University of Pretoria

Department of Economics Working Paper Series Price Gap Anomaly in the US Stock Market The Whole Story Alex Plastun Sumy State University Xolani Sibande University of Pretoria Rangan Gupta University of Pretoria Mark E Wohar University of Nebraska and Loughborough University Working Paper 2019-63 August 2019 __________________________________________________________ Department of Economics University of Pretoria 0002 Pretoria South Africa Tel +27 12 420 2413

Price Gap Anomaly in the US Stock Market TheWhole Story

Alex Plastunlowast Xolani Sibandedagger Rangan GuptaDagger Mark E Woharsect

August 12 2019

Abstract

This paper analyses the price gap anomaly in the US stock market (comprisedof the DJI SampP 500 and NASDAQ) covering the period 1928 to 2018 This paperaims to investigate whether or not price gaps create market inefficiencies Pricegaps occur when the current dayrsquos opening price is different from the previousdayrsquos closing price due orders placed before the opening of the market Severalhypotheses are tested using various statistical tests (Studentrsquos t-test ANOVAMann-Whitney test) regression analysis and special methods that is the mod-ified cumulative returns and the trading simulation approaches We find strongevidence in favour of abnormal price movements after price gaps We observe thatduring a gap day prices tend to change in the direction of the gap A tradingstrategy based on this anomaly was efficient in that its results were not randomindicating that this market was not efficient The momentum effect was found tobe temporary and no evidence of seasonality in price gaps was found Lastly ourresults were also contrary to the myth that price gaps tend to get filled

Keywords Price Gap Anomaly Trading Strategy Stock Market Momentum EffectEfficient Market HypothesisJEL Codes G12 C63

lowastFaculty of Economics and Management Sumy State University Sumy Ukraine Emailoplastungmailcom This author gratefully acknowledges financial support from the Ministry of Ed-ucation and Science of Ukraine (0117U003936)

daggerDepartment of Economics University of Pretoria Pretoria South Africa Emailxolanissgmailcom

DaggerDepartment of Economics University of Pretoria Pretoria South Africa Email ran-ganguptaupacza

sectCorresponding Author College of Business Administration University of Nebraska USASchool of Business and Economics Loughborough University Leicestershire LE11 3TU UK Emailmwoharunomahaedu

1

1 Introduction

The Efficient Market Hypothesis (EMH) contends that markets are efficient when pricesreflect all relevant information This has been empirically shown not to be the caseby academics and practitioners Anomalies in their various forms exist in internationalstock markets The study of anomalies therefore remains an active area in the financeliterature including that of price anomalies

According to Caporale and Plastun (2017) prices gaps occur when the current dayrsquosopening price is different from the previous dayrsquos closing price due to the orders placedbefore the opening of the market The empirical literature on the price gap anomalyis broadly focused on the confirmation of this anomaly (see Yuan (2015) and Caporaleet al (2016) for example) and the ascertainment of exploitable profits which may arise(see Caporale and Plastun (2017) and Plastun et al (2019a) for example) Howeverthis literature remains limited in terms of its application to the US stock market

This paper aims to investigate the existence of the price gap anomaly and its evo-lution in the US stock market in order to determine whether the price gap anomalygenerates exploitable profits Specifically we focus on the Dow Jones Industrial Aver-age index (DJI) the SampP 500 index (SampP 500) and the NASDAQ Our main focus isthe SampP 500 which has the longest sample (1928 and 2018) Several statistical tests(Studentrsquos t test ANOVA test Mann-Whitney test and cumulative abnormal returnsapproach) and trading simulation approach will be used Also we employ the simulationapproach to determine whether the price gap anomaly generates exploitable profits

A study of this nature focusing on the such a long period in the US stock markethas not been conducted previously constituting a gap in the literature To this endfollowing is a brief review of the relevant literature a discussion on the data and themethodology the results and a conclusion

2 Literature Review

According to Fama (1965) and Fama (1970) a market in which investment decisions aremade under the assumption that that security prices rsquofullyrsquo reflect all available informa-tion can be considered to be efficient Furthermore the extent to which information isreflected in security prices can be categorised and tested in two different forms that isthe weak form where only historical information affects security prices and the strongform where an investor has private information regarding the price of a security There-fore the EMH is simply the assertion that information is rsquofullyrsquo reflected in securityprices that is no investor has an opportunity to profit through arbitrage

However Grossman and Stiglitz (1980) Shiller (2000) Akerlof and Shiller (2009)Schwert (2003) and Mandelbrot (1997) amongst other have challenged the EMH on

2

a number of grounds At a theoretical level Grossman and Stiglitz (1980) argue thatinformation in reality is costly therefore prices cannot fully reflect all the availableinformation Shiller (2000) and Akerlof and Shiller (2009) highlight the irrational be-haviour of investors as such as mass panic as a key argument against the EMH Schwert(2003) shows how underlying market anomalies disappear after discovery as marketagents implement these anomalous strategies Others such as Mandelbrot (1997) empir-ically show that price distributions suffer from fat tails and long memory amongst others

Three types of anomalies have been studied in the literature that is seasonal sizeand price anomalies (see Jacobsen et al (2005)) According to Bildik (2004) anomaliesindicate market inefficiency or inadequacies in the underlying asset pricing model andtend to disappear after discovery as traders adapt to their existence There are nu-merous reasons for the existence of anomalies for example Basu (1977) identified priceanomalies by discovering that value stocks had higher risk-adjusted returns comparedto growth stocks

The price gap anomaly falls within this categorisation of anomalies The price gapanomaly is in essence related to the day of the week effect Cross (1973) was the first toconfirm that the distribution of stock prices changes according to the day of the weekand in particular between Friday and Monday Other such as Cross (1973) Gibbonsand Hess (1981) Cai et al (2006) French (1980) and Agrawal and Tandon (1994) findthat the day of the week effect was indeed most pronounced on Fridays and MondaysThis is otherwise known as the weekend effect as studied by Fortune (1999) and Fortune(1998) amongst others In summary Caporale and Plastun (2017) cite the following asthe most common reasons for the existence of price gaps

bull Significant time differences between closing and opening prices caused by holidaysand weekends

bull The advent of after-hours trading

bull Unexpected events that have a bearing on security prices such as earnings andprofit warning reports

bull Market shocks that can cause significant and sudden shifts in the supply anddemand of financial assets

bull Other reasons

Seasonal or calendar anomalies have received the most attention in the literatureStudies such as Plastun et al (2019b) and Lakonishok and Smidt (1988) amongst oth-ers demonstrate the evolution of calendar anomalies from a rsquogoldenrsquo age in the middleof the 20th century to their disappearance in recent years Studies on the evolution ofthe price gap anomaly are less common with a few exceptions such as Yuan (2015)Caporale and Plastun (2017) and Plastun et al (2019b)

3

However studies investigating the overreactive hypothesis (large market openingprice changes followed by significant correction) are more common (see Grant et al(2005) Fung et al (2010) and Caporale et al (2016) amongst others) For exampleGrant et al (2005) in the US stock index futures markets over 15 years found that sig-nificant intraday price reversals and also that the strength of the overreaction was morepronounced with large positive opening market price changes However Grant et al(2005) could not conclude if the price gap anomaly led to exploitable profits

Determining whether the price gap anomaly generates exploitable profits remainsa gap in the literature According to Jensen (1978) for an anomaly to be statisticallysignificant it must generate excess returns Only recently Plastun et al (2019b) appliedthe trading simulation approach to the Ukraine stock market and found that a tradingstrategy based on the price gap anomaly generate profits

3 Data and Methodology

Three US stock market indexes are analysed and tested that is the DJI covering theperiod 1985 to 2018 the SampP 500 covering the period 1928 to 2018 and NASDAQ overthe period 1949 to 2018 This data is from the Global Financial Data1 database Thedata were then split into 10-year sub-periods to allow us to explore the evolution of pricegap anomaly 10-year sub-periods also provide enough data points for robust statisticaltesting Table 1 below provides summary statistics for three markets

The following hypotheses are tested in this study

bull H1 Price gap anomaly exists

H1minus1 Prices tend to rise after positive gaps

H1minus2 Prices tend to fall after negative gaps

bull H2 Price gap anomaly evolves

bull H3 There is seasonality in price gaps

1The data is available for download at httpswwwglobalfinancialdatacom

4

Price Gap Anomaly in the US Stock Market TheWhole Story

Alex Plastunlowast Xolani Sibandedagger Rangan GuptaDagger Mark E Woharsect

August 12 2019

Abstract

This paper analyses the price gap anomaly in the US stock market (comprisedof the DJI SampP 500 and NASDAQ) covering the period 1928 to 2018 This paperaims to investigate whether or not price gaps create market inefficiencies Pricegaps occur when the current dayrsquos opening price is different from the previousdayrsquos closing price due orders placed before the opening of the market Severalhypotheses are tested using various statistical tests (Studentrsquos t-test ANOVAMann-Whitney test) regression analysis and special methods that is the mod-ified cumulative returns and the trading simulation approaches We find strongevidence in favour of abnormal price movements after price gaps We observe thatduring a gap day prices tend to change in the direction of the gap A tradingstrategy based on this anomaly was efficient in that its results were not randomindicating that this market was not efficient The momentum effect was found tobe temporary and no evidence of seasonality in price gaps was found Lastly ourresults were also contrary to the myth that price gaps tend to get filled

Keywords Price Gap Anomaly Trading Strategy Stock Market Momentum EffectEfficient Market HypothesisJEL Codes G12 C63

lowastFaculty of Economics and Management Sumy State University Sumy Ukraine Emailoplastungmailcom This author gratefully acknowledges financial support from the Ministry of Ed-ucation and Science of Ukraine (0117U003936)

daggerDepartment of Economics University of Pretoria Pretoria South Africa Emailxolanissgmailcom

DaggerDepartment of Economics University of Pretoria Pretoria South Africa Email ran-ganguptaupacza

sectCorresponding Author College of Business Administration University of Nebraska USASchool of Business and Economics Loughborough University Leicestershire LE11 3TU UK Emailmwoharunomahaedu

1

1 Introduction

The Efficient Market Hypothesis (EMH) contends that markets are efficient when pricesreflect all relevant information This has been empirically shown not to be the caseby academics and practitioners Anomalies in their various forms exist in internationalstock markets The study of anomalies therefore remains an active area in the financeliterature including that of price anomalies

According to Caporale and Plastun (2017) prices gaps occur when the current dayrsquosopening price is different from the previous dayrsquos closing price due to the orders placedbefore the opening of the market The empirical literature on the price gap anomalyis broadly focused on the confirmation of this anomaly (see Yuan (2015) and Caporaleet al (2016) for example) and the ascertainment of exploitable profits which may arise(see Caporale and Plastun (2017) and Plastun et al (2019a) for example) Howeverthis literature remains limited in terms of its application to the US stock market

This paper aims to investigate the existence of the price gap anomaly and its evo-lution in the US stock market in order to determine whether the price gap anomalygenerates exploitable profits Specifically we focus on the Dow Jones Industrial Aver-age index (DJI) the SampP 500 index (SampP 500) and the NASDAQ Our main focus isthe SampP 500 which has the longest sample (1928 and 2018) Several statistical tests(Studentrsquos t test ANOVA test Mann-Whitney test and cumulative abnormal returnsapproach) and trading simulation approach will be used Also we employ the simulationapproach to determine whether the price gap anomaly generates exploitable profits

A study of this nature focusing on the such a long period in the US stock markethas not been conducted previously constituting a gap in the literature To this endfollowing is a brief review of the relevant literature a discussion on the data and themethodology the results and a conclusion

2 Literature Review

According to Fama (1965) and Fama (1970) a market in which investment decisions aremade under the assumption that that security prices rsquofullyrsquo reflect all available informa-tion can be considered to be efficient Furthermore the extent to which information isreflected in security prices can be categorised and tested in two different forms that isthe weak form where only historical information affects security prices and the strongform where an investor has private information regarding the price of a security There-fore the EMH is simply the assertion that information is rsquofullyrsquo reflected in securityprices that is no investor has an opportunity to profit through arbitrage

However Grossman and Stiglitz (1980) Shiller (2000) Akerlof and Shiller (2009)Schwert (2003) and Mandelbrot (1997) amongst other have challenged the EMH on

2

a number of grounds At a theoretical level Grossman and Stiglitz (1980) argue thatinformation in reality is costly therefore prices cannot fully reflect all the availableinformation Shiller (2000) and Akerlof and Shiller (2009) highlight the irrational be-haviour of investors as such as mass panic as a key argument against the EMH Schwert(2003) shows how underlying market anomalies disappear after discovery as marketagents implement these anomalous strategies Others such as Mandelbrot (1997) empir-ically show that price distributions suffer from fat tails and long memory amongst others

Three types of anomalies have been studied in the literature that is seasonal sizeand price anomalies (see Jacobsen et al (2005)) According to Bildik (2004) anomaliesindicate market inefficiency or inadequacies in the underlying asset pricing model andtend to disappear after discovery as traders adapt to their existence There are nu-merous reasons for the existence of anomalies for example Basu (1977) identified priceanomalies by discovering that value stocks had higher risk-adjusted returns comparedto growth stocks

The price gap anomaly falls within this categorisation of anomalies The price gapanomaly is in essence related to the day of the week effect Cross (1973) was the first toconfirm that the distribution of stock prices changes according to the day of the weekand in particular between Friday and Monday Other such as Cross (1973) Gibbonsand Hess (1981) Cai et al (2006) French (1980) and Agrawal and Tandon (1994) findthat the day of the week effect was indeed most pronounced on Fridays and MondaysThis is otherwise known as the weekend effect as studied by Fortune (1999) and Fortune(1998) amongst others In summary Caporale and Plastun (2017) cite the following asthe most common reasons for the existence of price gaps

bull Significant time differences between closing and opening prices caused by holidaysand weekends

bull The advent of after-hours trading

bull Unexpected events that have a bearing on security prices such as earnings andprofit warning reports

bull Market shocks that can cause significant and sudden shifts in the supply anddemand of financial assets

bull Other reasons

Seasonal or calendar anomalies have received the most attention in the literatureStudies such as Plastun et al (2019b) and Lakonishok and Smidt (1988) amongst oth-ers demonstrate the evolution of calendar anomalies from a rsquogoldenrsquo age in the middleof the 20th century to their disappearance in recent years Studies on the evolution ofthe price gap anomaly are less common with a few exceptions such as Yuan (2015)Caporale and Plastun (2017) and Plastun et al (2019b)

3

However studies investigating the overreactive hypothesis (large market openingprice changes followed by significant correction) are more common (see Grant et al(2005) Fung et al (2010) and Caporale et al (2016) amongst others) For exampleGrant et al (2005) in the US stock index futures markets over 15 years found that sig-nificant intraday price reversals and also that the strength of the overreaction was morepronounced with large positive opening market price changes However Grant et al(2005) could not conclude if the price gap anomaly led to exploitable profits

Determining whether the price gap anomaly generates exploitable profits remainsa gap in the literature According to Jensen (1978) for an anomaly to be statisticallysignificant it must generate excess returns Only recently Plastun et al (2019b) appliedthe trading simulation approach to the Ukraine stock market and found that a tradingstrategy based on the price gap anomaly generate profits

3 Data and Methodology

Three US stock market indexes are analysed and tested that is the DJI covering theperiod 1985 to 2018 the SampP 500 covering the period 1928 to 2018 and NASDAQ overthe period 1949 to 2018 This data is from the Global Financial Data1 database Thedata were then split into 10-year sub-periods to allow us to explore the evolution of pricegap anomaly 10-year sub-periods also provide enough data points for robust statisticaltesting Table 1 below provides summary statistics for three markets

The following hypotheses are tested in this study

bull H1 Price gap anomaly exists

H1minus1 Prices tend to rise after positive gaps

H1minus2 Prices tend to fall after negative gaps

bull H2 Price gap anomaly evolves

bull H3 There is seasonality in price gaps

1The data is available for download at httpswwwglobalfinancialdatacom

4

1 Introduction

The Efficient Market Hypothesis (EMH) contends that markets are efficient when pricesreflect all relevant information This has been empirically shown not to be the caseby academics and practitioners Anomalies in their various forms exist in internationalstock markets The study of anomalies therefore remains an active area in the financeliterature including that of price anomalies

According to Caporale and Plastun (2017) prices gaps occur when the current dayrsquosopening price is different from the previous dayrsquos closing price due to the orders placedbefore the opening of the market The empirical literature on the price gap anomalyis broadly focused on the confirmation of this anomaly (see Yuan (2015) and Caporaleet al (2016) for example) and the ascertainment of exploitable profits which may arise(see Caporale and Plastun (2017) and Plastun et al (2019a) for example) Howeverthis literature remains limited in terms of its application to the US stock market

This paper aims to investigate the existence of the price gap anomaly and its evo-lution in the US stock market in order to determine whether the price gap anomalygenerates exploitable profits Specifically we focus on the Dow Jones Industrial Aver-age index (DJI) the SampP 500 index (SampP 500) and the NASDAQ Our main focus isthe SampP 500 which has the longest sample (1928 and 2018) Several statistical tests(Studentrsquos t test ANOVA test Mann-Whitney test and cumulative abnormal returnsapproach) and trading simulation approach will be used Also we employ the simulationapproach to determine whether the price gap anomaly generates exploitable profits

A study of this nature focusing on the such a long period in the US stock markethas not been conducted previously constituting a gap in the literature To this endfollowing is a brief review of the relevant literature a discussion on the data and themethodology the results and a conclusion

2 Literature Review

According to Fama (1965) and Fama (1970) a market in which investment decisions aremade under the assumption that that security prices rsquofullyrsquo reflect all available informa-tion can be considered to be efficient Furthermore the extent to which information isreflected in security prices can be categorised and tested in two different forms that isthe weak form where only historical information affects security prices and the strongform where an investor has private information regarding the price of a security There-fore the EMH is simply the assertion that information is rsquofullyrsquo reflected in securityprices that is no investor has an opportunity to profit through arbitrage

However Grossman and Stiglitz (1980) Shiller (2000) Akerlof and Shiller (2009)Schwert (2003) and Mandelbrot (1997) amongst other have challenged the EMH on

2

a number of grounds At a theoretical level Grossman and Stiglitz (1980) argue thatinformation in reality is costly therefore prices cannot fully reflect all the availableinformation Shiller (2000) and Akerlof and Shiller (2009) highlight the irrational be-haviour of investors as such as mass panic as a key argument against the EMH Schwert(2003) shows how underlying market anomalies disappear after discovery as marketagents implement these anomalous strategies Others such as Mandelbrot (1997) empir-ically show that price distributions suffer from fat tails and long memory amongst others

Three types of anomalies have been studied in the literature that is seasonal sizeand price anomalies (see Jacobsen et al (2005)) According to Bildik (2004) anomaliesindicate market inefficiency or inadequacies in the underlying asset pricing model andtend to disappear after discovery as traders adapt to their existence There are nu-merous reasons for the existence of anomalies for example Basu (1977) identified priceanomalies by discovering that value stocks had higher risk-adjusted returns comparedto growth stocks

The price gap anomaly falls within this categorisation of anomalies The price gapanomaly is in essence related to the day of the week effect Cross (1973) was the first toconfirm that the distribution of stock prices changes according to the day of the weekand in particular between Friday and Monday Other such as Cross (1973) Gibbonsand Hess (1981) Cai et al (2006) French (1980) and Agrawal and Tandon (1994) findthat the day of the week effect was indeed most pronounced on Fridays and MondaysThis is otherwise known as the weekend effect as studied by Fortune (1999) and Fortune(1998) amongst others In summary Caporale and Plastun (2017) cite the following asthe most common reasons for the existence of price gaps

bull Significant time differences between closing and opening prices caused by holidaysand weekends

bull The advent of after-hours trading

bull Unexpected events that have a bearing on security prices such as earnings andprofit warning reports

bull Market shocks that can cause significant and sudden shifts in the supply anddemand of financial assets

bull Other reasons

Seasonal or calendar anomalies have received the most attention in the literatureStudies such as Plastun et al (2019b) and Lakonishok and Smidt (1988) amongst oth-ers demonstrate the evolution of calendar anomalies from a rsquogoldenrsquo age in the middleof the 20th century to their disappearance in recent years Studies on the evolution ofthe price gap anomaly are less common with a few exceptions such as Yuan (2015)Caporale and Plastun (2017) and Plastun et al (2019b)

3

However studies investigating the overreactive hypothesis (large market openingprice changes followed by significant correction) are more common (see Grant et al(2005) Fung et al (2010) and Caporale et al (2016) amongst others) For exampleGrant et al (2005) in the US stock index futures markets over 15 years found that sig-nificant intraday price reversals and also that the strength of the overreaction was morepronounced with large positive opening market price changes However Grant et al(2005) could not conclude if the price gap anomaly led to exploitable profits

Determining whether the price gap anomaly generates exploitable profits remainsa gap in the literature According to Jensen (1978) for an anomaly to be statisticallysignificant it must generate excess returns Only recently Plastun et al (2019b) appliedthe trading simulation approach to the Ukraine stock market and found that a tradingstrategy based on the price gap anomaly generate profits

3 Data and Methodology

Three US stock market indexes are analysed and tested that is the DJI covering theperiod 1985 to 2018 the SampP 500 covering the period 1928 to 2018 and NASDAQ overthe period 1949 to 2018 This data is from the Global Financial Data1 database Thedata were then split into 10-year sub-periods to allow us to explore the evolution of pricegap anomaly 10-year sub-periods also provide enough data points for robust statisticaltesting Table 1 below provides summary statistics for three markets

The following hypotheses are tested in this study

bull H1 Price gap anomaly exists

H1minus1 Prices tend to rise after positive gaps

H1minus2 Prices tend to fall after negative gaps

bull H2 Price gap anomaly evolves

bull H3 There is seasonality in price gaps

1The data is available for download at httpswwwglobalfinancialdatacom

4

a number of grounds At a theoretical level Grossman and Stiglitz (1980) argue thatinformation in reality is costly therefore prices cannot fully reflect all the availableinformation Shiller (2000) and Akerlof and Shiller (2009) highlight the irrational be-haviour of investors as such as mass panic as a key argument against the EMH Schwert(2003) shows how underlying market anomalies disappear after discovery as marketagents implement these anomalous strategies Others such as Mandelbrot (1997) empir-ically show that price distributions suffer from fat tails and long memory amongst others

Three types of anomalies have been studied in the literature that is seasonal sizeand price anomalies (see Jacobsen et al (2005)) According to Bildik (2004) anomaliesindicate market inefficiency or inadequacies in the underlying asset pricing model andtend to disappear after discovery as traders adapt to their existence There are nu-merous reasons for the existence of anomalies for example Basu (1977) identified priceanomalies by discovering that value stocks had higher risk-adjusted returns comparedto growth stocks

The price gap anomaly falls within this categorisation of anomalies The price gapanomaly is in essence related to the day of the week effect Cross (1973) was the first toconfirm that the distribution of stock prices changes according to the day of the weekand in particular between Friday and Monday Other such as Cross (1973) Gibbonsand Hess (1981) Cai et al (2006) French (1980) and Agrawal and Tandon (1994) findthat the day of the week effect was indeed most pronounced on Fridays and MondaysThis is otherwise known as the weekend effect as studied by Fortune (1999) and Fortune(1998) amongst others In summary Caporale and Plastun (2017) cite the following asthe most common reasons for the existence of price gaps

bull Significant time differences between closing and opening prices caused by holidaysand weekends

bull The advent of after-hours trading

bull Unexpected events that have a bearing on security prices such as earnings andprofit warning reports

bull Market shocks that can cause significant and sudden shifts in the supply anddemand of financial assets

bull Other reasons

Seasonal or calendar anomalies have received the most attention in the literatureStudies such as Plastun et al (2019b) and Lakonishok and Smidt (1988) amongst oth-ers demonstrate the evolution of calendar anomalies from a rsquogoldenrsquo age in the middleof the 20th century to their disappearance in recent years Studies on the evolution ofthe price gap anomaly are less common with a few exceptions such as Yuan (2015)Caporale and Plastun (2017) and Plastun et al (2019b)

3

However studies investigating the overreactive hypothesis (large market openingprice changes followed by significant correction) are more common (see Grant et al(2005) Fung et al (2010) and Caporale et al (2016) amongst others) For exampleGrant et al (2005) in the US stock index futures markets over 15 years found that sig-nificant intraday price reversals and also that the strength of the overreaction was morepronounced with large positive opening market price changes However Grant et al(2005) could not conclude if the price gap anomaly led to exploitable profits

Determining whether the price gap anomaly generates exploitable profits remainsa gap in the literature According to Jensen (1978) for an anomaly to be statisticallysignificant it must generate excess returns Only recently Plastun et al (2019b) appliedthe trading simulation approach to the Ukraine stock market and found that a tradingstrategy based on the price gap anomaly generate profits

3 Data and Methodology

Three US stock market indexes are analysed and tested that is the DJI covering theperiod 1985 to 2018 the SampP 500 covering the period 1928 to 2018 and NASDAQ overthe period 1949 to 2018 This data is from the Global Financial Data1 database Thedata were then split into 10-year sub-periods to allow us to explore the evolution of pricegap anomaly 10-year sub-periods also provide enough data points for robust statisticaltesting Table 1 below provides summary statistics for three markets

The following hypotheses are tested in this study

bull H1 Price gap anomaly exists

H1minus1 Prices tend to rise after positive gaps

H1minus2 Prices tend to fall after negative gaps

bull H2 Price gap anomaly evolves

bull H3 There is seasonality in price gaps

1The data is available for download at httpswwwglobalfinancialdatacom

4

However studies investigating the overreactive hypothesis (large market openingprice changes followed by significant correction) are more common (see Grant et al(2005) Fung et al (2010) and Caporale et al (2016) amongst others) For exampleGrant et al (2005) in the US stock index futures markets over 15 years found that sig-nificant intraday price reversals and also that the strength of the overreaction was morepronounced with large positive opening market price changes However Grant et al(2005) could not conclude if the price gap anomaly led to exploitable profits

Determining whether the price gap anomaly generates exploitable profits remainsa gap in the literature According to Jensen (1978) for an anomaly to be statisticallysignificant it must generate excess returns Only recently Plastun et al (2019b) appliedthe trading simulation approach to the Ukraine stock market and found that a tradingstrategy based on the price gap anomaly generate profits

3 Data and Methodology

Three US stock market indexes are analysed and tested that is the DJI covering theperiod 1985 to 2018 the SampP 500 covering the period 1928 to 2018 and NASDAQ overthe period 1949 to 2018 This data is from the Global Financial Data1 database Thedata were then split into 10-year sub-periods to allow us to explore the evolution of pricegap anomaly 10-year sub-periods also provide enough data points for robust statisticaltesting Table 1 below provides summary statistics for three markets

The following hypotheses are tested in this study

bull H1 Price gap anomaly exists

H1minus1 Prices tend to rise after positive gaps

H1minus2 Prices tend to fall after negative gaps

bull H2 Price gap anomaly evolves

bull H3 There is seasonality in price gaps

1The data is available for download at httpswwwglobalfinancialdatacom

4

Table 1 Descriptive statistics for data (close prices)

Parameter DJI SampP 500 NASDAQMean 941167 42138 11152Median 983553 9449 25612Maximum 2682839 293075 810969Minimum 124205 441 893Std Dev 599052 63378 163616Skewness 067 176 194Kurtosis 002 237 354Sum 80846216 10068052 19738969Observations 8590 23893 17700

Testing H1 determines whether or not the price gap anomalies are inconsistent withmarket efficiency To achieve this sub-hypothesis H1minus1 and H1minus2 are also tested Theaim is to show that prices do behave abnormally after price gaps Testing H2 providesinformation about the evolution of price gap anomaly over time Testing H3 ascertainswhether any days of the week are more favourable for price gaps that is whether pricegaps are seasonal The statistical aim is therefore to establish whether returns inrsquonormalrsquo periods follow the same distribution as returns in rsquoabnormalrsquo periods when theprice gap anomaly is present To this end Gapi in the following manner

Gapi =

983061Openi

Closeiminus1

minus 1

983062lowast 100 (1)

where Gapi is the gap size on the gap day in percentage Openi is the opening price onthe gap day and Closeiminus1 is the closing price on the day prior to the gap day

In addition we define Ri as

Ri =

983061Openi

Closeiminus 1

983062lowast 100 (2)

where Ri is the return on the ith day in percentage Openi is the opening priceClosei is the close price on the ith day and Closeiminus1 is the open price on the ithminus 1 dayThe OpeniClosei relation is used in order to avoid incorporating the price gap as withthe standard CloseiCloseiminus1

To identify statistically significant differences between normal and abnormal periodsthat is periods when the price gap anomaly is prevalent in the market and when it is

5

not we also run the following regressions

Rt = a0 + a1Dt + 983171t (3)

where Rt is the return in period t a0 is the mean return in a normal period a1 is themean return in an abnormal period Dt is a dummy variable equal to 1 in abnormalperiods and 0 in normal period and 983171t is the random error term The sign and statis-tical significance of the dummy coefficients indicate the existence or not of price gapsanomalies

To avoid methodological bias we utilise the modified cumulative abnormal returnsapproach (MCAR) which was developed by Plastun et al (2019b) based on the work ofMacKinlay (1997) and recently utilised by Plastun et al (2019a) in the Ukraine stockmarket to detect price gap anomalies Plastun et al (2019b) developed this MCARapproach in the context of calendar anomalies and their evolution over time In thispaper we summarise the MCAR approach however further details of the MCAR canbe found in Plastun et al (2019b) Abnormal returns are defined as follows

ARt = Rt minus E(Rt) (4)

where Rt is the return and ARt is the abnormal return at time t E(Rt) is the iscorresponding average return computed over the entire sample as follows

E(Rt) =

9830611

T

983062983131T

i=1Ri (5)

where T is the sample size

The cumulative abnormal return denoted as CARi is simply the sum of the abnormalreturns

CARi =983131T

i=1ARi (6)

A trend in cumulative abnormal returns data confirms abnormal returns A simpleregression model is built to estimate the trend component A high multiple Rminussquaredand overall model significance (F minus test) and the statistical significance (pminus values) ofthe coefficients confirm or reject the presence of trend in the abnormal returns

In instances where a price gap anomaly is detected we test whether it gives riseto exploitable profits using the trading simulation approach The trading simulationapproach replicates the actions of a trader given the price anomaly trading strategy Ifthis trading strategy generates 50 per cent or more profitable trades and produces anoverall financial result of more than zero (excluding transaction costs) this indicates

6

that this strategy is efficient A z minus test is then conducted to ensure that the results ofthe trading strategy are not random using a 5 per cent level of significance

4 Results

The results of the SampP 500 are presented and contrasted with those of the DJI and theNASDAQ We focus on the SampP 500 specifically as it has the longest sample and there-fore can offer better insights as compared to the DJI and the NASDAQ The summaryresults for the DJI and the NASDAQ can be found in Appendix A The results of theshort term price behaviour tests are in Appendix B The detailed results of the overalldata sets for all indexes can be found in Appendices C to E Similarly the detailedresults of the sub-periods within the overall data sets can be found in Appendices F toH

41 Price gap size

First an appropriate gap size must be as a criterion for gap detection Caporale andPlastun (2017) show that the gap size significantly influences the number of detectedanomalies To confirm this we analyse SampP 500 data for the 2009-2018 sub-period Ascan be seen from Table 2 a small gap size choice generates too many gaps to be consid-ered as anomalies A large gap size provides very few cases for analysis and may leadto statistical insignificance of the results For this study (which is primarily based onstatistical analysis and tests) the number of observations should be around 100 to makeresults statistically significant This represents less than 10 per cent of the populationand hence can be considered anomalies As a result gap size is not constant and maydiffer from index to index and between sub-periods (see Table 3 and Table A1) Thisinconsistency in the gap size can be considered additional evidence in favour of pricegap anomaly evolution

7

Tab

le2

Gap

size

andthenumber

ofdetectedgapscase

ofSampP500dataover

theperiod2009-2018

Gap

size

010

020

030

040

050

060

070

080

090

100

gapsin

prices

4105

1970

1090

571

345

202

135

087

067

052

Number

ofdetectedgaps

1038

497

275

144

8751

3422

1713

Number

ofdetectednegativegaps

468

230

130

6944

3120

109

8Number

ofdetectedpositivegaps

570

267

145

7543

2014

128

5

8

Table 3 Gap size used for different sub-periods over the period 1929-2018

Period SampP 5001929-1938 1201949-1958 1201959-1968 0701969-1978 0011979-1988 0031989-1998 0011999-2008 0082009-2018 034Overall data set 070

42 Price gap seasonality

Caporale and Plastun (2017) show that in foreign exchange and commodity marketsprice gaps tend to appear on Mondays According to their results more than 95 percent of price gaps in foreign exchange markets compared to 65 per cent of price gaps incommodity markets appeared on Mondays This is rather reasonable because marketsare closed on weekends and as the result of any significant event over the weekend willlead to price gaps on Monday Surprisingly this is not the case in this instance (withstock markets) as can be seen in Tables 4 and A2 Therefore H3 is rejected

Table 4 Day of the week and gaps

Day of the week SampP 500Monday 023Tuesday 02Wednesday 02Thursday 018Friday 019

43 Short term price behaviour

Next we analyse short-term price behaviour in the US stock market around price gapsto investigate the presence of possible price patterns before and after price gaps Wecalculate the number of days with positive (or negative) returns after a positive (or neg-ative) price gaps divided by the total number of price gaps If this ratio or momentum

9

effect is much higher than 50 per cent this indicates abnormal price behaviour and asthe results confirm our hypotheses

The results are presented in Appendix B We find no convincing evidence in favour ofmomentum effect after price gaps (Table B1) and before them (Table B2) In generalprice gaps are not generated by previous price dynamics (NASDAQ index is an exceptionas negative gaps appear in 70 per cent of the cases after downward price movements andafter positive gaps in 67 per cent of the cases upward price movements are observed)Our results (see Table B3 for details) also indicate that the probability that price gapswill be filled within 5 days after appearance is very low at around 20 per cent

44 Price gap evolution

Overall in probabilistic terms price gaps do not generate any stable patterns But therecan be patterns in terms of size of price movements after gaps To check this we will testH1 and H2 To incorporate price direction in results of analysis H1 we further test forH1minus1 and H1minus2 The results for the overall data sets are presented in Appendices C toE for the cases of DJI SampP 500 and NASDAQ respectively To ease the interpretationof results we have summarised them in Table 5 and Table A3

Table 5 shows strong evidence confirming H1 in the SampP 500 Similarly Table A3confirms H1 for the NASDAQ but not for the DJI The difference between the DJI SampP500 and NASDAQ results can be explained by the differences in samples (DJI sampleis much shorter) This suggests that price gap anomaly may evolve and is therefore apreliminary confirmation of H2

Tables 6 and 7 confirm H1minus1 in the SampP 500 on the day of the price gap That ison the price gap day prices tend towards the direction of the price gap However thisis not the case for the day after the price gap therefore H1minus2 is not confirmed It canbe concluded that the SampP 500 roughly needs a day to absorb new information Never-theless even a day can be enough to create a profitable trading strategy and generateabnormal profits from trading

Similar results on the NASDAQ can be found in Tables A6 and A7 The longersample of the NASDAQ allows for the evolution of the price anomaly H1minus1 is there-fore confirmed on the day of the price gap anomaly and the day after the price gapanomaly (in both instances only until the 1990s and has since disappeared) H1minus2 inboth instances is confirmed up until the 1990s The results of the DJI did not providestrong evidence in favour of H1minus1 and H1minus2 on the day after the price gap but sim-ilar to the SampP 500 evidence was strong on the day of the price gap (see Tables A4and A5) These results confirm in the main the price gap anomaly is a reality in theUS stock market and that it evolves over time that is from prevalence to disappearance

10

Tab

le5

Overallstatisticalresults

SampP500

PeriodM

ethod

Average

analysis

t-test

ANOVA

test

Man

n-

Whitney

test

Regression

analysis

with

dummy

variab

les

Modified

CAR

approach

Overall

Gap

day

+-

-+

-+

3Gap

day

(Positivegaps)

++

++

++

6Gap

day

(Negativegaps)

++

++

++

6Day

aftergap(P

ositivegaps)

++

-+

++

5Day

aftergap(N

egativegaps)

++

--

++

4

Note+

indicates

thattheanom

alyis

confirm

edand-indicates

thatan

omaly

isnot

confirm

edThehigher

theoverallrating

the

strongertheeviden

ceofthean

omaly

11

Tab

le6

H1minus1summarystatisticalresults

SampP500sub-periods

PeriodM

ethod

Average

analysis

t-test

ANOVA

test

Man

n-

Whitney

test

Regression

analysis

withdummy

variab

les

Modified

CAR

approach

Overall

Dayofanomaly

1929-1938

++

++

++

61939-1948

+-

-+

-+

31949-1958

++

++

++

61959-1968

++

++

++

61969-1978

++

++

++

61979-1988

++

++

++

61989-1998

++

++

++

61999-2008

++

++

++

62009-2018

++

++

++

6Dayafteranomaly

1929-1938

+-

--

-+

21939-1948

++

++

++

61949-1958

+-

+-

++

51959-1968

++

++

++

61969-1978

+-

+-

++

41979-1988

+-

--

--

11989-1998

--

--

--

01999-2008

--

--

--

02009-2018

--

--

--

0

Note+

indicates

thattheanom

alyis

confirm

edand-indicates

thatan

omaly

isnot

confirm

edThehigher

theoverallrating

the

strongertheeviden

ceofthean

omaly

12

Tab

le7

H1minus2statisticalresults

SampP500sub-periods

PeriodM

ethod

Average

analysis

t-test

ANOVA

test

Man

n-

Whitney

test

Regression

analysiswith

dummy

variab

les

Modified

CAR

approach

Overall

Dayofanomaly

1929-1938

++

++

++

61939-1948

++

++

++

61949-1958

++

++

++

61959-1968

++

++

++

61969-1978

++

++

++

61979-1988

++

++

++

61989-1998

++

++

++

61999-2008

++

++

++

62009-2018

++

++

++

6Dayafteranomaly

1929-1938

+-

--

-+

21939-1948

++

++

++

61949-1958

--

--

--

01959-1968

--

--

-+

11969-1978

++

++

++

61979-1988

--

--

--

01989-1998

--

--

--

01999-2008

+-

--

-+

22009-2018

+-

+-

++

4

Note+

indicates

thattheanom

alyis

confirm

edand-indicates

thatan

omaly

isnot

confirm

edThehigher

theoverallrating

the

strongertheeviden

ceofthean

omaly

13

45 Trading simulation

The algorithm of the trading strategy is to buysell at the start of the updown gapday and close this position at the end of this day To test this strategy data for the DJIand SampP 500 are used (for this case the price anomaly still exists based on the day itoccurred) The results for DJI are presented in Table A8 and for the SampP 500 in Table8 For the SampP 500 and DJI the trading strategy built on price gap anomaly is efficientand its results differ from random

Table 8 Trading simulation results of the price gap anomaly for the SampP 500

Period Gaptype

Numberof

tradesunits

Numberof suc-cessfultradesunits

Numberof suc-cessfultrades

Profit

Profit peryear

z-test Result

1929-1938 Up 131 130 992 1816 182 1065 passedDown 110 108 982 1893 189 876 passed

1939-1948 Up 110 67 609 106 11 09 failedDown 122 79 648 518 52 465 passed

1949-1958 Up 106 105 991 1765 176 3191 passedDown 104 103 99 1891 189 2356 passed

1959-1968 Up 108 106 981 1331 113 2441 passedDown 92 91 989 948 95 2214 passed

1969-1978 Up 85 71 835 1128 113 1361 passedDown 96 90 938 1262 126 2118 passed

1979-1988 Up 92 63 685 54 54 495 passedDown 123 81 659 519 52 496 passed

1989-1998 Up 117 72 615 267 27 295 passedDown 99 61 616 228 23 32 passed

1999-2008 Up 99 65 657 828 83 373 passedDown 110 72 655 987 99 438 passed

2009-2018 Up 106 71 67 59 59 416 passedDown 107 65 607 56 56 362 passed

14

Figure 1 Trading simulation results of the price gap anomaly for the SampP 500

Note The primary axis refers to the percentage profit per year and the secondary to thez minus test statistic

One more interesting fact (see Figure 1) is the decrease of trading strategy efficiencyThis is indirect evidence in favour of evolution of the US stock market and its movementfrom less efficient to more efficient state Overall it can be concluded that the price gapanomaly is a real market anomaly The US stock market loses its efficiency after pricegaps This effect is temporary and lasts only for a day Still even this time is enoughto exploit the hole in the market efficiency and generate abnormal profits from trading

5 Conclusion

We analysed price gap anomaly in the US stock market by using information from threestock market indexes(DJI SampP 500 and NASDAQ) We tested three hypotheses of in-terest that is H1 the price gap anomaly exists H1minus1 prices tend to rise after positivegaps H1minus2 prices tend to fall after negative gaps H2 the price gap anomaly evolvesand H3 there is seasonality in price gaps Various statistical methods including para-metric tests (Students t-tests ANOVA) non-parametric tests (Mann-Whitney test)regression analysis with dummy variables MCAR approach and the trading simulationapproach were utilised

We conclude that the US stock market in the main did not exhibit seasonality in pricegaps Therefore H3 is rejected Furthermore no evidence was found that price gaps inthe US stock market were filled within five days of their occurrence However strongevidence in favour of abnormal price movements after the gaps were found confirming

15

H1 and H2 Particularly on the day of the occurrence of the gap and not on the dayafter the price gap In the DJI and the SampP 500 this pattern persists indicating thatthese markets take a day to incorporate new information As the results of the tradingsimulation indicate a day is enough to profit from a price gap anomaly trading strategyin the DJI and the SampP 500

Similar to other studies and other anomalies (see McLean and Pontiff (2016) Ca-jueiro and Tabak (2004) and Tiwari et al (2019) for example) the price gap anomalyevolved It is less prevalent since the 1990s as shown in the SampP 500 and NASDAQThis pattern of evolution is common amongst most stock market anomalies (see Plastunet al (2019b) on calendar anomalies amongst others) Our findings therefore add onto the existing literature Finally in the main our results are against the EMH and aretherefore interesting to both practitioners and academics

16

References

Agrawal A and Tandon K (1994) Anomalies or illusions evidence from stock marketsin eighteen countries Journal of international Money and Finance 13(1)83ndash106

Akerlof G A and Shiller R J (2009) Animal Spirits How human psychology drivesthe economy and why it matters for global capitalism Princeton University Press

Basu S (1977) Investment performance of common stocks in relation to their price-earnings ratios A test of the efficient market hypothesis The Journal of Finance32(3)663ndash682

Bildik R (2004) Are calendar anomalies still alive Evidence from istanbul stockexchange SSRN Electronic Journal 2004

Cai J Li Y and Qi Y (2006) The day-of-the-week effect New evidence from theChinese stock market Chinese Economy 39(2)71ndash88

Cajueiro D O and Tabak B M (2004) The Hurst exponent over time testing theassertion that emerging markets are becoming more efficient Physica A StatisticalMechanics and its Applications 336(3-4)521ndash537

Caporale G M Gil-Alana L Plastun A and Makarenko I (2016) Intraday anoma-lies and market efficiency A trading robot analysis Computational Economics47(2)275ndash295

Caporale G M and Plastun A (2017) Price gaps Another market anomaly Invest-ment Analysts Journal 46(4)279ndash293

Cross F (1973) The behavior of stock prices on Fridays and Mondays FinancialAnalysts Journal 29(6)67ndash69

Fama E F (1965) The behavior of stock-market prices The Journal of Business38(1)34ndash105

Fama E F (1970) Efficient capital markets A review of theory and empirical workThe Journal of Finance 25(2)383ndash417

Fortune P (1998) Weekends can be rough revisiting the weekend effect in stock pricesTechnical report

Fortune P (1999) Are stock returns different over weekends A jump diffusion analysisof the weekend effect New England Economic Review 103ndash19

French K R (1980) Stock returns and the weekend effect Journal of FinancialEconomics 8(1)55ndash69

Fung A K-W Lam K and Lam K-M (2010) Do the prices of stock index futuresin asia overreact to us market returns Journal of Empirical Finance 17(3)428ndash440

17

Gibbons M R and Hess P (1981) Day of the week effects and asset returns Journalof business pages 579ndash596

Grant J L Wolf A and Yu S (2005) Intraday price reversals in the us stock indexfutures market A 15-year study Journal of Banking amp Finance 29(5)1311ndash1327

Grossman S J and Stiglitz J E (1980) On the impossibility of informationallyefficient markets The American Economic Review 70(3)393ndash408

Jacobsen B Mamun A and Visaltanachoti N (2005) Seasonal size and valueanomalies

Jensen M (1978) Some anomalous evidence regarding market efficiency Journal ofFinancial Economics 6(23 (1978))95ndash101

Lakonishok J and Smidt S (1988) Are seasonal anomalies real A ninety-year per-spective The Review of Financial Studies 1(4)403ndash425

MacKinlay A (1997) Event studies in economics and finance Journal of EconomicLiterature (35)113ndash39

Mandelbrot B B (1997) The variation of certain speculative prices In Fractals andscaling in finance pages 371ndash418 Springer

McLean R D and Pontiff J (2016) Does academic research destroy stock returnpredictability The Journal of Finance 71(1)5ndash32

Plastun A Makarenko I Khomutenko L Shcherbak S and Tryfonova O (2019a)Exploring price gap anomaly in the ukrainian stock market Investment Managementamp Financial Innovations 16(2)150

Plastun A Sibande X Gupta R and Wohar M E (2019b) Rise and fall of calendaranomalies over a century The North American Journal of Economics and Finance49181ndash205

Schwert G W (2003) Chapter 15 anomalies and market efficiency In FinancialMarkets and Asset Pricing volume 1 of Handbook of the Economics of Finance pages939 ndash 974 Elsevier

Shiller R J (2000) Irrational exuberance Princeton University

Tiwari A K Aye G C and Gupta R (2019) Stock market efficiency analysis usinglong spans of data A multifractal detrended fluctuation approach Finance ResearchLetters 28398ndash411

Yuan Y (2015) Market-wide attention trading and stock returns Journal of FinancialEconomics 116(3)548ndash564

18

Appendices

A DJI and NASDAQ Summary Results

A1 Overall Results

Table A1 Gap size used for different sub-periods over the period 1929-2018

Period DJI NASDAQ1929-1938 - -1939-1948 - -1949-1958 - 0711959-1968 - 0951969-1978 - 1351979-1988 - 1101989-1998 040 0681999-2008 007 1502009-2018 020 110Overall data set 030 110

Table A2 Day of the week and gaps

Day of the week DJI NASDAQMonday 024 02Tuesday 02 02Wednesday 017 02Thursday 019 019Friday 021 02

A2 Statistical tests

Table A3 Results of the statistical tests for the overall data sets

PeriodMethod Averageanalysis

t-test ANOVAtest

Mann-Whitney

test

Regressionanalysiswith

dummyvariables

ModifiedCAR

approach

Overall

Dow Jones Index overall data setGap day - - - - - + 1Gap day (Positive gaps) + - - - - - 1Gap day (Negative gaps) + - - - - + 2Day after gap (Positive gaps) + - - - - - 1Day after gap (Negative gaps) + - - + - + 3

NASDAQ overall data setGap day + + + + + + 6Gap day (Positive gaps) + + + + + + 6Gap day (Negative gaps) + + + + + + 6Day after gap (Positive gaps) + + + + + + 6Day after gap (Negative gaps) + + + + + + 6

Note + indicates that the anomaly is confirmed and - indicates that anomaly is not confirmedThe higher the overall rating the stronger the evidence of the anomaly

19

Table A4 Results of the statistical tests for H1minus1 DJI

Period Averageanalysis

t-test ANOVA test Mann-Whitney

test

Regressionanalysis with

dummyvariables

ModifiedCAR

approach

Overall

Day of anomaly1989-1998 + - - - - + 21999-2008 + + + + + + 62009-2018 + + + + + + 6

Day after anomaly1989-1998 + - - - - + 21999-2008 + - - - - + 22009-2018 - - - - - - 0

Note + indicates that the anomaly is confirmed and - indicates that anomaly is not confirmedThe higher the overall rating the stronger the evidence of the anomaly

Table A5 Results of the statistical tests for H1minus2 DJI

Period Averageanalysis

t-test ANOVA test Mann-Whitneytest

Regressionanalysis with

dummyvariables

Modified CARapproach

Overall

Day of anomaly1989-1998 - - - - - - 01999-2008 + + + + + + 62009-2018 + + + + + + 6

Day after anomaly1989-1998 + - - - - + 21999-2008 + - - - - - 12009-2018 + - - - - + 2

Note + indicates that the anomaly is confirmed and - indicates that anomaly is not confirmedThe higher the overall rating the stronger the evidence of the anomaly

Table A6 Results of the statistical tests for H1minus1 NASDAQ

PeriodMethod Averageanalysis

t-test ANOVA test Mann-Whitney

test

Regressionanalysis with

dummyvariables

ModifiedCAR

approach

Overall

Day of anomaly1949-1958 + + + + + + 61959-1968 + + + + + + 61969-1978 + + + + + + 61979-1988 + + + + + + 61989-1998 + - - - - + 21999-2008 + - + + + + 52009-2018 + + + + + + 6

Day after anomaly1949-1958 + + + + + + 61959-1968 + + + + + + 61969-1978 + + + + + + 61979-1988 + + + + + + 61989-1998 + - + - + + 41999-2008 - - - - - - 02009-2018 + - - - - + 2

Note + indicates that the anomaly is confirmed and - indicates that anomaly is not confirmedThe higher the overall rating the stronger the evidence of the anomaly

20

Table A7 Results of the statistical tests for H1minus2 NASDAQ

PeriodMethod Averageanalysis

t-test ANOVA test Mann-Whitney

test

Regressionanalysis with

dummyvariables

ModifiedCAR

approach

Overall

Day of anomaly1949-1958 + + + + + + 61959-1968 + + + + + + 61969-1978 + + + + + + 61979-1988 + + + + + + 61989-1998 - - - - - + 11999-2008 - - + - - - 12009-2018 - - - - - - 0

Day after anomaly1949-1958 + + + + + + 61959-1968 + + + + + + 61969-1978 + + + + + + 61979-1988 + + + + + + 61989-1998 + - - - - - 11999-2008 - - - - - + 12009-2018 + - - + + + 4

Note + indicates that the anomaly is confirmed and - indicates that anomaly is not confirmedThe higher the overall rating the stronger the evidence of the anomaly

A3 Trading Simulation Results

Table A8 Trading simulation results of the price gap anomaly for the DJI 1989-2018

Period Gap type Number oftradesunits

Number ofsuccessfultradesunits

Number ofsuccessfultrades

Profit Profit per year

z-test Result

1989-1998 Up 102 46 451 -11 -01 011 failedDown 116 49 422 -267 -27 242 passed

1999-2008 Up 73 51 699 665 66 37 passedDown 143 81 566 641 64 331 passed

2009-2018 Up 127 88 693 308 31 327 passedDown 81 47 58 196 2 184 passed

21

B Short-term price behavior in DJI SampP 500 and

NASDAQ Price gaps (overall data sets)

Table B1 Momentum effect in the US stock market after the gap

Instrument Parameter Number of days after the gap1 2 3

Dow Jones Index Positive gaps 53 57 61Negative gaps 50 50 47

All gaps 51 54 54SampP 500 Index Positive gaps 40 63 60

Negative gaps 4 52 45All gaps 4 58 53

NASDAQ Positive gaps 32 65 67Negative gaps 24 63 59

All gaps 28 64 63

Table B2 Momentum effect in the US stock market before the gap

Instrument Parameter Number of days before the gap1 2 3

Dow Jones Index Positive gaps 56 49 52Negative gaps 54 49 49

All gaps 55 49 50SampP 500 Index Positive gaps 57 57 52

Negative gaps 60 59 54All gaps 58 58 53

NASDAQ Positive gaps 61 56 54Negative gaps 68 69 70

All gaps 64 63 63

Table B3 Fill gap effect in the US stock market

Instrument Parameter Number of days after the gap1 2 3 4 5

Dow Jones Index Positive gaps 22 28 26 30 28Negative gaps 25 33 36 42 46

All gaps 24 30 31 35 37SampP 500 Index Positive gaps 0 6 11 16 19

Negative gaps 1 10 19 26 27All gaps 1 8 15 20 23

NASDAQ Positive gaps 8 13 18 21 19Negative gaps 7 11 17 21 25

All gaps 8 12 18 21 22

22

C Detailed statistical results DJI overall data

C1 Average analysis

Table C1 Average analysis

Parameter Gap day Gap day(Positive gaps)

Gap day(Negative gaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Mean return (gap day) 003 006 0 005 -003Mean return (non-gap day) 004 004 004 004 004Anomaly not confirmed not confirmed confirmed not confirmed confirmed

C2 Parametric tests Students t-test

Table C2 T-test

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

t-criterion 016 042 053 015 104t-critical (=095) 196 196 196 196 196Null hypothesis not rejected not rejected not rejected not rejected not rejected

C3 Parametric tests ANOVA

Table C3 ANOVA

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

F 0036 018 053 003 14p-value 085 067 047 086 024F critical 384 384 384 384 384Null hypothesis not rejected not rejected not rejected not rejected not rejected

C4 Non-parametric tests Kruskal-Wallis test

Table C4 Kruskal -Wallis test

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Adjusted H 082 012 126 0 455df 1 1 1 1 1P value 037 073 026 095 003Critical value 384 384 384 384 384Null hypothesis not rejected not rejected not rejected not rejected rejected

23

C5 Regression analysis with dummy variables

Table C5 Regression analysis with dummy variables

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

a0 00004 (000) 00004 (000) 00004 (000) 00004 (000) 00004 (000)a1 -00001 (-019) 00002 (067) -00004 (047) 00001 (086) -00007 (024)Anomaly not confirmed not confirmed not confirmed not confirmed not confirmed

C6 Modified CAR approach

Table C6 Modified CAR approach

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Multiple R 049 05 025 0 092F-test 23347 (000) 12913 (000) 2207 (000) 000 (098) 1822 (000)a0 -00041 (060) 00128 (006) -00267 (000) 00354 (000) 00319 (000)a1 -00003 (000) -00003 (000) -00002 (000) 00000 (098) -00008 (000)Anomaly confirmed confirmed confirmed not confirmed confirmed

24

D Detailed statistical results SampP 500 overall data

D1 Average analysis

Table D1 Average analysis

Parameter Gap day Gap day(Positive gaps)

Gap day(Negative gaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Mean return (gap day) 006 115 -129 017 -011Mean return (non-gap day) 002 002 002 002 002Anomaly confirmed confirmed confirmed confirmed confirmed

D2 Parametric tests Students t-test

Table D2 T-test

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

t-criterion 092 4546 3579 485 271t-critical (=095) 196 196 196 196 196Null hypothesis not rejected rejected rejected rejected rejected

D3 Parametric tests ANOVA

Table D3 ANOVA

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

F 155 116211 126952 1866 136p-value 022 0 0 0 0F critical 384 384 384 384 384Null hypothesis not rejected rejected rejected not rejected not rejected

D4 Non-parametric tests Kruskal-Wallis test

Table D4 Kruskal-Wallis test

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Adjusted H 1352 70516 47237 3946 004df 1 1 1 1 1P value 0 0 0 0 084Critical value 384 384 384 384 384Null hypothesis rejected rejected rejected rejected not rejected

25

D5 Regression analysis with dummy variables

Table D5 Regression analysis with dummy variables

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

a0 00002 (000) 00002 (000) 00002 (000) 00002 (000) 00002 (000)a1 00003 (021) 00113 (000) -00132 (000) 00014 (000) -00014 (000)Anomaly not confirmed confirmed confirmed confirmed confirmed

D6 Modified CAR approach

Table D6 Modified CAR approach

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Multiple R 051 099 099 099 096F-test 69486 (000) 325351 (000) 1457582 (000) 6345973 (000) 1213344 (000)a0 -01003(000) 04081 (000) -05444 (000) -01088 (000) 00272 (000)a1 00002 (000) 00106 (000) -00127 (000) 00016 (000) -00016 (000)Anomaly confirmed confirmed confirmed confirmed confirmed

26

E Detailed statistical results NASDAQ overall data

E1 Average analysis

Table E1 Average analysis

Parameter Gap day Gap day(Positive gaps)

Gap day(Negative gaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Mean return (gap day) -009 084 -090 022 -037Mean return (non-gap day) 003 003 003 003 003Anomaly confirmed confirmed confirmed confirmed confirmed

E2 Parametric tests Students t-test

Table E2 T-test

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

t-criterion 230 1257 1341 306 664t-critical (=095) 196 196 196 196 196Null hypothesis rejected rejected rejected rejected rejected

E3 Parametric tests ANOVA

Table E3 ANOVA

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

F 2289 62720 88402 3330 17356p-value 0 0 0 0 0F critical 384 384 384 384 384Null hypothesis rejected rejected rejected rejected rejected

E4 Non-parametric tests Kruskal-Wallis test

Table E4 Kruskal-Wallis test

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Adjusted H 1892 36022 45248 4695 10437df 1 1 1 1 1P value 0 0 0 0 0Critical value 384 384 384 384 384Null hypothesis rejected rejected rejected rejected rejected

27

E5 Regression analysis with dummy variables

Table E5 Regression analysis with dummy variables

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

a0 00003 (000) 00003 (000) 00003 (000) 00003 (000) 00003 (000)a1 -00012 (000) 00081 (000) -00093 (000) 00018 (000) -00040 (000)Anomaly confirmed confirmed confirmed confirmed confirmed

E6 Modified CAR approach

Table E6 Modified CAR approach

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Multiple R 069 092 092 072 097F-test 133255 (000) 361102 (000) 442376 (000) 72903 (000) 1082812 (000)a0 -10646 (000) 11373 (000) -12888 (000) 03928 (000) -02297 (000)a1 -00011 (000) 00073 (000) -00097 (000) 00017 (000) -00039 (000)Anomaly confirmed confirmed confirmed confirmed confirmed

28

F Detailed statistical results DJI sub-periods

F1 Average analysis

Table F1 Average analysis

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 Mean return (gapday)

-001 023 015 -004

Mean return(non-gap day)

007 007 007 007

Anomaly confirmed confirmed confirmed confirmed1999-2008 Mean return (gap

day)090 -045 013 -004

Mean return(non-gap day)

-004 -004 -004 -004

Anomaly confirmed confirmed confirmed confirmed2009-2018 Mean return (gap

day)024 -024 0 -004

Mean return(non-gap day)

004 004 004 004

Anomaly confirmed confirmed not confirmed confirmed

F2 Parametric tests Students t-test

Table F2 T-test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 t-criterion 083 165 087 139t-critical (=095) 196 196 196 196Null hypothesis not rejected not rejected not rejected not rejected

1999-2008 t-criterion 347 351 054 047t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected rejected

2009-2018 t-criterion 265 207 051 058t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

F3 Parametric tests ANOVA

Table F3 ANOVA

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 F 085 409 093 179p-value 035 004 033 018

F critical 384 384 384 384Null hypothesis not rejected rejected not rejected not rejected

1999-2008 F 5405 3196 065 072p-value 0 0 042 039

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

2009-2018 F 554 697 024 058p-value 001 0 062 044

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

29

F4 Non-parametric tests Kruskal-Wallis test

Table F4 Kruskal-Wallis test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 Adjusted H 113 211 113 332df 1 1 1 1

P value 029 015 029 007Null hypothesis not rejected not rejected not rejected not rejected

1999-2008 Adjusted H 1484 1414 003 139df 1 1 1 1

P value 0 0 086 024Null hypothesis rejected rejected not rejected not rejected

2009-2018 Adjusted H 506 68 051 171df 1 1 1 1

P value 002 001 047 019Null hypothesis rejected rejected not rejected not rejected

F5 Regression analysis with dummy variables

Table F5 Regression analysis with dummy variables

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 a0 000068 (000) 00007 (000) 00007 (000) 00007 (000)a1 -000078 (035) 00016 (004) 00008 (033) -00011 (018)

Anomaly not confirmed confirmed not confirmed not confirmed1999-2008 a0 00004 (008) 00004 (008) 00004 (006) 00004 (008)

a1 00087 (000) -00049 (000) 00009 (042) -00008 (039)Anomaly confirmed confirmed not confirmed not confirmed

2009-2018 a0 00004 (006) 00004 (006) 00004 (006) 00004 (006)a1 00021 (001) -00028 (001) -00004 (062) -00008 (047)

Anomaly confirmed confirmed not confirmed not confirmed

F6 Modified CAR approach

Table F6 Modified CAR approach

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 Multiple R 083 088 082 086F-test 22779 (000) 40583 (000) 20401 (000) 3269454 (000)a0 00042 (023) 00017 (073) 00014 (058) -00266 (000)a1 -00009 (000) 00015 (000) 00006 (000) -00009 (000)

Anomaly confirmed confirmed confirmed confirmed1999-2008 Multiple R 095 093 076 019

F-test 62658 (000) 84712 (000) 10056 (000) 492 (003)a0 -00972 (000) 00365 (000) -00198 (000) -00115 (021)a1 00086 (000) -00042 (000) 00014 (000) 00002 (003)

Anomaly confirmed confirmed confirmed not confirmed2009-2018 Multiple R 096 082 08 05

F-test 150452 (000) 16731 (000) 22287 (000) 2620 (000)a0 00548 (000) -00618 (000) 00031 (020) -00112 (000)a1 00013 (000) -00014 (000) -00005 (000) -00004 (000)

Anomaly confirmed confirmed not confirmed confirmed

30

G Detailed statistical results NASDAQ sub-periods

G1 Average analysis

Table G1 Average analysis

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 Mean return (gapday)

094 -111 0189 -029

Mean return(non-gap day)

007 007 007 007

Anomaly confirmed confirmed confirmed confirmed1959-1968 Mean return (gap

day)133 -147 033 -039

Mean return(non-gap day)

006 006 006 006

Anomaly confirmed confirmed confirmed confirmed1969-1978 Mean return (gap

day)19 -186 057 -068

Mean return(non-gap day)

005 005 005 005

Anomaly confirmed confirmed confirmed confirmed1979-1988 Mean return (gap

day)138 -162 066 -04

Mean return(non-gap day)

008 008 008 008

Anomaly confirmed confirmed confirmed confirmed1989-1998 Mean return (gap

day)016 012 018 -009

Mean return(non-gap day)

002 002 002 002

Anomaly confirmed not confirmed confirmed confirmed1999-2008 Mean return (gap

day)38E-3 027 -036 -013

Mean return(non-gap day)

-01 -01 -01 -01

Anomaly confirmed not confirmed not confirmed not confirmed2009-2018 Mean return (gap

day)039 009 013 -025

Mean return(non-gap day)

001 001 001 001

Anomaly confirmed not confirmed confirmed confirmed

G2 Parametric tests Students t-test

Table G2 T-test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 t-criterion 3194 3076 201 559t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected rejected

1959-1968 t-criterion 1399 2246 443 382t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected rejected

1969-1978 t-criterion 261 4358 417 786t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected rejected

1979-1988 t-criterion 1847 1445 709 395t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected rejected

1989-1998 t-criterion 13 066 126 093t-critical (=095) 196 196 196 196Null hypothesis not rejected not rejected not rejected not rejected

1999-2008 t-criterion 192 106 111 009t-critical (=095) 196 196 196 196Null hypothesis not rejected not rejected not rejected not rejected

2009-2018 t-criterion 27 05 089 188t-critical (=095) 196 196 196 196Null hypothesis rejected not rejected not rejected not rejected

31

G3 Parametric tests ANOVA

Table G3 ANOVA

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 F 88153 190609 1272 14521p-value 0 0 0 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1959-1968 F 93974 149771 4715 10418p-value 0 0 0 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1969-1978 F 84546 145429 6295 18241p-value 0 0 0 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1979-1988 F 66952 110482 13138 8626p-value 0 0 0 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1989-1998 F 323 138 43 168p-value 007 024 003 019

F critical 384 384 384 384Null hypothesis not rejected not rejected rejected not rejected

1999-2008 F 106 512 327 003p-value 001 002 007 085

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

2009-2018 F 169 069 175 93p-value 0 04 018 0

F critical 384 384 384 384Null hypothesis rejected not rejected not rejected rejected

G4 Non-parametric tests Kruskal-Wallis test

Table G4 Kruskal-Wallis test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 Adjusted H 26254 32592 1464 3962df 1 1 1 1

P value 0 0 0 0Null hypothesis rejected rejected rejected rejected

1959-1968 Adjusted H 28235 27989 2736 332df 1 1 1 1

P value 0 0 0 0Null hypothesis rejected rejected rejected rejected

1969-1978 Adjusted H 22202 33777 3311 7591df 1 1 1 1

P value 0 0 0 0Null hypothesis rejected rejected rejected rejected

1979-1988 Adjusted H 23282 25292 4812 3964df 1 1 1 1

P value 0 0 0 0Null hypothesis rejected rejected rejected rejected

1989-1998 Adjusted H 381 017 175 132df 1 1 1 1

P value 005 068 019 025Null hypothesis not rejected not rejected not rejected not rejected

1999-2008 Adjusted H 855 023 044 004df 1 1 1 1

P value 0 063 051 084Null hypothesis rejected not rejected not rejected not rejected

2009-2018 Adjusted H 1063 009 257 709df 1 1 1 1

P value 0 077 011 001Null hypothesis rejected not rejected not rejected rejected

32

G5 Regression analysis with dummy variables

Table G5 Regression analysis with dummy variables

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 a0 00007 (000) 00007 (000) 00007 (000) 00007 (000)a1 00088 (000) -00119 (000) 00011 (000) -00036 (000)

Anomaly confirmed confirmed confirmed confirmed1959-1968 a0 00006 (000) 00006 (000) 00006 (000) 00006 (000)

a1 00128 (000) -00153 (000) 00027 (000) -00046 (000)Anomaly confirmed confirmed confirmed confirmed

1969-1978 a0 00005 (000) 00005 (000) 00005 (000) 00005 (000)a1 00185 (000) -00192 (000) 00053 (000) -00073 (000)

Anomaly confirmed confirmed confirmed confirmed1979-1988 a0 00008 (000) 00008 (000) 00008 (000) 00008 (000)

a1 00131 (000) -00172 (000) 00059 (000) -00048 (000)Anomaly confirmed confirmed confirmed confirmed

1989-1998 a0 00002 (027) 00002 (028) 00002 (028) 00002 (027)a1 00014 (007) 00010 (024) 00017 (004) -00011 (019)

Anomaly not confirmed not confirmed confirmed not confirmed1999-2008 a0 00001 (059) 00001 (062) 00001 (059) 00001 (060)

a1 00037 (000) 00026 (002) -00038 (000) -00014 (019)Anomaly confirmed not confirmed not confirmed not confirmed

2009-2018 a0 00001 (049) 00001 (049) 00001 (049) 00001 (049)a1 00038 (000) 00007 (040) 00012 (018) -00027 (000)

Anomaly confirmed not confirmed not confirmed confirmed

G6 Modified CAR approach

Table G6 Modified CAR approach

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 Multiple R 099 099 093 098F-test 5753605 (000) 100470(000) 6280421 283281a0 -00091 (000) -00349 (000) 00056 (001) 00015 (073)a1 00083 (000) -00110 (000) 00010 (000) -00031 (000)

Anomaly confirmed confirmed confirmed confirmed1959-1968 Multiple R 099 099 099 099

F-test 3923274 (000) 3005562 (000) 443198 (000) 372583 (000)a0 00096 (000) 00073 (016) -00082 (000) -00095 (004)a1 00116 (001) -00149 (000) 00025 (000) -00047 (000)

Anomaly confirmed confirmed confirmed confirmed1969-1978 Multiple R 099 099 098 099

F-test 4302608 (000) 2723953 (000) 179969 (000) 639745a0 00246 (000) -00002 (000) 00217 (000) -00514 (000)a1 00176 (000) -00182 (000) 00049 (000) -00062 (000)

Anomaly confirmed confirmed confirmed confirmed1979-1988 Multiple R 099 099 099 099

F-test 5872335 (000) 1182609 (000) 1083558 (000) 910089 (000)a0 00136 (000) -01081 (000) -00285 (000) -00101 (000)a1 00131 (000) -00167 (000) 00062 (000) -00048 (000)

Anomaly confirmed confirmed confirmed confirmed1989-1998 Multiple R 09 056 069 016

F-test 46947 (000) 4885 (000) 10131 (000) 263 (011)a0 00102 (002) -00261 (000) -0016 (001) -00237 (000)a1 00015 (000) 00010 (000) 0001 (000) 00002 (011)

Anomaly confirmed confirmed confirmed not confirmed1999-2008 Multiple R 093 087 073 037

F-test 71863 (000) 32530 (000) 13273 (000) 1669 (000)a0 00185 (004) 00311 (000) -00130 (039) -00546 (000)a1 00037 (000) 00032 (000) -00026 (000) -00007 (000)

Anomaly confirmed not confirmed not confirmed confirmed2009-2018 Multiple R 089 001 096 091

F-test 40818 (000) 000 (094) 116744 (000) 53770 (000)a0 01436 (000) -01099 (000) -01036 (000) 00697 (000)a1 00030 (000) 00000 (094) 00024 (000) -00021 (000)

Anomaly confirmed not confirmed confirmed confirmed

33

H Detailed statistical results SampP 500 sub-periods

H1 Average analysis

Table H1 Average analysis

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 Mean return (gapday)

138 -171 004 -014

Mean return(non-gap day)

0 0 0 0

Anomaly confirmed confirmed confirmed confirmed1939-1948 Mean return (gap

day)001 -042 172 -195

Mean return(non-gap day)

003 003 003 003

Anomaly confirmed confirmed confirmed confirmed1949-1958 Mean return (gap

day)165 -18 02 002

Mean return(non-gap day)

006 006 006 006

Anomaly confirmed confirmed confirmed not confirmed1959-1968 Mean return (gap

day)104 -102 015 0

Mean return(non-gap day)

002 002 002 002

Anomaly confirmed confirmed confirmed not confirmed1969-1978 Mean return (gap

day)131 -13 019 -03

Mean return(non-gap day)

0 0 0 0

Anomaly confirmed confirmed confirmed confirmed1979-1988 Mean return (gap

day)058 -042 015 003

Mean return(non-gap day)

005 005 005 005

Anomaly confirmed confirmed confirmed not confirmed1989-1998 Mean return (gap

day)02 -023 -002 01

Mean return(non-gap day)

007 007 007 007

Anomaly confirmed confirmed not confirmed not confirmed1999-2008 Mean return (gap

day)083 -089 -023 -005

Mean return(non-gap day)

001 001 001 001

Anomaly confirmed confirmed not confirmed confirmed2009-2018 Mean return (gap

day)055 -052 001 -015

Mean return(non-gap day)

004 004 004 004

Anomaly confirmed confirmed not confirmed confirmed

34

H2 Parametric tests Students t-test

Table H2 T-test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 t-criterion 101 85 029 048t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

1939-1948 t-criterion 064 479 3074 225t-critical (=095) 196 196 196 196Null hypothesis not rejected rejected rejected rejected

1949-1958 t-criterion 2964 2383 193 041t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

1959-1968 t-criterion 2281 2157 21 023t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected not rejected

1969-1978 t-criterion 1318 2034 187 321t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected rejected

1979-1988 t-criterion 435 535 07 037t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

1989-1998 t-criterion 201 396 132 052t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

1999-2008 t-criterion 362 433 117 022t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

2009-2018 t-criterion 375 382 027 132t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

H3 Parametric tests ANOVA

Table H3 ANOVA

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 F 6281 8032 005 051p-value 0 0 082 047

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

1939-1948 F 056 2603 34854 51034p-value 045 0 0 0

F critical 384 384 384 384Null hypothesis not rejected rejected rejected rejected

1949-1958 F 100174 128997 897 062p-value 0 0 0 043

F critical 384 384 384 384Null hypothesis rejected rejected rejected not rejected

1959-1968 F 36831 32858 617 01p-value 0 0 001 074

F critical 384 384 384 384Null hypothesis rejected rejected rejected not rejected

1969-1978 F 26601 3063 53 152p-value 0 0 002 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1979-1988 F 23 245 076 009p-value 0 0 039 077

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

1989-1998 F 399 1156 118 015p-value 004 0 027 069

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

1999-2008 F 4253 5622 365 024p-value 0 0 006 062

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

2009-2018 F 3064 3656 01 43p-value 0 0 075 004

F critical 384 384 384 384Null hypothesis rejected rejected not rejected rejected

35

H4 Non-parametric tests Kruskal -Wallis test

Table H4 Kruskal-Wallis test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 Adjusted H 9982 5913 332 14df 1 1 1 1

P value 0 0 007 024Null hypothesis rejected rejected not rejected not rejected

1939-1948 Adjusted H 494 1999 23387 24927df 1 1 1 1

P value 003 0 0 0Null hypothesis rejected rejected rejected rejected

1949-1958 Adjusted H 28728 28175 348 15df 1 1 1 1

P value 0 0 006 022Null hypothesis rejected rejected not rejected not rejected

1959-1968 Adjusted H 25729 21437 701 063df 1 1 1 1

P value 0 0 001 043Null hypothesis rejected rejected rejected not rejected

1969-1978 Adjusted H 14407 20078 27 1706df 1 1 1 1

P value 0 0 01 0Null hypothesis rejected rejected not rejected rejected

1979-1988 Adjusted H 1788 2836 027 034df 1 1 1 1

P value 0 0 06 056Null hypothesis rejected rejected not rejected not rejected

1989-1998 Adjusted H 251 1431 111 044df 1 1 1 1

P value 011 0 029 051Null hypothesis not rejected rejected not rejected not rejected

1999-2008 Adjusted H 1812 1788 042 002df 1 1 1 1

P value 0 0 052 089Null hypothesis rejected rejected not rejected not rejected

2009-2018 Adjusted H 1314 1783 074 37df 1 1 1 1

P value 0 0 039 005Null hypothesis rejected rejected not rejected not rejected

36

H5 Regression analysis with dummy variables

Table H5 Regression analysis with dummy variables

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 a0 00000 (097) 00000 (004) 00000 (097) 00000 (097)a1 00138 (000) -00172 (000) 00004 (082) -00014 (047)

Anomaly confirmed confirmed not confirmed not confirmed1939-1948 a0 00003 (015) 00003 (015) 00003 (015) 00003 (015)

a1 00007 (045) -00045 (000) 00170 (000) -00199 (000)Anomaly not confirmed confirmed confirmed confirmed

1949-1958 a0 00006 (000) 00006 (000) 00006 (000) 00006 (000)a1 00160 (000) -00188 (000) 00016 (000) -00004 (043)

Anomaly confirmed confirmed confirmed not confirmed1959-1968 a0 00002 (007) 00002 (004) 00002 (008) 00002 (008)

a1 00103 (000) -00105 (000) 00014 (001) -00002 (074)Anomaly confirmed confirmed confirmed not confirmed

1969-1978 a0 00000 (078) 00000 (078) 00000 (078) 00000 (078)a1 00132 (000) -00132 (000) 00019 (002) -00030 (000)

Anomaly confirmed confirmed confirmed confirmed1979-1988 a0 00006 (001) 00006 (001) 00006 (001) 00006 (000)

a1 00053 (000) -00048 (000) 00009 (040) -00003 (075)Anomaly confirmed confirmed not confirmed not confirmed

1989-1998 a0 00007 (000) 00007 (000) 00007 (000) 00007 (000)a1 00016 (005) -00030 (000) -00009 (026) 00003 (072)

Anomaly confirmed confirmed not confirmed not confirmed1999-2008 a0 00001 (075) 00001 (075) 00001 (075) 00001 (076)

a1 00083 (000) -00091 (000) -00024 (005) -00006 (062)Anomaly confirmed confirmed not confirmed not confirmed

2009-2018 a0 00004 (003) 00004 (000) 00004 (003) 00004 (003)a1 00051 (000) -00059 (000) -00003 (075) -00019 (003)

Anomaly confirmed confirmed not confirmed confirmed

37

H6 Modified CAR approach

Table H6 Modified CAR approach

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 Multiple R 096 095 046 046F-test 175935 (000) 96500 (000) 3534 (000) 2880 (000)a0 -01070 (000) 01958 (000) 00405 (000) 00535 (000)a1 00121 (000) -00160 (000) 00006 (000) -00014 (000)

Anomaly confirmed confirmed confirmed confirmed1939-1948 Multiple R 08 099 099 099

F-test 18777 (000) 755727 (000) 3572830 (000) 2696099 (000)a0 00019 (073) -00346 (000) -00373 (000) 00912 (000)a1 00012 (000) -00044 (000) 00168 (000) -00197 (000)

Anomaly confirmed confirmed confirmed confirmed1949-1958 Multiple R 099 099 094 015

F-test 1021705 (000) 7171257 (000) 75858 (000) 242 (012)a0 -00176 (000) -00191 (000) 00095 (000) -00498 (000)a1 00154 (000) -00181 (000) 00013 (000) -00002 (012)

Anomaly confirmed confirmed confirmed not confirmed1959-1968 Multiple R 099 099 094 078

F-test 1463311 (000) 6002659 (000) 82273 (000) 14352 (000)a0 -00112 (000) 00004 (085) 00151 (000) 00389 (000)a1 00098 (000) -00102 (000) 00011 (000) -00009 (000)

Anomaly confirmed confirmed confirmed confirmed1969-1978 Multiple R 098 099 093 099

F-test 241655 (000) 1451901 (000) 57333 (000) 368160 (000)a0 -00433 (000) 00276 (000) 00099 (002) -00144 (000)a1 00132 (000) -00134 (000) 00020 (000) -00030 (000)

Anomaly confirmed confirmed confirmed confirmed1979-1988 Multiple R 092 078 023 008

F-test 53757 (000) 18707 (000) 487 (003) 085 (036)a0 00813 (000) -02508 (000) 00204 (000) -00235 (000)a1 00036 (000) -00031 (000) -00003 (003) -00001 (036)

Anomaly confirmed confirmed not confirmed not confirmed1989-1998 Multiple R 079 099 074 044

F-test 19705(000) 761967 (000) 14133 (000) 2369 (000)a0 00268 (000) 00023 (021) -00381 (000) 00087 (000)a1 00013 (000) -00028 (000) -00008 (000) 00002 (000)

Anomaly confirmed confirmed not confirmed not confirmed1999-2008 Multiple R 091 093 071 065

F-test 47218 (000) 76564 (000) 9843 (000) 7768 (000)a0 -01493 (000) 01351 (000) 00397 (000) 00007 (093)a1 00081 (000) -00083 (000) -00026 (000) -00011 (000)

Anomaly confirmed confirmed not confirmed confirmed2009-2018 Multiple R 086 087 083 074

F-test 29971 (000) 32484 (000) 23228 (000) 12764 (000)a0 01711 (000) -02250 (000) 00407 (000) -00472 (000)a1 00038 (000) -00044 (000) -00010 (000) -00012 (000)

Anomaly confirmed confirmed not confirmed confirmed

38

not we also run the following regressions

Rt = a0 + a1Dt + 983171t (3)

where Rt is the return in period t a0 is the mean return in a normal period a1 is themean return in an abnormal period Dt is a dummy variable equal to 1 in abnormalperiods and 0 in normal period and 983171t is the random error term The sign and statis-tical significance of the dummy coefficients indicate the existence or not of price gapsanomalies

To avoid methodological bias we utilise the modified cumulative abnormal returnsapproach (MCAR) which was developed by Plastun et al (2019b) based on the work ofMacKinlay (1997) and recently utilised by Plastun et al (2019a) in the Ukraine stockmarket to detect price gap anomalies Plastun et al (2019b) developed this MCARapproach in the context of calendar anomalies and their evolution over time In thispaper we summarise the MCAR approach however further details of the MCAR canbe found in Plastun et al (2019b) Abnormal returns are defined as follows

ARt = Rt minus E(Rt) (4)

where Rt is the return and ARt is the abnormal return at time t E(Rt) is the iscorresponding average return computed over the entire sample as follows

E(Rt) =

9830611

T

983062983131T

i=1Ri (5)

where T is the sample size

The cumulative abnormal return denoted as CARi is simply the sum of the abnormalreturns

CARi =983131T

i=1ARi (6)

A trend in cumulative abnormal returns data confirms abnormal returns A simpleregression model is built to estimate the trend component A high multiple Rminussquaredand overall model significance (F minus test) and the statistical significance (pminus values) ofthe coefficients confirm or reject the presence of trend in the abnormal returns

In instances where a price gap anomaly is detected we test whether it gives riseto exploitable profits using the trading simulation approach The trading simulationapproach replicates the actions of a trader given the price anomaly trading strategy Ifthis trading strategy generates 50 per cent or more profitable trades and produces anoverall financial result of more than zero (excluding transaction costs) this indicates

6

that this strategy is efficient A z minus test is then conducted to ensure that the results ofthe trading strategy are not random using a 5 per cent level of significance

4 Results

The results of the SampP 500 are presented and contrasted with those of the DJI and theNASDAQ We focus on the SampP 500 specifically as it has the longest sample and there-fore can offer better insights as compared to the DJI and the NASDAQ The summaryresults for the DJI and the NASDAQ can be found in Appendix A The results of theshort term price behaviour tests are in Appendix B The detailed results of the overalldata sets for all indexes can be found in Appendices C to E Similarly the detailedresults of the sub-periods within the overall data sets can be found in Appendices F toH

41 Price gap size

First an appropriate gap size must be as a criterion for gap detection Caporale andPlastun (2017) show that the gap size significantly influences the number of detectedanomalies To confirm this we analyse SampP 500 data for the 2009-2018 sub-period Ascan be seen from Table 2 a small gap size choice generates too many gaps to be consid-ered as anomalies A large gap size provides very few cases for analysis and may leadto statistical insignificance of the results For this study (which is primarily based onstatistical analysis and tests) the number of observations should be around 100 to makeresults statistically significant This represents less than 10 per cent of the populationand hence can be considered anomalies As a result gap size is not constant and maydiffer from index to index and between sub-periods (see Table 3 and Table A1) Thisinconsistency in the gap size can be considered additional evidence in favour of pricegap anomaly evolution

7

Tab

le2

Gap

size

andthenumber

ofdetectedgapscase

ofSampP500dataover

theperiod2009-2018

Gap

size

010

020

030

040

050

060

070

080

090

100

gapsin

prices

4105

1970

1090

571

345

202

135

087

067

052

Number

ofdetectedgaps

1038

497

275

144

8751

3422

1713

Number

ofdetectednegativegaps

468

230

130

6944

3120

109

8Number

ofdetectedpositivegaps

570

267

145

7543

2014

128

5

8

Table 3 Gap size used for different sub-periods over the period 1929-2018

Period SampP 5001929-1938 1201949-1958 1201959-1968 0701969-1978 0011979-1988 0031989-1998 0011999-2008 0082009-2018 034Overall data set 070

42 Price gap seasonality

Caporale and Plastun (2017) show that in foreign exchange and commodity marketsprice gaps tend to appear on Mondays According to their results more than 95 percent of price gaps in foreign exchange markets compared to 65 per cent of price gaps incommodity markets appeared on Mondays This is rather reasonable because marketsare closed on weekends and as the result of any significant event over the weekend willlead to price gaps on Monday Surprisingly this is not the case in this instance (withstock markets) as can be seen in Tables 4 and A2 Therefore H3 is rejected

Table 4 Day of the week and gaps

Day of the week SampP 500Monday 023Tuesday 02Wednesday 02Thursday 018Friday 019

43 Short term price behaviour

Next we analyse short-term price behaviour in the US stock market around price gapsto investigate the presence of possible price patterns before and after price gaps Wecalculate the number of days with positive (or negative) returns after a positive (or neg-ative) price gaps divided by the total number of price gaps If this ratio or momentum

9

effect is much higher than 50 per cent this indicates abnormal price behaviour and asthe results confirm our hypotheses

The results are presented in Appendix B We find no convincing evidence in favour ofmomentum effect after price gaps (Table B1) and before them (Table B2) In generalprice gaps are not generated by previous price dynamics (NASDAQ index is an exceptionas negative gaps appear in 70 per cent of the cases after downward price movements andafter positive gaps in 67 per cent of the cases upward price movements are observed)Our results (see Table B3 for details) also indicate that the probability that price gapswill be filled within 5 days after appearance is very low at around 20 per cent

44 Price gap evolution

Overall in probabilistic terms price gaps do not generate any stable patterns But therecan be patterns in terms of size of price movements after gaps To check this we will testH1 and H2 To incorporate price direction in results of analysis H1 we further test forH1minus1 and H1minus2 The results for the overall data sets are presented in Appendices C toE for the cases of DJI SampP 500 and NASDAQ respectively To ease the interpretationof results we have summarised them in Table 5 and Table A3

Table 5 shows strong evidence confirming H1 in the SampP 500 Similarly Table A3confirms H1 for the NASDAQ but not for the DJI The difference between the DJI SampP500 and NASDAQ results can be explained by the differences in samples (DJI sampleis much shorter) This suggests that price gap anomaly may evolve and is therefore apreliminary confirmation of H2

Tables 6 and 7 confirm H1minus1 in the SampP 500 on the day of the price gap That ison the price gap day prices tend towards the direction of the price gap However thisis not the case for the day after the price gap therefore H1minus2 is not confirmed It canbe concluded that the SampP 500 roughly needs a day to absorb new information Never-theless even a day can be enough to create a profitable trading strategy and generateabnormal profits from trading

Similar results on the NASDAQ can be found in Tables A6 and A7 The longersample of the NASDAQ allows for the evolution of the price anomaly H1minus1 is there-fore confirmed on the day of the price gap anomaly and the day after the price gapanomaly (in both instances only until the 1990s and has since disappeared) H1minus2 inboth instances is confirmed up until the 1990s The results of the DJI did not providestrong evidence in favour of H1minus1 and H1minus2 on the day after the price gap but sim-ilar to the SampP 500 evidence was strong on the day of the price gap (see Tables A4and A5) These results confirm in the main the price gap anomaly is a reality in theUS stock market and that it evolves over time that is from prevalence to disappearance

10

Tab

le5

Overallstatisticalresults

SampP500

PeriodM

ethod

Average

analysis

t-test

ANOVA

test

Man

n-

Whitney

test

Regression

analysis

with

dummy

variab

les

Modified

CAR

approach

Overall

Gap

day

+-

-+

-+

3Gap

day

(Positivegaps)

++

++

++

6Gap

day

(Negativegaps)

++

++

++

6Day

aftergap(P

ositivegaps)

++

-+

++

5Day

aftergap(N

egativegaps)

++

--

++

4

Note+

indicates

thattheanom

alyis

confirm

edand-indicates

thatan

omaly

isnot

confirm

edThehigher

theoverallrating

the

strongertheeviden

ceofthean

omaly

11

Tab

le6

H1minus1summarystatisticalresults

SampP500sub-periods

PeriodM

ethod

Average

analysis

t-test

ANOVA

test

Man

n-

Whitney

test

Regression

analysis

withdummy

variab

les

Modified

CAR

approach

Overall

Dayofanomaly

1929-1938

++

++

++

61939-1948

+-

-+

-+

31949-1958

++

++

++

61959-1968

++

++

++

61969-1978

++

++

++

61979-1988

++

++

++

61989-1998

++

++

++

61999-2008

++

++

++

62009-2018

++

++

++

6Dayafteranomaly

1929-1938

+-

--

-+

21939-1948

++

++

++

61949-1958

+-

+-

++

51959-1968

++

++

++

61969-1978

+-

+-

++

41979-1988

+-

--

--

11989-1998

--

--

--

01999-2008

--

--

--

02009-2018

--

--

--

0

Note+

indicates

thattheanom

alyis

confirm

edand-indicates

thatan

omaly

isnot

confirm

edThehigher

theoverallrating

the

strongertheeviden

ceofthean

omaly

12

Tab

le7

H1minus2statisticalresults

SampP500sub-periods

PeriodM

ethod

Average

analysis

t-test

ANOVA

test

Man

n-

Whitney

test

Regression

analysiswith

dummy

variab

les

Modified

CAR

approach

Overall

Dayofanomaly

1929-1938

++

++

++

61939-1948

++

++

++

61949-1958

++

++

++

61959-1968

++

++

++

61969-1978

++

++

++

61979-1988

++

++

++

61989-1998

++

++

++

61999-2008

++

++

++

62009-2018

++

++

++

6Dayafteranomaly

1929-1938

+-

--

-+

21939-1948

++

++

++

61949-1958

--

--

--

01959-1968

--

--

-+

11969-1978

++

++

++

61979-1988

--

--

--

01989-1998

--

--

--

01999-2008

+-

--

-+

22009-2018

+-

+-

++

4

Note+

indicates

thattheanom

alyis

confirm

edand-indicates

thatan

omaly

isnot

confirm

edThehigher

theoverallrating

the

strongertheeviden

ceofthean

omaly

13

45 Trading simulation

The algorithm of the trading strategy is to buysell at the start of the updown gapday and close this position at the end of this day To test this strategy data for the DJIand SampP 500 are used (for this case the price anomaly still exists based on the day itoccurred) The results for DJI are presented in Table A8 and for the SampP 500 in Table8 For the SampP 500 and DJI the trading strategy built on price gap anomaly is efficientand its results differ from random

Table 8 Trading simulation results of the price gap anomaly for the SampP 500

Period Gaptype

Numberof

tradesunits

Numberof suc-cessfultradesunits

Numberof suc-cessfultrades

Profit

Profit peryear

z-test Result

1929-1938 Up 131 130 992 1816 182 1065 passedDown 110 108 982 1893 189 876 passed

1939-1948 Up 110 67 609 106 11 09 failedDown 122 79 648 518 52 465 passed

1949-1958 Up 106 105 991 1765 176 3191 passedDown 104 103 99 1891 189 2356 passed

1959-1968 Up 108 106 981 1331 113 2441 passedDown 92 91 989 948 95 2214 passed

1969-1978 Up 85 71 835 1128 113 1361 passedDown 96 90 938 1262 126 2118 passed

1979-1988 Up 92 63 685 54 54 495 passedDown 123 81 659 519 52 496 passed

1989-1998 Up 117 72 615 267 27 295 passedDown 99 61 616 228 23 32 passed

1999-2008 Up 99 65 657 828 83 373 passedDown 110 72 655 987 99 438 passed

2009-2018 Up 106 71 67 59 59 416 passedDown 107 65 607 56 56 362 passed

14

Figure 1 Trading simulation results of the price gap anomaly for the SampP 500

Note The primary axis refers to the percentage profit per year and the secondary to thez minus test statistic

One more interesting fact (see Figure 1) is the decrease of trading strategy efficiencyThis is indirect evidence in favour of evolution of the US stock market and its movementfrom less efficient to more efficient state Overall it can be concluded that the price gapanomaly is a real market anomaly The US stock market loses its efficiency after pricegaps This effect is temporary and lasts only for a day Still even this time is enoughto exploit the hole in the market efficiency and generate abnormal profits from trading

5 Conclusion

We analysed price gap anomaly in the US stock market by using information from threestock market indexes(DJI SampP 500 and NASDAQ) We tested three hypotheses of in-terest that is H1 the price gap anomaly exists H1minus1 prices tend to rise after positivegaps H1minus2 prices tend to fall after negative gaps H2 the price gap anomaly evolvesand H3 there is seasonality in price gaps Various statistical methods including para-metric tests (Students t-tests ANOVA) non-parametric tests (Mann-Whitney test)regression analysis with dummy variables MCAR approach and the trading simulationapproach were utilised

We conclude that the US stock market in the main did not exhibit seasonality in pricegaps Therefore H3 is rejected Furthermore no evidence was found that price gaps inthe US stock market were filled within five days of their occurrence However strongevidence in favour of abnormal price movements after the gaps were found confirming

15

H1 and H2 Particularly on the day of the occurrence of the gap and not on the dayafter the price gap In the DJI and the SampP 500 this pattern persists indicating thatthese markets take a day to incorporate new information As the results of the tradingsimulation indicate a day is enough to profit from a price gap anomaly trading strategyin the DJI and the SampP 500

Similar to other studies and other anomalies (see McLean and Pontiff (2016) Ca-jueiro and Tabak (2004) and Tiwari et al (2019) for example) the price gap anomalyevolved It is less prevalent since the 1990s as shown in the SampP 500 and NASDAQThis pattern of evolution is common amongst most stock market anomalies (see Plastunet al (2019b) on calendar anomalies amongst others) Our findings therefore add onto the existing literature Finally in the main our results are against the EMH and aretherefore interesting to both practitioners and academics

16

References

Agrawal A and Tandon K (1994) Anomalies or illusions evidence from stock marketsin eighteen countries Journal of international Money and Finance 13(1)83ndash106

Akerlof G A and Shiller R J (2009) Animal Spirits How human psychology drivesthe economy and why it matters for global capitalism Princeton University Press

Basu S (1977) Investment performance of common stocks in relation to their price-earnings ratios A test of the efficient market hypothesis The Journal of Finance32(3)663ndash682

Bildik R (2004) Are calendar anomalies still alive Evidence from istanbul stockexchange SSRN Electronic Journal 2004

Cai J Li Y and Qi Y (2006) The day-of-the-week effect New evidence from theChinese stock market Chinese Economy 39(2)71ndash88

Cajueiro D O and Tabak B M (2004) The Hurst exponent over time testing theassertion that emerging markets are becoming more efficient Physica A StatisticalMechanics and its Applications 336(3-4)521ndash537

Caporale G M Gil-Alana L Plastun A and Makarenko I (2016) Intraday anoma-lies and market efficiency A trading robot analysis Computational Economics47(2)275ndash295

Caporale G M and Plastun A (2017) Price gaps Another market anomaly Invest-ment Analysts Journal 46(4)279ndash293

Cross F (1973) The behavior of stock prices on Fridays and Mondays FinancialAnalysts Journal 29(6)67ndash69

Fama E F (1965) The behavior of stock-market prices The Journal of Business38(1)34ndash105

Fama E F (1970) Efficient capital markets A review of theory and empirical workThe Journal of Finance 25(2)383ndash417

Fortune P (1998) Weekends can be rough revisiting the weekend effect in stock pricesTechnical report

Fortune P (1999) Are stock returns different over weekends A jump diffusion analysisof the weekend effect New England Economic Review 103ndash19

French K R (1980) Stock returns and the weekend effect Journal of FinancialEconomics 8(1)55ndash69

Fung A K-W Lam K and Lam K-M (2010) Do the prices of stock index futuresin asia overreact to us market returns Journal of Empirical Finance 17(3)428ndash440

17

Gibbons M R and Hess P (1981) Day of the week effects and asset returns Journalof business pages 579ndash596

Grant J L Wolf A and Yu S (2005) Intraday price reversals in the us stock indexfutures market A 15-year study Journal of Banking amp Finance 29(5)1311ndash1327

Grossman S J and Stiglitz J E (1980) On the impossibility of informationallyefficient markets The American Economic Review 70(3)393ndash408

Jacobsen B Mamun A and Visaltanachoti N (2005) Seasonal size and valueanomalies

Jensen M (1978) Some anomalous evidence regarding market efficiency Journal ofFinancial Economics 6(23 (1978))95ndash101

Lakonishok J and Smidt S (1988) Are seasonal anomalies real A ninety-year per-spective The Review of Financial Studies 1(4)403ndash425

MacKinlay A (1997) Event studies in economics and finance Journal of EconomicLiterature (35)113ndash39

Mandelbrot B B (1997) The variation of certain speculative prices In Fractals andscaling in finance pages 371ndash418 Springer

McLean R D and Pontiff J (2016) Does academic research destroy stock returnpredictability The Journal of Finance 71(1)5ndash32

Plastun A Makarenko I Khomutenko L Shcherbak S and Tryfonova O (2019a)Exploring price gap anomaly in the ukrainian stock market Investment Managementamp Financial Innovations 16(2)150

Plastun A Sibande X Gupta R and Wohar M E (2019b) Rise and fall of calendaranomalies over a century The North American Journal of Economics and Finance49181ndash205

Schwert G W (2003) Chapter 15 anomalies and market efficiency In FinancialMarkets and Asset Pricing volume 1 of Handbook of the Economics of Finance pages939 ndash 974 Elsevier

Shiller R J (2000) Irrational exuberance Princeton University

Tiwari A K Aye G C and Gupta R (2019) Stock market efficiency analysis usinglong spans of data A multifractal detrended fluctuation approach Finance ResearchLetters 28398ndash411

Yuan Y (2015) Market-wide attention trading and stock returns Journal of FinancialEconomics 116(3)548ndash564

18

Appendices

A DJI and NASDAQ Summary Results

A1 Overall Results

Table A1 Gap size used for different sub-periods over the period 1929-2018

Period DJI NASDAQ1929-1938 - -1939-1948 - -1949-1958 - 0711959-1968 - 0951969-1978 - 1351979-1988 - 1101989-1998 040 0681999-2008 007 1502009-2018 020 110Overall data set 030 110

Table A2 Day of the week and gaps

Day of the week DJI NASDAQMonday 024 02Tuesday 02 02Wednesday 017 02Thursday 019 019Friday 021 02

A2 Statistical tests

Table A3 Results of the statistical tests for the overall data sets

PeriodMethod Averageanalysis

t-test ANOVAtest

Mann-Whitney

test

Regressionanalysiswith

dummyvariables

ModifiedCAR

approach

Overall

Dow Jones Index overall data setGap day - - - - - + 1Gap day (Positive gaps) + - - - - - 1Gap day (Negative gaps) + - - - - + 2Day after gap (Positive gaps) + - - - - - 1Day after gap (Negative gaps) + - - + - + 3

NASDAQ overall data setGap day + + + + + + 6Gap day (Positive gaps) + + + + + + 6Gap day (Negative gaps) + + + + + + 6Day after gap (Positive gaps) + + + + + + 6Day after gap (Negative gaps) + + + + + + 6

Note + indicates that the anomaly is confirmed and - indicates that anomaly is not confirmedThe higher the overall rating the stronger the evidence of the anomaly

19

Table A4 Results of the statistical tests for H1minus1 DJI

Period Averageanalysis

t-test ANOVA test Mann-Whitney

test

Regressionanalysis with

dummyvariables

ModifiedCAR

approach

Overall

Day of anomaly1989-1998 + - - - - + 21999-2008 + + + + + + 62009-2018 + + + + + + 6

Day after anomaly1989-1998 + - - - - + 21999-2008 + - - - - + 22009-2018 - - - - - - 0

Note + indicates that the anomaly is confirmed and - indicates that anomaly is not confirmedThe higher the overall rating the stronger the evidence of the anomaly

Table A5 Results of the statistical tests for H1minus2 DJI

Period Averageanalysis

t-test ANOVA test Mann-Whitneytest

Regressionanalysis with

dummyvariables

Modified CARapproach

Overall

Day of anomaly1989-1998 - - - - - - 01999-2008 + + + + + + 62009-2018 + + + + + + 6

Day after anomaly1989-1998 + - - - - + 21999-2008 + - - - - - 12009-2018 + - - - - + 2

Note + indicates that the anomaly is confirmed and - indicates that anomaly is not confirmedThe higher the overall rating the stronger the evidence of the anomaly

Table A6 Results of the statistical tests for H1minus1 NASDAQ

PeriodMethod Averageanalysis

t-test ANOVA test Mann-Whitney

test

Regressionanalysis with

dummyvariables

ModifiedCAR

approach

Overall

Day of anomaly1949-1958 + + + + + + 61959-1968 + + + + + + 61969-1978 + + + + + + 61979-1988 + + + + + + 61989-1998 + - - - - + 21999-2008 + - + + + + 52009-2018 + + + + + + 6

Day after anomaly1949-1958 + + + + + + 61959-1968 + + + + + + 61969-1978 + + + + + + 61979-1988 + + + + + + 61989-1998 + - + - + + 41999-2008 - - - - - - 02009-2018 + - - - - + 2

Note + indicates that the anomaly is confirmed and - indicates that anomaly is not confirmedThe higher the overall rating the stronger the evidence of the anomaly

20

Table A7 Results of the statistical tests for H1minus2 NASDAQ

PeriodMethod Averageanalysis

t-test ANOVA test Mann-Whitney

test

Regressionanalysis with

dummyvariables

ModifiedCAR

approach

Overall

Day of anomaly1949-1958 + + + + + + 61959-1968 + + + + + + 61969-1978 + + + + + + 61979-1988 + + + + + + 61989-1998 - - - - - + 11999-2008 - - + - - - 12009-2018 - - - - - - 0

Day after anomaly1949-1958 + + + + + + 61959-1968 + + + + + + 61969-1978 + + + + + + 61979-1988 + + + + + + 61989-1998 + - - - - - 11999-2008 - - - - - + 12009-2018 + - - + + + 4

Note + indicates that the anomaly is confirmed and - indicates that anomaly is not confirmedThe higher the overall rating the stronger the evidence of the anomaly

A3 Trading Simulation Results

Table A8 Trading simulation results of the price gap anomaly for the DJI 1989-2018

Period Gap type Number oftradesunits

Number ofsuccessfultradesunits

Number ofsuccessfultrades

Profit Profit per year

z-test Result

1989-1998 Up 102 46 451 -11 -01 011 failedDown 116 49 422 -267 -27 242 passed

1999-2008 Up 73 51 699 665 66 37 passedDown 143 81 566 641 64 331 passed

2009-2018 Up 127 88 693 308 31 327 passedDown 81 47 58 196 2 184 passed

21

B Short-term price behavior in DJI SampP 500 and

NASDAQ Price gaps (overall data sets)

Table B1 Momentum effect in the US stock market after the gap

Instrument Parameter Number of days after the gap1 2 3

Dow Jones Index Positive gaps 53 57 61Negative gaps 50 50 47

All gaps 51 54 54SampP 500 Index Positive gaps 40 63 60

Negative gaps 4 52 45All gaps 4 58 53

NASDAQ Positive gaps 32 65 67Negative gaps 24 63 59

All gaps 28 64 63

Table B2 Momentum effect in the US stock market before the gap

Instrument Parameter Number of days before the gap1 2 3

Dow Jones Index Positive gaps 56 49 52Negative gaps 54 49 49

All gaps 55 49 50SampP 500 Index Positive gaps 57 57 52

Negative gaps 60 59 54All gaps 58 58 53

NASDAQ Positive gaps 61 56 54Negative gaps 68 69 70

All gaps 64 63 63

Table B3 Fill gap effect in the US stock market

Instrument Parameter Number of days after the gap1 2 3 4 5

Dow Jones Index Positive gaps 22 28 26 30 28Negative gaps 25 33 36 42 46

All gaps 24 30 31 35 37SampP 500 Index Positive gaps 0 6 11 16 19

Negative gaps 1 10 19 26 27All gaps 1 8 15 20 23

NASDAQ Positive gaps 8 13 18 21 19Negative gaps 7 11 17 21 25

All gaps 8 12 18 21 22

22

C Detailed statistical results DJI overall data

C1 Average analysis

Table C1 Average analysis

Parameter Gap day Gap day(Positive gaps)

Gap day(Negative gaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Mean return (gap day) 003 006 0 005 -003Mean return (non-gap day) 004 004 004 004 004Anomaly not confirmed not confirmed confirmed not confirmed confirmed

C2 Parametric tests Students t-test

Table C2 T-test

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

t-criterion 016 042 053 015 104t-critical (=095) 196 196 196 196 196Null hypothesis not rejected not rejected not rejected not rejected not rejected

C3 Parametric tests ANOVA

Table C3 ANOVA

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

F 0036 018 053 003 14p-value 085 067 047 086 024F critical 384 384 384 384 384Null hypothesis not rejected not rejected not rejected not rejected not rejected

C4 Non-parametric tests Kruskal-Wallis test

Table C4 Kruskal -Wallis test

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Adjusted H 082 012 126 0 455df 1 1 1 1 1P value 037 073 026 095 003Critical value 384 384 384 384 384Null hypothesis not rejected not rejected not rejected not rejected rejected

23

C5 Regression analysis with dummy variables

Table C5 Regression analysis with dummy variables

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

a0 00004 (000) 00004 (000) 00004 (000) 00004 (000) 00004 (000)a1 -00001 (-019) 00002 (067) -00004 (047) 00001 (086) -00007 (024)Anomaly not confirmed not confirmed not confirmed not confirmed not confirmed

C6 Modified CAR approach

Table C6 Modified CAR approach

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Multiple R 049 05 025 0 092F-test 23347 (000) 12913 (000) 2207 (000) 000 (098) 1822 (000)a0 -00041 (060) 00128 (006) -00267 (000) 00354 (000) 00319 (000)a1 -00003 (000) -00003 (000) -00002 (000) 00000 (098) -00008 (000)Anomaly confirmed confirmed confirmed not confirmed confirmed

24

D Detailed statistical results SampP 500 overall data

D1 Average analysis

Table D1 Average analysis

Parameter Gap day Gap day(Positive gaps)

Gap day(Negative gaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Mean return (gap day) 006 115 -129 017 -011Mean return (non-gap day) 002 002 002 002 002Anomaly confirmed confirmed confirmed confirmed confirmed

D2 Parametric tests Students t-test

Table D2 T-test

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

t-criterion 092 4546 3579 485 271t-critical (=095) 196 196 196 196 196Null hypothesis not rejected rejected rejected rejected rejected

D3 Parametric tests ANOVA

Table D3 ANOVA

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

F 155 116211 126952 1866 136p-value 022 0 0 0 0F critical 384 384 384 384 384Null hypothesis not rejected rejected rejected not rejected not rejected

D4 Non-parametric tests Kruskal-Wallis test

Table D4 Kruskal-Wallis test

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Adjusted H 1352 70516 47237 3946 004df 1 1 1 1 1P value 0 0 0 0 084Critical value 384 384 384 384 384Null hypothesis rejected rejected rejected rejected not rejected

25

D5 Regression analysis with dummy variables

Table D5 Regression analysis with dummy variables

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

a0 00002 (000) 00002 (000) 00002 (000) 00002 (000) 00002 (000)a1 00003 (021) 00113 (000) -00132 (000) 00014 (000) -00014 (000)Anomaly not confirmed confirmed confirmed confirmed confirmed

D6 Modified CAR approach

Table D6 Modified CAR approach

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Multiple R 051 099 099 099 096F-test 69486 (000) 325351 (000) 1457582 (000) 6345973 (000) 1213344 (000)a0 -01003(000) 04081 (000) -05444 (000) -01088 (000) 00272 (000)a1 00002 (000) 00106 (000) -00127 (000) 00016 (000) -00016 (000)Anomaly confirmed confirmed confirmed confirmed confirmed

26

E Detailed statistical results NASDAQ overall data

E1 Average analysis

Table E1 Average analysis

Parameter Gap day Gap day(Positive gaps)

Gap day(Negative gaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Mean return (gap day) -009 084 -090 022 -037Mean return (non-gap day) 003 003 003 003 003Anomaly confirmed confirmed confirmed confirmed confirmed

E2 Parametric tests Students t-test

Table E2 T-test

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

t-criterion 230 1257 1341 306 664t-critical (=095) 196 196 196 196 196Null hypothesis rejected rejected rejected rejected rejected

E3 Parametric tests ANOVA

Table E3 ANOVA

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

F 2289 62720 88402 3330 17356p-value 0 0 0 0 0F critical 384 384 384 384 384Null hypothesis rejected rejected rejected rejected rejected

E4 Non-parametric tests Kruskal-Wallis test

Table E4 Kruskal-Wallis test

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Adjusted H 1892 36022 45248 4695 10437df 1 1 1 1 1P value 0 0 0 0 0Critical value 384 384 384 384 384Null hypothesis rejected rejected rejected rejected rejected

27

E5 Regression analysis with dummy variables

Table E5 Regression analysis with dummy variables

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

a0 00003 (000) 00003 (000) 00003 (000) 00003 (000) 00003 (000)a1 -00012 (000) 00081 (000) -00093 (000) 00018 (000) -00040 (000)Anomaly confirmed confirmed confirmed confirmed confirmed

E6 Modified CAR approach

Table E6 Modified CAR approach

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Multiple R 069 092 092 072 097F-test 133255 (000) 361102 (000) 442376 (000) 72903 (000) 1082812 (000)a0 -10646 (000) 11373 (000) -12888 (000) 03928 (000) -02297 (000)a1 -00011 (000) 00073 (000) -00097 (000) 00017 (000) -00039 (000)Anomaly confirmed confirmed confirmed confirmed confirmed

28

F Detailed statistical results DJI sub-periods

F1 Average analysis

Table F1 Average analysis

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 Mean return (gapday)

-001 023 015 -004

Mean return(non-gap day)

007 007 007 007

Anomaly confirmed confirmed confirmed confirmed1999-2008 Mean return (gap

day)090 -045 013 -004

Mean return(non-gap day)

-004 -004 -004 -004

Anomaly confirmed confirmed confirmed confirmed2009-2018 Mean return (gap

day)024 -024 0 -004

Mean return(non-gap day)

004 004 004 004

Anomaly confirmed confirmed not confirmed confirmed

F2 Parametric tests Students t-test

Table F2 T-test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 t-criterion 083 165 087 139t-critical (=095) 196 196 196 196Null hypothesis not rejected not rejected not rejected not rejected

1999-2008 t-criterion 347 351 054 047t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected rejected

2009-2018 t-criterion 265 207 051 058t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

F3 Parametric tests ANOVA

Table F3 ANOVA

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 F 085 409 093 179p-value 035 004 033 018

F critical 384 384 384 384Null hypothesis not rejected rejected not rejected not rejected

1999-2008 F 5405 3196 065 072p-value 0 0 042 039

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

2009-2018 F 554 697 024 058p-value 001 0 062 044

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

29

F4 Non-parametric tests Kruskal-Wallis test

Table F4 Kruskal-Wallis test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 Adjusted H 113 211 113 332df 1 1 1 1

P value 029 015 029 007Null hypothesis not rejected not rejected not rejected not rejected

1999-2008 Adjusted H 1484 1414 003 139df 1 1 1 1

P value 0 0 086 024Null hypothesis rejected rejected not rejected not rejected

2009-2018 Adjusted H 506 68 051 171df 1 1 1 1

P value 002 001 047 019Null hypothesis rejected rejected not rejected not rejected

F5 Regression analysis with dummy variables

Table F5 Regression analysis with dummy variables

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 a0 000068 (000) 00007 (000) 00007 (000) 00007 (000)a1 -000078 (035) 00016 (004) 00008 (033) -00011 (018)

Anomaly not confirmed confirmed not confirmed not confirmed1999-2008 a0 00004 (008) 00004 (008) 00004 (006) 00004 (008)

a1 00087 (000) -00049 (000) 00009 (042) -00008 (039)Anomaly confirmed confirmed not confirmed not confirmed

2009-2018 a0 00004 (006) 00004 (006) 00004 (006) 00004 (006)a1 00021 (001) -00028 (001) -00004 (062) -00008 (047)

Anomaly confirmed confirmed not confirmed not confirmed

F6 Modified CAR approach

Table F6 Modified CAR approach

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 Multiple R 083 088 082 086F-test 22779 (000) 40583 (000) 20401 (000) 3269454 (000)a0 00042 (023) 00017 (073) 00014 (058) -00266 (000)a1 -00009 (000) 00015 (000) 00006 (000) -00009 (000)

Anomaly confirmed confirmed confirmed confirmed1999-2008 Multiple R 095 093 076 019

F-test 62658 (000) 84712 (000) 10056 (000) 492 (003)a0 -00972 (000) 00365 (000) -00198 (000) -00115 (021)a1 00086 (000) -00042 (000) 00014 (000) 00002 (003)

Anomaly confirmed confirmed confirmed not confirmed2009-2018 Multiple R 096 082 08 05

F-test 150452 (000) 16731 (000) 22287 (000) 2620 (000)a0 00548 (000) -00618 (000) 00031 (020) -00112 (000)a1 00013 (000) -00014 (000) -00005 (000) -00004 (000)

Anomaly confirmed confirmed not confirmed confirmed

30

G Detailed statistical results NASDAQ sub-periods

G1 Average analysis

Table G1 Average analysis

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 Mean return (gapday)

094 -111 0189 -029

Mean return(non-gap day)

007 007 007 007

Anomaly confirmed confirmed confirmed confirmed1959-1968 Mean return (gap

day)133 -147 033 -039

Mean return(non-gap day)

006 006 006 006

Anomaly confirmed confirmed confirmed confirmed1969-1978 Mean return (gap

day)19 -186 057 -068

Mean return(non-gap day)

005 005 005 005

Anomaly confirmed confirmed confirmed confirmed1979-1988 Mean return (gap

day)138 -162 066 -04

Mean return(non-gap day)

008 008 008 008

Anomaly confirmed confirmed confirmed confirmed1989-1998 Mean return (gap

day)016 012 018 -009

Mean return(non-gap day)

002 002 002 002

Anomaly confirmed not confirmed confirmed confirmed1999-2008 Mean return (gap

day)38E-3 027 -036 -013

Mean return(non-gap day)

-01 -01 -01 -01

Anomaly confirmed not confirmed not confirmed not confirmed2009-2018 Mean return (gap

day)039 009 013 -025

Mean return(non-gap day)

001 001 001 001

Anomaly confirmed not confirmed confirmed confirmed

G2 Parametric tests Students t-test

Table G2 T-test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 t-criterion 3194 3076 201 559t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected rejected

1959-1968 t-criterion 1399 2246 443 382t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected rejected

1969-1978 t-criterion 261 4358 417 786t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected rejected

1979-1988 t-criterion 1847 1445 709 395t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected rejected

1989-1998 t-criterion 13 066 126 093t-critical (=095) 196 196 196 196Null hypothesis not rejected not rejected not rejected not rejected

1999-2008 t-criterion 192 106 111 009t-critical (=095) 196 196 196 196Null hypothesis not rejected not rejected not rejected not rejected

2009-2018 t-criterion 27 05 089 188t-critical (=095) 196 196 196 196Null hypothesis rejected not rejected not rejected not rejected

31

G3 Parametric tests ANOVA

Table G3 ANOVA

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 F 88153 190609 1272 14521p-value 0 0 0 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1959-1968 F 93974 149771 4715 10418p-value 0 0 0 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1969-1978 F 84546 145429 6295 18241p-value 0 0 0 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1979-1988 F 66952 110482 13138 8626p-value 0 0 0 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1989-1998 F 323 138 43 168p-value 007 024 003 019

F critical 384 384 384 384Null hypothesis not rejected not rejected rejected not rejected

1999-2008 F 106 512 327 003p-value 001 002 007 085

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

2009-2018 F 169 069 175 93p-value 0 04 018 0

F critical 384 384 384 384Null hypothesis rejected not rejected not rejected rejected

G4 Non-parametric tests Kruskal-Wallis test

Table G4 Kruskal-Wallis test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 Adjusted H 26254 32592 1464 3962df 1 1 1 1

P value 0 0 0 0Null hypothesis rejected rejected rejected rejected

1959-1968 Adjusted H 28235 27989 2736 332df 1 1 1 1

P value 0 0 0 0Null hypothesis rejected rejected rejected rejected

1969-1978 Adjusted H 22202 33777 3311 7591df 1 1 1 1

P value 0 0 0 0Null hypothesis rejected rejected rejected rejected

1979-1988 Adjusted H 23282 25292 4812 3964df 1 1 1 1

P value 0 0 0 0Null hypothesis rejected rejected rejected rejected

1989-1998 Adjusted H 381 017 175 132df 1 1 1 1

P value 005 068 019 025Null hypothesis not rejected not rejected not rejected not rejected

1999-2008 Adjusted H 855 023 044 004df 1 1 1 1

P value 0 063 051 084Null hypothesis rejected not rejected not rejected not rejected

2009-2018 Adjusted H 1063 009 257 709df 1 1 1 1

P value 0 077 011 001Null hypothesis rejected not rejected not rejected rejected

32

G5 Regression analysis with dummy variables

Table G5 Regression analysis with dummy variables

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 a0 00007 (000) 00007 (000) 00007 (000) 00007 (000)a1 00088 (000) -00119 (000) 00011 (000) -00036 (000)

Anomaly confirmed confirmed confirmed confirmed1959-1968 a0 00006 (000) 00006 (000) 00006 (000) 00006 (000)

a1 00128 (000) -00153 (000) 00027 (000) -00046 (000)Anomaly confirmed confirmed confirmed confirmed

1969-1978 a0 00005 (000) 00005 (000) 00005 (000) 00005 (000)a1 00185 (000) -00192 (000) 00053 (000) -00073 (000)

Anomaly confirmed confirmed confirmed confirmed1979-1988 a0 00008 (000) 00008 (000) 00008 (000) 00008 (000)

a1 00131 (000) -00172 (000) 00059 (000) -00048 (000)Anomaly confirmed confirmed confirmed confirmed

1989-1998 a0 00002 (027) 00002 (028) 00002 (028) 00002 (027)a1 00014 (007) 00010 (024) 00017 (004) -00011 (019)

Anomaly not confirmed not confirmed confirmed not confirmed1999-2008 a0 00001 (059) 00001 (062) 00001 (059) 00001 (060)

a1 00037 (000) 00026 (002) -00038 (000) -00014 (019)Anomaly confirmed not confirmed not confirmed not confirmed

2009-2018 a0 00001 (049) 00001 (049) 00001 (049) 00001 (049)a1 00038 (000) 00007 (040) 00012 (018) -00027 (000)

Anomaly confirmed not confirmed not confirmed confirmed

G6 Modified CAR approach

Table G6 Modified CAR approach

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 Multiple R 099 099 093 098F-test 5753605 (000) 100470(000) 6280421 283281a0 -00091 (000) -00349 (000) 00056 (001) 00015 (073)a1 00083 (000) -00110 (000) 00010 (000) -00031 (000)

Anomaly confirmed confirmed confirmed confirmed1959-1968 Multiple R 099 099 099 099

F-test 3923274 (000) 3005562 (000) 443198 (000) 372583 (000)a0 00096 (000) 00073 (016) -00082 (000) -00095 (004)a1 00116 (001) -00149 (000) 00025 (000) -00047 (000)

Anomaly confirmed confirmed confirmed confirmed1969-1978 Multiple R 099 099 098 099

F-test 4302608 (000) 2723953 (000) 179969 (000) 639745a0 00246 (000) -00002 (000) 00217 (000) -00514 (000)a1 00176 (000) -00182 (000) 00049 (000) -00062 (000)

Anomaly confirmed confirmed confirmed confirmed1979-1988 Multiple R 099 099 099 099

F-test 5872335 (000) 1182609 (000) 1083558 (000) 910089 (000)a0 00136 (000) -01081 (000) -00285 (000) -00101 (000)a1 00131 (000) -00167 (000) 00062 (000) -00048 (000)

Anomaly confirmed confirmed confirmed confirmed1989-1998 Multiple R 09 056 069 016

F-test 46947 (000) 4885 (000) 10131 (000) 263 (011)a0 00102 (002) -00261 (000) -0016 (001) -00237 (000)a1 00015 (000) 00010 (000) 0001 (000) 00002 (011)

Anomaly confirmed confirmed confirmed not confirmed1999-2008 Multiple R 093 087 073 037

F-test 71863 (000) 32530 (000) 13273 (000) 1669 (000)a0 00185 (004) 00311 (000) -00130 (039) -00546 (000)a1 00037 (000) 00032 (000) -00026 (000) -00007 (000)

Anomaly confirmed not confirmed not confirmed confirmed2009-2018 Multiple R 089 001 096 091

F-test 40818 (000) 000 (094) 116744 (000) 53770 (000)a0 01436 (000) -01099 (000) -01036 (000) 00697 (000)a1 00030 (000) 00000 (094) 00024 (000) -00021 (000)

Anomaly confirmed not confirmed confirmed confirmed

33

H Detailed statistical results SampP 500 sub-periods

H1 Average analysis

Table H1 Average analysis

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 Mean return (gapday)

138 -171 004 -014

Mean return(non-gap day)

0 0 0 0

Anomaly confirmed confirmed confirmed confirmed1939-1948 Mean return (gap

day)001 -042 172 -195

Mean return(non-gap day)

003 003 003 003

Anomaly confirmed confirmed confirmed confirmed1949-1958 Mean return (gap

day)165 -18 02 002

Mean return(non-gap day)

006 006 006 006

Anomaly confirmed confirmed confirmed not confirmed1959-1968 Mean return (gap

day)104 -102 015 0

Mean return(non-gap day)

002 002 002 002

Anomaly confirmed confirmed confirmed not confirmed1969-1978 Mean return (gap

day)131 -13 019 -03

Mean return(non-gap day)

0 0 0 0

Anomaly confirmed confirmed confirmed confirmed1979-1988 Mean return (gap

day)058 -042 015 003

Mean return(non-gap day)

005 005 005 005

Anomaly confirmed confirmed confirmed not confirmed1989-1998 Mean return (gap

day)02 -023 -002 01

Mean return(non-gap day)

007 007 007 007

Anomaly confirmed confirmed not confirmed not confirmed1999-2008 Mean return (gap

day)083 -089 -023 -005

Mean return(non-gap day)

001 001 001 001

Anomaly confirmed confirmed not confirmed confirmed2009-2018 Mean return (gap

day)055 -052 001 -015

Mean return(non-gap day)

004 004 004 004

Anomaly confirmed confirmed not confirmed confirmed

34

H2 Parametric tests Students t-test

Table H2 T-test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 t-criterion 101 85 029 048t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

1939-1948 t-criterion 064 479 3074 225t-critical (=095) 196 196 196 196Null hypothesis not rejected rejected rejected rejected

1949-1958 t-criterion 2964 2383 193 041t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

1959-1968 t-criterion 2281 2157 21 023t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected not rejected

1969-1978 t-criterion 1318 2034 187 321t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected rejected

1979-1988 t-criterion 435 535 07 037t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

1989-1998 t-criterion 201 396 132 052t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

1999-2008 t-criterion 362 433 117 022t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

2009-2018 t-criterion 375 382 027 132t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

H3 Parametric tests ANOVA

Table H3 ANOVA

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 F 6281 8032 005 051p-value 0 0 082 047

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

1939-1948 F 056 2603 34854 51034p-value 045 0 0 0

F critical 384 384 384 384Null hypothesis not rejected rejected rejected rejected

1949-1958 F 100174 128997 897 062p-value 0 0 0 043

F critical 384 384 384 384Null hypothesis rejected rejected rejected not rejected

1959-1968 F 36831 32858 617 01p-value 0 0 001 074

F critical 384 384 384 384Null hypothesis rejected rejected rejected not rejected

1969-1978 F 26601 3063 53 152p-value 0 0 002 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1979-1988 F 23 245 076 009p-value 0 0 039 077

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

1989-1998 F 399 1156 118 015p-value 004 0 027 069

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

1999-2008 F 4253 5622 365 024p-value 0 0 006 062

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

2009-2018 F 3064 3656 01 43p-value 0 0 075 004

F critical 384 384 384 384Null hypothesis rejected rejected not rejected rejected

35

H4 Non-parametric tests Kruskal -Wallis test

Table H4 Kruskal-Wallis test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 Adjusted H 9982 5913 332 14df 1 1 1 1

P value 0 0 007 024Null hypothesis rejected rejected not rejected not rejected

1939-1948 Adjusted H 494 1999 23387 24927df 1 1 1 1

P value 003 0 0 0Null hypothesis rejected rejected rejected rejected

1949-1958 Adjusted H 28728 28175 348 15df 1 1 1 1

P value 0 0 006 022Null hypothesis rejected rejected not rejected not rejected

1959-1968 Adjusted H 25729 21437 701 063df 1 1 1 1

P value 0 0 001 043Null hypothesis rejected rejected rejected not rejected

1969-1978 Adjusted H 14407 20078 27 1706df 1 1 1 1

P value 0 0 01 0Null hypothesis rejected rejected not rejected rejected

1979-1988 Adjusted H 1788 2836 027 034df 1 1 1 1

P value 0 0 06 056Null hypothesis rejected rejected not rejected not rejected

1989-1998 Adjusted H 251 1431 111 044df 1 1 1 1

P value 011 0 029 051Null hypothesis not rejected rejected not rejected not rejected

1999-2008 Adjusted H 1812 1788 042 002df 1 1 1 1

P value 0 0 052 089Null hypothesis rejected rejected not rejected not rejected

2009-2018 Adjusted H 1314 1783 074 37df 1 1 1 1

P value 0 0 039 005Null hypothesis rejected rejected not rejected not rejected

36

H5 Regression analysis with dummy variables

Table H5 Regression analysis with dummy variables

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 a0 00000 (097) 00000 (004) 00000 (097) 00000 (097)a1 00138 (000) -00172 (000) 00004 (082) -00014 (047)

Anomaly confirmed confirmed not confirmed not confirmed1939-1948 a0 00003 (015) 00003 (015) 00003 (015) 00003 (015)

a1 00007 (045) -00045 (000) 00170 (000) -00199 (000)Anomaly not confirmed confirmed confirmed confirmed

1949-1958 a0 00006 (000) 00006 (000) 00006 (000) 00006 (000)a1 00160 (000) -00188 (000) 00016 (000) -00004 (043)

Anomaly confirmed confirmed confirmed not confirmed1959-1968 a0 00002 (007) 00002 (004) 00002 (008) 00002 (008)

a1 00103 (000) -00105 (000) 00014 (001) -00002 (074)Anomaly confirmed confirmed confirmed not confirmed

1969-1978 a0 00000 (078) 00000 (078) 00000 (078) 00000 (078)a1 00132 (000) -00132 (000) 00019 (002) -00030 (000)

Anomaly confirmed confirmed confirmed confirmed1979-1988 a0 00006 (001) 00006 (001) 00006 (001) 00006 (000)

a1 00053 (000) -00048 (000) 00009 (040) -00003 (075)Anomaly confirmed confirmed not confirmed not confirmed

1989-1998 a0 00007 (000) 00007 (000) 00007 (000) 00007 (000)a1 00016 (005) -00030 (000) -00009 (026) 00003 (072)

Anomaly confirmed confirmed not confirmed not confirmed1999-2008 a0 00001 (075) 00001 (075) 00001 (075) 00001 (076)

a1 00083 (000) -00091 (000) -00024 (005) -00006 (062)Anomaly confirmed confirmed not confirmed not confirmed

2009-2018 a0 00004 (003) 00004 (000) 00004 (003) 00004 (003)a1 00051 (000) -00059 (000) -00003 (075) -00019 (003)

Anomaly confirmed confirmed not confirmed confirmed

37

H6 Modified CAR approach

Table H6 Modified CAR approach

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 Multiple R 096 095 046 046F-test 175935 (000) 96500 (000) 3534 (000) 2880 (000)a0 -01070 (000) 01958 (000) 00405 (000) 00535 (000)a1 00121 (000) -00160 (000) 00006 (000) -00014 (000)

Anomaly confirmed confirmed confirmed confirmed1939-1948 Multiple R 08 099 099 099

F-test 18777 (000) 755727 (000) 3572830 (000) 2696099 (000)a0 00019 (073) -00346 (000) -00373 (000) 00912 (000)a1 00012 (000) -00044 (000) 00168 (000) -00197 (000)

Anomaly confirmed confirmed confirmed confirmed1949-1958 Multiple R 099 099 094 015

F-test 1021705 (000) 7171257 (000) 75858 (000) 242 (012)a0 -00176 (000) -00191 (000) 00095 (000) -00498 (000)a1 00154 (000) -00181 (000) 00013 (000) -00002 (012)

Anomaly confirmed confirmed confirmed not confirmed1959-1968 Multiple R 099 099 094 078

F-test 1463311 (000) 6002659 (000) 82273 (000) 14352 (000)a0 -00112 (000) 00004 (085) 00151 (000) 00389 (000)a1 00098 (000) -00102 (000) 00011 (000) -00009 (000)

Anomaly confirmed confirmed confirmed confirmed1969-1978 Multiple R 098 099 093 099

F-test 241655 (000) 1451901 (000) 57333 (000) 368160 (000)a0 -00433 (000) 00276 (000) 00099 (002) -00144 (000)a1 00132 (000) -00134 (000) 00020 (000) -00030 (000)

Anomaly confirmed confirmed confirmed confirmed1979-1988 Multiple R 092 078 023 008

F-test 53757 (000) 18707 (000) 487 (003) 085 (036)a0 00813 (000) -02508 (000) 00204 (000) -00235 (000)a1 00036 (000) -00031 (000) -00003 (003) -00001 (036)

Anomaly confirmed confirmed not confirmed not confirmed1989-1998 Multiple R 079 099 074 044

F-test 19705(000) 761967 (000) 14133 (000) 2369 (000)a0 00268 (000) 00023 (021) -00381 (000) 00087 (000)a1 00013 (000) -00028 (000) -00008 (000) 00002 (000)

Anomaly confirmed confirmed not confirmed not confirmed1999-2008 Multiple R 091 093 071 065

F-test 47218 (000) 76564 (000) 9843 (000) 7768 (000)a0 -01493 (000) 01351 (000) 00397 (000) 00007 (093)a1 00081 (000) -00083 (000) -00026 (000) -00011 (000)

Anomaly confirmed confirmed not confirmed confirmed2009-2018 Multiple R 086 087 083 074

F-test 29971 (000) 32484 (000) 23228 (000) 12764 (000)a0 01711 (000) -02250 (000) 00407 (000) -00472 (000)a1 00038 (000) -00044 (000) -00010 (000) -00012 (000)

Anomaly confirmed confirmed not confirmed confirmed

38

that this strategy is efficient A z minus test is then conducted to ensure that the results ofthe trading strategy are not random using a 5 per cent level of significance

4 Results

The results of the SampP 500 are presented and contrasted with those of the DJI and theNASDAQ We focus on the SampP 500 specifically as it has the longest sample and there-fore can offer better insights as compared to the DJI and the NASDAQ The summaryresults for the DJI and the NASDAQ can be found in Appendix A The results of theshort term price behaviour tests are in Appendix B The detailed results of the overalldata sets for all indexes can be found in Appendices C to E Similarly the detailedresults of the sub-periods within the overall data sets can be found in Appendices F toH

41 Price gap size

First an appropriate gap size must be as a criterion for gap detection Caporale andPlastun (2017) show that the gap size significantly influences the number of detectedanomalies To confirm this we analyse SampP 500 data for the 2009-2018 sub-period Ascan be seen from Table 2 a small gap size choice generates too many gaps to be consid-ered as anomalies A large gap size provides very few cases for analysis and may leadto statistical insignificance of the results For this study (which is primarily based onstatistical analysis and tests) the number of observations should be around 100 to makeresults statistically significant This represents less than 10 per cent of the populationand hence can be considered anomalies As a result gap size is not constant and maydiffer from index to index and between sub-periods (see Table 3 and Table A1) Thisinconsistency in the gap size can be considered additional evidence in favour of pricegap anomaly evolution

7

Tab

le2

Gap

size

andthenumber

ofdetectedgapscase

ofSampP500dataover

theperiod2009-2018

Gap

size

010

020

030

040

050

060

070

080

090

100

gapsin

prices

4105

1970

1090

571

345

202

135

087

067

052

Number

ofdetectedgaps

1038

497

275

144

8751

3422

1713

Number

ofdetectednegativegaps

468

230

130

6944

3120

109

8Number

ofdetectedpositivegaps

570

267

145

7543

2014

128

5

8

Table 3 Gap size used for different sub-periods over the period 1929-2018

Period SampP 5001929-1938 1201949-1958 1201959-1968 0701969-1978 0011979-1988 0031989-1998 0011999-2008 0082009-2018 034Overall data set 070

42 Price gap seasonality

Caporale and Plastun (2017) show that in foreign exchange and commodity marketsprice gaps tend to appear on Mondays According to their results more than 95 percent of price gaps in foreign exchange markets compared to 65 per cent of price gaps incommodity markets appeared on Mondays This is rather reasonable because marketsare closed on weekends and as the result of any significant event over the weekend willlead to price gaps on Monday Surprisingly this is not the case in this instance (withstock markets) as can be seen in Tables 4 and A2 Therefore H3 is rejected

Table 4 Day of the week and gaps

Day of the week SampP 500Monday 023Tuesday 02Wednesday 02Thursday 018Friday 019

43 Short term price behaviour

Next we analyse short-term price behaviour in the US stock market around price gapsto investigate the presence of possible price patterns before and after price gaps Wecalculate the number of days with positive (or negative) returns after a positive (or neg-ative) price gaps divided by the total number of price gaps If this ratio or momentum

9

effect is much higher than 50 per cent this indicates abnormal price behaviour and asthe results confirm our hypotheses

The results are presented in Appendix B We find no convincing evidence in favour ofmomentum effect after price gaps (Table B1) and before them (Table B2) In generalprice gaps are not generated by previous price dynamics (NASDAQ index is an exceptionas negative gaps appear in 70 per cent of the cases after downward price movements andafter positive gaps in 67 per cent of the cases upward price movements are observed)Our results (see Table B3 for details) also indicate that the probability that price gapswill be filled within 5 days after appearance is very low at around 20 per cent

44 Price gap evolution

Overall in probabilistic terms price gaps do not generate any stable patterns But therecan be patterns in terms of size of price movements after gaps To check this we will testH1 and H2 To incorporate price direction in results of analysis H1 we further test forH1minus1 and H1minus2 The results for the overall data sets are presented in Appendices C toE for the cases of DJI SampP 500 and NASDAQ respectively To ease the interpretationof results we have summarised them in Table 5 and Table A3

Table 5 shows strong evidence confirming H1 in the SampP 500 Similarly Table A3confirms H1 for the NASDAQ but not for the DJI The difference between the DJI SampP500 and NASDAQ results can be explained by the differences in samples (DJI sampleis much shorter) This suggests that price gap anomaly may evolve and is therefore apreliminary confirmation of H2

Tables 6 and 7 confirm H1minus1 in the SampP 500 on the day of the price gap That ison the price gap day prices tend towards the direction of the price gap However thisis not the case for the day after the price gap therefore H1minus2 is not confirmed It canbe concluded that the SampP 500 roughly needs a day to absorb new information Never-theless even a day can be enough to create a profitable trading strategy and generateabnormal profits from trading

Similar results on the NASDAQ can be found in Tables A6 and A7 The longersample of the NASDAQ allows for the evolution of the price anomaly H1minus1 is there-fore confirmed on the day of the price gap anomaly and the day after the price gapanomaly (in both instances only until the 1990s and has since disappeared) H1minus2 inboth instances is confirmed up until the 1990s The results of the DJI did not providestrong evidence in favour of H1minus1 and H1minus2 on the day after the price gap but sim-ilar to the SampP 500 evidence was strong on the day of the price gap (see Tables A4and A5) These results confirm in the main the price gap anomaly is a reality in theUS stock market and that it evolves over time that is from prevalence to disappearance

10

Tab

le5

Overallstatisticalresults

SampP500

PeriodM

ethod

Average

analysis

t-test

ANOVA

test

Man

n-

Whitney

test

Regression

analysis

with

dummy

variab

les

Modified

CAR

approach

Overall

Gap

day

+-

-+

-+

3Gap

day

(Positivegaps)

++

++

++

6Gap

day

(Negativegaps)

++

++

++

6Day

aftergap(P

ositivegaps)

++

-+

++

5Day

aftergap(N

egativegaps)

++

--

++

4

Note+

indicates

thattheanom

alyis

confirm

edand-indicates

thatan

omaly

isnot

confirm

edThehigher

theoverallrating

the

strongertheeviden

ceofthean

omaly

11

Tab

le6

H1minus1summarystatisticalresults

SampP500sub-periods

PeriodM

ethod

Average

analysis

t-test

ANOVA

test

Man

n-

Whitney

test

Regression

analysis

withdummy

variab

les

Modified

CAR

approach

Overall

Dayofanomaly

1929-1938

++

++

++

61939-1948

+-

-+

-+

31949-1958

++

++

++

61959-1968

++

++

++

61969-1978

++

++

++

61979-1988

++

++

++

61989-1998

++

++

++

61999-2008

++

++

++

62009-2018

++

++

++

6Dayafteranomaly

1929-1938

+-

--

-+

21939-1948

++

++

++

61949-1958

+-

+-

++

51959-1968

++

++

++

61969-1978

+-

+-

++

41979-1988

+-

--

--

11989-1998

--

--

--

01999-2008

--

--

--

02009-2018

--

--

--

0

Note+

indicates

thattheanom

alyis

confirm

edand-indicates

thatan

omaly

isnot

confirm

edThehigher

theoverallrating

the

strongertheeviden

ceofthean

omaly

12

Tab

le7

H1minus2statisticalresults

SampP500sub-periods

PeriodM

ethod

Average

analysis

t-test

ANOVA

test

Man

n-

Whitney

test

Regression

analysiswith

dummy

variab

les

Modified

CAR

approach

Overall

Dayofanomaly

1929-1938

++

++

++

61939-1948

++

++

++

61949-1958

++

++

++

61959-1968

++

++

++

61969-1978

++

++

++

61979-1988

++

++

++

61989-1998

++

++

++

61999-2008

++

++

++

62009-2018

++

++

++

6Dayafteranomaly

1929-1938

+-

--

-+

21939-1948

++

++

++

61949-1958

--

--

--

01959-1968

--

--

-+

11969-1978

++

++

++

61979-1988

--

--

--

01989-1998

--

--

--

01999-2008

+-

--

-+

22009-2018

+-

+-

++

4

Note+

indicates

thattheanom

alyis

confirm

edand-indicates

thatan

omaly

isnot

confirm

edThehigher

theoverallrating

the

strongertheeviden

ceofthean

omaly

13

45 Trading simulation

The algorithm of the trading strategy is to buysell at the start of the updown gapday and close this position at the end of this day To test this strategy data for the DJIand SampP 500 are used (for this case the price anomaly still exists based on the day itoccurred) The results for DJI are presented in Table A8 and for the SampP 500 in Table8 For the SampP 500 and DJI the trading strategy built on price gap anomaly is efficientand its results differ from random

Table 8 Trading simulation results of the price gap anomaly for the SampP 500

Period Gaptype

Numberof

tradesunits

Numberof suc-cessfultradesunits

Numberof suc-cessfultrades

Profit

Profit peryear

z-test Result

1929-1938 Up 131 130 992 1816 182 1065 passedDown 110 108 982 1893 189 876 passed

1939-1948 Up 110 67 609 106 11 09 failedDown 122 79 648 518 52 465 passed

1949-1958 Up 106 105 991 1765 176 3191 passedDown 104 103 99 1891 189 2356 passed

1959-1968 Up 108 106 981 1331 113 2441 passedDown 92 91 989 948 95 2214 passed

1969-1978 Up 85 71 835 1128 113 1361 passedDown 96 90 938 1262 126 2118 passed

1979-1988 Up 92 63 685 54 54 495 passedDown 123 81 659 519 52 496 passed

1989-1998 Up 117 72 615 267 27 295 passedDown 99 61 616 228 23 32 passed

1999-2008 Up 99 65 657 828 83 373 passedDown 110 72 655 987 99 438 passed

2009-2018 Up 106 71 67 59 59 416 passedDown 107 65 607 56 56 362 passed

14

Figure 1 Trading simulation results of the price gap anomaly for the SampP 500

Note The primary axis refers to the percentage profit per year and the secondary to thez minus test statistic

One more interesting fact (see Figure 1) is the decrease of trading strategy efficiencyThis is indirect evidence in favour of evolution of the US stock market and its movementfrom less efficient to more efficient state Overall it can be concluded that the price gapanomaly is a real market anomaly The US stock market loses its efficiency after pricegaps This effect is temporary and lasts only for a day Still even this time is enoughto exploit the hole in the market efficiency and generate abnormal profits from trading

5 Conclusion

We analysed price gap anomaly in the US stock market by using information from threestock market indexes(DJI SampP 500 and NASDAQ) We tested three hypotheses of in-terest that is H1 the price gap anomaly exists H1minus1 prices tend to rise after positivegaps H1minus2 prices tend to fall after negative gaps H2 the price gap anomaly evolvesand H3 there is seasonality in price gaps Various statistical methods including para-metric tests (Students t-tests ANOVA) non-parametric tests (Mann-Whitney test)regression analysis with dummy variables MCAR approach and the trading simulationapproach were utilised

We conclude that the US stock market in the main did not exhibit seasonality in pricegaps Therefore H3 is rejected Furthermore no evidence was found that price gaps inthe US stock market were filled within five days of their occurrence However strongevidence in favour of abnormal price movements after the gaps were found confirming

15

H1 and H2 Particularly on the day of the occurrence of the gap and not on the dayafter the price gap In the DJI and the SampP 500 this pattern persists indicating thatthese markets take a day to incorporate new information As the results of the tradingsimulation indicate a day is enough to profit from a price gap anomaly trading strategyin the DJI and the SampP 500

Similar to other studies and other anomalies (see McLean and Pontiff (2016) Ca-jueiro and Tabak (2004) and Tiwari et al (2019) for example) the price gap anomalyevolved It is less prevalent since the 1990s as shown in the SampP 500 and NASDAQThis pattern of evolution is common amongst most stock market anomalies (see Plastunet al (2019b) on calendar anomalies amongst others) Our findings therefore add onto the existing literature Finally in the main our results are against the EMH and aretherefore interesting to both practitioners and academics

16

References

Agrawal A and Tandon K (1994) Anomalies or illusions evidence from stock marketsin eighteen countries Journal of international Money and Finance 13(1)83ndash106

Akerlof G A and Shiller R J (2009) Animal Spirits How human psychology drivesthe economy and why it matters for global capitalism Princeton University Press

Basu S (1977) Investment performance of common stocks in relation to their price-earnings ratios A test of the efficient market hypothesis The Journal of Finance32(3)663ndash682

Bildik R (2004) Are calendar anomalies still alive Evidence from istanbul stockexchange SSRN Electronic Journal 2004

Cai J Li Y and Qi Y (2006) The day-of-the-week effect New evidence from theChinese stock market Chinese Economy 39(2)71ndash88

Cajueiro D O and Tabak B M (2004) The Hurst exponent over time testing theassertion that emerging markets are becoming more efficient Physica A StatisticalMechanics and its Applications 336(3-4)521ndash537

Caporale G M Gil-Alana L Plastun A and Makarenko I (2016) Intraday anoma-lies and market efficiency A trading robot analysis Computational Economics47(2)275ndash295

Caporale G M and Plastun A (2017) Price gaps Another market anomaly Invest-ment Analysts Journal 46(4)279ndash293

Cross F (1973) The behavior of stock prices on Fridays and Mondays FinancialAnalysts Journal 29(6)67ndash69

Fama E F (1965) The behavior of stock-market prices The Journal of Business38(1)34ndash105

Fama E F (1970) Efficient capital markets A review of theory and empirical workThe Journal of Finance 25(2)383ndash417

Fortune P (1998) Weekends can be rough revisiting the weekend effect in stock pricesTechnical report

Fortune P (1999) Are stock returns different over weekends A jump diffusion analysisof the weekend effect New England Economic Review 103ndash19

French K R (1980) Stock returns and the weekend effect Journal of FinancialEconomics 8(1)55ndash69

Fung A K-W Lam K and Lam K-M (2010) Do the prices of stock index futuresin asia overreact to us market returns Journal of Empirical Finance 17(3)428ndash440

17

Gibbons M R and Hess P (1981) Day of the week effects and asset returns Journalof business pages 579ndash596

Grant J L Wolf A and Yu S (2005) Intraday price reversals in the us stock indexfutures market A 15-year study Journal of Banking amp Finance 29(5)1311ndash1327

Grossman S J and Stiglitz J E (1980) On the impossibility of informationallyefficient markets The American Economic Review 70(3)393ndash408

Jacobsen B Mamun A and Visaltanachoti N (2005) Seasonal size and valueanomalies

Jensen M (1978) Some anomalous evidence regarding market efficiency Journal ofFinancial Economics 6(23 (1978))95ndash101

Lakonishok J and Smidt S (1988) Are seasonal anomalies real A ninety-year per-spective The Review of Financial Studies 1(4)403ndash425

MacKinlay A (1997) Event studies in economics and finance Journal of EconomicLiterature (35)113ndash39

Mandelbrot B B (1997) The variation of certain speculative prices In Fractals andscaling in finance pages 371ndash418 Springer

McLean R D and Pontiff J (2016) Does academic research destroy stock returnpredictability The Journal of Finance 71(1)5ndash32

Plastun A Makarenko I Khomutenko L Shcherbak S and Tryfonova O (2019a)Exploring price gap anomaly in the ukrainian stock market Investment Managementamp Financial Innovations 16(2)150

Plastun A Sibande X Gupta R and Wohar M E (2019b) Rise and fall of calendaranomalies over a century The North American Journal of Economics and Finance49181ndash205

Schwert G W (2003) Chapter 15 anomalies and market efficiency In FinancialMarkets and Asset Pricing volume 1 of Handbook of the Economics of Finance pages939 ndash 974 Elsevier

Shiller R J (2000) Irrational exuberance Princeton University

Tiwari A K Aye G C and Gupta R (2019) Stock market efficiency analysis usinglong spans of data A multifractal detrended fluctuation approach Finance ResearchLetters 28398ndash411

Yuan Y (2015) Market-wide attention trading and stock returns Journal of FinancialEconomics 116(3)548ndash564

18

Appendices

A DJI and NASDAQ Summary Results

A1 Overall Results

Table A1 Gap size used for different sub-periods over the period 1929-2018

Period DJI NASDAQ1929-1938 - -1939-1948 - -1949-1958 - 0711959-1968 - 0951969-1978 - 1351979-1988 - 1101989-1998 040 0681999-2008 007 1502009-2018 020 110Overall data set 030 110

Table A2 Day of the week and gaps

Day of the week DJI NASDAQMonday 024 02Tuesday 02 02Wednesday 017 02Thursday 019 019Friday 021 02

A2 Statistical tests

Table A3 Results of the statistical tests for the overall data sets

PeriodMethod Averageanalysis

t-test ANOVAtest

Mann-Whitney

test

Regressionanalysiswith

dummyvariables

ModifiedCAR

approach

Overall

Dow Jones Index overall data setGap day - - - - - + 1Gap day (Positive gaps) + - - - - - 1Gap day (Negative gaps) + - - - - + 2Day after gap (Positive gaps) + - - - - - 1Day after gap (Negative gaps) + - - + - + 3

NASDAQ overall data setGap day + + + + + + 6Gap day (Positive gaps) + + + + + + 6Gap day (Negative gaps) + + + + + + 6Day after gap (Positive gaps) + + + + + + 6Day after gap (Negative gaps) + + + + + + 6

Note + indicates that the anomaly is confirmed and - indicates that anomaly is not confirmedThe higher the overall rating the stronger the evidence of the anomaly

19

Table A4 Results of the statistical tests for H1minus1 DJI

Period Averageanalysis

t-test ANOVA test Mann-Whitney

test

Regressionanalysis with

dummyvariables

ModifiedCAR

approach

Overall

Day of anomaly1989-1998 + - - - - + 21999-2008 + + + + + + 62009-2018 + + + + + + 6

Day after anomaly1989-1998 + - - - - + 21999-2008 + - - - - + 22009-2018 - - - - - - 0

Note + indicates that the anomaly is confirmed and - indicates that anomaly is not confirmedThe higher the overall rating the stronger the evidence of the anomaly

Table A5 Results of the statistical tests for H1minus2 DJI

Period Averageanalysis

t-test ANOVA test Mann-Whitneytest

Regressionanalysis with

dummyvariables

Modified CARapproach

Overall

Day of anomaly1989-1998 - - - - - - 01999-2008 + + + + + + 62009-2018 + + + + + + 6

Day after anomaly1989-1998 + - - - - + 21999-2008 + - - - - - 12009-2018 + - - - - + 2

Note + indicates that the anomaly is confirmed and - indicates that anomaly is not confirmedThe higher the overall rating the stronger the evidence of the anomaly

Table A6 Results of the statistical tests for H1minus1 NASDAQ

PeriodMethod Averageanalysis

t-test ANOVA test Mann-Whitney

test

Regressionanalysis with

dummyvariables

ModifiedCAR

approach

Overall

Day of anomaly1949-1958 + + + + + + 61959-1968 + + + + + + 61969-1978 + + + + + + 61979-1988 + + + + + + 61989-1998 + - - - - + 21999-2008 + - + + + + 52009-2018 + + + + + + 6

Day after anomaly1949-1958 + + + + + + 61959-1968 + + + + + + 61969-1978 + + + + + + 61979-1988 + + + + + + 61989-1998 + - + - + + 41999-2008 - - - - - - 02009-2018 + - - - - + 2

Note + indicates that the anomaly is confirmed and - indicates that anomaly is not confirmedThe higher the overall rating the stronger the evidence of the anomaly

20

Table A7 Results of the statistical tests for H1minus2 NASDAQ

PeriodMethod Averageanalysis

t-test ANOVA test Mann-Whitney

test

Regressionanalysis with

dummyvariables

ModifiedCAR

approach

Overall

Day of anomaly1949-1958 + + + + + + 61959-1968 + + + + + + 61969-1978 + + + + + + 61979-1988 + + + + + + 61989-1998 - - - - - + 11999-2008 - - + - - - 12009-2018 - - - - - - 0

Day after anomaly1949-1958 + + + + + + 61959-1968 + + + + + + 61969-1978 + + + + + + 61979-1988 + + + + + + 61989-1998 + - - - - - 11999-2008 - - - - - + 12009-2018 + - - + + + 4

Note + indicates that the anomaly is confirmed and - indicates that anomaly is not confirmedThe higher the overall rating the stronger the evidence of the anomaly

A3 Trading Simulation Results

Table A8 Trading simulation results of the price gap anomaly for the DJI 1989-2018

Period Gap type Number oftradesunits

Number ofsuccessfultradesunits

Number ofsuccessfultrades

Profit Profit per year

z-test Result

1989-1998 Up 102 46 451 -11 -01 011 failedDown 116 49 422 -267 -27 242 passed

1999-2008 Up 73 51 699 665 66 37 passedDown 143 81 566 641 64 331 passed

2009-2018 Up 127 88 693 308 31 327 passedDown 81 47 58 196 2 184 passed

21

B Short-term price behavior in DJI SampP 500 and

NASDAQ Price gaps (overall data sets)

Table B1 Momentum effect in the US stock market after the gap

Instrument Parameter Number of days after the gap1 2 3

Dow Jones Index Positive gaps 53 57 61Negative gaps 50 50 47

All gaps 51 54 54SampP 500 Index Positive gaps 40 63 60

Negative gaps 4 52 45All gaps 4 58 53

NASDAQ Positive gaps 32 65 67Negative gaps 24 63 59

All gaps 28 64 63

Table B2 Momentum effect in the US stock market before the gap

Instrument Parameter Number of days before the gap1 2 3

Dow Jones Index Positive gaps 56 49 52Negative gaps 54 49 49

All gaps 55 49 50SampP 500 Index Positive gaps 57 57 52

Negative gaps 60 59 54All gaps 58 58 53

NASDAQ Positive gaps 61 56 54Negative gaps 68 69 70

All gaps 64 63 63

Table B3 Fill gap effect in the US stock market

Instrument Parameter Number of days after the gap1 2 3 4 5

Dow Jones Index Positive gaps 22 28 26 30 28Negative gaps 25 33 36 42 46

All gaps 24 30 31 35 37SampP 500 Index Positive gaps 0 6 11 16 19

Negative gaps 1 10 19 26 27All gaps 1 8 15 20 23

NASDAQ Positive gaps 8 13 18 21 19Negative gaps 7 11 17 21 25

All gaps 8 12 18 21 22

22

C Detailed statistical results DJI overall data

C1 Average analysis

Table C1 Average analysis

Parameter Gap day Gap day(Positive gaps)

Gap day(Negative gaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Mean return (gap day) 003 006 0 005 -003Mean return (non-gap day) 004 004 004 004 004Anomaly not confirmed not confirmed confirmed not confirmed confirmed

C2 Parametric tests Students t-test

Table C2 T-test

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

t-criterion 016 042 053 015 104t-critical (=095) 196 196 196 196 196Null hypothesis not rejected not rejected not rejected not rejected not rejected

C3 Parametric tests ANOVA

Table C3 ANOVA

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

F 0036 018 053 003 14p-value 085 067 047 086 024F critical 384 384 384 384 384Null hypothesis not rejected not rejected not rejected not rejected not rejected

C4 Non-parametric tests Kruskal-Wallis test

Table C4 Kruskal -Wallis test

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Adjusted H 082 012 126 0 455df 1 1 1 1 1P value 037 073 026 095 003Critical value 384 384 384 384 384Null hypothesis not rejected not rejected not rejected not rejected rejected

23

C5 Regression analysis with dummy variables

Table C5 Regression analysis with dummy variables

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

a0 00004 (000) 00004 (000) 00004 (000) 00004 (000) 00004 (000)a1 -00001 (-019) 00002 (067) -00004 (047) 00001 (086) -00007 (024)Anomaly not confirmed not confirmed not confirmed not confirmed not confirmed

C6 Modified CAR approach

Table C6 Modified CAR approach

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Multiple R 049 05 025 0 092F-test 23347 (000) 12913 (000) 2207 (000) 000 (098) 1822 (000)a0 -00041 (060) 00128 (006) -00267 (000) 00354 (000) 00319 (000)a1 -00003 (000) -00003 (000) -00002 (000) 00000 (098) -00008 (000)Anomaly confirmed confirmed confirmed not confirmed confirmed

24

D Detailed statistical results SampP 500 overall data

D1 Average analysis

Table D1 Average analysis

Parameter Gap day Gap day(Positive gaps)

Gap day(Negative gaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Mean return (gap day) 006 115 -129 017 -011Mean return (non-gap day) 002 002 002 002 002Anomaly confirmed confirmed confirmed confirmed confirmed

D2 Parametric tests Students t-test

Table D2 T-test

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

t-criterion 092 4546 3579 485 271t-critical (=095) 196 196 196 196 196Null hypothesis not rejected rejected rejected rejected rejected

D3 Parametric tests ANOVA

Table D3 ANOVA

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

F 155 116211 126952 1866 136p-value 022 0 0 0 0F critical 384 384 384 384 384Null hypothesis not rejected rejected rejected not rejected not rejected

D4 Non-parametric tests Kruskal-Wallis test

Table D4 Kruskal-Wallis test

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Adjusted H 1352 70516 47237 3946 004df 1 1 1 1 1P value 0 0 0 0 084Critical value 384 384 384 384 384Null hypothesis rejected rejected rejected rejected not rejected

25

D5 Regression analysis with dummy variables

Table D5 Regression analysis with dummy variables

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

a0 00002 (000) 00002 (000) 00002 (000) 00002 (000) 00002 (000)a1 00003 (021) 00113 (000) -00132 (000) 00014 (000) -00014 (000)Anomaly not confirmed confirmed confirmed confirmed confirmed

D6 Modified CAR approach

Table D6 Modified CAR approach

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Multiple R 051 099 099 099 096F-test 69486 (000) 325351 (000) 1457582 (000) 6345973 (000) 1213344 (000)a0 -01003(000) 04081 (000) -05444 (000) -01088 (000) 00272 (000)a1 00002 (000) 00106 (000) -00127 (000) 00016 (000) -00016 (000)Anomaly confirmed confirmed confirmed confirmed confirmed

26

E Detailed statistical results NASDAQ overall data

E1 Average analysis

Table E1 Average analysis

Parameter Gap day Gap day(Positive gaps)

Gap day(Negative gaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Mean return (gap day) -009 084 -090 022 -037Mean return (non-gap day) 003 003 003 003 003Anomaly confirmed confirmed confirmed confirmed confirmed

E2 Parametric tests Students t-test

Table E2 T-test

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

t-criterion 230 1257 1341 306 664t-critical (=095) 196 196 196 196 196Null hypothesis rejected rejected rejected rejected rejected

E3 Parametric tests ANOVA

Table E3 ANOVA

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

F 2289 62720 88402 3330 17356p-value 0 0 0 0 0F critical 384 384 384 384 384Null hypothesis rejected rejected rejected rejected rejected

E4 Non-parametric tests Kruskal-Wallis test

Table E4 Kruskal-Wallis test

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Adjusted H 1892 36022 45248 4695 10437df 1 1 1 1 1P value 0 0 0 0 0Critical value 384 384 384 384 384Null hypothesis rejected rejected rejected rejected rejected

27

E5 Regression analysis with dummy variables

Table E5 Regression analysis with dummy variables

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

a0 00003 (000) 00003 (000) 00003 (000) 00003 (000) 00003 (000)a1 -00012 (000) 00081 (000) -00093 (000) 00018 (000) -00040 (000)Anomaly confirmed confirmed confirmed confirmed confirmed

E6 Modified CAR approach

Table E6 Modified CAR approach

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Multiple R 069 092 092 072 097F-test 133255 (000) 361102 (000) 442376 (000) 72903 (000) 1082812 (000)a0 -10646 (000) 11373 (000) -12888 (000) 03928 (000) -02297 (000)a1 -00011 (000) 00073 (000) -00097 (000) 00017 (000) -00039 (000)Anomaly confirmed confirmed confirmed confirmed confirmed

28

F Detailed statistical results DJI sub-periods

F1 Average analysis

Table F1 Average analysis

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 Mean return (gapday)

-001 023 015 -004

Mean return(non-gap day)

007 007 007 007

Anomaly confirmed confirmed confirmed confirmed1999-2008 Mean return (gap

day)090 -045 013 -004

Mean return(non-gap day)

-004 -004 -004 -004

Anomaly confirmed confirmed confirmed confirmed2009-2018 Mean return (gap

day)024 -024 0 -004

Mean return(non-gap day)

004 004 004 004

Anomaly confirmed confirmed not confirmed confirmed

F2 Parametric tests Students t-test

Table F2 T-test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 t-criterion 083 165 087 139t-critical (=095) 196 196 196 196Null hypothesis not rejected not rejected not rejected not rejected

1999-2008 t-criterion 347 351 054 047t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected rejected

2009-2018 t-criterion 265 207 051 058t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

F3 Parametric tests ANOVA

Table F3 ANOVA

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 F 085 409 093 179p-value 035 004 033 018

F critical 384 384 384 384Null hypothesis not rejected rejected not rejected not rejected

1999-2008 F 5405 3196 065 072p-value 0 0 042 039

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

2009-2018 F 554 697 024 058p-value 001 0 062 044

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

29

F4 Non-parametric tests Kruskal-Wallis test

Table F4 Kruskal-Wallis test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 Adjusted H 113 211 113 332df 1 1 1 1

P value 029 015 029 007Null hypothesis not rejected not rejected not rejected not rejected

1999-2008 Adjusted H 1484 1414 003 139df 1 1 1 1

P value 0 0 086 024Null hypothesis rejected rejected not rejected not rejected

2009-2018 Adjusted H 506 68 051 171df 1 1 1 1

P value 002 001 047 019Null hypothesis rejected rejected not rejected not rejected

F5 Regression analysis with dummy variables

Table F5 Regression analysis with dummy variables

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 a0 000068 (000) 00007 (000) 00007 (000) 00007 (000)a1 -000078 (035) 00016 (004) 00008 (033) -00011 (018)

Anomaly not confirmed confirmed not confirmed not confirmed1999-2008 a0 00004 (008) 00004 (008) 00004 (006) 00004 (008)

a1 00087 (000) -00049 (000) 00009 (042) -00008 (039)Anomaly confirmed confirmed not confirmed not confirmed

2009-2018 a0 00004 (006) 00004 (006) 00004 (006) 00004 (006)a1 00021 (001) -00028 (001) -00004 (062) -00008 (047)

Anomaly confirmed confirmed not confirmed not confirmed

F6 Modified CAR approach

Table F6 Modified CAR approach

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 Multiple R 083 088 082 086F-test 22779 (000) 40583 (000) 20401 (000) 3269454 (000)a0 00042 (023) 00017 (073) 00014 (058) -00266 (000)a1 -00009 (000) 00015 (000) 00006 (000) -00009 (000)

Anomaly confirmed confirmed confirmed confirmed1999-2008 Multiple R 095 093 076 019

F-test 62658 (000) 84712 (000) 10056 (000) 492 (003)a0 -00972 (000) 00365 (000) -00198 (000) -00115 (021)a1 00086 (000) -00042 (000) 00014 (000) 00002 (003)

Anomaly confirmed confirmed confirmed not confirmed2009-2018 Multiple R 096 082 08 05

F-test 150452 (000) 16731 (000) 22287 (000) 2620 (000)a0 00548 (000) -00618 (000) 00031 (020) -00112 (000)a1 00013 (000) -00014 (000) -00005 (000) -00004 (000)

Anomaly confirmed confirmed not confirmed confirmed

30

G Detailed statistical results NASDAQ sub-periods

G1 Average analysis

Table G1 Average analysis

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 Mean return (gapday)

094 -111 0189 -029

Mean return(non-gap day)

007 007 007 007

Anomaly confirmed confirmed confirmed confirmed1959-1968 Mean return (gap

day)133 -147 033 -039

Mean return(non-gap day)

006 006 006 006

Anomaly confirmed confirmed confirmed confirmed1969-1978 Mean return (gap

day)19 -186 057 -068

Mean return(non-gap day)

005 005 005 005

Anomaly confirmed confirmed confirmed confirmed1979-1988 Mean return (gap

day)138 -162 066 -04

Mean return(non-gap day)

008 008 008 008

Anomaly confirmed confirmed confirmed confirmed1989-1998 Mean return (gap

day)016 012 018 -009

Mean return(non-gap day)

002 002 002 002

Anomaly confirmed not confirmed confirmed confirmed1999-2008 Mean return (gap

day)38E-3 027 -036 -013

Mean return(non-gap day)

-01 -01 -01 -01

Anomaly confirmed not confirmed not confirmed not confirmed2009-2018 Mean return (gap

day)039 009 013 -025

Mean return(non-gap day)

001 001 001 001

Anomaly confirmed not confirmed confirmed confirmed

G2 Parametric tests Students t-test

Table G2 T-test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 t-criterion 3194 3076 201 559t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected rejected

1959-1968 t-criterion 1399 2246 443 382t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected rejected

1969-1978 t-criterion 261 4358 417 786t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected rejected

1979-1988 t-criterion 1847 1445 709 395t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected rejected

1989-1998 t-criterion 13 066 126 093t-critical (=095) 196 196 196 196Null hypothesis not rejected not rejected not rejected not rejected

1999-2008 t-criterion 192 106 111 009t-critical (=095) 196 196 196 196Null hypothesis not rejected not rejected not rejected not rejected

2009-2018 t-criterion 27 05 089 188t-critical (=095) 196 196 196 196Null hypothesis rejected not rejected not rejected not rejected

31

G3 Parametric tests ANOVA

Table G3 ANOVA

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 F 88153 190609 1272 14521p-value 0 0 0 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1959-1968 F 93974 149771 4715 10418p-value 0 0 0 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1969-1978 F 84546 145429 6295 18241p-value 0 0 0 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1979-1988 F 66952 110482 13138 8626p-value 0 0 0 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1989-1998 F 323 138 43 168p-value 007 024 003 019

F critical 384 384 384 384Null hypothesis not rejected not rejected rejected not rejected

1999-2008 F 106 512 327 003p-value 001 002 007 085

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

2009-2018 F 169 069 175 93p-value 0 04 018 0

F critical 384 384 384 384Null hypothesis rejected not rejected not rejected rejected

G4 Non-parametric tests Kruskal-Wallis test

Table G4 Kruskal-Wallis test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 Adjusted H 26254 32592 1464 3962df 1 1 1 1

P value 0 0 0 0Null hypothesis rejected rejected rejected rejected

1959-1968 Adjusted H 28235 27989 2736 332df 1 1 1 1

P value 0 0 0 0Null hypothesis rejected rejected rejected rejected

1969-1978 Adjusted H 22202 33777 3311 7591df 1 1 1 1

P value 0 0 0 0Null hypothesis rejected rejected rejected rejected

1979-1988 Adjusted H 23282 25292 4812 3964df 1 1 1 1

P value 0 0 0 0Null hypothesis rejected rejected rejected rejected

1989-1998 Adjusted H 381 017 175 132df 1 1 1 1

P value 005 068 019 025Null hypothesis not rejected not rejected not rejected not rejected

1999-2008 Adjusted H 855 023 044 004df 1 1 1 1

P value 0 063 051 084Null hypothesis rejected not rejected not rejected not rejected

2009-2018 Adjusted H 1063 009 257 709df 1 1 1 1

P value 0 077 011 001Null hypothesis rejected not rejected not rejected rejected

32

G5 Regression analysis with dummy variables

Table G5 Regression analysis with dummy variables

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 a0 00007 (000) 00007 (000) 00007 (000) 00007 (000)a1 00088 (000) -00119 (000) 00011 (000) -00036 (000)

Anomaly confirmed confirmed confirmed confirmed1959-1968 a0 00006 (000) 00006 (000) 00006 (000) 00006 (000)

a1 00128 (000) -00153 (000) 00027 (000) -00046 (000)Anomaly confirmed confirmed confirmed confirmed

1969-1978 a0 00005 (000) 00005 (000) 00005 (000) 00005 (000)a1 00185 (000) -00192 (000) 00053 (000) -00073 (000)

Anomaly confirmed confirmed confirmed confirmed1979-1988 a0 00008 (000) 00008 (000) 00008 (000) 00008 (000)

a1 00131 (000) -00172 (000) 00059 (000) -00048 (000)Anomaly confirmed confirmed confirmed confirmed

1989-1998 a0 00002 (027) 00002 (028) 00002 (028) 00002 (027)a1 00014 (007) 00010 (024) 00017 (004) -00011 (019)

Anomaly not confirmed not confirmed confirmed not confirmed1999-2008 a0 00001 (059) 00001 (062) 00001 (059) 00001 (060)

a1 00037 (000) 00026 (002) -00038 (000) -00014 (019)Anomaly confirmed not confirmed not confirmed not confirmed

2009-2018 a0 00001 (049) 00001 (049) 00001 (049) 00001 (049)a1 00038 (000) 00007 (040) 00012 (018) -00027 (000)

Anomaly confirmed not confirmed not confirmed confirmed

G6 Modified CAR approach

Table G6 Modified CAR approach

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 Multiple R 099 099 093 098F-test 5753605 (000) 100470(000) 6280421 283281a0 -00091 (000) -00349 (000) 00056 (001) 00015 (073)a1 00083 (000) -00110 (000) 00010 (000) -00031 (000)

Anomaly confirmed confirmed confirmed confirmed1959-1968 Multiple R 099 099 099 099

F-test 3923274 (000) 3005562 (000) 443198 (000) 372583 (000)a0 00096 (000) 00073 (016) -00082 (000) -00095 (004)a1 00116 (001) -00149 (000) 00025 (000) -00047 (000)

Anomaly confirmed confirmed confirmed confirmed1969-1978 Multiple R 099 099 098 099

F-test 4302608 (000) 2723953 (000) 179969 (000) 639745a0 00246 (000) -00002 (000) 00217 (000) -00514 (000)a1 00176 (000) -00182 (000) 00049 (000) -00062 (000)

Anomaly confirmed confirmed confirmed confirmed1979-1988 Multiple R 099 099 099 099

F-test 5872335 (000) 1182609 (000) 1083558 (000) 910089 (000)a0 00136 (000) -01081 (000) -00285 (000) -00101 (000)a1 00131 (000) -00167 (000) 00062 (000) -00048 (000)

Anomaly confirmed confirmed confirmed confirmed1989-1998 Multiple R 09 056 069 016

F-test 46947 (000) 4885 (000) 10131 (000) 263 (011)a0 00102 (002) -00261 (000) -0016 (001) -00237 (000)a1 00015 (000) 00010 (000) 0001 (000) 00002 (011)

Anomaly confirmed confirmed confirmed not confirmed1999-2008 Multiple R 093 087 073 037

F-test 71863 (000) 32530 (000) 13273 (000) 1669 (000)a0 00185 (004) 00311 (000) -00130 (039) -00546 (000)a1 00037 (000) 00032 (000) -00026 (000) -00007 (000)

Anomaly confirmed not confirmed not confirmed confirmed2009-2018 Multiple R 089 001 096 091

F-test 40818 (000) 000 (094) 116744 (000) 53770 (000)a0 01436 (000) -01099 (000) -01036 (000) 00697 (000)a1 00030 (000) 00000 (094) 00024 (000) -00021 (000)

Anomaly confirmed not confirmed confirmed confirmed

33

H Detailed statistical results SampP 500 sub-periods

H1 Average analysis

Table H1 Average analysis

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 Mean return (gapday)

138 -171 004 -014

Mean return(non-gap day)

0 0 0 0

Anomaly confirmed confirmed confirmed confirmed1939-1948 Mean return (gap

day)001 -042 172 -195

Mean return(non-gap day)

003 003 003 003

Anomaly confirmed confirmed confirmed confirmed1949-1958 Mean return (gap

day)165 -18 02 002

Mean return(non-gap day)

006 006 006 006

Anomaly confirmed confirmed confirmed not confirmed1959-1968 Mean return (gap

day)104 -102 015 0

Mean return(non-gap day)

002 002 002 002

Anomaly confirmed confirmed confirmed not confirmed1969-1978 Mean return (gap

day)131 -13 019 -03

Mean return(non-gap day)

0 0 0 0

Anomaly confirmed confirmed confirmed confirmed1979-1988 Mean return (gap

day)058 -042 015 003

Mean return(non-gap day)

005 005 005 005

Anomaly confirmed confirmed confirmed not confirmed1989-1998 Mean return (gap

day)02 -023 -002 01

Mean return(non-gap day)

007 007 007 007

Anomaly confirmed confirmed not confirmed not confirmed1999-2008 Mean return (gap

day)083 -089 -023 -005

Mean return(non-gap day)

001 001 001 001

Anomaly confirmed confirmed not confirmed confirmed2009-2018 Mean return (gap

day)055 -052 001 -015

Mean return(non-gap day)

004 004 004 004

Anomaly confirmed confirmed not confirmed confirmed

34

H2 Parametric tests Students t-test

Table H2 T-test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 t-criterion 101 85 029 048t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

1939-1948 t-criterion 064 479 3074 225t-critical (=095) 196 196 196 196Null hypothesis not rejected rejected rejected rejected

1949-1958 t-criterion 2964 2383 193 041t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

1959-1968 t-criterion 2281 2157 21 023t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected not rejected

1969-1978 t-criterion 1318 2034 187 321t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected rejected

1979-1988 t-criterion 435 535 07 037t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

1989-1998 t-criterion 201 396 132 052t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

1999-2008 t-criterion 362 433 117 022t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

2009-2018 t-criterion 375 382 027 132t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

H3 Parametric tests ANOVA

Table H3 ANOVA

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 F 6281 8032 005 051p-value 0 0 082 047

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

1939-1948 F 056 2603 34854 51034p-value 045 0 0 0

F critical 384 384 384 384Null hypothesis not rejected rejected rejected rejected

1949-1958 F 100174 128997 897 062p-value 0 0 0 043

F critical 384 384 384 384Null hypothesis rejected rejected rejected not rejected

1959-1968 F 36831 32858 617 01p-value 0 0 001 074

F critical 384 384 384 384Null hypothesis rejected rejected rejected not rejected

1969-1978 F 26601 3063 53 152p-value 0 0 002 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1979-1988 F 23 245 076 009p-value 0 0 039 077

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

1989-1998 F 399 1156 118 015p-value 004 0 027 069

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

1999-2008 F 4253 5622 365 024p-value 0 0 006 062

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

2009-2018 F 3064 3656 01 43p-value 0 0 075 004

F critical 384 384 384 384Null hypothesis rejected rejected not rejected rejected

35

H4 Non-parametric tests Kruskal -Wallis test

Table H4 Kruskal-Wallis test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 Adjusted H 9982 5913 332 14df 1 1 1 1

P value 0 0 007 024Null hypothesis rejected rejected not rejected not rejected

1939-1948 Adjusted H 494 1999 23387 24927df 1 1 1 1

P value 003 0 0 0Null hypothesis rejected rejected rejected rejected

1949-1958 Adjusted H 28728 28175 348 15df 1 1 1 1

P value 0 0 006 022Null hypothesis rejected rejected not rejected not rejected

1959-1968 Adjusted H 25729 21437 701 063df 1 1 1 1

P value 0 0 001 043Null hypothesis rejected rejected rejected not rejected

1969-1978 Adjusted H 14407 20078 27 1706df 1 1 1 1

P value 0 0 01 0Null hypothesis rejected rejected not rejected rejected

1979-1988 Adjusted H 1788 2836 027 034df 1 1 1 1

P value 0 0 06 056Null hypothesis rejected rejected not rejected not rejected

1989-1998 Adjusted H 251 1431 111 044df 1 1 1 1

P value 011 0 029 051Null hypothesis not rejected rejected not rejected not rejected

1999-2008 Adjusted H 1812 1788 042 002df 1 1 1 1

P value 0 0 052 089Null hypothesis rejected rejected not rejected not rejected

2009-2018 Adjusted H 1314 1783 074 37df 1 1 1 1

P value 0 0 039 005Null hypothesis rejected rejected not rejected not rejected

36

H5 Regression analysis with dummy variables

Table H5 Regression analysis with dummy variables

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 a0 00000 (097) 00000 (004) 00000 (097) 00000 (097)a1 00138 (000) -00172 (000) 00004 (082) -00014 (047)

Anomaly confirmed confirmed not confirmed not confirmed1939-1948 a0 00003 (015) 00003 (015) 00003 (015) 00003 (015)

a1 00007 (045) -00045 (000) 00170 (000) -00199 (000)Anomaly not confirmed confirmed confirmed confirmed

1949-1958 a0 00006 (000) 00006 (000) 00006 (000) 00006 (000)a1 00160 (000) -00188 (000) 00016 (000) -00004 (043)

Anomaly confirmed confirmed confirmed not confirmed1959-1968 a0 00002 (007) 00002 (004) 00002 (008) 00002 (008)

a1 00103 (000) -00105 (000) 00014 (001) -00002 (074)Anomaly confirmed confirmed confirmed not confirmed

1969-1978 a0 00000 (078) 00000 (078) 00000 (078) 00000 (078)a1 00132 (000) -00132 (000) 00019 (002) -00030 (000)

Anomaly confirmed confirmed confirmed confirmed1979-1988 a0 00006 (001) 00006 (001) 00006 (001) 00006 (000)

a1 00053 (000) -00048 (000) 00009 (040) -00003 (075)Anomaly confirmed confirmed not confirmed not confirmed

1989-1998 a0 00007 (000) 00007 (000) 00007 (000) 00007 (000)a1 00016 (005) -00030 (000) -00009 (026) 00003 (072)

Anomaly confirmed confirmed not confirmed not confirmed1999-2008 a0 00001 (075) 00001 (075) 00001 (075) 00001 (076)

a1 00083 (000) -00091 (000) -00024 (005) -00006 (062)Anomaly confirmed confirmed not confirmed not confirmed

2009-2018 a0 00004 (003) 00004 (000) 00004 (003) 00004 (003)a1 00051 (000) -00059 (000) -00003 (075) -00019 (003)

Anomaly confirmed confirmed not confirmed confirmed

37

H6 Modified CAR approach

Table H6 Modified CAR approach

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 Multiple R 096 095 046 046F-test 175935 (000) 96500 (000) 3534 (000) 2880 (000)a0 -01070 (000) 01958 (000) 00405 (000) 00535 (000)a1 00121 (000) -00160 (000) 00006 (000) -00014 (000)

Anomaly confirmed confirmed confirmed confirmed1939-1948 Multiple R 08 099 099 099

F-test 18777 (000) 755727 (000) 3572830 (000) 2696099 (000)a0 00019 (073) -00346 (000) -00373 (000) 00912 (000)a1 00012 (000) -00044 (000) 00168 (000) -00197 (000)

Anomaly confirmed confirmed confirmed confirmed1949-1958 Multiple R 099 099 094 015

F-test 1021705 (000) 7171257 (000) 75858 (000) 242 (012)a0 -00176 (000) -00191 (000) 00095 (000) -00498 (000)a1 00154 (000) -00181 (000) 00013 (000) -00002 (012)

Anomaly confirmed confirmed confirmed not confirmed1959-1968 Multiple R 099 099 094 078

F-test 1463311 (000) 6002659 (000) 82273 (000) 14352 (000)a0 -00112 (000) 00004 (085) 00151 (000) 00389 (000)a1 00098 (000) -00102 (000) 00011 (000) -00009 (000)

Anomaly confirmed confirmed confirmed confirmed1969-1978 Multiple R 098 099 093 099

F-test 241655 (000) 1451901 (000) 57333 (000) 368160 (000)a0 -00433 (000) 00276 (000) 00099 (002) -00144 (000)a1 00132 (000) -00134 (000) 00020 (000) -00030 (000)

Anomaly confirmed confirmed confirmed confirmed1979-1988 Multiple R 092 078 023 008

F-test 53757 (000) 18707 (000) 487 (003) 085 (036)a0 00813 (000) -02508 (000) 00204 (000) -00235 (000)a1 00036 (000) -00031 (000) -00003 (003) -00001 (036)

Anomaly confirmed confirmed not confirmed not confirmed1989-1998 Multiple R 079 099 074 044

F-test 19705(000) 761967 (000) 14133 (000) 2369 (000)a0 00268 (000) 00023 (021) -00381 (000) 00087 (000)a1 00013 (000) -00028 (000) -00008 (000) 00002 (000)

Anomaly confirmed confirmed not confirmed not confirmed1999-2008 Multiple R 091 093 071 065

F-test 47218 (000) 76564 (000) 9843 (000) 7768 (000)a0 -01493 (000) 01351 (000) 00397 (000) 00007 (093)a1 00081 (000) -00083 (000) -00026 (000) -00011 (000)

Anomaly confirmed confirmed not confirmed confirmed2009-2018 Multiple R 086 087 083 074

F-test 29971 (000) 32484 (000) 23228 (000) 12764 (000)a0 01711 (000) -02250 (000) 00407 (000) -00472 (000)a1 00038 (000) -00044 (000) -00010 (000) -00012 (000)

Anomaly confirmed confirmed not confirmed confirmed

38

Tab

le2

Gap

size

andthenumber

ofdetectedgapscase

ofSampP500dataover

theperiod2009-2018

Gap

size

010

020

030

040

050

060

070

080

090

100

gapsin

prices

4105

1970

1090

571

345

202

135

087

067

052

Number

ofdetectedgaps

1038

497

275

144

8751

3422

1713

Number

ofdetectednegativegaps

468

230

130

6944

3120

109

8Number

ofdetectedpositivegaps

570

267

145

7543

2014

128

5

8

Table 3 Gap size used for different sub-periods over the period 1929-2018

Period SampP 5001929-1938 1201949-1958 1201959-1968 0701969-1978 0011979-1988 0031989-1998 0011999-2008 0082009-2018 034Overall data set 070

42 Price gap seasonality

Caporale and Plastun (2017) show that in foreign exchange and commodity marketsprice gaps tend to appear on Mondays According to their results more than 95 percent of price gaps in foreign exchange markets compared to 65 per cent of price gaps incommodity markets appeared on Mondays This is rather reasonable because marketsare closed on weekends and as the result of any significant event over the weekend willlead to price gaps on Monday Surprisingly this is not the case in this instance (withstock markets) as can be seen in Tables 4 and A2 Therefore H3 is rejected

Table 4 Day of the week and gaps

Day of the week SampP 500Monday 023Tuesday 02Wednesday 02Thursday 018Friday 019

43 Short term price behaviour

Next we analyse short-term price behaviour in the US stock market around price gapsto investigate the presence of possible price patterns before and after price gaps Wecalculate the number of days with positive (or negative) returns after a positive (or neg-ative) price gaps divided by the total number of price gaps If this ratio or momentum

9

effect is much higher than 50 per cent this indicates abnormal price behaviour and asthe results confirm our hypotheses

The results are presented in Appendix B We find no convincing evidence in favour ofmomentum effect after price gaps (Table B1) and before them (Table B2) In generalprice gaps are not generated by previous price dynamics (NASDAQ index is an exceptionas negative gaps appear in 70 per cent of the cases after downward price movements andafter positive gaps in 67 per cent of the cases upward price movements are observed)Our results (see Table B3 for details) also indicate that the probability that price gapswill be filled within 5 days after appearance is very low at around 20 per cent

44 Price gap evolution

Overall in probabilistic terms price gaps do not generate any stable patterns But therecan be patterns in terms of size of price movements after gaps To check this we will testH1 and H2 To incorporate price direction in results of analysis H1 we further test forH1minus1 and H1minus2 The results for the overall data sets are presented in Appendices C toE for the cases of DJI SampP 500 and NASDAQ respectively To ease the interpretationof results we have summarised them in Table 5 and Table A3

Table 5 shows strong evidence confirming H1 in the SampP 500 Similarly Table A3confirms H1 for the NASDAQ but not for the DJI The difference between the DJI SampP500 and NASDAQ results can be explained by the differences in samples (DJI sampleis much shorter) This suggests that price gap anomaly may evolve and is therefore apreliminary confirmation of H2

Tables 6 and 7 confirm H1minus1 in the SampP 500 on the day of the price gap That ison the price gap day prices tend towards the direction of the price gap However thisis not the case for the day after the price gap therefore H1minus2 is not confirmed It canbe concluded that the SampP 500 roughly needs a day to absorb new information Never-theless even a day can be enough to create a profitable trading strategy and generateabnormal profits from trading

Similar results on the NASDAQ can be found in Tables A6 and A7 The longersample of the NASDAQ allows for the evolution of the price anomaly H1minus1 is there-fore confirmed on the day of the price gap anomaly and the day after the price gapanomaly (in both instances only until the 1990s and has since disappeared) H1minus2 inboth instances is confirmed up until the 1990s The results of the DJI did not providestrong evidence in favour of H1minus1 and H1minus2 on the day after the price gap but sim-ilar to the SampP 500 evidence was strong on the day of the price gap (see Tables A4and A5) These results confirm in the main the price gap anomaly is a reality in theUS stock market and that it evolves over time that is from prevalence to disappearance

10

Tab

le5

Overallstatisticalresults

SampP500

PeriodM

ethod

Average

analysis

t-test

ANOVA

test

Man

n-

Whitney

test

Regression

analysis

with

dummy

variab

les

Modified

CAR

approach

Overall

Gap

day

+-

-+

-+

3Gap

day

(Positivegaps)

++

++

++

6Gap

day

(Negativegaps)

++

++

++

6Day

aftergap(P

ositivegaps)

++

-+

++

5Day

aftergap(N

egativegaps)

++

--

++

4

Note+

indicates

thattheanom

alyis

confirm

edand-indicates

thatan

omaly

isnot

confirm

edThehigher

theoverallrating

the

strongertheeviden

ceofthean

omaly

11

Tab

le6

H1minus1summarystatisticalresults

SampP500sub-periods

PeriodM

ethod

Average

analysis

t-test

ANOVA

test

Man

n-

Whitney

test

Regression

analysis

withdummy

variab

les

Modified

CAR

approach

Overall

Dayofanomaly

1929-1938

++

++

++

61939-1948

+-

-+

-+

31949-1958

++

++

++

61959-1968

++

++

++

61969-1978

++

++

++

61979-1988

++

++

++

61989-1998

++

++

++

61999-2008

++

++

++

62009-2018

++

++

++

6Dayafteranomaly

1929-1938

+-

--

-+

21939-1948

++

++

++

61949-1958

+-

+-

++

51959-1968

++

++

++

61969-1978

+-

+-

++

41979-1988

+-

--

--

11989-1998

--

--

--

01999-2008

--

--

--

02009-2018

--

--

--

0

Note+

indicates

thattheanom

alyis

confirm

edand-indicates

thatan

omaly

isnot

confirm

edThehigher

theoverallrating

the

strongertheeviden

ceofthean

omaly

12

Tab

le7

H1minus2statisticalresults

SampP500sub-periods

PeriodM

ethod

Average

analysis

t-test

ANOVA

test

Man

n-

Whitney

test

Regression

analysiswith

dummy

variab

les

Modified

CAR

approach

Overall

Dayofanomaly

1929-1938

++

++

++

61939-1948

++

++

++

61949-1958

++

++

++

61959-1968

++

++

++

61969-1978

++

++

++

61979-1988

++

++

++

61989-1998

++

++

++

61999-2008

++

++

++

62009-2018

++

++

++

6Dayafteranomaly

1929-1938

+-

--

-+

21939-1948

++

++

++

61949-1958

--

--

--

01959-1968

--

--

-+

11969-1978

++

++

++

61979-1988

--

--

--

01989-1998

--

--

--

01999-2008

+-

--

-+

22009-2018

+-

+-

++

4

Note+

indicates

thattheanom

alyis

confirm

edand-indicates

thatan

omaly

isnot

confirm

edThehigher

theoverallrating

the

strongertheeviden

ceofthean

omaly

13

45 Trading simulation

The algorithm of the trading strategy is to buysell at the start of the updown gapday and close this position at the end of this day To test this strategy data for the DJIand SampP 500 are used (for this case the price anomaly still exists based on the day itoccurred) The results for DJI are presented in Table A8 and for the SampP 500 in Table8 For the SampP 500 and DJI the trading strategy built on price gap anomaly is efficientand its results differ from random

Table 8 Trading simulation results of the price gap anomaly for the SampP 500

Period Gaptype

Numberof

tradesunits

Numberof suc-cessfultradesunits

Numberof suc-cessfultrades

Profit

Profit peryear

z-test Result

1929-1938 Up 131 130 992 1816 182 1065 passedDown 110 108 982 1893 189 876 passed

1939-1948 Up 110 67 609 106 11 09 failedDown 122 79 648 518 52 465 passed

1949-1958 Up 106 105 991 1765 176 3191 passedDown 104 103 99 1891 189 2356 passed

1959-1968 Up 108 106 981 1331 113 2441 passedDown 92 91 989 948 95 2214 passed

1969-1978 Up 85 71 835 1128 113 1361 passedDown 96 90 938 1262 126 2118 passed

1979-1988 Up 92 63 685 54 54 495 passedDown 123 81 659 519 52 496 passed

1989-1998 Up 117 72 615 267 27 295 passedDown 99 61 616 228 23 32 passed

1999-2008 Up 99 65 657 828 83 373 passedDown 110 72 655 987 99 438 passed

2009-2018 Up 106 71 67 59 59 416 passedDown 107 65 607 56 56 362 passed

14

Figure 1 Trading simulation results of the price gap anomaly for the SampP 500

Note The primary axis refers to the percentage profit per year and the secondary to thez minus test statistic

One more interesting fact (see Figure 1) is the decrease of trading strategy efficiencyThis is indirect evidence in favour of evolution of the US stock market and its movementfrom less efficient to more efficient state Overall it can be concluded that the price gapanomaly is a real market anomaly The US stock market loses its efficiency after pricegaps This effect is temporary and lasts only for a day Still even this time is enoughto exploit the hole in the market efficiency and generate abnormal profits from trading

5 Conclusion

We analysed price gap anomaly in the US stock market by using information from threestock market indexes(DJI SampP 500 and NASDAQ) We tested three hypotheses of in-terest that is H1 the price gap anomaly exists H1minus1 prices tend to rise after positivegaps H1minus2 prices tend to fall after negative gaps H2 the price gap anomaly evolvesand H3 there is seasonality in price gaps Various statistical methods including para-metric tests (Students t-tests ANOVA) non-parametric tests (Mann-Whitney test)regression analysis with dummy variables MCAR approach and the trading simulationapproach were utilised

We conclude that the US stock market in the main did not exhibit seasonality in pricegaps Therefore H3 is rejected Furthermore no evidence was found that price gaps inthe US stock market were filled within five days of their occurrence However strongevidence in favour of abnormal price movements after the gaps were found confirming

15

H1 and H2 Particularly on the day of the occurrence of the gap and not on the dayafter the price gap In the DJI and the SampP 500 this pattern persists indicating thatthese markets take a day to incorporate new information As the results of the tradingsimulation indicate a day is enough to profit from a price gap anomaly trading strategyin the DJI and the SampP 500

Similar to other studies and other anomalies (see McLean and Pontiff (2016) Ca-jueiro and Tabak (2004) and Tiwari et al (2019) for example) the price gap anomalyevolved It is less prevalent since the 1990s as shown in the SampP 500 and NASDAQThis pattern of evolution is common amongst most stock market anomalies (see Plastunet al (2019b) on calendar anomalies amongst others) Our findings therefore add onto the existing literature Finally in the main our results are against the EMH and aretherefore interesting to both practitioners and academics

16

References

Agrawal A and Tandon K (1994) Anomalies or illusions evidence from stock marketsin eighteen countries Journal of international Money and Finance 13(1)83ndash106

Akerlof G A and Shiller R J (2009) Animal Spirits How human psychology drivesthe economy and why it matters for global capitalism Princeton University Press

Basu S (1977) Investment performance of common stocks in relation to their price-earnings ratios A test of the efficient market hypothesis The Journal of Finance32(3)663ndash682

Bildik R (2004) Are calendar anomalies still alive Evidence from istanbul stockexchange SSRN Electronic Journal 2004

Cai J Li Y and Qi Y (2006) The day-of-the-week effect New evidence from theChinese stock market Chinese Economy 39(2)71ndash88

Cajueiro D O and Tabak B M (2004) The Hurst exponent over time testing theassertion that emerging markets are becoming more efficient Physica A StatisticalMechanics and its Applications 336(3-4)521ndash537

Caporale G M Gil-Alana L Plastun A and Makarenko I (2016) Intraday anoma-lies and market efficiency A trading robot analysis Computational Economics47(2)275ndash295

Caporale G M and Plastun A (2017) Price gaps Another market anomaly Invest-ment Analysts Journal 46(4)279ndash293

Cross F (1973) The behavior of stock prices on Fridays and Mondays FinancialAnalysts Journal 29(6)67ndash69

Fama E F (1965) The behavior of stock-market prices The Journal of Business38(1)34ndash105

Fama E F (1970) Efficient capital markets A review of theory and empirical workThe Journal of Finance 25(2)383ndash417

Fortune P (1998) Weekends can be rough revisiting the weekend effect in stock pricesTechnical report

Fortune P (1999) Are stock returns different over weekends A jump diffusion analysisof the weekend effect New England Economic Review 103ndash19

French K R (1980) Stock returns and the weekend effect Journal of FinancialEconomics 8(1)55ndash69

Fung A K-W Lam K and Lam K-M (2010) Do the prices of stock index futuresin asia overreact to us market returns Journal of Empirical Finance 17(3)428ndash440

17

Gibbons M R and Hess P (1981) Day of the week effects and asset returns Journalof business pages 579ndash596

Grant J L Wolf A and Yu S (2005) Intraday price reversals in the us stock indexfutures market A 15-year study Journal of Banking amp Finance 29(5)1311ndash1327

Grossman S J and Stiglitz J E (1980) On the impossibility of informationallyefficient markets The American Economic Review 70(3)393ndash408

Jacobsen B Mamun A and Visaltanachoti N (2005) Seasonal size and valueanomalies

Jensen M (1978) Some anomalous evidence regarding market efficiency Journal ofFinancial Economics 6(23 (1978))95ndash101

Lakonishok J and Smidt S (1988) Are seasonal anomalies real A ninety-year per-spective The Review of Financial Studies 1(4)403ndash425

MacKinlay A (1997) Event studies in economics and finance Journal of EconomicLiterature (35)113ndash39

Mandelbrot B B (1997) The variation of certain speculative prices In Fractals andscaling in finance pages 371ndash418 Springer

McLean R D and Pontiff J (2016) Does academic research destroy stock returnpredictability The Journal of Finance 71(1)5ndash32

Plastun A Makarenko I Khomutenko L Shcherbak S and Tryfonova O (2019a)Exploring price gap anomaly in the ukrainian stock market Investment Managementamp Financial Innovations 16(2)150

Plastun A Sibande X Gupta R and Wohar M E (2019b) Rise and fall of calendaranomalies over a century The North American Journal of Economics and Finance49181ndash205

Schwert G W (2003) Chapter 15 anomalies and market efficiency In FinancialMarkets and Asset Pricing volume 1 of Handbook of the Economics of Finance pages939 ndash 974 Elsevier

Shiller R J (2000) Irrational exuberance Princeton University

Tiwari A K Aye G C and Gupta R (2019) Stock market efficiency analysis usinglong spans of data A multifractal detrended fluctuation approach Finance ResearchLetters 28398ndash411

Yuan Y (2015) Market-wide attention trading and stock returns Journal of FinancialEconomics 116(3)548ndash564

18

Appendices

A DJI and NASDAQ Summary Results

A1 Overall Results

Table A1 Gap size used for different sub-periods over the period 1929-2018

Period DJI NASDAQ1929-1938 - -1939-1948 - -1949-1958 - 0711959-1968 - 0951969-1978 - 1351979-1988 - 1101989-1998 040 0681999-2008 007 1502009-2018 020 110Overall data set 030 110

Table A2 Day of the week and gaps

Day of the week DJI NASDAQMonday 024 02Tuesday 02 02Wednesday 017 02Thursday 019 019Friday 021 02

A2 Statistical tests

Table A3 Results of the statistical tests for the overall data sets

PeriodMethod Averageanalysis

t-test ANOVAtest

Mann-Whitney

test

Regressionanalysiswith

dummyvariables

ModifiedCAR

approach

Overall

Dow Jones Index overall data setGap day - - - - - + 1Gap day (Positive gaps) + - - - - - 1Gap day (Negative gaps) + - - - - + 2Day after gap (Positive gaps) + - - - - - 1Day after gap (Negative gaps) + - - + - + 3

NASDAQ overall data setGap day + + + + + + 6Gap day (Positive gaps) + + + + + + 6Gap day (Negative gaps) + + + + + + 6Day after gap (Positive gaps) + + + + + + 6Day after gap (Negative gaps) + + + + + + 6

Note + indicates that the anomaly is confirmed and - indicates that anomaly is not confirmedThe higher the overall rating the stronger the evidence of the anomaly

19

Table A4 Results of the statistical tests for H1minus1 DJI

Period Averageanalysis

t-test ANOVA test Mann-Whitney

test

Regressionanalysis with

dummyvariables

ModifiedCAR

approach

Overall

Day of anomaly1989-1998 + - - - - + 21999-2008 + + + + + + 62009-2018 + + + + + + 6

Day after anomaly1989-1998 + - - - - + 21999-2008 + - - - - + 22009-2018 - - - - - - 0

Note + indicates that the anomaly is confirmed and - indicates that anomaly is not confirmedThe higher the overall rating the stronger the evidence of the anomaly

Table A5 Results of the statistical tests for H1minus2 DJI

Period Averageanalysis

t-test ANOVA test Mann-Whitneytest

Regressionanalysis with

dummyvariables

Modified CARapproach

Overall

Day of anomaly1989-1998 - - - - - - 01999-2008 + + + + + + 62009-2018 + + + + + + 6

Day after anomaly1989-1998 + - - - - + 21999-2008 + - - - - - 12009-2018 + - - - - + 2

Note + indicates that the anomaly is confirmed and - indicates that anomaly is not confirmedThe higher the overall rating the stronger the evidence of the anomaly

Table A6 Results of the statistical tests for H1minus1 NASDAQ

PeriodMethod Averageanalysis

t-test ANOVA test Mann-Whitney

test

Regressionanalysis with

dummyvariables

ModifiedCAR

approach

Overall

Day of anomaly1949-1958 + + + + + + 61959-1968 + + + + + + 61969-1978 + + + + + + 61979-1988 + + + + + + 61989-1998 + - - - - + 21999-2008 + - + + + + 52009-2018 + + + + + + 6

Day after anomaly1949-1958 + + + + + + 61959-1968 + + + + + + 61969-1978 + + + + + + 61979-1988 + + + + + + 61989-1998 + - + - + + 41999-2008 - - - - - - 02009-2018 + - - - - + 2

Note + indicates that the anomaly is confirmed and - indicates that anomaly is not confirmedThe higher the overall rating the stronger the evidence of the anomaly

20

Table A7 Results of the statistical tests for H1minus2 NASDAQ

PeriodMethod Averageanalysis

t-test ANOVA test Mann-Whitney

test

Regressionanalysis with

dummyvariables

ModifiedCAR

approach

Overall

Day of anomaly1949-1958 + + + + + + 61959-1968 + + + + + + 61969-1978 + + + + + + 61979-1988 + + + + + + 61989-1998 - - - - - + 11999-2008 - - + - - - 12009-2018 - - - - - - 0

Day after anomaly1949-1958 + + + + + + 61959-1968 + + + + + + 61969-1978 + + + + + + 61979-1988 + + + + + + 61989-1998 + - - - - - 11999-2008 - - - - - + 12009-2018 + - - + + + 4

Note + indicates that the anomaly is confirmed and - indicates that anomaly is not confirmedThe higher the overall rating the stronger the evidence of the anomaly

A3 Trading Simulation Results

Table A8 Trading simulation results of the price gap anomaly for the DJI 1989-2018

Period Gap type Number oftradesunits

Number ofsuccessfultradesunits

Number ofsuccessfultrades

Profit Profit per year

z-test Result

1989-1998 Up 102 46 451 -11 -01 011 failedDown 116 49 422 -267 -27 242 passed

1999-2008 Up 73 51 699 665 66 37 passedDown 143 81 566 641 64 331 passed

2009-2018 Up 127 88 693 308 31 327 passedDown 81 47 58 196 2 184 passed

21

B Short-term price behavior in DJI SampP 500 and

NASDAQ Price gaps (overall data sets)

Table B1 Momentum effect in the US stock market after the gap

Instrument Parameter Number of days after the gap1 2 3

Dow Jones Index Positive gaps 53 57 61Negative gaps 50 50 47

All gaps 51 54 54SampP 500 Index Positive gaps 40 63 60

Negative gaps 4 52 45All gaps 4 58 53

NASDAQ Positive gaps 32 65 67Negative gaps 24 63 59

All gaps 28 64 63

Table B2 Momentum effect in the US stock market before the gap

Instrument Parameter Number of days before the gap1 2 3

Dow Jones Index Positive gaps 56 49 52Negative gaps 54 49 49

All gaps 55 49 50SampP 500 Index Positive gaps 57 57 52

Negative gaps 60 59 54All gaps 58 58 53

NASDAQ Positive gaps 61 56 54Negative gaps 68 69 70

All gaps 64 63 63

Table B3 Fill gap effect in the US stock market

Instrument Parameter Number of days after the gap1 2 3 4 5

Dow Jones Index Positive gaps 22 28 26 30 28Negative gaps 25 33 36 42 46

All gaps 24 30 31 35 37SampP 500 Index Positive gaps 0 6 11 16 19

Negative gaps 1 10 19 26 27All gaps 1 8 15 20 23

NASDAQ Positive gaps 8 13 18 21 19Negative gaps 7 11 17 21 25

All gaps 8 12 18 21 22

22

C Detailed statistical results DJI overall data

C1 Average analysis

Table C1 Average analysis

Parameter Gap day Gap day(Positive gaps)

Gap day(Negative gaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Mean return (gap day) 003 006 0 005 -003Mean return (non-gap day) 004 004 004 004 004Anomaly not confirmed not confirmed confirmed not confirmed confirmed

C2 Parametric tests Students t-test

Table C2 T-test

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

t-criterion 016 042 053 015 104t-critical (=095) 196 196 196 196 196Null hypothesis not rejected not rejected not rejected not rejected not rejected

C3 Parametric tests ANOVA

Table C3 ANOVA

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

F 0036 018 053 003 14p-value 085 067 047 086 024F critical 384 384 384 384 384Null hypothesis not rejected not rejected not rejected not rejected not rejected

C4 Non-parametric tests Kruskal-Wallis test

Table C4 Kruskal -Wallis test

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Adjusted H 082 012 126 0 455df 1 1 1 1 1P value 037 073 026 095 003Critical value 384 384 384 384 384Null hypothesis not rejected not rejected not rejected not rejected rejected

23

C5 Regression analysis with dummy variables

Table C5 Regression analysis with dummy variables

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

a0 00004 (000) 00004 (000) 00004 (000) 00004 (000) 00004 (000)a1 -00001 (-019) 00002 (067) -00004 (047) 00001 (086) -00007 (024)Anomaly not confirmed not confirmed not confirmed not confirmed not confirmed

C6 Modified CAR approach

Table C6 Modified CAR approach

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Multiple R 049 05 025 0 092F-test 23347 (000) 12913 (000) 2207 (000) 000 (098) 1822 (000)a0 -00041 (060) 00128 (006) -00267 (000) 00354 (000) 00319 (000)a1 -00003 (000) -00003 (000) -00002 (000) 00000 (098) -00008 (000)Anomaly confirmed confirmed confirmed not confirmed confirmed

24

D Detailed statistical results SampP 500 overall data

D1 Average analysis

Table D1 Average analysis

Parameter Gap day Gap day(Positive gaps)

Gap day(Negative gaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Mean return (gap day) 006 115 -129 017 -011Mean return (non-gap day) 002 002 002 002 002Anomaly confirmed confirmed confirmed confirmed confirmed

D2 Parametric tests Students t-test

Table D2 T-test

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

t-criterion 092 4546 3579 485 271t-critical (=095) 196 196 196 196 196Null hypothesis not rejected rejected rejected rejected rejected

D3 Parametric tests ANOVA

Table D3 ANOVA

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

F 155 116211 126952 1866 136p-value 022 0 0 0 0F critical 384 384 384 384 384Null hypothesis not rejected rejected rejected not rejected not rejected

D4 Non-parametric tests Kruskal-Wallis test

Table D4 Kruskal-Wallis test

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Adjusted H 1352 70516 47237 3946 004df 1 1 1 1 1P value 0 0 0 0 084Critical value 384 384 384 384 384Null hypothesis rejected rejected rejected rejected not rejected

25

D5 Regression analysis with dummy variables

Table D5 Regression analysis with dummy variables

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

a0 00002 (000) 00002 (000) 00002 (000) 00002 (000) 00002 (000)a1 00003 (021) 00113 (000) -00132 (000) 00014 (000) -00014 (000)Anomaly not confirmed confirmed confirmed confirmed confirmed

D6 Modified CAR approach

Table D6 Modified CAR approach

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Multiple R 051 099 099 099 096F-test 69486 (000) 325351 (000) 1457582 (000) 6345973 (000) 1213344 (000)a0 -01003(000) 04081 (000) -05444 (000) -01088 (000) 00272 (000)a1 00002 (000) 00106 (000) -00127 (000) 00016 (000) -00016 (000)Anomaly confirmed confirmed confirmed confirmed confirmed

26

E Detailed statistical results NASDAQ overall data

E1 Average analysis

Table E1 Average analysis

Parameter Gap day Gap day(Positive gaps)

Gap day(Negative gaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Mean return (gap day) -009 084 -090 022 -037Mean return (non-gap day) 003 003 003 003 003Anomaly confirmed confirmed confirmed confirmed confirmed

E2 Parametric tests Students t-test

Table E2 T-test

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

t-criterion 230 1257 1341 306 664t-critical (=095) 196 196 196 196 196Null hypothesis rejected rejected rejected rejected rejected

E3 Parametric tests ANOVA

Table E3 ANOVA

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

F 2289 62720 88402 3330 17356p-value 0 0 0 0 0F critical 384 384 384 384 384Null hypothesis rejected rejected rejected rejected rejected

E4 Non-parametric tests Kruskal-Wallis test

Table E4 Kruskal-Wallis test

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Adjusted H 1892 36022 45248 4695 10437df 1 1 1 1 1P value 0 0 0 0 0Critical value 384 384 384 384 384Null hypothesis rejected rejected rejected rejected rejected

27

E5 Regression analysis with dummy variables

Table E5 Regression analysis with dummy variables

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

a0 00003 (000) 00003 (000) 00003 (000) 00003 (000) 00003 (000)a1 -00012 (000) 00081 (000) -00093 (000) 00018 (000) -00040 (000)Anomaly confirmed confirmed confirmed confirmed confirmed

E6 Modified CAR approach

Table E6 Modified CAR approach

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Multiple R 069 092 092 072 097F-test 133255 (000) 361102 (000) 442376 (000) 72903 (000) 1082812 (000)a0 -10646 (000) 11373 (000) -12888 (000) 03928 (000) -02297 (000)a1 -00011 (000) 00073 (000) -00097 (000) 00017 (000) -00039 (000)Anomaly confirmed confirmed confirmed confirmed confirmed

28

F Detailed statistical results DJI sub-periods

F1 Average analysis

Table F1 Average analysis

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 Mean return (gapday)

-001 023 015 -004

Mean return(non-gap day)

007 007 007 007

Anomaly confirmed confirmed confirmed confirmed1999-2008 Mean return (gap

day)090 -045 013 -004

Mean return(non-gap day)

-004 -004 -004 -004

Anomaly confirmed confirmed confirmed confirmed2009-2018 Mean return (gap

day)024 -024 0 -004

Mean return(non-gap day)

004 004 004 004

Anomaly confirmed confirmed not confirmed confirmed

F2 Parametric tests Students t-test

Table F2 T-test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 t-criterion 083 165 087 139t-critical (=095) 196 196 196 196Null hypothesis not rejected not rejected not rejected not rejected

1999-2008 t-criterion 347 351 054 047t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected rejected

2009-2018 t-criterion 265 207 051 058t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

F3 Parametric tests ANOVA

Table F3 ANOVA

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 F 085 409 093 179p-value 035 004 033 018

F critical 384 384 384 384Null hypothesis not rejected rejected not rejected not rejected

1999-2008 F 5405 3196 065 072p-value 0 0 042 039

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

2009-2018 F 554 697 024 058p-value 001 0 062 044

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

29

F4 Non-parametric tests Kruskal-Wallis test

Table F4 Kruskal-Wallis test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 Adjusted H 113 211 113 332df 1 1 1 1

P value 029 015 029 007Null hypothesis not rejected not rejected not rejected not rejected

1999-2008 Adjusted H 1484 1414 003 139df 1 1 1 1

P value 0 0 086 024Null hypothesis rejected rejected not rejected not rejected

2009-2018 Adjusted H 506 68 051 171df 1 1 1 1

P value 002 001 047 019Null hypothesis rejected rejected not rejected not rejected

F5 Regression analysis with dummy variables

Table F5 Regression analysis with dummy variables

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 a0 000068 (000) 00007 (000) 00007 (000) 00007 (000)a1 -000078 (035) 00016 (004) 00008 (033) -00011 (018)

Anomaly not confirmed confirmed not confirmed not confirmed1999-2008 a0 00004 (008) 00004 (008) 00004 (006) 00004 (008)

a1 00087 (000) -00049 (000) 00009 (042) -00008 (039)Anomaly confirmed confirmed not confirmed not confirmed

2009-2018 a0 00004 (006) 00004 (006) 00004 (006) 00004 (006)a1 00021 (001) -00028 (001) -00004 (062) -00008 (047)

Anomaly confirmed confirmed not confirmed not confirmed

F6 Modified CAR approach

Table F6 Modified CAR approach

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 Multiple R 083 088 082 086F-test 22779 (000) 40583 (000) 20401 (000) 3269454 (000)a0 00042 (023) 00017 (073) 00014 (058) -00266 (000)a1 -00009 (000) 00015 (000) 00006 (000) -00009 (000)

Anomaly confirmed confirmed confirmed confirmed1999-2008 Multiple R 095 093 076 019

F-test 62658 (000) 84712 (000) 10056 (000) 492 (003)a0 -00972 (000) 00365 (000) -00198 (000) -00115 (021)a1 00086 (000) -00042 (000) 00014 (000) 00002 (003)

Anomaly confirmed confirmed confirmed not confirmed2009-2018 Multiple R 096 082 08 05

F-test 150452 (000) 16731 (000) 22287 (000) 2620 (000)a0 00548 (000) -00618 (000) 00031 (020) -00112 (000)a1 00013 (000) -00014 (000) -00005 (000) -00004 (000)

Anomaly confirmed confirmed not confirmed confirmed

30

G Detailed statistical results NASDAQ sub-periods

G1 Average analysis

Table G1 Average analysis

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 Mean return (gapday)

094 -111 0189 -029

Mean return(non-gap day)

007 007 007 007

Anomaly confirmed confirmed confirmed confirmed1959-1968 Mean return (gap

day)133 -147 033 -039

Mean return(non-gap day)

006 006 006 006

Anomaly confirmed confirmed confirmed confirmed1969-1978 Mean return (gap

day)19 -186 057 -068

Mean return(non-gap day)

005 005 005 005

Anomaly confirmed confirmed confirmed confirmed1979-1988 Mean return (gap

day)138 -162 066 -04

Mean return(non-gap day)

008 008 008 008

Anomaly confirmed confirmed confirmed confirmed1989-1998 Mean return (gap

day)016 012 018 -009

Mean return(non-gap day)

002 002 002 002

Anomaly confirmed not confirmed confirmed confirmed1999-2008 Mean return (gap

day)38E-3 027 -036 -013

Mean return(non-gap day)

-01 -01 -01 -01

Anomaly confirmed not confirmed not confirmed not confirmed2009-2018 Mean return (gap

day)039 009 013 -025

Mean return(non-gap day)

001 001 001 001

Anomaly confirmed not confirmed confirmed confirmed

G2 Parametric tests Students t-test

Table G2 T-test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 t-criterion 3194 3076 201 559t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected rejected

1959-1968 t-criterion 1399 2246 443 382t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected rejected

1969-1978 t-criterion 261 4358 417 786t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected rejected

1979-1988 t-criterion 1847 1445 709 395t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected rejected

1989-1998 t-criterion 13 066 126 093t-critical (=095) 196 196 196 196Null hypothesis not rejected not rejected not rejected not rejected

1999-2008 t-criterion 192 106 111 009t-critical (=095) 196 196 196 196Null hypothesis not rejected not rejected not rejected not rejected

2009-2018 t-criterion 27 05 089 188t-critical (=095) 196 196 196 196Null hypothesis rejected not rejected not rejected not rejected

31

G3 Parametric tests ANOVA

Table G3 ANOVA

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 F 88153 190609 1272 14521p-value 0 0 0 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1959-1968 F 93974 149771 4715 10418p-value 0 0 0 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1969-1978 F 84546 145429 6295 18241p-value 0 0 0 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1979-1988 F 66952 110482 13138 8626p-value 0 0 0 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1989-1998 F 323 138 43 168p-value 007 024 003 019

F critical 384 384 384 384Null hypothesis not rejected not rejected rejected not rejected

1999-2008 F 106 512 327 003p-value 001 002 007 085

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

2009-2018 F 169 069 175 93p-value 0 04 018 0

F critical 384 384 384 384Null hypothesis rejected not rejected not rejected rejected

G4 Non-parametric tests Kruskal-Wallis test

Table G4 Kruskal-Wallis test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 Adjusted H 26254 32592 1464 3962df 1 1 1 1

P value 0 0 0 0Null hypothesis rejected rejected rejected rejected

1959-1968 Adjusted H 28235 27989 2736 332df 1 1 1 1

P value 0 0 0 0Null hypothesis rejected rejected rejected rejected

1969-1978 Adjusted H 22202 33777 3311 7591df 1 1 1 1

P value 0 0 0 0Null hypothesis rejected rejected rejected rejected

1979-1988 Adjusted H 23282 25292 4812 3964df 1 1 1 1

P value 0 0 0 0Null hypothesis rejected rejected rejected rejected

1989-1998 Adjusted H 381 017 175 132df 1 1 1 1

P value 005 068 019 025Null hypothesis not rejected not rejected not rejected not rejected

1999-2008 Adjusted H 855 023 044 004df 1 1 1 1

P value 0 063 051 084Null hypothesis rejected not rejected not rejected not rejected

2009-2018 Adjusted H 1063 009 257 709df 1 1 1 1

P value 0 077 011 001Null hypothesis rejected not rejected not rejected rejected

32

G5 Regression analysis with dummy variables

Table G5 Regression analysis with dummy variables

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 a0 00007 (000) 00007 (000) 00007 (000) 00007 (000)a1 00088 (000) -00119 (000) 00011 (000) -00036 (000)

Anomaly confirmed confirmed confirmed confirmed1959-1968 a0 00006 (000) 00006 (000) 00006 (000) 00006 (000)

a1 00128 (000) -00153 (000) 00027 (000) -00046 (000)Anomaly confirmed confirmed confirmed confirmed

1969-1978 a0 00005 (000) 00005 (000) 00005 (000) 00005 (000)a1 00185 (000) -00192 (000) 00053 (000) -00073 (000)

Anomaly confirmed confirmed confirmed confirmed1979-1988 a0 00008 (000) 00008 (000) 00008 (000) 00008 (000)

a1 00131 (000) -00172 (000) 00059 (000) -00048 (000)Anomaly confirmed confirmed confirmed confirmed

1989-1998 a0 00002 (027) 00002 (028) 00002 (028) 00002 (027)a1 00014 (007) 00010 (024) 00017 (004) -00011 (019)

Anomaly not confirmed not confirmed confirmed not confirmed1999-2008 a0 00001 (059) 00001 (062) 00001 (059) 00001 (060)

a1 00037 (000) 00026 (002) -00038 (000) -00014 (019)Anomaly confirmed not confirmed not confirmed not confirmed

2009-2018 a0 00001 (049) 00001 (049) 00001 (049) 00001 (049)a1 00038 (000) 00007 (040) 00012 (018) -00027 (000)

Anomaly confirmed not confirmed not confirmed confirmed

G6 Modified CAR approach

Table G6 Modified CAR approach

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 Multiple R 099 099 093 098F-test 5753605 (000) 100470(000) 6280421 283281a0 -00091 (000) -00349 (000) 00056 (001) 00015 (073)a1 00083 (000) -00110 (000) 00010 (000) -00031 (000)

Anomaly confirmed confirmed confirmed confirmed1959-1968 Multiple R 099 099 099 099

F-test 3923274 (000) 3005562 (000) 443198 (000) 372583 (000)a0 00096 (000) 00073 (016) -00082 (000) -00095 (004)a1 00116 (001) -00149 (000) 00025 (000) -00047 (000)

Anomaly confirmed confirmed confirmed confirmed1969-1978 Multiple R 099 099 098 099

F-test 4302608 (000) 2723953 (000) 179969 (000) 639745a0 00246 (000) -00002 (000) 00217 (000) -00514 (000)a1 00176 (000) -00182 (000) 00049 (000) -00062 (000)

Anomaly confirmed confirmed confirmed confirmed1979-1988 Multiple R 099 099 099 099

F-test 5872335 (000) 1182609 (000) 1083558 (000) 910089 (000)a0 00136 (000) -01081 (000) -00285 (000) -00101 (000)a1 00131 (000) -00167 (000) 00062 (000) -00048 (000)

Anomaly confirmed confirmed confirmed confirmed1989-1998 Multiple R 09 056 069 016

F-test 46947 (000) 4885 (000) 10131 (000) 263 (011)a0 00102 (002) -00261 (000) -0016 (001) -00237 (000)a1 00015 (000) 00010 (000) 0001 (000) 00002 (011)

Anomaly confirmed confirmed confirmed not confirmed1999-2008 Multiple R 093 087 073 037

F-test 71863 (000) 32530 (000) 13273 (000) 1669 (000)a0 00185 (004) 00311 (000) -00130 (039) -00546 (000)a1 00037 (000) 00032 (000) -00026 (000) -00007 (000)

Anomaly confirmed not confirmed not confirmed confirmed2009-2018 Multiple R 089 001 096 091

F-test 40818 (000) 000 (094) 116744 (000) 53770 (000)a0 01436 (000) -01099 (000) -01036 (000) 00697 (000)a1 00030 (000) 00000 (094) 00024 (000) -00021 (000)

Anomaly confirmed not confirmed confirmed confirmed

33

H Detailed statistical results SampP 500 sub-periods

H1 Average analysis

Table H1 Average analysis

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 Mean return (gapday)

138 -171 004 -014

Mean return(non-gap day)

0 0 0 0

Anomaly confirmed confirmed confirmed confirmed1939-1948 Mean return (gap

day)001 -042 172 -195

Mean return(non-gap day)

003 003 003 003

Anomaly confirmed confirmed confirmed confirmed1949-1958 Mean return (gap

day)165 -18 02 002

Mean return(non-gap day)

006 006 006 006

Anomaly confirmed confirmed confirmed not confirmed1959-1968 Mean return (gap

day)104 -102 015 0

Mean return(non-gap day)

002 002 002 002

Anomaly confirmed confirmed confirmed not confirmed1969-1978 Mean return (gap

day)131 -13 019 -03

Mean return(non-gap day)

0 0 0 0

Anomaly confirmed confirmed confirmed confirmed1979-1988 Mean return (gap

day)058 -042 015 003

Mean return(non-gap day)

005 005 005 005

Anomaly confirmed confirmed confirmed not confirmed1989-1998 Mean return (gap

day)02 -023 -002 01

Mean return(non-gap day)

007 007 007 007

Anomaly confirmed confirmed not confirmed not confirmed1999-2008 Mean return (gap

day)083 -089 -023 -005

Mean return(non-gap day)

001 001 001 001

Anomaly confirmed confirmed not confirmed confirmed2009-2018 Mean return (gap

day)055 -052 001 -015

Mean return(non-gap day)

004 004 004 004

Anomaly confirmed confirmed not confirmed confirmed

34

H2 Parametric tests Students t-test

Table H2 T-test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 t-criterion 101 85 029 048t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

1939-1948 t-criterion 064 479 3074 225t-critical (=095) 196 196 196 196Null hypothesis not rejected rejected rejected rejected

1949-1958 t-criterion 2964 2383 193 041t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

1959-1968 t-criterion 2281 2157 21 023t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected not rejected

1969-1978 t-criterion 1318 2034 187 321t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected rejected

1979-1988 t-criterion 435 535 07 037t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

1989-1998 t-criterion 201 396 132 052t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

1999-2008 t-criterion 362 433 117 022t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

2009-2018 t-criterion 375 382 027 132t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

H3 Parametric tests ANOVA

Table H3 ANOVA

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 F 6281 8032 005 051p-value 0 0 082 047

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

1939-1948 F 056 2603 34854 51034p-value 045 0 0 0

F critical 384 384 384 384Null hypothesis not rejected rejected rejected rejected

1949-1958 F 100174 128997 897 062p-value 0 0 0 043

F critical 384 384 384 384Null hypothesis rejected rejected rejected not rejected

1959-1968 F 36831 32858 617 01p-value 0 0 001 074

F critical 384 384 384 384Null hypothesis rejected rejected rejected not rejected

1969-1978 F 26601 3063 53 152p-value 0 0 002 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1979-1988 F 23 245 076 009p-value 0 0 039 077

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

1989-1998 F 399 1156 118 015p-value 004 0 027 069

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

1999-2008 F 4253 5622 365 024p-value 0 0 006 062

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

2009-2018 F 3064 3656 01 43p-value 0 0 075 004

F critical 384 384 384 384Null hypothesis rejected rejected not rejected rejected

35

H4 Non-parametric tests Kruskal -Wallis test

Table H4 Kruskal-Wallis test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 Adjusted H 9982 5913 332 14df 1 1 1 1

P value 0 0 007 024Null hypothesis rejected rejected not rejected not rejected

1939-1948 Adjusted H 494 1999 23387 24927df 1 1 1 1

P value 003 0 0 0Null hypothesis rejected rejected rejected rejected

1949-1958 Adjusted H 28728 28175 348 15df 1 1 1 1

P value 0 0 006 022Null hypothesis rejected rejected not rejected not rejected

1959-1968 Adjusted H 25729 21437 701 063df 1 1 1 1

P value 0 0 001 043Null hypothesis rejected rejected rejected not rejected

1969-1978 Adjusted H 14407 20078 27 1706df 1 1 1 1

P value 0 0 01 0Null hypothesis rejected rejected not rejected rejected

1979-1988 Adjusted H 1788 2836 027 034df 1 1 1 1

P value 0 0 06 056Null hypothesis rejected rejected not rejected not rejected

1989-1998 Adjusted H 251 1431 111 044df 1 1 1 1

P value 011 0 029 051Null hypothesis not rejected rejected not rejected not rejected

1999-2008 Adjusted H 1812 1788 042 002df 1 1 1 1

P value 0 0 052 089Null hypothesis rejected rejected not rejected not rejected

2009-2018 Adjusted H 1314 1783 074 37df 1 1 1 1

P value 0 0 039 005Null hypothesis rejected rejected not rejected not rejected

36

H5 Regression analysis with dummy variables

Table H5 Regression analysis with dummy variables

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 a0 00000 (097) 00000 (004) 00000 (097) 00000 (097)a1 00138 (000) -00172 (000) 00004 (082) -00014 (047)

Anomaly confirmed confirmed not confirmed not confirmed1939-1948 a0 00003 (015) 00003 (015) 00003 (015) 00003 (015)

a1 00007 (045) -00045 (000) 00170 (000) -00199 (000)Anomaly not confirmed confirmed confirmed confirmed

1949-1958 a0 00006 (000) 00006 (000) 00006 (000) 00006 (000)a1 00160 (000) -00188 (000) 00016 (000) -00004 (043)

Anomaly confirmed confirmed confirmed not confirmed1959-1968 a0 00002 (007) 00002 (004) 00002 (008) 00002 (008)

a1 00103 (000) -00105 (000) 00014 (001) -00002 (074)Anomaly confirmed confirmed confirmed not confirmed

1969-1978 a0 00000 (078) 00000 (078) 00000 (078) 00000 (078)a1 00132 (000) -00132 (000) 00019 (002) -00030 (000)

Anomaly confirmed confirmed confirmed confirmed1979-1988 a0 00006 (001) 00006 (001) 00006 (001) 00006 (000)

a1 00053 (000) -00048 (000) 00009 (040) -00003 (075)Anomaly confirmed confirmed not confirmed not confirmed

1989-1998 a0 00007 (000) 00007 (000) 00007 (000) 00007 (000)a1 00016 (005) -00030 (000) -00009 (026) 00003 (072)

Anomaly confirmed confirmed not confirmed not confirmed1999-2008 a0 00001 (075) 00001 (075) 00001 (075) 00001 (076)

a1 00083 (000) -00091 (000) -00024 (005) -00006 (062)Anomaly confirmed confirmed not confirmed not confirmed

2009-2018 a0 00004 (003) 00004 (000) 00004 (003) 00004 (003)a1 00051 (000) -00059 (000) -00003 (075) -00019 (003)

Anomaly confirmed confirmed not confirmed confirmed

37

H6 Modified CAR approach

Table H6 Modified CAR approach

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 Multiple R 096 095 046 046F-test 175935 (000) 96500 (000) 3534 (000) 2880 (000)a0 -01070 (000) 01958 (000) 00405 (000) 00535 (000)a1 00121 (000) -00160 (000) 00006 (000) -00014 (000)

Anomaly confirmed confirmed confirmed confirmed1939-1948 Multiple R 08 099 099 099

F-test 18777 (000) 755727 (000) 3572830 (000) 2696099 (000)a0 00019 (073) -00346 (000) -00373 (000) 00912 (000)a1 00012 (000) -00044 (000) 00168 (000) -00197 (000)

Anomaly confirmed confirmed confirmed confirmed1949-1958 Multiple R 099 099 094 015

F-test 1021705 (000) 7171257 (000) 75858 (000) 242 (012)a0 -00176 (000) -00191 (000) 00095 (000) -00498 (000)a1 00154 (000) -00181 (000) 00013 (000) -00002 (012)

Anomaly confirmed confirmed confirmed not confirmed1959-1968 Multiple R 099 099 094 078

F-test 1463311 (000) 6002659 (000) 82273 (000) 14352 (000)a0 -00112 (000) 00004 (085) 00151 (000) 00389 (000)a1 00098 (000) -00102 (000) 00011 (000) -00009 (000)

Anomaly confirmed confirmed confirmed confirmed1969-1978 Multiple R 098 099 093 099

F-test 241655 (000) 1451901 (000) 57333 (000) 368160 (000)a0 -00433 (000) 00276 (000) 00099 (002) -00144 (000)a1 00132 (000) -00134 (000) 00020 (000) -00030 (000)

Anomaly confirmed confirmed confirmed confirmed1979-1988 Multiple R 092 078 023 008

F-test 53757 (000) 18707 (000) 487 (003) 085 (036)a0 00813 (000) -02508 (000) 00204 (000) -00235 (000)a1 00036 (000) -00031 (000) -00003 (003) -00001 (036)

Anomaly confirmed confirmed not confirmed not confirmed1989-1998 Multiple R 079 099 074 044

F-test 19705(000) 761967 (000) 14133 (000) 2369 (000)a0 00268 (000) 00023 (021) -00381 (000) 00087 (000)a1 00013 (000) -00028 (000) -00008 (000) 00002 (000)

Anomaly confirmed confirmed not confirmed not confirmed1999-2008 Multiple R 091 093 071 065

F-test 47218 (000) 76564 (000) 9843 (000) 7768 (000)a0 -01493 (000) 01351 (000) 00397 (000) 00007 (093)a1 00081 (000) -00083 (000) -00026 (000) -00011 (000)

Anomaly confirmed confirmed not confirmed confirmed2009-2018 Multiple R 086 087 083 074

F-test 29971 (000) 32484 (000) 23228 (000) 12764 (000)a0 01711 (000) -02250 (000) 00407 (000) -00472 (000)a1 00038 (000) -00044 (000) -00010 (000) -00012 (000)

Anomaly confirmed confirmed not confirmed confirmed

38

Table 3 Gap size used for different sub-periods over the period 1929-2018

Period SampP 5001929-1938 1201949-1958 1201959-1968 0701969-1978 0011979-1988 0031989-1998 0011999-2008 0082009-2018 034Overall data set 070

42 Price gap seasonality

Caporale and Plastun (2017) show that in foreign exchange and commodity marketsprice gaps tend to appear on Mondays According to their results more than 95 percent of price gaps in foreign exchange markets compared to 65 per cent of price gaps incommodity markets appeared on Mondays This is rather reasonable because marketsare closed on weekends and as the result of any significant event over the weekend willlead to price gaps on Monday Surprisingly this is not the case in this instance (withstock markets) as can be seen in Tables 4 and A2 Therefore H3 is rejected

Table 4 Day of the week and gaps

Day of the week SampP 500Monday 023Tuesday 02Wednesday 02Thursday 018Friday 019

43 Short term price behaviour

Next we analyse short-term price behaviour in the US stock market around price gapsto investigate the presence of possible price patterns before and after price gaps Wecalculate the number of days with positive (or negative) returns after a positive (or neg-ative) price gaps divided by the total number of price gaps If this ratio or momentum

9

effect is much higher than 50 per cent this indicates abnormal price behaviour and asthe results confirm our hypotheses

The results are presented in Appendix B We find no convincing evidence in favour ofmomentum effect after price gaps (Table B1) and before them (Table B2) In generalprice gaps are not generated by previous price dynamics (NASDAQ index is an exceptionas negative gaps appear in 70 per cent of the cases after downward price movements andafter positive gaps in 67 per cent of the cases upward price movements are observed)Our results (see Table B3 for details) also indicate that the probability that price gapswill be filled within 5 days after appearance is very low at around 20 per cent

44 Price gap evolution

Overall in probabilistic terms price gaps do not generate any stable patterns But therecan be patterns in terms of size of price movements after gaps To check this we will testH1 and H2 To incorporate price direction in results of analysis H1 we further test forH1minus1 and H1minus2 The results for the overall data sets are presented in Appendices C toE for the cases of DJI SampP 500 and NASDAQ respectively To ease the interpretationof results we have summarised them in Table 5 and Table A3

Table 5 shows strong evidence confirming H1 in the SampP 500 Similarly Table A3confirms H1 for the NASDAQ but not for the DJI The difference between the DJI SampP500 and NASDAQ results can be explained by the differences in samples (DJI sampleis much shorter) This suggests that price gap anomaly may evolve and is therefore apreliminary confirmation of H2

Tables 6 and 7 confirm H1minus1 in the SampP 500 on the day of the price gap That ison the price gap day prices tend towards the direction of the price gap However thisis not the case for the day after the price gap therefore H1minus2 is not confirmed It canbe concluded that the SampP 500 roughly needs a day to absorb new information Never-theless even a day can be enough to create a profitable trading strategy and generateabnormal profits from trading

Similar results on the NASDAQ can be found in Tables A6 and A7 The longersample of the NASDAQ allows for the evolution of the price anomaly H1minus1 is there-fore confirmed on the day of the price gap anomaly and the day after the price gapanomaly (in both instances only until the 1990s and has since disappeared) H1minus2 inboth instances is confirmed up until the 1990s The results of the DJI did not providestrong evidence in favour of H1minus1 and H1minus2 on the day after the price gap but sim-ilar to the SampP 500 evidence was strong on the day of the price gap (see Tables A4and A5) These results confirm in the main the price gap anomaly is a reality in theUS stock market and that it evolves over time that is from prevalence to disappearance

10

Tab

le5

Overallstatisticalresults

SampP500

PeriodM

ethod

Average

analysis

t-test

ANOVA

test

Man

n-

Whitney

test

Regression

analysis

with

dummy

variab

les

Modified

CAR

approach

Overall

Gap

day

+-

-+

-+

3Gap

day

(Positivegaps)

++

++

++

6Gap

day

(Negativegaps)

++

++

++

6Day

aftergap(P

ositivegaps)

++

-+

++

5Day

aftergap(N

egativegaps)

++

--

++

4

Note+

indicates

thattheanom

alyis

confirm

edand-indicates

thatan

omaly

isnot

confirm

edThehigher

theoverallrating

the

strongertheeviden

ceofthean

omaly

11

Tab

le6

H1minus1summarystatisticalresults

SampP500sub-periods

PeriodM

ethod

Average

analysis

t-test

ANOVA

test

Man

n-

Whitney

test

Regression

analysis

withdummy

variab

les

Modified

CAR

approach

Overall

Dayofanomaly

1929-1938

++

++

++

61939-1948

+-

-+

-+

31949-1958

++

++

++

61959-1968

++

++

++

61969-1978

++

++

++

61979-1988

++

++

++

61989-1998

++

++

++

61999-2008

++

++

++

62009-2018

++

++

++

6Dayafteranomaly

1929-1938

+-

--

-+

21939-1948

++

++

++

61949-1958

+-

+-

++

51959-1968

++

++

++

61969-1978

+-

+-

++

41979-1988

+-

--

--

11989-1998

--

--

--

01999-2008

--

--

--

02009-2018

--

--

--

0

Note+

indicates

thattheanom

alyis

confirm

edand-indicates

thatan

omaly

isnot

confirm

edThehigher

theoverallrating

the

strongertheeviden

ceofthean

omaly

12

Tab

le7

H1minus2statisticalresults

SampP500sub-periods

PeriodM

ethod

Average

analysis

t-test

ANOVA

test

Man

n-

Whitney

test

Regression

analysiswith

dummy

variab

les

Modified

CAR

approach

Overall

Dayofanomaly

1929-1938

++

++

++

61939-1948

++

++

++

61949-1958

++

++

++

61959-1968

++

++

++

61969-1978

++

++

++

61979-1988

++

++

++

61989-1998

++

++

++

61999-2008

++

++

++

62009-2018

++

++

++

6Dayafteranomaly

1929-1938

+-

--

-+

21939-1948

++

++

++

61949-1958

--

--

--

01959-1968

--

--

-+

11969-1978

++

++

++

61979-1988

--

--

--

01989-1998

--

--

--

01999-2008

+-

--

-+

22009-2018

+-

+-

++

4

Note+

indicates

thattheanom

alyis

confirm

edand-indicates

thatan

omaly

isnot

confirm

edThehigher

theoverallrating

the

strongertheeviden

ceofthean

omaly

13

45 Trading simulation

The algorithm of the trading strategy is to buysell at the start of the updown gapday and close this position at the end of this day To test this strategy data for the DJIand SampP 500 are used (for this case the price anomaly still exists based on the day itoccurred) The results for DJI are presented in Table A8 and for the SampP 500 in Table8 For the SampP 500 and DJI the trading strategy built on price gap anomaly is efficientand its results differ from random

Table 8 Trading simulation results of the price gap anomaly for the SampP 500

Period Gaptype

Numberof

tradesunits

Numberof suc-cessfultradesunits

Numberof suc-cessfultrades

Profit

Profit peryear

z-test Result

1929-1938 Up 131 130 992 1816 182 1065 passedDown 110 108 982 1893 189 876 passed

1939-1948 Up 110 67 609 106 11 09 failedDown 122 79 648 518 52 465 passed

1949-1958 Up 106 105 991 1765 176 3191 passedDown 104 103 99 1891 189 2356 passed

1959-1968 Up 108 106 981 1331 113 2441 passedDown 92 91 989 948 95 2214 passed

1969-1978 Up 85 71 835 1128 113 1361 passedDown 96 90 938 1262 126 2118 passed

1979-1988 Up 92 63 685 54 54 495 passedDown 123 81 659 519 52 496 passed

1989-1998 Up 117 72 615 267 27 295 passedDown 99 61 616 228 23 32 passed

1999-2008 Up 99 65 657 828 83 373 passedDown 110 72 655 987 99 438 passed

2009-2018 Up 106 71 67 59 59 416 passedDown 107 65 607 56 56 362 passed

14

Figure 1 Trading simulation results of the price gap anomaly for the SampP 500

Note The primary axis refers to the percentage profit per year and the secondary to thez minus test statistic

One more interesting fact (see Figure 1) is the decrease of trading strategy efficiencyThis is indirect evidence in favour of evolution of the US stock market and its movementfrom less efficient to more efficient state Overall it can be concluded that the price gapanomaly is a real market anomaly The US stock market loses its efficiency after pricegaps This effect is temporary and lasts only for a day Still even this time is enoughto exploit the hole in the market efficiency and generate abnormal profits from trading

5 Conclusion

We analysed price gap anomaly in the US stock market by using information from threestock market indexes(DJI SampP 500 and NASDAQ) We tested three hypotheses of in-terest that is H1 the price gap anomaly exists H1minus1 prices tend to rise after positivegaps H1minus2 prices tend to fall after negative gaps H2 the price gap anomaly evolvesand H3 there is seasonality in price gaps Various statistical methods including para-metric tests (Students t-tests ANOVA) non-parametric tests (Mann-Whitney test)regression analysis with dummy variables MCAR approach and the trading simulationapproach were utilised

We conclude that the US stock market in the main did not exhibit seasonality in pricegaps Therefore H3 is rejected Furthermore no evidence was found that price gaps inthe US stock market were filled within five days of their occurrence However strongevidence in favour of abnormal price movements after the gaps were found confirming

15

H1 and H2 Particularly on the day of the occurrence of the gap and not on the dayafter the price gap In the DJI and the SampP 500 this pattern persists indicating thatthese markets take a day to incorporate new information As the results of the tradingsimulation indicate a day is enough to profit from a price gap anomaly trading strategyin the DJI and the SampP 500

Similar to other studies and other anomalies (see McLean and Pontiff (2016) Ca-jueiro and Tabak (2004) and Tiwari et al (2019) for example) the price gap anomalyevolved It is less prevalent since the 1990s as shown in the SampP 500 and NASDAQThis pattern of evolution is common amongst most stock market anomalies (see Plastunet al (2019b) on calendar anomalies amongst others) Our findings therefore add onto the existing literature Finally in the main our results are against the EMH and aretherefore interesting to both practitioners and academics

16

References

Agrawal A and Tandon K (1994) Anomalies or illusions evidence from stock marketsin eighteen countries Journal of international Money and Finance 13(1)83ndash106

Akerlof G A and Shiller R J (2009) Animal Spirits How human psychology drivesthe economy and why it matters for global capitalism Princeton University Press

Basu S (1977) Investment performance of common stocks in relation to their price-earnings ratios A test of the efficient market hypothesis The Journal of Finance32(3)663ndash682

Bildik R (2004) Are calendar anomalies still alive Evidence from istanbul stockexchange SSRN Electronic Journal 2004

Cai J Li Y and Qi Y (2006) The day-of-the-week effect New evidence from theChinese stock market Chinese Economy 39(2)71ndash88

Cajueiro D O and Tabak B M (2004) The Hurst exponent over time testing theassertion that emerging markets are becoming more efficient Physica A StatisticalMechanics and its Applications 336(3-4)521ndash537

Caporale G M Gil-Alana L Plastun A and Makarenko I (2016) Intraday anoma-lies and market efficiency A trading robot analysis Computational Economics47(2)275ndash295

Caporale G M and Plastun A (2017) Price gaps Another market anomaly Invest-ment Analysts Journal 46(4)279ndash293

Cross F (1973) The behavior of stock prices on Fridays and Mondays FinancialAnalysts Journal 29(6)67ndash69

Fama E F (1965) The behavior of stock-market prices The Journal of Business38(1)34ndash105

Fama E F (1970) Efficient capital markets A review of theory and empirical workThe Journal of Finance 25(2)383ndash417

Fortune P (1998) Weekends can be rough revisiting the weekend effect in stock pricesTechnical report

Fortune P (1999) Are stock returns different over weekends A jump diffusion analysisof the weekend effect New England Economic Review 103ndash19

French K R (1980) Stock returns and the weekend effect Journal of FinancialEconomics 8(1)55ndash69

Fung A K-W Lam K and Lam K-M (2010) Do the prices of stock index futuresin asia overreact to us market returns Journal of Empirical Finance 17(3)428ndash440

17

Gibbons M R and Hess P (1981) Day of the week effects and asset returns Journalof business pages 579ndash596

Grant J L Wolf A and Yu S (2005) Intraday price reversals in the us stock indexfutures market A 15-year study Journal of Banking amp Finance 29(5)1311ndash1327

Grossman S J and Stiglitz J E (1980) On the impossibility of informationallyefficient markets The American Economic Review 70(3)393ndash408

Jacobsen B Mamun A and Visaltanachoti N (2005) Seasonal size and valueanomalies

Jensen M (1978) Some anomalous evidence regarding market efficiency Journal ofFinancial Economics 6(23 (1978))95ndash101

Lakonishok J and Smidt S (1988) Are seasonal anomalies real A ninety-year per-spective The Review of Financial Studies 1(4)403ndash425

MacKinlay A (1997) Event studies in economics and finance Journal of EconomicLiterature (35)113ndash39

Mandelbrot B B (1997) The variation of certain speculative prices In Fractals andscaling in finance pages 371ndash418 Springer

McLean R D and Pontiff J (2016) Does academic research destroy stock returnpredictability The Journal of Finance 71(1)5ndash32

Plastun A Makarenko I Khomutenko L Shcherbak S and Tryfonova O (2019a)Exploring price gap anomaly in the ukrainian stock market Investment Managementamp Financial Innovations 16(2)150

Plastun A Sibande X Gupta R and Wohar M E (2019b) Rise and fall of calendaranomalies over a century The North American Journal of Economics and Finance49181ndash205

Schwert G W (2003) Chapter 15 anomalies and market efficiency In FinancialMarkets and Asset Pricing volume 1 of Handbook of the Economics of Finance pages939 ndash 974 Elsevier

Shiller R J (2000) Irrational exuberance Princeton University

Tiwari A K Aye G C and Gupta R (2019) Stock market efficiency analysis usinglong spans of data A multifractal detrended fluctuation approach Finance ResearchLetters 28398ndash411

Yuan Y (2015) Market-wide attention trading and stock returns Journal of FinancialEconomics 116(3)548ndash564

18

Appendices

A DJI and NASDAQ Summary Results

A1 Overall Results

Table A1 Gap size used for different sub-periods over the period 1929-2018

Period DJI NASDAQ1929-1938 - -1939-1948 - -1949-1958 - 0711959-1968 - 0951969-1978 - 1351979-1988 - 1101989-1998 040 0681999-2008 007 1502009-2018 020 110Overall data set 030 110

Table A2 Day of the week and gaps

Day of the week DJI NASDAQMonday 024 02Tuesday 02 02Wednesday 017 02Thursday 019 019Friday 021 02

A2 Statistical tests

Table A3 Results of the statistical tests for the overall data sets

PeriodMethod Averageanalysis

t-test ANOVAtest

Mann-Whitney

test

Regressionanalysiswith

dummyvariables

ModifiedCAR

approach

Overall

Dow Jones Index overall data setGap day - - - - - + 1Gap day (Positive gaps) + - - - - - 1Gap day (Negative gaps) + - - - - + 2Day after gap (Positive gaps) + - - - - - 1Day after gap (Negative gaps) + - - + - + 3

NASDAQ overall data setGap day + + + + + + 6Gap day (Positive gaps) + + + + + + 6Gap day (Negative gaps) + + + + + + 6Day after gap (Positive gaps) + + + + + + 6Day after gap (Negative gaps) + + + + + + 6

Note + indicates that the anomaly is confirmed and - indicates that anomaly is not confirmedThe higher the overall rating the stronger the evidence of the anomaly

19

Table A4 Results of the statistical tests for H1minus1 DJI

Period Averageanalysis

t-test ANOVA test Mann-Whitney

test

Regressionanalysis with

dummyvariables

ModifiedCAR

approach

Overall

Day of anomaly1989-1998 + - - - - + 21999-2008 + + + + + + 62009-2018 + + + + + + 6

Day after anomaly1989-1998 + - - - - + 21999-2008 + - - - - + 22009-2018 - - - - - - 0

Note + indicates that the anomaly is confirmed and - indicates that anomaly is not confirmedThe higher the overall rating the stronger the evidence of the anomaly

Table A5 Results of the statistical tests for H1minus2 DJI

Period Averageanalysis

t-test ANOVA test Mann-Whitneytest

Regressionanalysis with

dummyvariables

Modified CARapproach

Overall

Day of anomaly1989-1998 - - - - - - 01999-2008 + + + + + + 62009-2018 + + + + + + 6

Day after anomaly1989-1998 + - - - - + 21999-2008 + - - - - - 12009-2018 + - - - - + 2

Note + indicates that the anomaly is confirmed and - indicates that anomaly is not confirmedThe higher the overall rating the stronger the evidence of the anomaly

Table A6 Results of the statistical tests for H1minus1 NASDAQ

PeriodMethod Averageanalysis

t-test ANOVA test Mann-Whitney

test

Regressionanalysis with

dummyvariables

ModifiedCAR

approach

Overall

Day of anomaly1949-1958 + + + + + + 61959-1968 + + + + + + 61969-1978 + + + + + + 61979-1988 + + + + + + 61989-1998 + - - - - + 21999-2008 + - + + + + 52009-2018 + + + + + + 6

Day after anomaly1949-1958 + + + + + + 61959-1968 + + + + + + 61969-1978 + + + + + + 61979-1988 + + + + + + 61989-1998 + - + - + + 41999-2008 - - - - - - 02009-2018 + - - - - + 2

Note + indicates that the anomaly is confirmed and - indicates that anomaly is not confirmedThe higher the overall rating the stronger the evidence of the anomaly

20

Table A7 Results of the statistical tests for H1minus2 NASDAQ

PeriodMethod Averageanalysis

t-test ANOVA test Mann-Whitney

test

Regressionanalysis with

dummyvariables

ModifiedCAR

approach

Overall

Day of anomaly1949-1958 + + + + + + 61959-1968 + + + + + + 61969-1978 + + + + + + 61979-1988 + + + + + + 61989-1998 - - - - - + 11999-2008 - - + - - - 12009-2018 - - - - - - 0

Day after anomaly1949-1958 + + + + + + 61959-1968 + + + + + + 61969-1978 + + + + + + 61979-1988 + + + + + + 61989-1998 + - - - - - 11999-2008 - - - - - + 12009-2018 + - - + + + 4

Note + indicates that the anomaly is confirmed and - indicates that anomaly is not confirmedThe higher the overall rating the stronger the evidence of the anomaly

A3 Trading Simulation Results

Table A8 Trading simulation results of the price gap anomaly for the DJI 1989-2018

Period Gap type Number oftradesunits

Number ofsuccessfultradesunits

Number ofsuccessfultrades

Profit Profit per year

z-test Result

1989-1998 Up 102 46 451 -11 -01 011 failedDown 116 49 422 -267 -27 242 passed

1999-2008 Up 73 51 699 665 66 37 passedDown 143 81 566 641 64 331 passed

2009-2018 Up 127 88 693 308 31 327 passedDown 81 47 58 196 2 184 passed

21

B Short-term price behavior in DJI SampP 500 and

NASDAQ Price gaps (overall data sets)

Table B1 Momentum effect in the US stock market after the gap

Instrument Parameter Number of days after the gap1 2 3

Dow Jones Index Positive gaps 53 57 61Negative gaps 50 50 47

All gaps 51 54 54SampP 500 Index Positive gaps 40 63 60

Negative gaps 4 52 45All gaps 4 58 53

NASDAQ Positive gaps 32 65 67Negative gaps 24 63 59

All gaps 28 64 63

Table B2 Momentum effect in the US stock market before the gap

Instrument Parameter Number of days before the gap1 2 3

Dow Jones Index Positive gaps 56 49 52Negative gaps 54 49 49

All gaps 55 49 50SampP 500 Index Positive gaps 57 57 52

Negative gaps 60 59 54All gaps 58 58 53

NASDAQ Positive gaps 61 56 54Negative gaps 68 69 70

All gaps 64 63 63

Table B3 Fill gap effect in the US stock market

Instrument Parameter Number of days after the gap1 2 3 4 5

Dow Jones Index Positive gaps 22 28 26 30 28Negative gaps 25 33 36 42 46

All gaps 24 30 31 35 37SampP 500 Index Positive gaps 0 6 11 16 19

Negative gaps 1 10 19 26 27All gaps 1 8 15 20 23

NASDAQ Positive gaps 8 13 18 21 19Negative gaps 7 11 17 21 25

All gaps 8 12 18 21 22

22

C Detailed statistical results DJI overall data

C1 Average analysis

Table C1 Average analysis

Parameter Gap day Gap day(Positive gaps)

Gap day(Negative gaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Mean return (gap day) 003 006 0 005 -003Mean return (non-gap day) 004 004 004 004 004Anomaly not confirmed not confirmed confirmed not confirmed confirmed

C2 Parametric tests Students t-test

Table C2 T-test

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

t-criterion 016 042 053 015 104t-critical (=095) 196 196 196 196 196Null hypothesis not rejected not rejected not rejected not rejected not rejected

C3 Parametric tests ANOVA

Table C3 ANOVA

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

F 0036 018 053 003 14p-value 085 067 047 086 024F critical 384 384 384 384 384Null hypothesis not rejected not rejected not rejected not rejected not rejected

C4 Non-parametric tests Kruskal-Wallis test

Table C4 Kruskal -Wallis test

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Adjusted H 082 012 126 0 455df 1 1 1 1 1P value 037 073 026 095 003Critical value 384 384 384 384 384Null hypothesis not rejected not rejected not rejected not rejected rejected

23

C5 Regression analysis with dummy variables

Table C5 Regression analysis with dummy variables

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

a0 00004 (000) 00004 (000) 00004 (000) 00004 (000) 00004 (000)a1 -00001 (-019) 00002 (067) -00004 (047) 00001 (086) -00007 (024)Anomaly not confirmed not confirmed not confirmed not confirmed not confirmed

C6 Modified CAR approach

Table C6 Modified CAR approach

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Multiple R 049 05 025 0 092F-test 23347 (000) 12913 (000) 2207 (000) 000 (098) 1822 (000)a0 -00041 (060) 00128 (006) -00267 (000) 00354 (000) 00319 (000)a1 -00003 (000) -00003 (000) -00002 (000) 00000 (098) -00008 (000)Anomaly confirmed confirmed confirmed not confirmed confirmed

24

D Detailed statistical results SampP 500 overall data

D1 Average analysis

Table D1 Average analysis

Parameter Gap day Gap day(Positive gaps)

Gap day(Negative gaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Mean return (gap day) 006 115 -129 017 -011Mean return (non-gap day) 002 002 002 002 002Anomaly confirmed confirmed confirmed confirmed confirmed

D2 Parametric tests Students t-test

Table D2 T-test

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

t-criterion 092 4546 3579 485 271t-critical (=095) 196 196 196 196 196Null hypothesis not rejected rejected rejected rejected rejected

D3 Parametric tests ANOVA

Table D3 ANOVA

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

F 155 116211 126952 1866 136p-value 022 0 0 0 0F critical 384 384 384 384 384Null hypothesis not rejected rejected rejected not rejected not rejected

D4 Non-parametric tests Kruskal-Wallis test

Table D4 Kruskal-Wallis test

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Adjusted H 1352 70516 47237 3946 004df 1 1 1 1 1P value 0 0 0 0 084Critical value 384 384 384 384 384Null hypothesis rejected rejected rejected rejected not rejected

25

D5 Regression analysis with dummy variables

Table D5 Regression analysis with dummy variables

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

a0 00002 (000) 00002 (000) 00002 (000) 00002 (000) 00002 (000)a1 00003 (021) 00113 (000) -00132 (000) 00014 (000) -00014 (000)Anomaly not confirmed confirmed confirmed confirmed confirmed

D6 Modified CAR approach

Table D6 Modified CAR approach

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Multiple R 051 099 099 099 096F-test 69486 (000) 325351 (000) 1457582 (000) 6345973 (000) 1213344 (000)a0 -01003(000) 04081 (000) -05444 (000) -01088 (000) 00272 (000)a1 00002 (000) 00106 (000) -00127 (000) 00016 (000) -00016 (000)Anomaly confirmed confirmed confirmed confirmed confirmed

26

E Detailed statistical results NASDAQ overall data

E1 Average analysis

Table E1 Average analysis

Parameter Gap day Gap day(Positive gaps)

Gap day(Negative gaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Mean return (gap day) -009 084 -090 022 -037Mean return (non-gap day) 003 003 003 003 003Anomaly confirmed confirmed confirmed confirmed confirmed

E2 Parametric tests Students t-test

Table E2 T-test

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

t-criterion 230 1257 1341 306 664t-critical (=095) 196 196 196 196 196Null hypothesis rejected rejected rejected rejected rejected

E3 Parametric tests ANOVA

Table E3 ANOVA

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

F 2289 62720 88402 3330 17356p-value 0 0 0 0 0F critical 384 384 384 384 384Null hypothesis rejected rejected rejected rejected rejected

E4 Non-parametric tests Kruskal-Wallis test

Table E4 Kruskal-Wallis test

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Adjusted H 1892 36022 45248 4695 10437df 1 1 1 1 1P value 0 0 0 0 0Critical value 384 384 384 384 384Null hypothesis rejected rejected rejected rejected rejected

27

E5 Regression analysis with dummy variables

Table E5 Regression analysis with dummy variables

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

a0 00003 (000) 00003 (000) 00003 (000) 00003 (000) 00003 (000)a1 -00012 (000) 00081 (000) -00093 (000) 00018 (000) -00040 (000)Anomaly confirmed confirmed confirmed confirmed confirmed

E6 Modified CAR approach

Table E6 Modified CAR approach

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Multiple R 069 092 092 072 097F-test 133255 (000) 361102 (000) 442376 (000) 72903 (000) 1082812 (000)a0 -10646 (000) 11373 (000) -12888 (000) 03928 (000) -02297 (000)a1 -00011 (000) 00073 (000) -00097 (000) 00017 (000) -00039 (000)Anomaly confirmed confirmed confirmed confirmed confirmed

28

F Detailed statistical results DJI sub-periods

F1 Average analysis

Table F1 Average analysis

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 Mean return (gapday)

-001 023 015 -004

Mean return(non-gap day)

007 007 007 007

Anomaly confirmed confirmed confirmed confirmed1999-2008 Mean return (gap

day)090 -045 013 -004

Mean return(non-gap day)

-004 -004 -004 -004

Anomaly confirmed confirmed confirmed confirmed2009-2018 Mean return (gap

day)024 -024 0 -004

Mean return(non-gap day)

004 004 004 004

Anomaly confirmed confirmed not confirmed confirmed

F2 Parametric tests Students t-test

Table F2 T-test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 t-criterion 083 165 087 139t-critical (=095) 196 196 196 196Null hypothesis not rejected not rejected not rejected not rejected

1999-2008 t-criterion 347 351 054 047t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected rejected

2009-2018 t-criterion 265 207 051 058t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

F3 Parametric tests ANOVA

Table F3 ANOVA

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 F 085 409 093 179p-value 035 004 033 018

F critical 384 384 384 384Null hypothesis not rejected rejected not rejected not rejected

1999-2008 F 5405 3196 065 072p-value 0 0 042 039

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

2009-2018 F 554 697 024 058p-value 001 0 062 044

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

29

F4 Non-parametric tests Kruskal-Wallis test

Table F4 Kruskal-Wallis test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 Adjusted H 113 211 113 332df 1 1 1 1

P value 029 015 029 007Null hypothesis not rejected not rejected not rejected not rejected

1999-2008 Adjusted H 1484 1414 003 139df 1 1 1 1

P value 0 0 086 024Null hypothesis rejected rejected not rejected not rejected

2009-2018 Adjusted H 506 68 051 171df 1 1 1 1

P value 002 001 047 019Null hypothesis rejected rejected not rejected not rejected

F5 Regression analysis with dummy variables

Table F5 Regression analysis with dummy variables

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 a0 000068 (000) 00007 (000) 00007 (000) 00007 (000)a1 -000078 (035) 00016 (004) 00008 (033) -00011 (018)

Anomaly not confirmed confirmed not confirmed not confirmed1999-2008 a0 00004 (008) 00004 (008) 00004 (006) 00004 (008)

a1 00087 (000) -00049 (000) 00009 (042) -00008 (039)Anomaly confirmed confirmed not confirmed not confirmed

2009-2018 a0 00004 (006) 00004 (006) 00004 (006) 00004 (006)a1 00021 (001) -00028 (001) -00004 (062) -00008 (047)

Anomaly confirmed confirmed not confirmed not confirmed

F6 Modified CAR approach

Table F6 Modified CAR approach

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 Multiple R 083 088 082 086F-test 22779 (000) 40583 (000) 20401 (000) 3269454 (000)a0 00042 (023) 00017 (073) 00014 (058) -00266 (000)a1 -00009 (000) 00015 (000) 00006 (000) -00009 (000)

Anomaly confirmed confirmed confirmed confirmed1999-2008 Multiple R 095 093 076 019

F-test 62658 (000) 84712 (000) 10056 (000) 492 (003)a0 -00972 (000) 00365 (000) -00198 (000) -00115 (021)a1 00086 (000) -00042 (000) 00014 (000) 00002 (003)

Anomaly confirmed confirmed confirmed not confirmed2009-2018 Multiple R 096 082 08 05

F-test 150452 (000) 16731 (000) 22287 (000) 2620 (000)a0 00548 (000) -00618 (000) 00031 (020) -00112 (000)a1 00013 (000) -00014 (000) -00005 (000) -00004 (000)

Anomaly confirmed confirmed not confirmed confirmed

30

G Detailed statistical results NASDAQ sub-periods

G1 Average analysis

Table G1 Average analysis

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 Mean return (gapday)

094 -111 0189 -029

Mean return(non-gap day)

007 007 007 007

Anomaly confirmed confirmed confirmed confirmed1959-1968 Mean return (gap

day)133 -147 033 -039

Mean return(non-gap day)

006 006 006 006

Anomaly confirmed confirmed confirmed confirmed1969-1978 Mean return (gap

day)19 -186 057 -068

Mean return(non-gap day)

005 005 005 005

Anomaly confirmed confirmed confirmed confirmed1979-1988 Mean return (gap

day)138 -162 066 -04

Mean return(non-gap day)

008 008 008 008

Anomaly confirmed confirmed confirmed confirmed1989-1998 Mean return (gap

day)016 012 018 -009

Mean return(non-gap day)

002 002 002 002

Anomaly confirmed not confirmed confirmed confirmed1999-2008 Mean return (gap

day)38E-3 027 -036 -013

Mean return(non-gap day)

-01 -01 -01 -01

Anomaly confirmed not confirmed not confirmed not confirmed2009-2018 Mean return (gap

day)039 009 013 -025

Mean return(non-gap day)

001 001 001 001

Anomaly confirmed not confirmed confirmed confirmed

G2 Parametric tests Students t-test

Table G2 T-test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 t-criterion 3194 3076 201 559t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected rejected

1959-1968 t-criterion 1399 2246 443 382t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected rejected

1969-1978 t-criterion 261 4358 417 786t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected rejected

1979-1988 t-criterion 1847 1445 709 395t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected rejected

1989-1998 t-criterion 13 066 126 093t-critical (=095) 196 196 196 196Null hypothesis not rejected not rejected not rejected not rejected

1999-2008 t-criterion 192 106 111 009t-critical (=095) 196 196 196 196Null hypothesis not rejected not rejected not rejected not rejected

2009-2018 t-criterion 27 05 089 188t-critical (=095) 196 196 196 196Null hypothesis rejected not rejected not rejected not rejected

31

G3 Parametric tests ANOVA

Table G3 ANOVA

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 F 88153 190609 1272 14521p-value 0 0 0 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1959-1968 F 93974 149771 4715 10418p-value 0 0 0 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1969-1978 F 84546 145429 6295 18241p-value 0 0 0 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1979-1988 F 66952 110482 13138 8626p-value 0 0 0 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1989-1998 F 323 138 43 168p-value 007 024 003 019

F critical 384 384 384 384Null hypothesis not rejected not rejected rejected not rejected

1999-2008 F 106 512 327 003p-value 001 002 007 085

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

2009-2018 F 169 069 175 93p-value 0 04 018 0

F critical 384 384 384 384Null hypothesis rejected not rejected not rejected rejected

G4 Non-parametric tests Kruskal-Wallis test

Table G4 Kruskal-Wallis test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 Adjusted H 26254 32592 1464 3962df 1 1 1 1

P value 0 0 0 0Null hypothesis rejected rejected rejected rejected

1959-1968 Adjusted H 28235 27989 2736 332df 1 1 1 1

P value 0 0 0 0Null hypothesis rejected rejected rejected rejected

1969-1978 Adjusted H 22202 33777 3311 7591df 1 1 1 1

P value 0 0 0 0Null hypothesis rejected rejected rejected rejected

1979-1988 Adjusted H 23282 25292 4812 3964df 1 1 1 1

P value 0 0 0 0Null hypothesis rejected rejected rejected rejected

1989-1998 Adjusted H 381 017 175 132df 1 1 1 1

P value 005 068 019 025Null hypothesis not rejected not rejected not rejected not rejected

1999-2008 Adjusted H 855 023 044 004df 1 1 1 1

P value 0 063 051 084Null hypothesis rejected not rejected not rejected not rejected

2009-2018 Adjusted H 1063 009 257 709df 1 1 1 1

P value 0 077 011 001Null hypothesis rejected not rejected not rejected rejected

32

G5 Regression analysis with dummy variables

Table G5 Regression analysis with dummy variables

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 a0 00007 (000) 00007 (000) 00007 (000) 00007 (000)a1 00088 (000) -00119 (000) 00011 (000) -00036 (000)

Anomaly confirmed confirmed confirmed confirmed1959-1968 a0 00006 (000) 00006 (000) 00006 (000) 00006 (000)

a1 00128 (000) -00153 (000) 00027 (000) -00046 (000)Anomaly confirmed confirmed confirmed confirmed

1969-1978 a0 00005 (000) 00005 (000) 00005 (000) 00005 (000)a1 00185 (000) -00192 (000) 00053 (000) -00073 (000)

Anomaly confirmed confirmed confirmed confirmed1979-1988 a0 00008 (000) 00008 (000) 00008 (000) 00008 (000)

a1 00131 (000) -00172 (000) 00059 (000) -00048 (000)Anomaly confirmed confirmed confirmed confirmed

1989-1998 a0 00002 (027) 00002 (028) 00002 (028) 00002 (027)a1 00014 (007) 00010 (024) 00017 (004) -00011 (019)

Anomaly not confirmed not confirmed confirmed not confirmed1999-2008 a0 00001 (059) 00001 (062) 00001 (059) 00001 (060)

a1 00037 (000) 00026 (002) -00038 (000) -00014 (019)Anomaly confirmed not confirmed not confirmed not confirmed

2009-2018 a0 00001 (049) 00001 (049) 00001 (049) 00001 (049)a1 00038 (000) 00007 (040) 00012 (018) -00027 (000)

Anomaly confirmed not confirmed not confirmed confirmed

G6 Modified CAR approach

Table G6 Modified CAR approach

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 Multiple R 099 099 093 098F-test 5753605 (000) 100470(000) 6280421 283281a0 -00091 (000) -00349 (000) 00056 (001) 00015 (073)a1 00083 (000) -00110 (000) 00010 (000) -00031 (000)

Anomaly confirmed confirmed confirmed confirmed1959-1968 Multiple R 099 099 099 099

F-test 3923274 (000) 3005562 (000) 443198 (000) 372583 (000)a0 00096 (000) 00073 (016) -00082 (000) -00095 (004)a1 00116 (001) -00149 (000) 00025 (000) -00047 (000)

Anomaly confirmed confirmed confirmed confirmed1969-1978 Multiple R 099 099 098 099

F-test 4302608 (000) 2723953 (000) 179969 (000) 639745a0 00246 (000) -00002 (000) 00217 (000) -00514 (000)a1 00176 (000) -00182 (000) 00049 (000) -00062 (000)

Anomaly confirmed confirmed confirmed confirmed1979-1988 Multiple R 099 099 099 099

F-test 5872335 (000) 1182609 (000) 1083558 (000) 910089 (000)a0 00136 (000) -01081 (000) -00285 (000) -00101 (000)a1 00131 (000) -00167 (000) 00062 (000) -00048 (000)

Anomaly confirmed confirmed confirmed confirmed1989-1998 Multiple R 09 056 069 016

F-test 46947 (000) 4885 (000) 10131 (000) 263 (011)a0 00102 (002) -00261 (000) -0016 (001) -00237 (000)a1 00015 (000) 00010 (000) 0001 (000) 00002 (011)

Anomaly confirmed confirmed confirmed not confirmed1999-2008 Multiple R 093 087 073 037

F-test 71863 (000) 32530 (000) 13273 (000) 1669 (000)a0 00185 (004) 00311 (000) -00130 (039) -00546 (000)a1 00037 (000) 00032 (000) -00026 (000) -00007 (000)

Anomaly confirmed not confirmed not confirmed confirmed2009-2018 Multiple R 089 001 096 091

F-test 40818 (000) 000 (094) 116744 (000) 53770 (000)a0 01436 (000) -01099 (000) -01036 (000) 00697 (000)a1 00030 (000) 00000 (094) 00024 (000) -00021 (000)

Anomaly confirmed not confirmed confirmed confirmed

33

H Detailed statistical results SampP 500 sub-periods

H1 Average analysis

Table H1 Average analysis

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 Mean return (gapday)

138 -171 004 -014

Mean return(non-gap day)

0 0 0 0

Anomaly confirmed confirmed confirmed confirmed1939-1948 Mean return (gap

day)001 -042 172 -195

Mean return(non-gap day)

003 003 003 003

Anomaly confirmed confirmed confirmed confirmed1949-1958 Mean return (gap

day)165 -18 02 002

Mean return(non-gap day)

006 006 006 006

Anomaly confirmed confirmed confirmed not confirmed1959-1968 Mean return (gap

day)104 -102 015 0

Mean return(non-gap day)

002 002 002 002

Anomaly confirmed confirmed confirmed not confirmed1969-1978 Mean return (gap

day)131 -13 019 -03

Mean return(non-gap day)

0 0 0 0

Anomaly confirmed confirmed confirmed confirmed1979-1988 Mean return (gap

day)058 -042 015 003

Mean return(non-gap day)

005 005 005 005

Anomaly confirmed confirmed confirmed not confirmed1989-1998 Mean return (gap

day)02 -023 -002 01

Mean return(non-gap day)

007 007 007 007

Anomaly confirmed confirmed not confirmed not confirmed1999-2008 Mean return (gap

day)083 -089 -023 -005

Mean return(non-gap day)

001 001 001 001

Anomaly confirmed confirmed not confirmed confirmed2009-2018 Mean return (gap

day)055 -052 001 -015

Mean return(non-gap day)

004 004 004 004

Anomaly confirmed confirmed not confirmed confirmed

34

H2 Parametric tests Students t-test

Table H2 T-test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 t-criterion 101 85 029 048t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

1939-1948 t-criterion 064 479 3074 225t-critical (=095) 196 196 196 196Null hypothesis not rejected rejected rejected rejected

1949-1958 t-criterion 2964 2383 193 041t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

1959-1968 t-criterion 2281 2157 21 023t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected not rejected

1969-1978 t-criterion 1318 2034 187 321t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected rejected

1979-1988 t-criterion 435 535 07 037t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

1989-1998 t-criterion 201 396 132 052t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

1999-2008 t-criterion 362 433 117 022t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

2009-2018 t-criterion 375 382 027 132t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

H3 Parametric tests ANOVA

Table H3 ANOVA

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 F 6281 8032 005 051p-value 0 0 082 047

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

1939-1948 F 056 2603 34854 51034p-value 045 0 0 0

F critical 384 384 384 384Null hypothesis not rejected rejected rejected rejected

1949-1958 F 100174 128997 897 062p-value 0 0 0 043

F critical 384 384 384 384Null hypothesis rejected rejected rejected not rejected

1959-1968 F 36831 32858 617 01p-value 0 0 001 074

F critical 384 384 384 384Null hypothesis rejected rejected rejected not rejected

1969-1978 F 26601 3063 53 152p-value 0 0 002 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1979-1988 F 23 245 076 009p-value 0 0 039 077

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

1989-1998 F 399 1156 118 015p-value 004 0 027 069

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

1999-2008 F 4253 5622 365 024p-value 0 0 006 062

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

2009-2018 F 3064 3656 01 43p-value 0 0 075 004

F critical 384 384 384 384Null hypothesis rejected rejected not rejected rejected

35

H4 Non-parametric tests Kruskal -Wallis test

Table H4 Kruskal-Wallis test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 Adjusted H 9982 5913 332 14df 1 1 1 1

P value 0 0 007 024Null hypothesis rejected rejected not rejected not rejected

1939-1948 Adjusted H 494 1999 23387 24927df 1 1 1 1

P value 003 0 0 0Null hypothesis rejected rejected rejected rejected

1949-1958 Adjusted H 28728 28175 348 15df 1 1 1 1

P value 0 0 006 022Null hypothesis rejected rejected not rejected not rejected

1959-1968 Adjusted H 25729 21437 701 063df 1 1 1 1

P value 0 0 001 043Null hypothesis rejected rejected rejected not rejected

1969-1978 Adjusted H 14407 20078 27 1706df 1 1 1 1

P value 0 0 01 0Null hypothesis rejected rejected not rejected rejected

1979-1988 Adjusted H 1788 2836 027 034df 1 1 1 1

P value 0 0 06 056Null hypothesis rejected rejected not rejected not rejected

1989-1998 Adjusted H 251 1431 111 044df 1 1 1 1

P value 011 0 029 051Null hypothesis not rejected rejected not rejected not rejected

1999-2008 Adjusted H 1812 1788 042 002df 1 1 1 1

P value 0 0 052 089Null hypothesis rejected rejected not rejected not rejected

2009-2018 Adjusted H 1314 1783 074 37df 1 1 1 1

P value 0 0 039 005Null hypothesis rejected rejected not rejected not rejected

36

H5 Regression analysis with dummy variables

Table H5 Regression analysis with dummy variables

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 a0 00000 (097) 00000 (004) 00000 (097) 00000 (097)a1 00138 (000) -00172 (000) 00004 (082) -00014 (047)

Anomaly confirmed confirmed not confirmed not confirmed1939-1948 a0 00003 (015) 00003 (015) 00003 (015) 00003 (015)

a1 00007 (045) -00045 (000) 00170 (000) -00199 (000)Anomaly not confirmed confirmed confirmed confirmed

1949-1958 a0 00006 (000) 00006 (000) 00006 (000) 00006 (000)a1 00160 (000) -00188 (000) 00016 (000) -00004 (043)

Anomaly confirmed confirmed confirmed not confirmed1959-1968 a0 00002 (007) 00002 (004) 00002 (008) 00002 (008)

a1 00103 (000) -00105 (000) 00014 (001) -00002 (074)Anomaly confirmed confirmed confirmed not confirmed

1969-1978 a0 00000 (078) 00000 (078) 00000 (078) 00000 (078)a1 00132 (000) -00132 (000) 00019 (002) -00030 (000)

Anomaly confirmed confirmed confirmed confirmed1979-1988 a0 00006 (001) 00006 (001) 00006 (001) 00006 (000)

a1 00053 (000) -00048 (000) 00009 (040) -00003 (075)Anomaly confirmed confirmed not confirmed not confirmed

1989-1998 a0 00007 (000) 00007 (000) 00007 (000) 00007 (000)a1 00016 (005) -00030 (000) -00009 (026) 00003 (072)

Anomaly confirmed confirmed not confirmed not confirmed1999-2008 a0 00001 (075) 00001 (075) 00001 (075) 00001 (076)

a1 00083 (000) -00091 (000) -00024 (005) -00006 (062)Anomaly confirmed confirmed not confirmed not confirmed

2009-2018 a0 00004 (003) 00004 (000) 00004 (003) 00004 (003)a1 00051 (000) -00059 (000) -00003 (075) -00019 (003)

Anomaly confirmed confirmed not confirmed confirmed

37

H6 Modified CAR approach

Table H6 Modified CAR approach

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 Multiple R 096 095 046 046F-test 175935 (000) 96500 (000) 3534 (000) 2880 (000)a0 -01070 (000) 01958 (000) 00405 (000) 00535 (000)a1 00121 (000) -00160 (000) 00006 (000) -00014 (000)

Anomaly confirmed confirmed confirmed confirmed1939-1948 Multiple R 08 099 099 099

F-test 18777 (000) 755727 (000) 3572830 (000) 2696099 (000)a0 00019 (073) -00346 (000) -00373 (000) 00912 (000)a1 00012 (000) -00044 (000) 00168 (000) -00197 (000)

Anomaly confirmed confirmed confirmed confirmed1949-1958 Multiple R 099 099 094 015

F-test 1021705 (000) 7171257 (000) 75858 (000) 242 (012)a0 -00176 (000) -00191 (000) 00095 (000) -00498 (000)a1 00154 (000) -00181 (000) 00013 (000) -00002 (012)

Anomaly confirmed confirmed confirmed not confirmed1959-1968 Multiple R 099 099 094 078

F-test 1463311 (000) 6002659 (000) 82273 (000) 14352 (000)a0 -00112 (000) 00004 (085) 00151 (000) 00389 (000)a1 00098 (000) -00102 (000) 00011 (000) -00009 (000)

Anomaly confirmed confirmed confirmed confirmed1969-1978 Multiple R 098 099 093 099

F-test 241655 (000) 1451901 (000) 57333 (000) 368160 (000)a0 -00433 (000) 00276 (000) 00099 (002) -00144 (000)a1 00132 (000) -00134 (000) 00020 (000) -00030 (000)

Anomaly confirmed confirmed confirmed confirmed1979-1988 Multiple R 092 078 023 008

F-test 53757 (000) 18707 (000) 487 (003) 085 (036)a0 00813 (000) -02508 (000) 00204 (000) -00235 (000)a1 00036 (000) -00031 (000) -00003 (003) -00001 (036)

Anomaly confirmed confirmed not confirmed not confirmed1989-1998 Multiple R 079 099 074 044

F-test 19705(000) 761967 (000) 14133 (000) 2369 (000)a0 00268 (000) 00023 (021) -00381 (000) 00087 (000)a1 00013 (000) -00028 (000) -00008 (000) 00002 (000)

Anomaly confirmed confirmed not confirmed not confirmed1999-2008 Multiple R 091 093 071 065

F-test 47218 (000) 76564 (000) 9843 (000) 7768 (000)a0 -01493 (000) 01351 (000) 00397 (000) 00007 (093)a1 00081 (000) -00083 (000) -00026 (000) -00011 (000)

Anomaly confirmed confirmed not confirmed confirmed2009-2018 Multiple R 086 087 083 074

F-test 29971 (000) 32484 (000) 23228 (000) 12764 (000)a0 01711 (000) -02250 (000) 00407 (000) -00472 (000)a1 00038 (000) -00044 (000) -00010 (000) -00012 (000)

Anomaly confirmed confirmed not confirmed confirmed

38

effect is much higher than 50 per cent this indicates abnormal price behaviour and asthe results confirm our hypotheses

The results are presented in Appendix B We find no convincing evidence in favour ofmomentum effect after price gaps (Table B1) and before them (Table B2) In generalprice gaps are not generated by previous price dynamics (NASDAQ index is an exceptionas negative gaps appear in 70 per cent of the cases after downward price movements andafter positive gaps in 67 per cent of the cases upward price movements are observed)Our results (see Table B3 for details) also indicate that the probability that price gapswill be filled within 5 days after appearance is very low at around 20 per cent

44 Price gap evolution

Overall in probabilistic terms price gaps do not generate any stable patterns But therecan be patterns in terms of size of price movements after gaps To check this we will testH1 and H2 To incorporate price direction in results of analysis H1 we further test forH1minus1 and H1minus2 The results for the overall data sets are presented in Appendices C toE for the cases of DJI SampP 500 and NASDAQ respectively To ease the interpretationof results we have summarised them in Table 5 and Table A3

Table 5 shows strong evidence confirming H1 in the SampP 500 Similarly Table A3confirms H1 for the NASDAQ but not for the DJI The difference between the DJI SampP500 and NASDAQ results can be explained by the differences in samples (DJI sampleis much shorter) This suggests that price gap anomaly may evolve and is therefore apreliminary confirmation of H2

Tables 6 and 7 confirm H1minus1 in the SampP 500 on the day of the price gap That ison the price gap day prices tend towards the direction of the price gap However thisis not the case for the day after the price gap therefore H1minus2 is not confirmed It canbe concluded that the SampP 500 roughly needs a day to absorb new information Never-theless even a day can be enough to create a profitable trading strategy and generateabnormal profits from trading

Similar results on the NASDAQ can be found in Tables A6 and A7 The longersample of the NASDAQ allows for the evolution of the price anomaly H1minus1 is there-fore confirmed on the day of the price gap anomaly and the day after the price gapanomaly (in both instances only until the 1990s and has since disappeared) H1minus2 inboth instances is confirmed up until the 1990s The results of the DJI did not providestrong evidence in favour of H1minus1 and H1minus2 on the day after the price gap but sim-ilar to the SampP 500 evidence was strong on the day of the price gap (see Tables A4and A5) These results confirm in the main the price gap anomaly is a reality in theUS stock market and that it evolves over time that is from prevalence to disappearance

10

Tab

le5

Overallstatisticalresults

SampP500

PeriodM

ethod

Average

analysis

t-test

ANOVA

test

Man

n-

Whitney

test

Regression

analysis

with

dummy

variab

les

Modified

CAR

approach

Overall

Gap

day

+-

-+

-+

3Gap

day

(Positivegaps)

++

++

++

6Gap

day

(Negativegaps)

++

++

++

6Day

aftergap(P

ositivegaps)

++

-+

++

5Day

aftergap(N

egativegaps)

++

--

++

4

Note+

indicates

thattheanom

alyis

confirm

edand-indicates

thatan

omaly

isnot

confirm

edThehigher

theoverallrating

the

strongertheeviden

ceofthean

omaly

11

Tab

le6

H1minus1summarystatisticalresults

SampP500sub-periods

PeriodM

ethod

Average

analysis

t-test

ANOVA

test

Man

n-

Whitney

test

Regression

analysis

withdummy

variab

les

Modified

CAR

approach

Overall

Dayofanomaly

1929-1938

++

++

++

61939-1948

+-

-+

-+

31949-1958

++

++

++

61959-1968

++

++

++

61969-1978

++

++

++

61979-1988

++

++

++

61989-1998

++

++

++

61999-2008

++

++

++

62009-2018

++

++

++

6Dayafteranomaly

1929-1938

+-

--

-+

21939-1948

++

++

++

61949-1958

+-

+-

++

51959-1968

++

++

++

61969-1978

+-

+-

++

41979-1988

+-

--

--

11989-1998

--

--

--

01999-2008

--

--

--

02009-2018

--

--

--

0

Note+

indicates

thattheanom

alyis

confirm

edand-indicates

thatan

omaly

isnot

confirm

edThehigher

theoverallrating

the

strongertheeviden

ceofthean

omaly

12

Tab

le7

H1minus2statisticalresults

SampP500sub-periods

PeriodM

ethod

Average

analysis

t-test

ANOVA

test

Man

n-

Whitney

test

Regression

analysiswith

dummy

variab

les

Modified

CAR

approach

Overall

Dayofanomaly

1929-1938

++

++

++

61939-1948

++

++

++

61949-1958

++

++

++

61959-1968

++

++

++

61969-1978

++

++

++

61979-1988

++

++

++

61989-1998

++

++

++

61999-2008

++

++

++

62009-2018

++

++

++

6Dayafteranomaly

1929-1938

+-

--

-+

21939-1948

++

++

++

61949-1958

--

--

--

01959-1968

--

--

-+

11969-1978

++

++

++

61979-1988

--

--

--

01989-1998

--

--

--

01999-2008

+-

--

-+

22009-2018

+-

+-

++

4

Note+

indicates

thattheanom

alyis

confirm

edand-indicates

thatan

omaly

isnot

confirm

edThehigher

theoverallrating

the

strongertheeviden

ceofthean

omaly

13

45 Trading simulation

The algorithm of the trading strategy is to buysell at the start of the updown gapday and close this position at the end of this day To test this strategy data for the DJIand SampP 500 are used (for this case the price anomaly still exists based on the day itoccurred) The results for DJI are presented in Table A8 and for the SampP 500 in Table8 For the SampP 500 and DJI the trading strategy built on price gap anomaly is efficientand its results differ from random

Table 8 Trading simulation results of the price gap anomaly for the SampP 500

Period Gaptype

Numberof

tradesunits

Numberof suc-cessfultradesunits

Numberof suc-cessfultrades

Profit

Profit peryear

z-test Result

1929-1938 Up 131 130 992 1816 182 1065 passedDown 110 108 982 1893 189 876 passed

1939-1948 Up 110 67 609 106 11 09 failedDown 122 79 648 518 52 465 passed

1949-1958 Up 106 105 991 1765 176 3191 passedDown 104 103 99 1891 189 2356 passed

1959-1968 Up 108 106 981 1331 113 2441 passedDown 92 91 989 948 95 2214 passed

1969-1978 Up 85 71 835 1128 113 1361 passedDown 96 90 938 1262 126 2118 passed

1979-1988 Up 92 63 685 54 54 495 passedDown 123 81 659 519 52 496 passed

1989-1998 Up 117 72 615 267 27 295 passedDown 99 61 616 228 23 32 passed

1999-2008 Up 99 65 657 828 83 373 passedDown 110 72 655 987 99 438 passed

2009-2018 Up 106 71 67 59 59 416 passedDown 107 65 607 56 56 362 passed

14

Figure 1 Trading simulation results of the price gap anomaly for the SampP 500

Note The primary axis refers to the percentage profit per year and the secondary to thez minus test statistic

One more interesting fact (see Figure 1) is the decrease of trading strategy efficiencyThis is indirect evidence in favour of evolution of the US stock market and its movementfrom less efficient to more efficient state Overall it can be concluded that the price gapanomaly is a real market anomaly The US stock market loses its efficiency after pricegaps This effect is temporary and lasts only for a day Still even this time is enoughto exploit the hole in the market efficiency and generate abnormal profits from trading

5 Conclusion

We analysed price gap anomaly in the US stock market by using information from threestock market indexes(DJI SampP 500 and NASDAQ) We tested three hypotheses of in-terest that is H1 the price gap anomaly exists H1minus1 prices tend to rise after positivegaps H1minus2 prices tend to fall after negative gaps H2 the price gap anomaly evolvesand H3 there is seasonality in price gaps Various statistical methods including para-metric tests (Students t-tests ANOVA) non-parametric tests (Mann-Whitney test)regression analysis with dummy variables MCAR approach and the trading simulationapproach were utilised

We conclude that the US stock market in the main did not exhibit seasonality in pricegaps Therefore H3 is rejected Furthermore no evidence was found that price gaps inthe US stock market were filled within five days of their occurrence However strongevidence in favour of abnormal price movements after the gaps were found confirming

15

H1 and H2 Particularly on the day of the occurrence of the gap and not on the dayafter the price gap In the DJI and the SampP 500 this pattern persists indicating thatthese markets take a day to incorporate new information As the results of the tradingsimulation indicate a day is enough to profit from a price gap anomaly trading strategyin the DJI and the SampP 500

Similar to other studies and other anomalies (see McLean and Pontiff (2016) Ca-jueiro and Tabak (2004) and Tiwari et al (2019) for example) the price gap anomalyevolved It is less prevalent since the 1990s as shown in the SampP 500 and NASDAQThis pattern of evolution is common amongst most stock market anomalies (see Plastunet al (2019b) on calendar anomalies amongst others) Our findings therefore add onto the existing literature Finally in the main our results are against the EMH and aretherefore interesting to both practitioners and academics

16

References

Agrawal A and Tandon K (1994) Anomalies or illusions evidence from stock marketsin eighteen countries Journal of international Money and Finance 13(1)83ndash106

Akerlof G A and Shiller R J (2009) Animal Spirits How human psychology drivesthe economy and why it matters for global capitalism Princeton University Press

Basu S (1977) Investment performance of common stocks in relation to their price-earnings ratios A test of the efficient market hypothesis The Journal of Finance32(3)663ndash682

Bildik R (2004) Are calendar anomalies still alive Evidence from istanbul stockexchange SSRN Electronic Journal 2004

Cai J Li Y and Qi Y (2006) The day-of-the-week effect New evidence from theChinese stock market Chinese Economy 39(2)71ndash88

Cajueiro D O and Tabak B M (2004) The Hurst exponent over time testing theassertion that emerging markets are becoming more efficient Physica A StatisticalMechanics and its Applications 336(3-4)521ndash537

Caporale G M Gil-Alana L Plastun A and Makarenko I (2016) Intraday anoma-lies and market efficiency A trading robot analysis Computational Economics47(2)275ndash295

Caporale G M and Plastun A (2017) Price gaps Another market anomaly Invest-ment Analysts Journal 46(4)279ndash293

Cross F (1973) The behavior of stock prices on Fridays and Mondays FinancialAnalysts Journal 29(6)67ndash69

Fama E F (1965) The behavior of stock-market prices The Journal of Business38(1)34ndash105

Fama E F (1970) Efficient capital markets A review of theory and empirical workThe Journal of Finance 25(2)383ndash417

Fortune P (1998) Weekends can be rough revisiting the weekend effect in stock pricesTechnical report

Fortune P (1999) Are stock returns different over weekends A jump diffusion analysisof the weekend effect New England Economic Review 103ndash19

French K R (1980) Stock returns and the weekend effect Journal of FinancialEconomics 8(1)55ndash69

Fung A K-W Lam K and Lam K-M (2010) Do the prices of stock index futuresin asia overreact to us market returns Journal of Empirical Finance 17(3)428ndash440

17

Gibbons M R and Hess P (1981) Day of the week effects and asset returns Journalof business pages 579ndash596

Grant J L Wolf A and Yu S (2005) Intraday price reversals in the us stock indexfutures market A 15-year study Journal of Banking amp Finance 29(5)1311ndash1327

Grossman S J and Stiglitz J E (1980) On the impossibility of informationallyefficient markets The American Economic Review 70(3)393ndash408

Jacobsen B Mamun A and Visaltanachoti N (2005) Seasonal size and valueanomalies

Jensen M (1978) Some anomalous evidence regarding market efficiency Journal ofFinancial Economics 6(23 (1978))95ndash101

Lakonishok J and Smidt S (1988) Are seasonal anomalies real A ninety-year per-spective The Review of Financial Studies 1(4)403ndash425

MacKinlay A (1997) Event studies in economics and finance Journal of EconomicLiterature (35)113ndash39

Mandelbrot B B (1997) The variation of certain speculative prices In Fractals andscaling in finance pages 371ndash418 Springer

McLean R D and Pontiff J (2016) Does academic research destroy stock returnpredictability The Journal of Finance 71(1)5ndash32

Plastun A Makarenko I Khomutenko L Shcherbak S and Tryfonova O (2019a)Exploring price gap anomaly in the ukrainian stock market Investment Managementamp Financial Innovations 16(2)150

Plastun A Sibande X Gupta R and Wohar M E (2019b) Rise and fall of calendaranomalies over a century The North American Journal of Economics and Finance49181ndash205

Schwert G W (2003) Chapter 15 anomalies and market efficiency In FinancialMarkets and Asset Pricing volume 1 of Handbook of the Economics of Finance pages939 ndash 974 Elsevier

Shiller R J (2000) Irrational exuberance Princeton University

Tiwari A K Aye G C and Gupta R (2019) Stock market efficiency analysis usinglong spans of data A multifractal detrended fluctuation approach Finance ResearchLetters 28398ndash411

Yuan Y (2015) Market-wide attention trading and stock returns Journal of FinancialEconomics 116(3)548ndash564

18

Appendices

A DJI and NASDAQ Summary Results

A1 Overall Results

Table A1 Gap size used for different sub-periods over the period 1929-2018

Period DJI NASDAQ1929-1938 - -1939-1948 - -1949-1958 - 0711959-1968 - 0951969-1978 - 1351979-1988 - 1101989-1998 040 0681999-2008 007 1502009-2018 020 110Overall data set 030 110

Table A2 Day of the week and gaps

Day of the week DJI NASDAQMonday 024 02Tuesday 02 02Wednesday 017 02Thursday 019 019Friday 021 02

A2 Statistical tests

Table A3 Results of the statistical tests for the overall data sets

PeriodMethod Averageanalysis

t-test ANOVAtest

Mann-Whitney

test

Regressionanalysiswith

dummyvariables

ModifiedCAR

approach

Overall

Dow Jones Index overall data setGap day - - - - - + 1Gap day (Positive gaps) + - - - - - 1Gap day (Negative gaps) + - - - - + 2Day after gap (Positive gaps) + - - - - - 1Day after gap (Negative gaps) + - - + - + 3

NASDAQ overall data setGap day + + + + + + 6Gap day (Positive gaps) + + + + + + 6Gap day (Negative gaps) + + + + + + 6Day after gap (Positive gaps) + + + + + + 6Day after gap (Negative gaps) + + + + + + 6

Note + indicates that the anomaly is confirmed and - indicates that anomaly is not confirmedThe higher the overall rating the stronger the evidence of the anomaly

19

Table A4 Results of the statistical tests for H1minus1 DJI

Period Averageanalysis

t-test ANOVA test Mann-Whitney

test

Regressionanalysis with

dummyvariables

ModifiedCAR

approach

Overall

Day of anomaly1989-1998 + - - - - + 21999-2008 + + + + + + 62009-2018 + + + + + + 6

Day after anomaly1989-1998 + - - - - + 21999-2008 + - - - - + 22009-2018 - - - - - - 0

Note + indicates that the anomaly is confirmed and - indicates that anomaly is not confirmedThe higher the overall rating the stronger the evidence of the anomaly

Table A5 Results of the statistical tests for H1minus2 DJI

Period Averageanalysis

t-test ANOVA test Mann-Whitneytest

Regressionanalysis with

dummyvariables

Modified CARapproach

Overall

Day of anomaly1989-1998 - - - - - - 01999-2008 + + + + + + 62009-2018 + + + + + + 6

Day after anomaly1989-1998 + - - - - + 21999-2008 + - - - - - 12009-2018 + - - - - + 2

Note + indicates that the anomaly is confirmed and - indicates that anomaly is not confirmedThe higher the overall rating the stronger the evidence of the anomaly

Table A6 Results of the statistical tests for H1minus1 NASDAQ

PeriodMethod Averageanalysis

t-test ANOVA test Mann-Whitney

test

Regressionanalysis with

dummyvariables

ModifiedCAR

approach

Overall

Day of anomaly1949-1958 + + + + + + 61959-1968 + + + + + + 61969-1978 + + + + + + 61979-1988 + + + + + + 61989-1998 + - - - - + 21999-2008 + - + + + + 52009-2018 + + + + + + 6

Day after anomaly1949-1958 + + + + + + 61959-1968 + + + + + + 61969-1978 + + + + + + 61979-1988 + + + + + + 61989-1998 + - + - + + 41999-2008 - - - - - - 02009-2018 + - - - - + 2

Note + indicates that the anomaly is confirmed and - indicates that anomaly is not confirmedThe higher the overall rating the stronger the evidence of the anomaly

20

Table A7 Results of the statistical tests for H1minus2 NASDAQ

PeriodMethod Averageanalysis

t-test ANOVA test Mann-Whitney

test

Regressionanalysis with

dummyvariables

ModifiedCAR

approach

Overall

Day of anomaly1949-1958 + + + + + + 61959-1968 + + + + + + 61969-1978 + + + + + + 61979-1988 + + + + + + 61989-1998 - - - - - + 11999-2008 - - + - - - 12009-2018 - - - - - - 0

Day after anomaly1949-1958 + + + + + + 61959-1968 + + + + + + 61969-1978 + + + + + + 61979-1988 + + + + + + 61989-1998 + - - - - - 11999-2008 - - - - - + 12009-2018 + - - + + + 4

Note + indicates that the anomaly is confirmed and - indicates that anomaly is not confirmedThe higher the overall rating the stronger the evidence of the anomaly

A3 Trading Simulation Results

Table A8 Trading simulation results of the price gap anomaly for the DJI 1989-2018

Period Gap type Number oftradesunits

Number ofsuccessfultradesunits

Number ofsuccessfultrades

Profit Profit per year

z-test Result

1989-1998 Up 102 46 451 -11 -01 011 failedDown 116 49 422 -267 -27 242 passed

1999-2008 Up 73 51 699 665 66 37 passedDown 143 81 566 641 64 331 passed

2009-2018 Up 127 88 693 308 31 327 passedDown 81 47 58 196 2 184 passed

21

B Short-term price behavior in DJI SampP 500 and

NASDAQ Price gaps (overall data sets)

Table B1 Momentum effect in the US stock market after the gap

Instrument Parameter Number of days after the gap1 2 3

Dow Jones Index Positive gaps 53 57 61Negative gaps 50 50 47

All gaps 51 54 54SampP 500 Index Positive gaps 40 63 60

Negative gaps 4 52 45All gaps 4 58 53

NASDAQ Positive gaps 32 65 67Negative gaps 24 63 59

All gaps 28 64 63

Table B2 Momentum effect in the US stock market before the gap

Instrument Parameter Number of days before the gap1 2 3

Dow Jones Index Positive gaps 56 49 52Negative gaps 54 49 49

All gaps 55 49 50SampP 500 Index Positive gaps 57 57 52

Negative gaps 60 59 54All gaps 58 58 53

NASDAQ Positive gaps 61 56 54Negative gaps 68 69 70

All gaps 64 63 63

Table B3 Fill gap effect in the US stock market

Instrument Parameter Number of days after the gap1 2 3 4 5

Dow Jones Index Positive gaps 22 28 26 30 28Negative gaps 25 33 36 42 46

All gaps 24 30 31 35 37SampP 500 Index Positive gaps 0 6 11 16 19

Negative gaps 1 10 19 26 27All gaps 1 8 15 20 23

NASDAQ Positive gaps 8 13 18 21 19Negative gaps 7 11 17 21 25

All gaps 8 12 18 21 22

22

C Detailed statistical results DJI overall data

C1 Average analysis

Table C1 Average analysis

Parameter Gap day Gap day(Positive gaps)

Gap day(Negative gaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Mean return (gap day) 003 006 0 005 -003Mean return (non-gap day) 004 004 004 004 004Anomaly not confirmed not confirmed confirmed not confirmed confirmed

C2 Parametric tests Students t-test

Table C2 T-test

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

t-criterion 016 042 053 015 104t-critical (=095) 196 196 196 196 196Null hypothesis not rejected not rejected not rejected not rejected not rejected

C3 Parametric tests ANOVA

Table C3 ANOVA

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

F 0036 018 053 003 14p-value 085 067 047 086 024F critical 384 384 384 384 384Null hypothesis not rejected not rejected not rejected not rejected not rejected

C4 Non-parametric tests Kruskal-Wallis test

Table C4 Kruskal -Wallis test

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Adjusted H 082 012 126 0 455df 1 1 1 1 1P value 037 073 026 095 003Critical value 384 384 384 384 384Null hypothesis not rejected not rejected not rejected not rejected rejected

23

C5 Regression analysis with dummy variables

Table C5 Regression analysis with dummy variables

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

a0 00004 (000) 00004 (000) 00004 (000) 00004 (000) 00004 (000)a1 -00001 (-019) 00002 (067) -00004 (047) 00001 (086) -00007 (024)Anomaly not confirmed not confirmed not confirmed not confirmed not confirmed

C6 Modified CAR approach

Table C6 Modified CAR approach

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Multiple R 049 05 025 0 092F-test 23347 (000) 12913 (000) 2207 (000) 000 (098) 1822 (000)a0 -00041 (060) 00128 (006) -00267 (000) 00354 (000) 00319 (000)a1 -00003 (000) -00003 (000) -00002 (000) 00000 (098) -00008 (000)Anomaly confirmed confirmed confirmed not confirmed confirmed

24

D Detailed statistical results SampP 500 overall data

D1 Average analysis

Table D1 Average analysis

Parameter Gap day Gap day(Positive gaps)

Gap day(Negative gaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Mean return (gap day) 006 115 -129 017 -011Mean return (non-gap day) 002 002 002 002 002Anomaly confirmed confirmed confirmed confirmed confirmed

D2 Parametric tests Students t-test

Table D2 T-test

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

t-criterion 092 4546 3579 485 271t-critical (=095) 196 196 196 196 196Null hypothesis not rejected rejected rejected rejected rejected

D3 Parametric tests ANOVA

Table D3 ANOVA

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

F 155 116211 126952 1866 136p-value 022 0 0 0 0F critical 384 384 384 384 384Null hypothesis not rejected rejected rejected not rejected not rejected

D4 Non-parametric tests Kruskal-Wallis test

Table D4 Kruskal-Wallis test

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Adjusted H 1352 70516 47237 3946 004df 1 1 1 1 1P value 0 0 0 0 084Critical value 384 384 384 384 384Null hypothesis rejected rejected rejected rejected not rejected

25

D5 Regression analysis with dummy variables

Table D5 Regression analysis with dummy variables

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

a0 00002 (000) 00002 (000) 00002 (000) 00002 (000) 00002 (000)a1 00003 (021) 00113 (000) -00132 (000) 00014 (000) -00014 (000)Anomaly not confirmed confirmed confirmed confirmed confirmed

D6 Modified CAR approach

Table D6 Modified CAR approach

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Multiple R 051 099 099 099 096F-test 69486 (000) 325351 (000) 1457582 (000) 6345973 (000) 1213344 (000)a0 -01003(000) 04081 (000) -05444 (000) -01088 (000) 00272 (000)a1 00002 (000) 00106 (000) -00127 (000) 00016 (000) -00016 (000)Anomaly confirmed confirmed confirmed confirmed confirmed

26

E Detailed statistical results NASDAQ overall data

E1 Average analysis

Table E1 Average analysis

Parameter Gap day Gap day(Positive gaps)

Gap day(Negative gaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Mean return (gap day) -009 084 -090 022 -037Mean return (non-gap day) 003 003 003 003 003Anomaly confirmed confirmed confirmed confirmed confirmed

E2 Parametric tests Students t-test

Table E2 T-test

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

t-criterion 230 1257 1341 306 664t-critical (=095) 196 196 196 196 196Null hypothesis rejected rejected rejected rejected rejected

E3 Parametric tests ANOVA

Table E3 ANOVA

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

F 2289 62720 88402 3330 17356p-value 0 0 0 0 0F critical 384 384 384 384 384Null hypothesis rejected rejected rejected rejected rejected

E4 Non-parametric tests Kruskal-Wallis test

Table E4 Kruskal-Wallis test

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Adjusted H 1892 36022 45248 4695 10437df 1 1 1 1 1P value 0 0 0 0 0Critical value 384 384 384 384 384Null hypothesis rejected rejected rejected rejected rejected

27

E5 Regression analysis with dummy variables

Table E5 Regression analysis with dummy variables

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

a0 00003 (000) 00003 (000) 00003 (000) 00003 (000) 00003 (000)a1 -00012 (000) 00081 (000) -00093 (000) 00018 (000) -00040 (000)Anomaly confirmed confirmed confirmed confirmed confirmed

E6 Modified CAR approach

Table E6 Modified CAR approach

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Multiple R 069 092 092 072 097F-test 133255 (000) 361102 (000) 442376 (000) 72903 (000) 1082812 (000)a0 -10646 (000) 11373 (000) -12888 (000) 03928 (000) -02297 (000)a1 -00011 (000) 00073 (000) -00097 (000) 00017 (000) -00039 (000)Anomaly confirmed confirmed confirmed confirmed confirmed

28

F Detailed statistical results DJI sub-periods

F1 Average analysis

Table F1 Average analysis

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 Mean return (gapday)

-001 023 015 -004

Mean return(non-gap day)

007 007 007 007

Anomaly confirmed confirmed confirmed confirmed1999-2008 Mean return (gap

day)090 -045 013 -004

Mean return(non-gap day)

-004 -004 -004 -004

Anomaly confirmed confirmed confirmed confirmed2009-2018 Mean return (gap

day)024 -024 0 -004

Mean return(non-gap day)

004 004 004 004

Anomaly confirmed confirmed not confirmed confirmed

F2 Parametric tests Students t-test

Table F2 T-test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 t-criterion 083 165 087 139t-critical (=095) 196 196 196 196Null hypothesis not rejected not rejected not rejected not rejected

1999-2008 t-criterion 347 351 054 047t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected rejected

2009-2018 t-criterion 265 207 051 058t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

F3 Parametric tests ANOVA

Table F3 ANOVA

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 F 085 409 093 179p-value 035 004 033 018

F critical 384 384 384 384Null hypothesis not rejected rejected not rejected not rejected

1999-2008 F 5405 3196 065 072p-value 0 0 042 039

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

2009-2018 F 554 697 024 058p-value 001 0 062 044

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

29

F4 Non-parametric tests Kruskal-Wallis test

Table F4 Kruskal-Wallis test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 Adjusted H 113 211 113 332df 1 1 1 1

P value 029 015 029 007Null hypothesis not rejected not rejected not rejected not rejected

1999-2008 Adjusted H 1484 1414 003 139df 1 1 1 1

P value 0 0 086 024Null hypothesis rejected rejected not rejected not rejected

2009-2018 Adjusted H 506 68 051 171df 1 1 1 1

P value 002 001 047 019Null hypothesis rejected rejected not rejected not rejected

F5 Regression analysis with dummy variables

Table F5 Regression analysis with dummy variables

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 a0 000068 (000) 00007 (000) 00007 (000) 00007 (000)a1 -000078 (035) 00016 (004) 00008 (033) -00011 (018)

Anomaly not confirmed confirmed not confirmed not confirmed1999-2008 a0 00004 (008) 00004 (008) 00004 (006) 00004 (008)

a1 00087 (000) -00049 (000) 00009 (042) -00008 (039)Anomaly confirmed confirmed not confirmed not confirmed

2009-2018 a0 00004 (006) 00004 (006) 00004 (006) 00004 (006)a1 00021 (001) -00028 (001) -00004 (062) -00008 (047)

Anomaly confirmed confirmed not confirmed not confirmed

F6 Modified CAR approach

Table F6 Modified CAR approach

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 Multiple R 083 088 082 086F-test 22779 (000) 40583 (000) 20401 (000) 3269454 (000)a0 00042 (023) 00017 (073) 00014 (058) -00266 (000)a1 -00009 (000) 00015 (000) 00006 (000) -00009 (000)

Anomaly confirmed confirmed confirmed confirmed1999-2008 Multiple R 095 093 076 019

F-test 62658 (000) 84712 (000) 10056 (000) 492 (003)a0 -00972 (000) 00365 (000) -00198 (000) -00115 (021)a1 00086 (000) -00042 (000) 00014 (000) 00002 (003)

Anomaly confirmed confirmed confirmed not confirmed2009-2018 Multiple R 096 082 08 05

F-test 150452 (000) 16731 (000) 22287 (000) 2620 (000)a0 00548 (000) -00618 (000) 00031 (020) -00112 (000)a1 00013 (000) -00014 (000) -00005 (000) -00004 (000)

Anomaly confirmed confirmed not confirmed confirmed

30

G Detailed statistical results NASDAQ sub-periods

G1 Average analysis

Table G1 Average analysis

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 Mean return (gapday)

094 -111 0189 -029

Mean return(non-gap day)

007 007 007 007

Anomaly confirmed confirmed confirmed confirmed1959-1968 Mean return (gap

day)133 -147 033 -039

Mean return(non-gap day)

006 006 006 006

Anomaly confirmed confirmed confirmed confirmed1969-1978 Mean return (gap

day)19 -186 057 -068

Mean return(non-gap day)

005 005 005 005

Anomaly confirmed confirmed confirmed confirmed1979-1988 Mean return (gap

day)138 -162 066 -04

Mean return(non-gap day)

008 008 008 008

Anomaly confirmed confirmed confirmed confirmed1989-1998 Mean return (gap

day)016 012 018 -009

Mean return(non-gap day)

002 002 002 002

Anomaly confirmed not confirmed confirmed confirmed1999-2008 Mean return (gap

day)38E-3 027 -036 -013

Mean return(non-gap day)

-01 -01 -01 -01

Anomaly confirmed not confirmed not confirmed not confirmed2009-2018 Mean return (gap

day)039 009 013 -025

Mean return(non-gap day)

001 001 001 001

Anomaly confirmed not confirmed confirmed confirmed

G2 Parametric tests Students t-test

Table G2 T-test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 t-criterion 3194 3076 201 559t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected rejected

1959-1968 t-criterion 1399 2246 443 382t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected rejected

1969-1978 t-criterion 261 4358 417 786t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected rejected

1979-1988 t-criterion 1847 1445 709 395t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected rejected

1989-1998 t-criterion 13 066 126 093t-critical (=095) 196 196 196 196Null hypothesis not rejected not rejected not rejected not rejected

1999-2008 t-criterion 192 106 111 009t-critical (=095) 196 196 196 196Null hypothesis not rejected not rejected not rejected not rejected

2009-2018 t-criterion 27 05 089 188t-critical (=095) 196 196 196 196Null hypothesis rejected not rejected not rejected not rejected

31

G3 Parametric tests ANOVA

Table G3 ANOVA

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 F 88153 190609 1272 14521p-value 0 0 0 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1959-1968 F 93974 149771 4715 10418p-value 0 0 0 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1969-1978 F 84546 145429 6295 18241p-value 0 0 0 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1979-1988 F 66952 110482 13138 8626p-value 0 0 0 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1989-1998 F 323 138 43 168p-value 007 024 003 019

F critical 384 384 384 384Null hypothesis not rejected not rejected rejected not rejected

1999-2008 F 106 512 327 003p-value 001 002 007 085

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

2009-2018 F 169 069 175 93p-value 0 04 018 0

F critical 384 384 384 384Null hypothesis rejected not rejected not rejected rejected

G4 Non-parametric tests Kruskal-Wallis test

Table G4 Kruskal-Wallis test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 Adjusted H 26254 32592 1464 3962df 1 1 1 1

P value 0 0 0 0Null hypothesis rejected rejected rejected rejected

1959-1968 Adjusted H 28235 27989 2736 332df 1 1 1 1

P value 0 0 0 0Null hypothesis rejected rejected rejected rejected

1969-1978 Adjusted H 22202 33777 3311 7591df 1 1 1 1

P value 0 0 0 0Null hypothesis rejected rejected rejected rejected

1979-1988 Adjusted H 23282 25292 4812 3964df 1 1 1 1

P value 0 0 0 0Null hypothesis rejected rejected rejected rejected

1989-1998 Adjusted H 381 017 175 132df 1 1 1 1

P value 005 068 019 025Null hypothesis not rejected not rejected not rejected not rejected

1999-2008 Adjusted H 855 023 044 004df 1 1 1 1

P value 0 063 051 084Null hypothesis rejected not rejected not rejected not rejected

2009-2018 Adjusted H 1063 009 257 709df 1 1 1 1

P value 0 077 011 001Null hypothesis rejected not rejected not rejected rejected

32

G5 Regression analysis with dummy variables

Table G5 Regression analysis with dummy variables

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 a0 00007 (000) 00007 (000) 00007 (000) 00007 (000)a1 00088 (000) -00119 (000) 00011 (000) -00036 (000)

Anomaly confirmed confirmed confirmed confirmed1959-1968 a0 00006 (000) 00006 (000) 00006 (000) 00006 (000)

a1 00128 (000) -00153 (000) 00027 (000) -00046 (000)Anomaly confirmed confirmed confirmed confirmed

1969-1978 a0 00005 (000) 00005 (000) 00005 (000) 00005 (000)a1 00185 (000) -00192 (000) 00053 (000) -00073 (000)

Anomaly confirmed confirmed confirmed confirmed1979-1988 a0 00008 (000) 00008 (000) 00008 (000) 00008 (000)

a1 00131 (000) -00172 (000) 00059 (000) -00048 (000)Anomaly confirmed confirmed confirmed confirmed

1989-1998 a0 00002 (027) 00002 (028) 00002 (028) 00002 (027)a1 00014 (007) 00010 (024) 00017 (004) -00011 (019)

Anomaly not confirmed not confirmed confirmed not confirmed1999-2008 a0 00001 (059) 00001 (062) 00001 (059) 00001 (060)

a1 00037 (000) 00026 (002) -00038 (000) -00014 (019)Anomaly confirmed not confirmed not confirmed not confirmed

2009-2018 a0 00001 (049) 00001 (049) 00001 (049) 00001 (049)a1 00038 (000) 00007 (040) 00012 (018) -00027 (000)

Anomaly confirmed not confirmed not confirmed confirmed

G6 Modified CAR approach

Table G6 Modified CAR approach

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 Multiple R 099 099 093 098F-test 5753605 (000) 100470(000) 6280421 283281a0 -00091 (000) -00349 (000) 00056 (001) 00015 (073)a1 00083 (000) -00110 (000) 00010 (000) -00031 (000)

Anomaly confirmed confirmed confirmed confirmed1959-1968 Multiple R 099 099 099 099

F-test 3923274 (000) 3005562 (000) 443198 (000) 372583 (000)a0 00096 (000) 00073 (016) -00082 (000) -00095 (004)a1 00116 (001) -00149 (000) 00025 (000) -00047 (000)

Anomaly confirmed confirmed confirmed confirmed1969-1978 Multiple R 099 099 098 099

F-test 4302608 (000) 2723953 (000) 179969 (000) 639745a0 00246 (000) -00002 (000) 00217 (000) -00514 (000)a1 00176 (000) -00182 (000) 00049 (000) -00062 (000)

Anomaly confirmed confirmed confirmed confirmed1979-1988 Multiple R 099 099 099 099

F-test 5872335 (000) 1182609 (000) 1083558 (000) 910089 (000)a0 00136 (000) -01081 (000) -00285 (000) -00101 (000)a1 00131 (000) -00167 (000) 00062 (000) -00048 (000)

Anomaly confirmed confirmed confirmed confirmed1989-1998 Multiple R 09 056 069 016

F-test 46947 (000) 4885 (000) 10131 (000) 263 (011)a0 00102 (002) -00261 (000) -0016 (001) -00237 (000)a1 00015 (000) 00010 (000) 0001 (000) 00002 (011)

Anomaly confirmed confirmed confirmed not confirmed1999-2008 Multiple R 093 087 073 037

F-test 71863 (000) 32530 (000) 13273 (000) 1669 (000)a0 00185 (004) 00311 (000) -00130 (039) -00546 (000)a1 00037 (000) 00032 (000) -00026 (000) -00007 (000)

Anomaly confirmed not confirmed not confirmed confirmed2009-2018 Multiple R 089 001 096 091

F-test 40818 (000) 000 (094) 116744 (000) 53770 (000)a0 01436 (000) -01099 (000) -01036 (000) 00697 (000)a1 00030 (000) 00000 (094) 00024 (000) -00021 (000)

Anomaly confirmed not confirmed confirmed confirmed

33

H Detailed statistical results SampP 500 sub-periods

H1 Average analysis

Table H1 Average analysis

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 Mean return (gapday)

138 -171 004 -014

Mean return(non-gap day)

0 0 0 0

Anomaly confirmed confirmed confirmed confirmed1939-1948 Mean return (gap

day)001 -042 172 -195

Mean return(non-gap day)

003 003 003 003

Anomaly confirmed confirmed confirmed confirmed1949-1958 Mean return (gap

day)165 -18 02 002

Mean return(non-gap day)

006 006 006 006

Anomaly confirmed confirmed confirmed not confirmed1959-1968 Mean return (gap

day)104 -102 015 0

Mean return(non-gap day)

002 002 002 002

Anomaly confirmed confirmed confirmed not confirmed1969-1978 Mean return (gap

day)131 -13 019 -03

Mean return(non-gap day)

0 0 0 0

Anomaly confirmed confirmed confirmed confirmed1979-1988 Mean return (gap

day)058 -042 015 003

Mean return(non-gap day)

005 005 005 005

Anomaly confirmed confirmed confirmed not confirmed1989-1998 Mean return (gap

day)02 -023 -002 01

Mean return(non-gap day)

007 007 007 007

Anomaly confirmed confirmed not confirmed not confirmed1999-2008 Mean return (gap

day)083 -089 -023 -005

Mean return(non-gap day)

001 001 001 001

Anomaly confirmed confirmed not confirmed confirmed2009-2018 Mean return (gap

day)055 -052 001 -015

Mean return(non-gap day)

004 004 004 004

Anomaly confirmed confirmed not confirmed confirmed

34

H2 Parametric tests Students t-test

Table H2 T-test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 t-criterion 101 85 029 048t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

1939-1948 t-criterion 064 479 3074 225t-critical (=095) 196 196 196 196Null hypothesis not rejected rejected rejected rejected

1949-1958 t-criterion 2964 2383 193 041t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

1959-1968 t-criterion 2281 2157 21 023t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected not rejected

1969-1978 t-criterion 1318 2034 187 321t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected rejected

1979-1988 t-criterion 435 535 07 037t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

1989-1998 t-criterion 201 396 132 052t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

1999-2008 t-criterion 362 433 117 022t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

2009-2018 t-criterion 375 382 027 132t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

H3 Parametric tests ANOVA

Table H3 ANOVA

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 F 6281 8032 005 051p-value 0 0 082 047

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

1939-1948 F 056 2603 34854 51034p-value 045 0 0 0

F critical 384 384 384 384Null hypothesis not rejected rejected rejected rejected

1949-1958 F 100174 128997 897 062p-value 0 0 0 043

F critical 384 384 384 384Null hypothesis rejected rejected rejected not rejected

1959-1968 F 36831 32858 617 01p-value 0 0 001 074

F critical 384 384 384 384Null hypothesis rejected rejected rejected not rejected

1969-1978 F 26601 3063 53 152p-value 0 0 002 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1979-1988 F 23 245 076 009p-value 0 0 039 077

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

1989-1998 F 399 1156 118 015p-value 004 0 027 069

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

1999-2008 F 4253 5622 365 024p-value 0 0 006 062

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

2009-2018 F 3064 3656 01 43p-value 0 0 075 004

F critical 384 384 384 384Null hypothesis rejected rejected not rejected rejected

35

H4 Non-parametric tests Kruskal -Wallis test

Table H4 Kruskal-Wallis test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 Adjusted H 9982 5913 332 14df 1 1 1 1

P value 0 0 007 024Null hypothesis rejected rejected not rejected not rejected

1939-1948 Adjusted H 494 1999 23387 24927df 1 1 1 1

P value 003 0 0 0Null hypothesis rejected rejected rejected rejected

1949-1958 Adjusted H 28728 28175 348 15df 1 1 1 1

P value 0 0 006 022Null hypothesis rejected rejected not rejected not rejected

1959-1968 Adjusted H 25729 21437 701 063df 1 1 1 1

P value 0 0 001 043Null hypothesis rejected rejected rejected not rejected

1969-1978 Adjusted H 14407 20078 27 1706df 1 1 1 1

P value 0 0 01 0Null hypothesis rejected rejected not rejected rejected

1979-1988 Adjusted H 1788 2836 027 034df 1 1 1 1

P value 0 0 06 056Null hypothesis rejected rejected not rejected not rejected

1989-1998 Adjusted H 251 1431 111 044df 1 1 1 1

P value 011 0 029 051Null hypothesis not rejected rejected not rejected not rejected

1999-2008 Adjusted H 1812 1788 042 002df 1 1 1 1

P value 0 0 052 089Null hypothesis rejected rejected not rejected not rejected

2009-2018 Adjusted H 1314 1783 074 37df 1 1 1 1

P value 0 0 039 005Null hypothesis rejected rejected not rejected not rejected

36

H5 Regression analysis with dummy variables

Table H5 Regression analysis with dummy variables

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 a0 00000 (097) 00000 (004) 00000 (097) 00000 (097)a1 00138 (000) -00172 (000) 00004 (082) -00014 (047)

Anomaly confirmed confirmed not confirmed not confirmed1939-1948 a0 00003 (015) 00003 (015) 00003 (015) 00003 (015)

a1 00007 (045) -00045 (000) 00170 (000) -00199 (000)Anomaly not confirmed confirmed confirmed confirmed

1949-1958 a0 00006 (000) 00006 (000) 00006 (000) 00006 (000)a1 00160 (000) -00188 (000) 00016 (000) -00004 (043)

Anomaly confirmed confirmed confirmed not confirmed1959-1968 a0 00002 (007) 00002 (004) 00002 (008) 00002 (008)

a1 00103 (000) -00105 (000) 00014 (001) -00002 (074)Anomaly confirmed confirmed confirmed not confirmed

1969-1978 a0 00000 (078) 00000 (078) 00000 (078) 00000 (078)a1 00132 (000) -00132 (000) 00019 (002) -00030 (000)

Anomaly confirmed confirmed confirmed confirmed1979-1988 a0 00006 (001) 00006 (001) 00006 (001) 00006 (000)

a1 00053 (000) -00048 (000) 00009 (040) -00003 (075)Anomaly confirmed confirmed not confirmed not confirmed

1989-1998 a0 00007 (000) 00007 (000) 00007 (000) 00007 (000)a1 00016 (005) -00030 (000) -00009 (026) 00003 (072)

Anomaly confirmed confirmed not confirmed not confirmed1999-2008 a0 00001 (075) 00001 (075) 00001 (075) 00001 (076)

a1 00083 (000) -00091 (000) -00024 (005) -00006 (062)Anomaly confirmed confirmed not confirmed not confirmed

2009-2018 a0 00004 (003) 00004 (000) 00004 (003) 00004 (003)a1 00051 (000) -00059 (000) -00003 (075) -00019 (003)

Anomaly confirmed confirmed not confirmed confirmed

37

H6 Modified CAR approach

Table H6 Modified CAR approach

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 Multiple R 096 095 046 046F-test 175935 (000) 96500 (000) 3534 (000) 2880 (000)a0 -01070 (000) 01958 (000) 00405 (000) 00535 (000)a1 00121 (000) -00160 (000) 00006 (000) -00014 (000)

Anomaly confirmed confirmed confirmed confirmed1939-1948 Multiple R 08 099 099 099

F-test 18777 (000) 755727 (000) 3572830 (000) 2696099 (000)a0 00019 (073) -00346 (000) -00373 (000) 00912 (000)a1 00012 (000) -00044 (000) 00168 (000) -00197 (000)

Anomaly confirmed confirmed confirmed confirmed1949-1958 Multiple R 099 099 094 015

F-test 1021705 (000) 7171257 (000) 75858 (000) 242 (012)a0 -00176 (000) -00191 (000) 00095 (000) -00498 (000)a1 00154 (000) -00181 (000) 00013 (000) -00002 (012)

Anomaly confirmed confirmed confirmed not confirmed1959-1968 Multiple R 099 099 094 078

F-test 1463311 (000) 6002659 (000) 82273 (000) 14352 (000)a0 -00112 (000) 00004 (085) 00151 (000) 00389 (000)a1 00098 (000) -00102 (000) 00011 (000) -00009 (000)

Anomaly confirmed confirmed confirmed confirmed1969-1978 Multiple R 098 099 093 099

F-test 241655 (000) 1451901 (000) 57333 (000) 368160 (000)a0 -00433 (000) 00276 (000) 00099 (002) -00144 (000)a1 00132 (000) -00134 (000) 00020 (000) -00030 (000)

Anomaly confirmed confirmed confirmed confirmed1979-1988 Multiple R 092 078 023 008

F-test 53757 (000) 18707 (000) 487 (003) 085 (036)a0 00813 (000) -02508 (000) 00204 (000) -00235 (000)a1 00036 (000) -00031 (000) -00003 (003) -00001 (036)

Anomaly confirmed confirmed not confirmed not confirmed1989-1998 Multiple R 079 099 074 044

F-test 19705(000) 761967 (000) 14133 (000) 2369 (000)a0 00268 (000) 00023 (021) -00381 (000) 00087 (000)a1 00013 (000) -00028 (000) -00008 (000) 00002 (000)

Anomaly confirmed confirmed not confirmed not confirmed1999-2008 Multiple R 091 093 071 065

F-test 47218 (000) 76564 (000) 9843 (000) 7768 (000)a0 -01493 (000) 01351 (000) 00397 (000) 00007 (093)a1 00081 (000) -00083 (000) -00026 (000) -00011 (000)

Anomaly confirmed confirmed not confirmed confirmed2009-2018 Multiple R 086 087 083 074

F-test 29971 (000) 32484 (000) 23228 (000) 12764 (000)a0 01711 (000) -02250 (000) 00407 (000) -00472 (000)a1 00038 (000) -00044 (000) -00010 (000) -00012 (000)

Anomaly confirmed confirmed not confirmed confirmed

38

Tab

le5

Overallstatisticalresults

SampP500

PeriodM

ethod

Average

analysis

t-test

ANOVA

test

Man

n-

Whitney

test

Regression

analysis

with

dummy

variab

les

Modified

CAR

approach

Overall

Gap

day

+-

-+

-+

3Gap

day

(Positivegaps)

++

++

++

6Gap

day

(Negativegaps)

++

++

++

6Day

aftergap(P

ositivegaps)

++

-+

++

5Day

aftergap(N

egativegaps)

++

--

++

4

Note+

indicates

thattheanom

alyis

confirm

edand-indicates

thatan

omaly

isnot

confirm

edThehigher

theoverallrating

the

strongertheeviden

ceofthean

omaly

11

Tab

le6

H1minus1summarystatisticalresults

SampP500sub-periods

PeriodM

ethod

Average

analysis

t-test

ANOVA

test

Man

n-

Whitney

test

Regression

analysis

withdummy

variab

les

Modified

CAR

approach

Overall

Dayofanomaly

1929-1938

++

++

++

61939-1948

+-

-+

-+

31949-1958

++

++

++

61959-1968

++

++

++

61969-1978

++

++

++

61979-1988

++

++

++

61989-1998

++

++

++

61999-2008

++

++

++

62009-2018

++

++

++

6Dayafteranomaly

1929-1938

+-

--

-+

21939-1948

++

++

++

61949-1958

+-

+-

++

51959-1968

++

++

++

61969-1978

+-

+-

++

41979-1988

+-

--

--

11989-1998

--

--

--

01999-2008

--

--

--

02009-2018

--

--

--

0

Note+

indicates

thattheanom

alyis

confirm

edand-indicates

thatan

omaly

isnot

confirm

edThehigher

theoverallrating

the

strongertheeviden

ceofthean

omaly

12

Tab

le7

H1minus2statisticalresults

SampP500sub-periods

PeriodM

ethod

Average

analysis

t-test

ANOVA

test

Man

n-

Whitney

test

Regression

analysiswith

dummy

variab

les

Modified

CAR

approach

Overall

Dayofanomaly

1929-1938

++

++

++

61939-1948

++

++

++

61949-1958

++

++

++

61959-1968

++

++

++

61969-1978

++

++

++

61979-1988

++

++

++

61989-1998

++

++

++

61999-2008

++

++

++

62009-2018

++

++

++

6Dayafteranomaly

1929-1938

+-

--

-+

21939-1948

++

++

++

61949-1958

--

--

--

01959-1968

--

--

-+

11969-1978

++

++

++

61979-1988

--

--

--

01989-1998

--

--

--

01999-2008

+-

--

-+

22009-2018

+-

+-

++

4

Note+

indicates

thattheanom

alyis

confirm

edand-indicates

thatan

omaly

isnot

confirm

edThehigher

theoverallrating

the

strongertheeviden

ceofthean

omaly

13

45 Trading simulation

The algorithm of the trading strategy is to buysell at the start of the updown gapday and close this position at the end of this day To test this strategy data for the DJIand SampP 500 are used (for this case the price anomaly still exists based on the day itoccurred) The results for DJI are presented in Table A8 and for the SampP 500 in Table8 For the SampP 500 and DJI the trading strategy built on price gap anomaly is efficientand its results differ from random

Table 8 Trading simulation results of the price gap anomaly for the SampP 500

Period Gaptype

Numberof

tradesunits

Numberof suc-cessfultradesunits

Numberof suc-cessfultrades

Profit

Profit peryear

z-test Result

1929-1938 Up 131 130 992 1816 182 1065 passedDown 110 108 982 1893 189 876 passed

1939-1948 Up 110 67 609 106 11 09 failedDown 122 79 648 518 52 465 passed

1949-1958 Up 106 105 991 1765 176 3191 passedDown 104 103 99 1891 189 2356 passed

1959-1968 Up 108 106 981 1331 113 2441 passedDown 92 91 989 948 95 2214 passed

1969-1978 Up 85 71 835 1128 113 1361 passedDown 96 90 938 1262 126 2118 passed

1979-1988 Up 92 63 685 54 54 495 passedDown 123 81 659 519 52 496 passed

1989-1998 Up 117 72 615 267 27 295 passedDown 99 61 616 228 23 32 passed

1999-2008 Up 99 65 657 828 83 373 passedDown 110 72 655 987 99 438 passed

2009-2018 Up 106 71 67 59 59 416 passedDown 107 65 607 56 56 362 passed

14

Figure 1 Trading simulation results of the price gap anomaly for the SampP 500

Note The primary axis refers to the percentage profit per year and the secondary to thez minus test statistic

One more interesting fact (see Figure 1) is the decrease of trading strategy efficiencyThis is indirect evidence in favour of evolution of the US stock market and its movementfrom less efficient to more efficient state Overall it can be concluded that the price gapanomaly is a real market anomaly The US stock market loses its efficiency after pricegaps This effect is temporary and lasts only for a day Still even this time is enoughto exploit the hole in the market efficiency and generate abnormal profits from trading

5 Conclusion

We analysed price gap anomaly in the US stock market by using information from threestock market indexes(DJI SampP 500 and NASDAQ) We tested three hypotheses of in-terest that is H1 the price gap anomaly exists H1minus1 prices tend to rise after positivegaps H1minus2 prices tend to fall after negative gaps H2 the price gap anomaly evolvesand H3 there is seasonality in price gaps Various statistical methods including para-metric tests (Students t-tests ANOVA) non-parametric tests (Mann-Whitney test)regression analysis with dummy variables MCAR approach and the trading simulationapproach were utilised

We conclude that the US stock market in the main did not exhibit seasonality in pricegaps Therefore H3 is rejected Furthermore no evidence was found that price gaps inthe US stock market were filled within five days of their occurrence However strongevidence in favour of abnormal price movements after the gaps were found confirming

15

H1 and H2 Particularly on the day of the occurrence of the gap and not on the dayafter the price gap In the DJI and the SampP 500 this pattern persists indicating thatthese markets take a day to incorporate new information As the results of the tradingsimulation indicate a day is enough to profit from a price gap anomaly trading strategyin the DJI and the SampP 500

Similar to other studies and other anomalies (see McLean and Pontiff (2016) Ca-jueiro and Tabak (2004) and Tiwari et al (2019) for example) the price gap anomalyevolved It is less prevalent since the 1990s as shown in the SampP 500 and NASDAQThis pattern of evolution is common amongst most stock market anomalies (see Plastunet al (2019b) on calendar anomalies amongst others) Our findings therefore add onto the existing literature Finally in the main our results are against the EMH and aretherefore interesting to both practitioners and academics

16

References

Agrawal A and Tandon K (1994) Anomalies or illusions evidence from stock marketsin eighteen countries Journal of international Money and Finance 13(1)83ndash106

Akerlof G A and Shiller R J (2009) Animal Spirits How human psychology drivesthe economy and why it matters for global capitalism Princeton University Press

Basu S (1977) Investment performance of common stocks in relation to their price-earnings ratios A test of the efficient market hypothesis The Journal of Finance32(3)663ndash682

Bildik R (2004) Are calendar anomalies still alive Evidence from istanbul stockexchange SSRN Electronic Journal 2004

Cai J Li Y and Qi Y (2006) The day-of-the-week effect New evidence from theChinese stock market Chinese Economy 39(2)71ndash88

Cajueiro D O and Tabak B M (2004) The Hurst exponent over time testing theassertion that emerging markets are becoming more efficient Physica A StatisticalMechanics and its Applications 336(3-4)521ndash537

Caporale G M Gil-Alana L Plastun A and Makarenko I (2016) Intraday anoma-lies and market efficiency A trading robot analysis Computational Economics47(2)275ndash295

Caporale G M and Plastun A (2017) Price gaps Another market anomaly Invest-ment Analysts Journal 46(4)279ndash293

Cross F (1973) The behavior of stock prices on Fridays and Mondays FinancialAnalysts Journal 29(6)67ndash69

Fama E F (1965) The behavior of stock-market prices The Journal of Business38(1)34ndash105

Fama E F (1970) Efficient capital markets A review of theory and empirical workThe Journal of Finance 25(2)383ndash417

Fortune P (1998) Weekends can be rough revisiting the weekend effect in stock pricesTechnical report

Fortune P (1999) Are stock returns different over weekends A jump diffusion analysisof the weekend effect New England Economic Review 103ndash19

French K R (1980) Stock returns and the weekend effect Journal of FinancialEconomics 8(1)55ndash69

Fung A K-W Lam K and Lam K-M (2010) Do the prices of stock index futuresin asia overreact to us market returns Journal of Empirical Finance 17(3)428ndash440

17

Gibbons M R and Hess P (1981) Day of the week effects and asset returns Journalof business pages 579ndash596

Grant J L Wolf A and Yu S (2005) Intraday price reversals in the us stock indexfutures market A 15-year study Journal of Banking amp Finance 29(5)1311ndash1327

Grossman S J and Stiglitz J E (1980) On the impossibility of informationallyefficient markets The American Economic Review 70(3)393ndash408

Jacobsen B Mamun A and Visaltanachoti N (2005) Seasonal size and valueanomalies

Jensen M (1978) Some anomalous evidence regarding market efficiency Journal ofFinancial Economics 6(23 (1978))95ndash101

Lakonishok J and Smidt S (1988) Are seasonal anomalies real A ninety-year per-spective The Review of Financial Studies 1(4)403ndash425

MacKinlay A (1997) Event studies in economics and finance Journal of EconomicLiterature (35)113ndash39

Mandelbrot B B (1997) The variation of certain speculative prices In Fractals andscaling in finance pages 371ndash418 Springer

McLean R D and Pontiff J (2016) Does academic research destroy stock returnpredictability The Journal of Finance 71(1)5ndash32

Plastun A Makarenko I Khomutenko L Shcherbak S and Tryfonova O (2019a)Exploring price gap anomaly in the ukrainian stock market Investment Managementamp Financial Innovations 16(2)150

Plastun A Sibande X Gupta R and Wohar M E (2019b) Rise and fall of calendaranomalies over a century The North American Journal of Economics and Finance49181ndash205

Schwert G W (2003) Chapter 15 anomalies and market efficiency In FinancialMarkets and Asset Pricing volume 1 of Handbook of the Economics of Finance pages939 ndash 974 Elsevier

Shiller R J (2000) Irrational exuberance Princeton University

Tiwari A K Aye G C and Gupta R (2019) Stock market efficiency analysis usinglong spans of data A multifractal detrended fluctuation approach Finance ResearchLetters 28398ndash411

Yuan Y (2015) Market-wide attention trading and stock returns Journal of FinancialEconomics 116(3)548ndash564

18

Appendices

A DJI and NASDAQ Summary Results

A1 Overall Results

Table A1 Gap size used for different sub-periods over the period 1929-2018

Period DJI NASDAQ1929-1938 - -1939-1948 - -1949-1958 - 0711959-1968 - 0951969-1978 - 1351979-1988 - 1101989-1998 040 0681999-2008 007 1502009-2018 020 110Overall data set 030 110

Table A2 Day of the week and gaps

Day of the week DJI NASDAQMonday 024 02Tuesday 02 02Wednesday 017 02Thursday 019 019Friday 021 02

A2 Statistical tests

Table A3 Results of the statistical tests for the overall data sets

PeriodMethod Averageanalysis

t-test ANOVAtest

Mann-Whitney

test

Regressionanalysiswith

dummyvariables

ModifiedCAR

approach

Overall

Dow Jones Index overall data setGap day - - - - - + 1Gap day (Positive gaps) + - - - - - 1Gap day (Negative gaps) + - - - - + 2Day after gap (Positive gaps) + - - - - - 1Day after gap (Negative gaps) + - - + - + 3

NASDAQ overall data setGap day + + + + + + 6Gap day (Positive gaps) + + + + + + 6Gap day (Negative gaps) + + + + + + 6Day after gap (Positive gaps) + + + + + + 6Day after gap (Negative gaps) + + + + + + 6

Note + indicates that the anomaly is confirmed and - indicates that anomaly is not confirmedThe higher the overall rating the stronger the evidence of the anomaly

19

Table A4 Results of the statistical tests for H1minus1 DJI

Period Averageanalysis

t-test ANOVA test Mann-Whitney

test

Regressionanalysis with

dummyvariables

ModifiedCAR

approach

Overall

Day of anomaly1989-1998 + - - - - + 21999-2008 + + + + + + 62009-2018 + + + + + + 6

Day after anomaly1989-1998 + - - - - + 21999-2008 + - - - - + 22009-2018 - - - - - - 0

Note + indicates that the anomaly is confirmed and - indicates that anomaly is not confirmedThe higher the overall rating the stronger the evidence of the anomaly

Table A5 Results of the statistical tests for H1minus2 DJI

Period Averageanalysis

t-test ANOVA test Mann-Whitneytest

Regressionanalysis with

dummyvariables

Modified CARapproach

Overall

Day of anomaly1989-1998 - - - - - - 01999-2008 + + + + + + 62009-2018 + + + + + + 6

Day after anomaly1989-1998 + - - - - + 21999-2008 + - - - - - 12009-2018 + - - - - + 2

Note + indicates that the anomaly is confirmed and - indicates that anomaly is not confirmedThe higher the overall rating the stronger the evidence of the anomaly

Table A6 Results of the statistical tests for H1minus1 NASDAQ

PeriodMethod Averageanalysis

t-test ANOVA test Mann-Whitney

test

Regressionanalysis with

dummyvariables

ModifiedCAR

approach

Overall

Day of anomaly1949-1958 + + + + + + 61959-1968 + + + + + + 61969-1978 + + + + + + 61979-1988 + + + + + + 61989-1998 + - - - - + 21999-2008 + - + + + + 52009-2018 + + + + + + 6

Day after anomaly1949-1958 + + + + + + 61959-1968 + + + + + + 61969-1978 + + + + + + 61979-1988 + + + + + + 61989-1998 + - + - + + 41999-2008 - - - - - - 02009-2018 + - - - - + 2

Note + indicates that the anomaly is confirmed and - indicates that anomaly is not confirmedThe higher the overall rating the stronger the evidence of the anomaly

20

Table A7 Results of the statistical tests for H1minus2 NASDAQ

PeriodMethod Averageanalysis

t-test ANOVA test Mann-Whitney

test

Regressionanalysis with

dummyvariables

ModifiedCAR

approach

Overall

Day of anomaly1949-1958 + + + + + + 61959-1968 + + + + + + 61969-1978 + + + + + + 61979-1988 + + + + + + 61989-1998 - - - - - + 11999-2008 - - + - - - 12009-2018 - - - - - - 0

Day after anomaly1949-1958 + + + + + + 61959-1968 + + + + + + 61969-1978 + + + + + + 61979-1988 + + + + + + 61989-1998 + - - - - - 11999-2008 - - - - - + 12009-2018 + - - + + + 4

Note + indicates that the anomaly is confirmed and - indicates that anomaly is not confirmedThe higher the overall rating the stronger the evidence of the anomaly

A3 Trading Simulation Results

Table A8 Trading simulation results of the price gap anomaly for the DJI 1989-2018

Period Gap type Number oftradesunits

Number ofsuccessfultradesunits

Number ofsuccessfultrades

Profit Profit per year

z-test Result

1989-1998 Up 102 46 451 -11 -01 011 failedDown 116 49 422 -267 -27 242 passed

1999-2008 Up 73 51 699 665 66 37 passedDown 143 81 566 641 64 331 passed

2009-2018 Up 127 88 693 308 31 327 passedDown 81 47 58 196 2 184 passed

21

B Short-term price behavior in DJI SampP 500 and

NASDAQ Price gaps (overall data sets)

Table B1 Momentum effect in the US stock market after the gap

Instrument Parameter Number of days after the gap1 2 3

Dow Jones Index Positive gaps 53 57 61Negative gaps 50 50 47

All gaps 51 54 54SampP 500 Index Positive gaps 40 63 60

Negative gaps 4 52 45All gaps 4 58 53

NASDAQ Positive gaps 32 65 67Negative gaps 24 63 59

All gaps 28 64 63

Table B2 Momentum effect in the US stock market before the gap

Instrument Parameter Number of days before the gap1 2 3

Dow Jones Index Positive gaps 56 49 52Negative gaps 54 49 49

All gaps 55 49 50SampP 500 Index Positive gaps 57 57 52

Negative gaps 60 59 54All gaps 58 58 53

NASDAQ Positive gaps 61 56 54Negative gaps 68 69 70

All gaps 64 63 63

Table B3 Fill gap effect in the US stock market

Instrument Parameter Number of days after the gap1 2 3 4 5

Dow Jones Index Positive gaps 22 28 26 30 28Negative gaps 25 33 36 42 46

All gaps 24 30 31 35 37SampP 500 Index Positive gaps 0 6 11 16 19

Negative gaps 1 10 19 26 27All gaps 1 8 15 20 23

NASDAQ Positive gaps 8 13 18 21 19Negative gaps 7 11 17 21 25

All gaps 8 12 18 21 22

22

C Detailed statistical results DJI overall data

C1 Average analysis

Table C1 Average analysis

Parameter Gap day Gap day(Positive gaps)

Gap day(Negative gaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Mean return (gap day) 003 006 0 005 -003Mean return (non-gap day) 004 004 004 004 004Anomaly not confirmed not confirmed confirmed not confirmed confirmed

C2 Parametric tests Students t-test

Table C2 T-test

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

t-criterion 016 042 053 015 104t-critical (=095) 196 196 196 196 196Null hypothesis not rejected not rejected not rejected not rejected not rejected

C3 Parametric tests ANOVA

Table C3 ANOVA

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

F 0036 018 053 003 14p-value 085 067 047 086 024F critical 384 384 384 384 384Null hypothesis not rejected not rejected not rejected not rejected not rejected

C4 Non-parametric tests Kruskal-Wallis test

Table C4 Kruskal -Wallis test

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Adjusted H 082 012 126 0 455df 1 1 1 1 1P value 037 073 026 095 003Critical value 384 384 384 384 384Null hypothesis not rejected not rejected not rejected not rejected rejected

23

C5 Regression analysis with dummy variables

Table C5 Regression analysis with dummy variables

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

a0 00004 (000) 00004 (000) 00004 (000) 00004 (000) 00004 (000)a1 -00001 (-019) 00002 (067) -00004 (047) 00001 (086) -00007 (024)Anomaly not confirmed not confirmed not confirmed not confirmed not confirmed

C6 Modified CAR approach

Table C6 Modified CAR approach

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Multiple R 049 05 025 0 092F-test 23347 (000) 12913 (000) 2207 (000) 000 (098) 1822 (000)a0 -00041 (060) 00128 (006) -00267 (000) 00354 (000) 00319 (000)a1 -00003 (000) -00003 (000) -00002 (000) 00000 (098) -00008 (000)Anomaly confirmed confirmed confirmed not confirmed confirmed

24

D Detailed statistical results SampP 500 overall data

D1 Average analysis

Table D1 Average analysis

Parameter Gap day Gap day(Positive gaps)

Gap day(Negative gaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Mean return (gap day) 006 115 -129 017 -011Mean return (non-gap day) 002 002 002 002 002Anomaly confirmed confirmed confirmed confirmed confirmed

D2 Parametric tests Students t-test

Table D2 T-test

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

t-criterion 092 4546 3579 485 271t-critical (=095) 196 196 196 196 196Null hypothesis not rejected rejected rejected rejected rejected

D3 Parametric tests ANOVA

Table D3 ANOVA

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

F 155 116211 126952 1866 136p-value 022 0 0 0 0F critical 384 384 384 384 384Null hypothesis not rejected rejected rejected not rejected not rejected

D4 Non-parametric tests Kruskal-Wallis test

Table D4 Kruskal-Wallis test

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Adjusted H 1352 70516 47237 3946 004df 1 1 1 1 1P value 0 0 0 0 084Critical value 384 384 384 384 384Null hypothesis rejected rejected rejected rejected not rejected

25

D5 Regression analysis with dummy variables

Table D5 Regression analysis with dummy variables

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

a0 00002 (000) 00002 (000) 00002 (000) 00002 (000) 00002 (000)a1 00003 (021) 00113 (000) -00132 (000) 00014 (000) -00014 (000)Anomaly not confirmed confirmed confirmed confirmed confirmed

D6 Modified CAR approach

Table D6 Modified CAR approach

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Multiple R 051 099 099 099 096F-test 69486 (000) 325351 (000) 1457582 (000) 6345973 (000) 1213344 (000)a0 -01003(000) 04081 (000) -05444 (000) -01088 (000) 00272 (000)a1 00002 (000) 00106 (000) -00127 (000) 00016 (000) -00016 (000)Anomaly confirmed confirmed confirmed confirmed confirmed

26

E Detailed statistical results NASDAQ overall data

E1 Average analysis

Table E1 Average analysis

Parameter Gap day Gap day(Positive gaps)

Gap day(Negative gaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Mean return (gap day) -009 084 -090 022 -037Mean return (non-gap day) 003 003 003 003 003Anomaly confirmed confirmed confirmed confirmed confirmed

E2 Parametric tests Students t-test

Table E2 T-test

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

t-criterion 230 1257 1341 306 664t-critical (=095) 196 196 196 196 196Null hypothesis rejected rejected rejected rejected rejected

E3 Parametric tests ANOVA

Table E3 ANOVA

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

F 2289 62720 88402 3330 17356p-value 0 0 0 0 0F critical 384 384 384 384 384Null hypothesis rejected rejected rejected rejected rejected

E4 Non-parametric tests Kruskal-Wallis test

Table E4 Kruskal-Wallis test

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Adjusted H 1892 36022 45248 4695 10437df 1 1 1 1 1P value 0 0 0 0 0Critical value 384 384 384 384 384Null hypothesis rejected rejected rejected rejected rejected

27

E5 Regression analysis with dummy variables

Table E5 Regression analysis with dummy variables

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

a0 00003 (000) 00003 (000) 00003 (000) 00003 (000) 00003 (000)a1 -00012 (000) 00081 (000) -00093 (000) 00018 (000) -00040 (000)Anomaly confirmed confirmed confirmed confirmed confirmed

E6 Modified CAR approach

Table E6 Modified CAR approach

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Multiple R 069 092 092 072 097F-test 133255 (000) 361102 (000) 442376 (000) 72903 (000) 1082812 (000)a0 -10646 (000) 11373 (000) -12888 (000) 03928 (000) -02297 (000)a1 -00011 (000) 00073 (000) -00097 (000) 00017 (000) -00039 (000)Anomaly confirmed confirmed confirmed confirmed confirmed

28

F Detailed statistical results DJI sub-periods

F1 Average analysis

Table F1 Average analysis

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 Mean return (gapday)

-001 023 015 -004

Mean return(non-gap day)

007 007 007 007

Anomaly confirmed confirmed confirmed confirmed1999-2008 Mean return (gap

day)090 -045 013 -004

Mean return(non-gap day)

-004 -004 -004 -004

Anomaly confirmed confirmed confirmed confirmed2009-2018 Mean return (gap

day)024 -024 0 -004

Mean return(non-gap day)

004 004 004 004

Anomaly confirmed confirmed not confirmed confirmed

F2 Parametric tests Students t-test

Table F2 T-test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 t-criterion 083 165 087 139t-critical (=095) 196 196 196 196Null hypothesis not rejected not rejected not rejected not rejected

1999-2008 t-criterion 347 351 054 047t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected rejected

2009-2018 t-criterion 265 207 051 058t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

F3 Parametric tests ANOVA

Table F3 ANOVA

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 F 085 409 093 179p-value 035 004 033 018

F critical 384 384 384 384Null hypothesis not rejected rejected not rejected not rejected

1999-2008 F 5405 3196 065 072p-value 0 0 042 039

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

2009-2018 F 554 697 024 058p-value 001 0 062 044

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

29

F4 Non-parametric tests Kruskal-Wallis test

Table F4 Kruskal-Wallis test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 Adjusted H 113 211 113 332df 1 1 1 1

P value 029 015 029 007Null hypothesis not rejected not rejected not rejected not rejected

1999-2008 Adjusted H 1484 1414 003 139df 1 1 1 1

P value 0 0 086 024Null hypothesis rejected rejected not rejected not rejected

2009-2018 Adjusted H 506 68 051 171df 1 1 1 1

P value 002 001 047 019Null hypothesis rejected rejected not rejected not rejected

F5 Regression analysis with dummy variables

Table F5 Regression analysis with dummy variables

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 a0 000068 (000) 00007 (000) 00007 (000) 00007 (000)a1 -000078 (035) 00016 (004) 00008 (033) -00011 (018)

Anomaly not confirmed confirmed not confirmed not confirmed1999-2008 a0 00004 (008) 00004 (008) 00004 (006) 00004 (008)

a1 00087 (000) -00049 (000) 00009 (042) -00008 (039)Anomaly confirmed confirmed not confirmed not confirmed

2009-2018 a0 00004 (006) 00004 (006) 00004 (006) 00004 (006)a1 00021 (001) -00028 (001) -00004 (062) -00008 (047)

Anomaly confirmed confirmed not confirmed not confirmed

F6 Modified CAR approach

Table F6 Modified CAR approach

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 Multiple R 083 088 082 086F-test 22779 (000) 40583 (000) 20401 (000) 3269454 (000)a0 00042 (023) 00017 (073) 00014 (058) -00266 (000)a1 -00009 (000) 00015 (000) 00006 (000) -00009 (000)

Anomaly confirmed confirmed confirmed confirmed1999-2008 Multiple R 095 093 076 019

F-test 62658 (000) 84712 (000) 10056 (000) 492 (003)a0 -00972 (000) 00365 (000) -00198 (000) -00115 (021)a1 00086 (000) -00042 (000) 00014 (000) 00002 (003)

Anomaly confirmed confirmed confirmed not confirmed2009-2018 Multiple R 096 082 08 05

F-test 150452 (000) 16731 (000) 22287 (000) 2620 (000)a0 00548 (000) -00618 (000) 00031 (020) -00112 (000)a1 00013 (000) -00014 (000) -00005 (000) -00004 (000)

Anomaly confirmed confirmed not confirmed confirmed

30

G Detailed statistical results NASDAQ sub-periods

G1 Average analysis

Table G1 Average analysis

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 Mean return (gapday)

094 -111 0189 -029

Mean return(non-gap day)

007 007 007 007

Anomaly confirmed confirmed confirmed confirmed1959-1968 Mean return (gap

day)133 -147 033 -039

Mean return(non-gap day)

006 006 006 006

Anomaly confirmed confirmed confirmed confirmed1969-1978 Mean return (gap

day)19 -186 057 -068

Mean return(non-gap day)

005 005 005 005

Anomaly confirmed confirmed confirmed confirmed1979-1988 Mean return (gap

day)138 -162 066 -04

Mean return(non-gap day)

008 008 008 008

Anomaly confirmed confirmed confirmed confirmed1989-1998 Mean return (gap

day)016 012 018 -009

Mean return(non-gap day)

002 002 002 002

Anomaly confirmed not confirmed confirmed confirmed1999-2008 Mean return (gap

day)38E-3 027 -036 -013

Mean return(non-gap day)

-01 -01 -01 -01

Anomaly confirmed not confirmed not confirmed not confirmed2009-2018 Mean return (gap

day)039 009 013 -025

Mean return(non-gap day)

001 001 001 001

Anomaly confirmed not confirmed confirmed confirmed

G2 Parametric tests Students t-test

Table G2 T-test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 t-criterion 3194 3076 201 559t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected rejected

1959-1968 t-criterion 1399 2246 443 382t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected rejected

1969-1978 t-criterion 261 4358 417 786t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected rejected

1979-1988 t-criterion 1847 1445 709 395t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected rejected

1989-1998 t-criterion 13 066 126 093t-critical (=095) 196 196 196 196Null hypothesis not rejected not rejected not rejected not rejected

1999-2008 t-criterion 192 106 111 009t-critical (=095) 196 196 196 196Null hypothesis not rejected not rejected not rejected not rejected

2009-2018 t-criterion 27 05 089 188t-critical (=095) 196 196 196 196Null hypothesis rejected not rejected not rejected not rejected

31

G3 Parametric tests ANOVA

Table G3 ANOVA

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 F 88153 190609 1272 14521p-value 0 0 0 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1959-1968 F 93974 149771 4715 10418p-value 0 0 0 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1969-1978 F 84546 145429 6295 18241p-value 0 0 0 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1979-1988 F 66952 110482 13138 8626p-value 0 0 0 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1989-1998 F 323 138 43 168p-value 007 024 003 019

F critical 384 384 384 384Null hypothesis not rejected not rejected rejected not rejected

1999-2008 F 106 512 327 003p-value 001 002 007 085

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

2009-2018 F 169 069 175 93p-value 0 04 018 0

F critical 384 384 384 384Null hypothesis rejected not rejected not rejected rejected

G4 Non-parametric tests Kruskal-Wallis test

Table G4 Kruskal-Wallis test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 Adjusted H 26254 32592 1464 3962df 1 1 1 1

P value 0 0 0 0Null hypothesis rejected rejected rejected rejected

1959-1968 Adjusted H 28235 27989 2736 332df 1 1 1 1

P value 0 0 0 0Null hypothesis rejected rejected rejected rejected

1969-1978 Adjusted H 22202 33777 3311 7591df 1 1 1 1

P value 0 0 0 0Null hypothesis rejected rejected rejected rejected

1979-1988 Adjusted H 23282 25292 4812 3964df 1 1 1 1

P value 0 0 0 0Null hypothesis rejected rejected rejected rejected

1989-1998 Adjusted H 381 017 175 132df 1 1 1 1

P value 005 068 019 025Null hypothesis not rejected not rejected not rejected not rejected

1999-2008 Adjusted H 855 023 044 004df 1 1 1 1

P value 0 063 051 084Null hypothesis rejected not rejected not rejected not rejected

2009-2018 Adjusted H 1063 009 257 709df 1 1 1 1

P value 0 077 011 001Null hypothesis rejected not rejected not rejected rejected

32

G5 Regression analysis with dummy variables

Table G5 Regression analysis with dummy variables

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 a0 00007 (000) 00007 (000) 00007 (000) 00007 (000)a1 00088 (000) -00119 (000) 00011 (000) -00036 (000)

Anomaly confirmed confirmed confirmed confirmed1959-1968 a0 00006 (000) 00006 (000) 00006 (000) 00006 (000)

a1 00128 (000) -00153 (000) 00027 (000) -00046 (000)Anomaly confirmed confirmed confirmed confirmed

1969-1978 a0 00005 (000) 00005 (000) 00005 (000) 00005 (000)a1 00185 (000) -00192 (000) 00053 (000) -00073 (000)

Anomaly confirmed confirmed confirmed confirmed1979-1988 a0 00008 (000) 00008 (000) 00008 (000) 00008 (000)

a1 00131 (000) -00172 (000) 00059 (000) -00048 (000)Anomaly confirmed confirmed confirmed confirmed

1989-1998 a0 00002 (027) 00002 (028) 00002 (028) 00002 (027)a1 00014 (007) 00010 (024) 00017 (004) -00011 (019)

Anomaly not confirmed not confirmed confirmed not confirmed1999-2008 a0 00001 (059) 00001 (062) 00001 (059) 00001 (060)

a1 00037 (000) 00026 (002) -00038 (000) -00014 (019)Anomaly confirmed not confirmed not confirmed not confirmed

2009-2018 a0 00001 (049) 00001 (049) 00001 (049) 00001 (049)a1 00038 (000) 00007 (040) 00012 (018) -00027 (000)

Anomaly confirmed not confirmed not confirmed confirmed

G6 Modified CAR approach

Table G6 Modified CAR approach

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 Multiple R 099 099 093 098F-test 5753605 (000) 100470(000) 6280421 283281a0 -00091 (000) -00349 (000) 00056 (001) 00015 (073)a1 00083 (000) -00110 (000) 00010 (000) -00031 (000)

Anomaly confirmed confirmed confirmed confirmed1959-1968 Multiple R 099 099 099 099

F-test 3923274 (000) 3005562 (000) 443198 (000) 372583 (000)a0 00096 (000) 00073 (016) -00082 (000) -00095 (004)a1 00116 (001) -00149 (000) 00025 (000) -00047 (000)

Anomaly confirmed confirmed confirmed confirmed1969-1978 Multiple R 099 099 098 099

F-test 4302608 (000) 2723953 (000) 179969 (000) 639745a0 00246 (000) -00002 (000) 00217 (000) -00514 (000)a1 00176 (000) -00182 (000) 00049 (000) -00062 (000)

Anomaly confirmed confirmed confirmed confirmed1979-1988 Multiple R 099 099 099 099

F-test 5872335 (000) 1182609 (000) 1083558 (000) 910089 (000)a0 00136 (000) -01081 (000) -00285 (000) -00101 (000)a1 00131 (000) -00167 (000) 00062 (000) -00048 (000)

Anomaly confirmed confirmed confirmed confirmed1989-1998 Multiple R 09 056 069 016

F-test 46947 (000) 4885 (000) 10131 (000) 263 (011)a0 00102 (002) -00261 (000) -0016 (001) -00237 (000)a1 00015 (000) 00010 (000) 0001 (000) 00002 (011)

Anomaly confirmed confirmed confirmed not confirmed1999-2008 Multiple R 093 087 073 037

F-test 71863 (000) 32530 (000) 13273 (000) 1669 (000)a0 00185 (004) 00311 (000) -00130 (039) -00546 (000)a1 00037 (000) 00032 (000) -00026 (000) -00007 (000)

Anomaly confirmed not confirmed not confirmed confirmed2009-2018 Multiple R 089 001 096 091

F-test 40818 (000) 000 (094) 116744 (000) 53770 (000)a0 01436 (000) -01099 (000) -01036 (000) 00697 (000)a1 00030 (000) 00000 (094) 00024 (000) -00021 (000)

Anomaly confirmed not confirmed confirmed confirmed

33

H Detailed statistical results SampP 500 sub-periods

H1 Average analysis

Table H1 Average analysis

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 Mean return (gapday)

138 -171 004 -014

Mean return(non-gap day)

0 0 0 0

Anomaly confirmed confirmed confirmed confirmed1939-1948 Mean return (gap

day)001 -042 172 -195

Mean return(non-gap day)

003 003 003 003

Anomaly confirmed confirmed confirmed confirmed1949-1958 Mean return (gap

day)165 -18 02 002

Mean return(non-gap day)

006 006 006 006

Anomaly confirmed confirmed confirmed not confirmed1959-1968 Mean return (gap

day)104 -102 015 0

Mean return(non-gap day)

002 002 002 002

Anomaly confirmed confirmed confirmed not confirmed1969-1978 Mean return (gap

day)131 -13 019 -03

Mean return(non-gap day)

0 0 0 0

Anomaly confirmed confirmed confirmed confirmed1979-1988 Mean return (gap

day)058 -042 015 003

Mean return(non-gap day)

005 005 005 005

Anomaly confirmed confirmed confirmed not confirmed1989-1998 Mean return (gap

day)02 -023 -002 01

Mean return(non-gap day)

007 007 007 007

Anomaly confirmed confirmed not confirmed not confirmed1999-2008 Mean return (gap

day)083 -089 -023 -005

Mean return(non-gap day)

001 001 001 001

Anomaly confirmed confirmed not confirmed confirmed2009-2018 Mean return (gap

day)055 -052 001 -015

Mean return(non-gap day)

004 004 004 004

Anomaly confirmed confirmed not confirmed confirmed

34

H2 Parametric tests Students t-test

Table H2 T-test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 t-criterion 101 85 029 048t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

1939-1948 t-criterion 064 479 3074 225t-critical (=095) 196 196 196 196Null hypothesis not rejected rejected rejected rejected

1949-1958 t-criterion 2964 2383 193 041t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

1959-1968 t-criterion 2281 2157 21 023t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected not rejected

1969-1978 t-criterion 1318 2034 187 321t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected rejected

1979-1988 t-criterion 435 535 07 037t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

1989-1998 t-criterion 201 396 132 052t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

1999-2008 t-criterion 362 433 117 022t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

2009-2018 t-criterion 375 382 027 132t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

H3 Parametric tests ANOVA

Table H3 ANOVA

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 F 6281 8032 005 051p-value 0 0 082 047

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

1939-1948 F 056 2603 34854 51034p-value 045 0 0 0

F critical 384 384 384 384Null hypothesis not rejected rejected rejected rejected

1949-1958 F 100174 128997 897 062p-value 0 0 0 043

F critical 384 384 384 384Null hypothesis rejected rejected rejected not rejected

1959-1968 F 36831 32858 617 01p-value 0 0 001 074

F critical 384 384 384 384Null hypothesis rejected rejected rejected not rejected

1969-1978 F 26601 3063 53 152p-value 0 0 002 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1979-1988 F 23 245 076 009p-value 0 0 039 077

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

1989-1998 F 399 1156 118 015p-value 004 0 027 069

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

1999-2008 F 4253 5622 365 024p-value 0 0 006 062

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

2009-2018 F 3064 3656 01 43p-value 0 0 075 004

F critical 384 384 384 384Null hypothesis rejected rejected not rejected rejected

35

H4 Non-parametric tests Kruskal -Wallis test

Table H4 Kruskal-Wallis test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 Adjusted H 9982 5913 332 14df 1 1 1 1

P value 0 0 007 024Null hypothesis rejected rejected not rejected not rejected

1939-1948 Adjusted H 494 1999 23387 24927df 1 1 1 1

P value 003 0 0 0Null hypothesis rejected rejected rejected rejected

1949-1958 Adjusted H 28728 28175 348 15df 1 1 1 1

P value 0 0 006 022Null hypothesis rejected rejected not rejected not rejected

1959-1968 Adjusted H 25729 21437 701 063df 1 1 1 1

P value 0 0 001 043Null hypothesis rejected rejected rejected not rejected

1969-1978 Adjusted H 14407 20078 27 1706df 1 1 1 1

P value 0 0 01 0Null hypothesis rejected rejected not rejected rejected

1979-1988 Adjusted H 1788 2836 027 034df 1 1 1 1

P value 0 0 06 056Null hypothesis rejected rejected not rejected not rejected

1989-1998 Adjusted H 251 1431 111 044df 1 1 1 1

P value 011 0 029 051Null hypothesis not rejected rejected not rejected not rejected

1999-2008 Adjusted H 1812 1788 042 002df 1 1 1 1

P value 0 0 052 089Null hypothesis rejected rejected not rejected not rejected

2009-2018 Adjusted H 1314 1783 074 37df 1 1 1 1

P value 0 0 039 005Null hypothesis rejected rejected not rejected not rejected

36

H5 Regression analysis with dummy variables

Table H5 Regression analysis with dummy variables

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 a0 00000 (097) 00000 (004) 00000 (097) 00000 (097)a1 00138 (000) -00172 (000) 00004 (082) -00014 (047)

Anomaly confirmed confirmed not confirmed not confirmed1939-1948 a0 00003 (015) 00003 (015) 00003 (015) 00003 (015)

a1 00007 (045) -00045 (000) 00170 (000) -00199 (000)Anomaly not confirmed confirmed confirmed confirmed

1949-1958 a0 00006 (000) 00006 (000) 00006 (000) 00006 (000)a1 00160 (000) -00188 (000) 00016 (000) -00004 (043)

Anomaly confirmed confirmed confirmed not confirmed1959-1968 a0 00002 (007) 00002 (004) 00002 (008) 00002 (008)

a1 00103 (000) -00105 (000) 00014 (001) -00002 (074)Anomaly confirmed confirmed confirmed not confirmed

1969-1978 a0 00000 (078) 00000 (078) 00000 (078) 00000 (078)a1 00132 (000) -00132 (000) 00019 (002) -00030 (000)

Anomaly confirmed confirmed confirmed confirmed1979-1988 a0 00006 (001) 00006 (001) 00006 (001) 00006 (000)

a1 00053 (000) -00048 (000) 00009 (040) -00003 (075)Anomaly confirmed confirmed not confirmed not confirmed

1989-1998 a0 00007 (000) 00007 (000) 00007 (000) 00007 (000)a1 00016 (005) -00030 (000) -00009 (026) 00003 (072)

Anomaly confirmed confirmed not confirmed not confirmed1999-2008 a0 00001 (075) 00001 (075) 00001 (075) 00001 (076)

a1 00083 (000) -00091 (000) -00024 (005) -00006 (062)Anomaly confirmed confirmed not confirmed not confirmed

2009-2018 a0 00004 (003) 00004 (000) 00004 (003) 00004 (003)a1 00051 (000) -00059 (000) -00003 (075) -00019 (003)

Anomaly confirmed confirmed not confirmed confirmed

37

H6 Modified CAR approach

Table H6 Modified CAR approach

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 Multiple R 096 095 046 046F-test 175935 (000) 96500 (000) 3534 (000) 2880 (000)a0 -01070 (000) 01958 (000) 00405 (000) 00535 (000)a1 00121 (000) -00160 (000) 00006 (000) -00014 (000)

Anomaly confirmed confirmed confirmed confirmed1939-1948 Multiple R 08 099 099 099

F-test 18777 (000) 755727 (000) 3572830 (000) 2696099 (000)a0 00019 (073) -00346 (000) -00373 (000) 00912 (000)a1 00012 (000) -00044 (000) 00168 (000) -00197 (000)

Anomaly confirmed confirmed confirmed confirmed1949-1958 Multiple R 099 099 094 015

F-test 1021705 (000) 7171257 (000) 75858 (000) 242 (012)a0 -00176 (000) -00191 (000) 00095 (000) -00498 (000)a1 00154 (000) -00181 (000) 00013 (000) -00002 (012)

Anomaly confirmed confirmed confirmed not confirmed1959-1968 Multiple R 099 099 094 078

F-test 1463311 (000) 6002659 (000) 82273 (000) 14352 (000)a0 -00112 (000) 00004 (085) 00151 (000) 00389 (000)a1 00098 (000) -00102 (000) 00011 (000) -00009 (000)

Anomaly confirmed confirmed confirmed confirmed1969-1978 Multiple R 098 099 093 099

F-test 241655 (000) 1451901 (000) 57333 (000) 368160 (000)a0 -00433 (000) 00276 (000) 00099 (002) -00144 (000)a1 00132 (000) -00134 (000) 00020 (000) -00030 (000)

Anomaly confirmed confirmed confirmed confirmed1979-1988 Multiple R 092 078 023 008

F-test 53757 (000) 18707 (000) 487 (003) 085 (036)a0 00813 (000) -02508 (000) 00204 (000) -00235 (000)a1 00036 (000) -00031 (000) -00003 (003) -00001 (036)

Anomaly confirmed confirmed not confirmed not confirmed1989-1998 Multiple R 079 099 074 044

F-test 19705(000) 761967 (000) 14133 (000) 2369 (000)a0 00268 (000) 00023 (021) -00381 (000) 00087 (000)a1 00013 (000) -00028 (000) -00008 (000) 00002 (000)

Anomaly confirmed confirmed not confirmed not confirmed1999-2008 Multiple R 091 093 071 065

F-test 47218 (000) 76564 (000) 9843 (000) 7768 (000)a0 -01493 (000) 01351 (000) 00397 (000) 00007 (093)a1 00081 (000) -00083 (000) -00026 (000) -00011 (000)

Anomaly confirmed confirmed not confirmed confirmed2009-2018 Multiple R 086 087 083 074

F-test 29971 (000) 32484 (000) 23228 (000) 12764 (000)a0 01711 (000) -02250 (000) 00407 (000) -00472 (000)a1 00038 (000) -00044 (000) -00010 (000) -00012 (000)

Anomaly confirmed confirmed not confirmed confirmed

38

Tab

le6

H1minus1summarystatisticalresults

SampP500sub-periods

PeriodM

ethod

Average

analysis

t-test

ANOVA

test

Man

n-

Whitney

test

Regression

analysis

withdummy

variab

les

Modified

CAR

approach

Overall

Dayofanomaly

1929-1938

++

++

++

61939-1948

+-

-+

-+

31949-1958

++

++

++

61959-1968

++

++

++

61969-1978

++

++

++

61979-1988

++

++

++

61989-1998

++

++

++

61999-2008

++

++

++

62009-2018

++

++

++

6Dayafteranomaly

1929-1938

+-

--

-+

21939-1948

++

++

++

61949-1958

+-

+-

++

51959-1968

++

++

++

61969-1978

+-

+-

++

41979-1988

+-

--

--

11989-1998

--

--

--

01999-2008

--

--

--

02009-2018

--

--

--

0

Note+

indicates

thattheanom

alyis

confirm

edand-indicates

thatan

omaly

isnot

confirm

edThehigher

theoverallrating

the

strongertheeviden

ceofthean

omaly

12

Tab

le7

H1minus2statisticalresults

SampP500sub-periods

PeriodM

ethod

Average

analysis

t-test

ANOVA

test

Man

n-

Whitney

test

Regression

analysiswith

dummy

variab

les

Modified

CAR

approach

Overall

Dayofanomaly

1929-1938

++

++

++

61939-1948

++

++

++

61949-1958

++

++

++

61959-1968

++

++

++

61969-1978

++

++

++

61979-1988

++

++

++

61989-1998

++

++

++

61999-2008

++

++

++

62009-2018

++

++

++

6Dayafteranomaly

1929-1938

+-

--

-+

21939-1948

++

++

++

61949-1958

--

--

--

01959-1968

--

--

-+

11969-1978

++

++

++

61979-1988

--

--

--

01989-1998

--

--

--

01999-2008

+-

--

-+

22009-2018

+-

+-

++

4

Note+

indicates

thattheanom

alyis

confirm

edand-indicates

thatan

omaly

isnot

confirm

edThehigher

theoverallrating

the

strongertheeviden

ceofthean

omaly

13

45 Trading simulation

The algorithm of the trading strategy is to buysell at the start of the updown gapday and close this position at the end of this day To test this strategy data for the DJIand SampP 500 are used (for this case the price anomaly still exists based on the day itoccurred) The results for DJI are presented in Table A8 and for the SampP 500 in Table8 For the SampP 500 and DJI the trading strategy built on price gap anomaly is efficientand its results differ from random

Table 8 Trading simulation results of the price gap anomaly for the SampP 500

Period Gaptype

Numberof

tradesunits

Numberof suc-cessfultradesunits

Numberof suc-cessfultrades

Profit

Profit peryear

z-test Result

1929-1938 Up 131 130 992 1816 182 1065 passedDown 110 108 982 1893 189 876 passed

1939-1948 Up 110 67 609 106 11 09 failedDown 122 79 648 518 52 465 passed

1949-1958 Up 106 105 991 1765 176 3191 passedDown 104 103 99 1891 189 2356 passed

1959-1968 Up 108 106 981 1331 113 2441 passedDown 92 91 989 948 95 2214 passed

1969-1978 Up 85 71 835 1128 113 1361 passedDown 96 90 938 1262 126 2118 passed

1979-1988 Up 92 63 685 54 54 495 passedDown 123 81 659 519 52 496 passed

1989-1998 Up 117 72 615 267 27 295 passedDown 99 61 616 228 23 32 passed

1999-2008 Up 99 65 657 828 83 373 passedDown 110 72 655 987 99 438 passed

2009-2018 Up 106 71 67 59 59 416 passedDown 107 65 607 56 56 362 passed

14

Figure 1 Trading simulation results of the price gap anomaly for the SampP 500

Note The primary axis refers to the percentage profit per year and the secondary to thez minus test statistic

One more interesting fact (see Figure 1) is the decrease of trading strategy efficiencyThis is indirect evidence in favour of evolution of the US stock market and its movementfrom less efficient to more efficient state Overall it can be concluded that the price gapanomaly is a real market anomaly The US stock market loses its efficiency after pricegaps This effect is temporary and lasts only for a day Still even this time is enoughto exploit the hole in the market efficiency and generate abnormal profits from trading

5 Conclusion

We analysed price gap anomaly in the US stock market by using information from threestock market indexes(DJI SampP 500 and NASDAQ) We tested three hypotheses of in-terest that is H1 the price gap anomaly exists H1minus1 prices tend to rise after positivegaps H1minus2 prices tend to fall after negative gaps H2 the price gap anomaly evolvesand H3 there is seasonality in price gaps Various statistical methods including para-metric tests (Students t-tests ANOVA) non-parametric tests (Mann-Whitney test)regression analysis with dummy variables MCAR approach and the trading simulationapproach were utilised

We conclude that the US stock market in the main did not exhibit seasonality in pricegaps Therefore H3 is rejected Furthermore no evidence was found that price gaps inthe US stock market were filled within five days of their occurrence However strongevidence in favour of abnormal price movements after the gaps were found confirming

15

H1 and H2 Particularly on the day of the occurrence of the gap and not on the dayafter the price gap In the DJI and the SampP 500 this pattern persists indicating thatthese markets take a day to incorporate new information As the results of the tradingsimulation indicate a day is enough to profit from a price gap anomaly trading strategyin the DJI and the SampP 500

Similar to other studies and other anomalies (see McLean and Pontiff (2016) Ca-jueiro and Tabak (2004) and Tiwari et al (2019) for example) the price gap anomalyevolved It is less prevalent since the 1990s as shown in the SampP 500 and NASDAQThis pattern of evolution is common amongst most stock market anomalies (see Plastunet al (2019b) on calendar anomalies amongst others) Our findings therefore add onto the existing literature Finally in the main our results are against the EMH and aretherefore interesting to both practitioners and academics

16

References

Agrawal A and Tandon K (1994) Anomalies or illusions evidence from stock marketsin eighteen countries Journal of international Money and Finance 13(1)83ndash106

Akerlof G A and Shiller R J (2009) Animal Spirits How human psychology drivesthe economy and why it matters for global capitalism Princeton University Press

Basu S (1977) Investment performance of common stocks in relation to their price-earnings ratios A test of the efficient market hypothesis The Journal of Finance32(3)663ndash682

Bildik R (2004) Are calendar anomalies still alive Evidence from istanbul stockexchange SSRN Electronic Journal 2004

Cai J Li Y and Qi Y (2006) The day-of-the-week effect New evidence from theChinese stock market Chinese Economy 39(2)71ndash88

Cajueiro D O and Tabak B M (2004) The Hurst exponent over time testing theassertion that emerging markets are becoming more efficient Physica A StatisticalMechanics and its Applications 336(3-4)521ndash537

Caporale G M Gil-Alana L Plastun A and Makarenko I (2016) Intraday anoma-lies and market efficiency A trading robot analysis Computational Economics47(2)275ndash295

Caporale G M and Plastun A (2017) Price gaps Another market anomaly Invest-ment Analysts Journal 46(4)279ndash293

Cross F (1973) The behavior of stock prices on Fridays and Mondays FinancialAnalysts Journal 29(6)67ndash69

Fama E F (1965) The behavior of stock-market prices The Journal of Business38(1)34ndash105

Fama E F (1970) Efficient capital markets A review of theory and empirical workThe Journal of Finance 25(2)383ndash417

Fortune P (1998) Weekends can be rough revisiting the weekend effect in stock pricesTechnical report

Fortune P (1999) Are stock returns different over weekends A jump diffusion analysisof the weekend effect New England Economic Review 103ndash19

French K R (1980) Stock returns and the weekend effect Journal of FinancialEconomics 8(1)55ndash69

Fung A K-W Lam K and Lam K-M (2010) Do the prices of stock index futuresin asia overreact to us market returns Journal of Empirical Finance 17(3)428ndash440

17

Gibbons M R and Hess P (1981) Day of the week effects and asset returns Journalof business pages 579ndash596

Grant J L Wolf A and Yu S (2005) Intraday price reversals in the us stock indexfutures market A 15-year study Journal of Banking amp Finance 29(5)1311ndash1327

Grossman S J and Stiglitz J E (1980) On the impossibility of informationallyefficient markets The American Economic Review 70(3)393ndash408

Jacobsen B Mamun A and Visaltanachoti N (2005) Seasonal size and valueanomalies

Jensen M (1978) Some anomalous evidence regarding market efficiency Journal ofFinancial Economics 6(23 (1978))95ndash101

Lakonishok J and Smidt S (1988) Are seasonal anomalies real A ninety-year per-spective The Review of Financial Studies 1(4)403ndash425

MacKinlay A (1997) Event studies in economics and finance Journal of EconomicLiterature (35)113ndash39

Mandelbrot B B (1997) The variation of certain speculative prices In Fractals andscaling in finance pages 371ndash418 Springer

McLean R D and Pontiff J (2016) Does academic research destroy stock returnpredictability The Journal of Finance 71(1)5ndash32

Plastun A Makarenko I Khomutenko L Shcherbak S and Tryfonova O (2019a)Exploring price gap anomaly in the ukrainian stock market Investment Managementamp Financial Innovations 16(2)150

Plastun A Sibande X Gupta R and Wohar M E (2019b) Rise and fall of calendaranomalies over a century The North American Journal of Economics and Finance49181ndash205

Schwert G W (2003) Chapter 15 anomalies and market efficiency In FinancialMarkets and Asset Pricing volume 1 of Handbook of the Economics of Finance pages939 ndash 974 Elsevier

Shiller R J (2000) Irrational exuberance Princeton University

Tiwari A K Aye G C and Gupta R (2019) Stock market efficiency analysis usinglong spans of data A multifractal detrended fluctuation approach Finance ResearchLetters 28398ndash411

Yuan Y (2015) Market-wide attention trading and stock returns Journal of FinancialEconomics 116(3)548ndash564

18

Appendices

A DJI and NASDAQ Summary Results

A1 Overall Results

Table A1 Gap size used for different sub-periods over the period 1929-2018

Period DJI NASDAQ1929-1938 - -1939-1948 - -1949-1958 - 0711959-1968 - 0951969-1978 - 1351979-1988 - 1101989-1998 040 0681999-2008 007 1502009-2018 020 110Overall data set 030 110

Table A2 Day of the week and gaps

Day of the week DJI NASDAQMonday 024 02Tuesday 02 02Wednesday 017 02Thursday 019 019Friday 021 02

A2 Statistical tests

Table A3 Results of the statistical tests for the overall data sets

PeriodMethod Averageanalysis

t-test ANOVAtest

Mann-Whitney

test

Regressionanalysiswith

dummyvariables

ModifiedCAR

approach

Overall

Dow Jones Index overall data setGap day - - - - - + 1Gap day (Positive gaps) + - - - - - 1Gap day (Negative gaps) + - - - - + 2Day after gap (Positive gaps) + - - - - - 1Day after gap (Negative gaps) + - - + - + 3

NASDAQ overall data setGap day + + + + + + 6Gap day (Positive gaps) + + + + + + 6Gap day (Negative gaps) + + + + + + 6Day after gap (Positive gaps) + + + + + + 6Day after gap (Negative gaps) + + + + + + 6

Note + indicates that the anomaly is confirmed and - indicates that anomaly is not confirmedThe higher the overall rating the stronger the evidence of the anomaly

19

Table A4 Results of the statistical tests for H1minus1 DJI

Period Averageanalysis

t-test ANOVA test Mann-Whitney

test

Regressionanalysis with

dummyvariables

ModifiedCAR

approach

Overall

Day of anomaly1989-1998 + - - - - + 21999-2008 + + + + + + 62009-2018 + + + + + + 6

Day after anomaly1989-1998 + - - - - + 21999-2008 + - - - - + 22009-2018 - - - - - - 0

Note + indicates that the anomaly is confirmed and - indicates that anomaly is not confirmedThe higher the overall rating the stronger the evidence of the anomaly

Table A5 Results of the statistical tests for H1minus2 DJI

Period Averageanalysis

t-test ANOVA test Mann-Whitneytest

Regressionanalysis with

dummyvariables

Modified CARapproach

Overall

Day of anomaly1989-1998 - - - - - - 01999-2008 + + + + + + 62009-2018 + + + + + + 6

Day after anomaly1989-1998 + - - - - + 21999-2008 + - - - - - 12009-2018 + - - - - + 2

Note + indicates that the anomaly is confirmed and - indicates that anomaly is not confirmedThe higher the overall rating the stronger the evidence of the anomaly

Table A6 Results of the statistical tests for H1minus1 NASDAQ

PeriodMethod Averageanalysis

t-test ANOVA test Mann-Whitney

test

Regressionanalysis with

dummyvariables

ModifiedCAR

approach

Overall

Day of anomaly1949-1958 + + + + + + 61959-1968 + + + + + + 61969-1978 + + + + + + 61979-1988 + + + + + + 61989-1998 + - - - - + 21999-2008 + - + + + + 52009-2018 + + + + + + 6

Day after anomaly1949-1958 + + + + + + 61959-1968 + + + + + + 61969-1978 + + + + + + 61979-1988 + + + + + + 61989-1998 + - + - + + 41999-2008 - - - - - - 02009-2018 + - - - - + 2

Note + indicates that the anomaly is confirmed and - indicates that anomaly is not confirmedThe higher the overall rating the stronger the evidence of the anomaly

20

Table A7 Results of the statistical tests for H1minus2 NASDAQ

PeriodMethod Averageanalysis

t-test ANOVA test Mann-Whitney

test

Regressionanalysis with

dummyvariables

ModifiedCAR

approach

Overall

Day of anomaly1949-1958 + + + + + + 61959-1968 + + + + + + 61969-1978 + + + + + + 61979-1988 + + + + + + 61989-1998 - - - - - + 11999-2008 - - + - - - 12009-2018 - - - - - - 0

Day after anomaly1949-1958 + + + + + + 61959-1968 + + + + + + 61969-1978 + + + + + + 61979-1988 + + + + + + 61989-1998 + - - - - - 11999-2008 - - - - - + 12009-2018 + - - + + + 4

Note + indicates that the anomaly is confirmed and - indicates that anomaly is not confirmedThe higher the overall rating the stronger the evidence of the anomaly

A3 Trading Simulation Results

Table A8 Trading simulation results of the price gap anomaly for the DJI 1989-2018

Period Gap type Number oftradesunits

Number ofsuccessfultradesunits

Number ofsuccessfultrades

Profit Profit per year

z-test Result

1989-1998 Up 102 46 451 -11 -01 011 failedDown 116 49 422 -267 -27 242 passed

1999-2008 Up 73 51 699 665 66 37 passedDown 143 81 566 641 64 331 passed

2009-2018 Up 127 88 693 308 31 327 passedDown 81 47 58 196 2 184 passed

21

B Short-term price behavior in DJI SampP 500 and

NASDAQ Price gaps (overall data sets)

Table B1 Momentum effect in the US stock market after the gap

Instrument Parameter Number of days after the gap1 2 3

Dow Jones Index Positive gaps 53 57 61Negative gaps 50 50 47

All gaps 51 54 54SampP 500 Index Positive gaps 40 63 60

Negative gaps 4 52 45All gaps 4 58 53

NASDAQ Positive gaps 32 65 67Negative gaps 24 63 59

All gaps 28 64 63

Table B2 Momentum effect in the US stock market before the gap

Instrument Parameter Number of days before the gap1 2 3

Dow Jones Index Positive gaps 56 49 52Negative gaps 54 49 49

All gaps 55 49 50SampP 500 Index Positive gaps 57 57 52

Negative gaps 60 59 54All gaps 58 58 53

NASDAQ Positive gaps 61 56 54Negative gaps 68 69 70

All gaps 64 63 63

Table B3 Fill gap effect in the US stock market

Instrument Parameter Number of days after the gap1 2 3 4 5

Dow Jones Index Positive gaps 22 28 26 30 28Negative gaps 25 33 36 42 46

All gaps 24 30 31 35 37SampP 500 Index Positive gaps 0 6 11 16 19

Negative gaps 1 10 19 26 27All gaps 1 8 15 20 23

NASDAQ Positive gaps 8 13 18 21 19Negative gaps 7 11 17 21 25

All gaps 8 12 18 21 22

22

C Detailed statistical results DJI overall data

C1 Average analysis

Table C1 Average analysis

Parameter Gap day Gap day(Positive gaps)

Gap day(Negative gaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Mean return (gap day) 003 006 0 005 -003Mean return (non-gap day) 004 004 004 004 004Anomaly not confirmed not confirmed confirmed not confirmed confirmed

C2 Parametric tests Students t-test

Table C2 T-test

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

t-criterion 016 042 053 015 104t-critical (=095) 196 196 196 196 196Null hypothesis not rejected not rejected not rejected not rejected not rejected

C3 Parametric tests ANOVA

Table C3 ANOVA

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

F 0036 018 053 003 14p-value 085 067 047 086 024F critical 384 384 384 384 384Null hypothesis not rejected not rejected not rejected not rejected not rejected

C4 Non-parametric tests Kruskal-Wallis test

Table C4 Kruskal -Wallis test

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Adjusted H 082 012 126 0 455df 1 1 1 1 1P value 037 073 026 095 003Critical value 384 384 384 384 384Null hypothesis not rejected not rejected not rejected not rejected rejected

23

C5 Regression analysis with dummy variables

Table C5 Regression analysis with dummy variables

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

a0 00004 (000) 00004 (000) 00004 (000) 00004 (000) 00004 (000)a1 -00001 (-019) 00002 (067) -00004 (047) 00001 (086) -00007 (024)Anomaly not confirmed not confirmed not confirmed not confirmed not confirmed

C6 Modified CAR approach

Table C6 Modified CAR approach

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Multiple R 049 05 025 0 092F-test 23347 (000) 12913 (000) 2207 (000) 000 (098) 1822 (000)a0 -00041 (060) 00128 (006) -00267 (000) 00354 (000) 00319 (000)a1 -00003 (000) -00003 (000) -00002 (000) 00000 (098) -00008 (000)Anomaly confirmed confirmed confirmed not confirmed confirmed

24

D Detailed statistical results SampP 500 overall data

D1 Average analysis

Table D1 Average analysis

Parameter Gap day Gap day(Positive gaps)

Gap day(Negative gaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Mean return (gap day) 006 115 -129 017 -011Mean return (non-gap day) 002 002 002 002 002Anomaly confirmed confirmed confirmed confirmed confirmed

D2 Parametric tests Students t-test

Table D2 T-test

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

t-criterion 092 4546 3579 485 271t-critical (=095) 196 196 196 196 196Null hypothesis not rejected rejected rejected rejected rejected

D3 Parametric tests ANOVA

Table D3 ANOVA

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

F 155 116211 126952 1866 136p-value 022 0 0 0 0F critical 384 384 384 384 384Null hypothesis not rejected rejected rejected not rejected not rejected

D4 Non-parametric tests Kruskal-Wallis test

Table D4 Kruskal-Wallis test

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Adjusted H 1352 70516 47237 3946 004df 1 1 1 1 1P value 0 0 0 0 084Critical value 384 384 384 384 384Null hypothesis rejected rejected rejected rejected not rejected

25

D5 Regression analysis with dummy variables

Table D5 Regression analysis with dummy variables

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

a0 00002 (000) 00002 (000) 00002 (000) 00002 (000) 00002 (000)a1 00003 (021) 00113 (000) -00132 (000) 00014 (000) -00014 (000)Anomaly not confirmed confirmed confirmed confirmed confirmed

D6 Modified CAR approach

Table D6 Modified CAR approach

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Multiple R 051 099 099 099 096F-test 69486 (000) 325351 (000) 1457582 (000) 6345973 (000) 1213344 (000)a0 -01003(000) 04081 (000) -05444 (000) -01088 (000) 00272 (000)a1 00002 (000) 00106 (000) -00127 (000) 00016 (000) -00016 (000)Anomaly confirmed confirmed confirmed confirmed confirmed

26

E Detailed statistical results NASDAQ overall data

E1 Average analysis

Table E1 Average analysis

Parameter Gap day Gap day(Positive gaps)

Gap day(Negative gaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Mean return (gap day) -009 084 -090 022 -037Mean return (non-gap day) 003 003 003 003 003Anomaly confirmed confirmed confirmed confirmed confirmed

E2 Parametric tests Students t-test

Table E2 T-test

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

t-criterion 230 1257 1341 306 664t-critical (=095) 196 196 196 196 196Null hypothesis rejected rejected rejected rejected rejected

E3 Parametric tests ANOVA

Table E3 ANOVA

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

F 2289 62720 88402 3330 17356p-value 0 0 0 0 0F critical 384 384 384 384 384Null hypothesis rejected rejected rejected rejected rejected

E4 Non-parametric tests Kruskal-Wallis test

Table E4 Kruskal-Wallis test

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Adjusted H 1892 36022 45248 4695 10437df 1 1 1 1 1P value 0 0 0 0 0Critical value 384 384 384 384 384Null hypothesis rejected rejected rejected rejected rejected

27

E5 Regression analysis with dummy variables

Table E5 Regression analysis with dummy variables

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

a0 00003 (000) 00003 (000) 00003 (000) 00003 (000) 00003 (000)a1 -00012 (000) 00081 (000) -00093 (000) 00018 (000) -00040 (000)Anomaly confirmed confirmed confirmed confirmed confirmed

E6 Modified CAR approach

Table E6 Modified CAR approach

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Multiple R 069 092 092 072 097F-test 133255 (000) 361102 (000) 442376 (000) 72903 (000) 1082812 (000)a0 -10646 (000) 11373 (000) -12888 (000) 03928 (000) -02297 (000)a1 -00011 (000) 00073 (000) -00097 (000) 00017 (000) -00039 (000)Anomaly confirmed confirmed confirmed confirmed confirmed

28

F Detailed statistical results DJI sub-periods

F1 Average analysis

Table F1 Average analysis

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 Mean return (gapday)

-001 023 015 -004

Mean return(non-gap day)

007 007 007 007

Anomaly confirmed confirmed confirmed confirmed1999-2008 Mean return (gap

day)090 -045 013 -004

Mean return(non-gap day)

-004 -004 -004 -004

Anomaly confirmed confirmed confirmed confirmed2009-2018 Mean return (gap

day)024 -024 0 -004

Mean return(non-gap day)

004 004 004 004

Anomaly confirmed confirmed not confirmed confirmed

F2 Parametric tests Students t-test

Table F2 T-test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 t-criterion 083 165 087 139t-critical (=095) 196 196 196 196Null hypothesis not rejected not rejected not rejected not rejected

1999-2008 t-criterion 347 351 054 047t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected rejected

2009-2018 t-criterion 265 207 051 058t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

F3 Parametric tests ANOVA

Table F3 ANOVA

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 F 085 409 093 179p-value 035 004 033 018

F critical 384 384 384 384Null hypothesis not rejected rejected not rejected not rejected

1999-2008 F 5405 3196 065 072p-value 0 0 042 039

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

2009-2018 F 554 697 024 058p-value 001 0 062 044

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

29

F4 Non-parametric tests Kruskal-Wallis test

Table F4 Kruskal-Wallis test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 Adjusted H 113 211 113 332df 1 1 1 1

P value 029 015 029 007Null hypothesis not rejected not rejected not rejected not rejected

1999-2008 Adjusted H 1484 1414 003 139df 1 1 1 1

P value 0 0 086 024Null hypothesis rejected rejected not rejected not rejected

2009-2018 Adjusted H 506 68 051 171df 1 1 1 1

P value 002 001 047 019Null hypothesis rejected rejected not rejected not rejected

F5 Regression analysis with dummy variables

Table F5 Regression analysis with dummy variables

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 a0 000068 (000) 00007 (000) 00007 (000) 00007 (000)a1 -000078 (035) 00016 (004) 00008 (033) -00011 (018)

Anomaly not confirmed confirmed not confirmed not confirmed1999-2008 a0 00004 (008) 00004 (008) 00004 (006) 00004 (008)

a1 00087 (000) -00049 (000) 00009 (042) -00008 (039)Anomaly confirmed confirmed not confirmed not confirmed

2009-2018 a0 00004 (006) 00004 (006) 00004 (006) 00004 (006)a1 00021 (001) -00028 (001) -00004 (062) -00008 (047)

Anomaly confirmed confirmed not confirmed not confirmed

F6 Modified CAR approach

Table F6 Modified CAR approach

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 Multiple R 083 088 082 086F-test 22779 (000) 40583 (000) 20401 (000) 3269454 (000)a0 00042 (023) 00017 (073) 00014 (058) -00266 (000)a1 -00009 (000) 00015 (000) 00006 (000) -00009 (000)

Anomaly confirmed confirmed confirmed confirmed1999-2008 Multiple R 095 093 076 019

F-test 62658 (000) 84712 (000) 10056 (000) 492 (003)a0 -00972 (000) 00365 (000) -00198 (000) -00115 (021)a1 00086 (000) -00042 (000) 00014 (000) 00002 (003)

Anomaly confirmed confirmed confirmed not confirmed2009-2018 Multiple R 096 082 08 05

F-test 150452 (000) 16731 (000) 22287 (000) 2620 (000)a0 00548 (000) -00618 (000) 00031 (020) -00112 (000)a1 00013 (000) -00014 (000) -00005 (000) -00004 (000)

Anomaly confirmed confirmed not confirmed confirmed

30

G Detailed statistical results NASDAQ sub-periods

G1 Average analysis

Table G1 Average analysis

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 Mean return (gapday)

094 -111 0189 -029

Mean return(non-gap day)

007 007 007 007

Anomaly confirmed confirmed confirmed confirmed1959-1968 Mean return (gap

day)133 -147 033 -039

Mean return(non-gap day)

006 006 006 006

Anomaly confirmed confirmed confirmed confirmed1969-1978 Mean return (gap

day)19 -186 057 -068

Mean return(non-gap day)

005 005 005 005

Anomaly confirmed confirmed confirmed confirmed1979-1988 Mean return (gap

day)138 -162 066 -04

Mean return(non-gap day)

008 008 008 008

Anomaly confirmed confirmed confirmed confirmed1989-1998 Mean return (gap

day)016 012 018 -009

Mean return(non-gap day)

002 002 002 002

Anomaly confirmed not confirmed confirmed confirmed1999-2008 Mean return (gap

day)38E-3 027 -036 -013

Mean return(non-gap day)

-01 -01 -01 -01

Anomaly confirmed not confirmed not confirmed not confirmed2009-2018 Mean return (gap

day)039 009 013 -025

Mean return(non-gap day)

001 001 001 001

Anomaly confirmed not confirmed confirmed confirmed

G2 Parametric tests Students t-test

Table G2 T-test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 t-criterion 3194 3076 201 559t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected rejected

1959-1968 t-criterion 1399 2246 443 382t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected rejected

1969-1978 t-criterion 261 4358 417 786t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected rejected

1979-1988 t-criterion 1847 1445 709 395t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected rejected

1989-1998 t-criterion 13 066 126 093t-critical (=095) 196 196 196 196Null hypothesis not rejected not rejected not rejected not rejected

1999-2008 t-criterion 192 106 111 009t-critical (=095) 196 196 196 196Null hypothesis not rejected not rejected not rejected not rejected

2009-2018 t-criterion 27 05 089 188t-critical (=095) 196 196 196 196Null hypothesis rejected not rejected not rejected not rejected

31

G3 Parametric tests ANOVA

Table G3 ANOVA

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 F 88153 190609 1272 14521p-value 0 0 0 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1959-1968 F 93974 149771 4715 10418p-value 0 0 0 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1969-1978 F 84546 145429 6295 18241p-value 0 0 0 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1979-1988 F 66952 110482 13138 8626p-value 0 0 0 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1989-1998 F 323 138 43 168p-value 007 024 003 019

F critical 384 384 384 384Null hypothesis not rejected not rejected rejected not rejected

1999-2008 F 106 512 327 003p-value 001 002 007 085

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

2009-2018 F 169 069 175 93p-value 0 04 018 0

F critical 384 384 384 384Null hypothesis rejected not rejected not rejected rejected

G4 Non-parametric tests Kruskal-Wallis test

Table G4 Kruskal-Wallis test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 Adjusted H 26254 32592 1464 3962df 1 1 1 1

P value 0 0 0 0Null hypothesis rejected rejected rejected rejected

1959-1968 Adjusted H 28235 27989 2736 332df 1 1 1 1

P value 0 0 0 0Null hypothesis rejected rejected rejected rejected

1969-1978 Adjusted H 22202 33777 3311 7591df 1 1 1 1

P value 0 0 0 0Null hypothesis rejected rejected rejected rejected

1979-1988 Adjusted H 23282 25292 4812 3964df 1 1 1 1

P value 0 0 0 0Null hypothesis rejected rejected rejected rejected

1989-1998 Adjusted H 381 017 175 132df 1 1 1 1

P value 005 068 019 025Null hypothesis not rejected not rejected not rejected not rejected

1999-2008 Adjusted H 855 023 044 004df 1 1 1 1

P value 0 063 051 084Null hypothesis rejected not rejected not rejected not rejected

2009-2018 Adjusted H 1063 009 257 709df 1 1 1 1

P value 0 077 011 001Null hypothesis rejected not rejected not rejected rejected

32

G5 Regression analysis with dummy variables

Table G5 Regression analysis with dummy variables

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 a0 00007 (000) 00007 (000) 00007 (000) 00007 (000)a1 00088 (000) -00119 (000) 00011 (000) -00036 (000)

Anomaly confirmed confirmed confirmed confirmed1959-1968 a0 00006 (000) 00006 (000) 00006 (000) 00006 (000)

a1 00128 (000) -00153 (000) 00027 (000) -00046 (000)Anomaly confirmed confirmed confirmed confirmed

1969-1978 a0 00005 (000) 00005 (000) 00005 (000) 00005 (000)a1 00185 (000) -00192 (000) 00053 (000) -00073 (000)

Anomaly confirmed confirmed confirmed confirmed1979-1988 a0 00008 (000) 00008 (000) 00008 (000) 00008 (000)

a1 00131 (000) -00172 (000) 00059 (000) -00048 (000)Anomaly confirmed confirmed confirmed confirmed

1989-1998 a0 00002 (027) 00002 (028) 00002 (028) 00002 (027)a1 00014 (007) 00010 (024) 00017 (004) -00011 (019)

Anomaly not confirmed not confirmed confirmed not confirmed1999-2008 a0 00001 (059) 00001 (062) 00001 (059) 00001 (060)

a1 00037 (000) 00026 (002) -00038 (000) -00014 (019)Anomaly confirmed not confirmed not confirmed not confirmed

2009-2018 a0 00001 (049) 00001 (049) 00001 (049) 00001 (049)a1 00038 (000) 00007 (040) 00012 (018) -00027 (000)

Anomaly confirmed not confirmed not confirmed confirmed

G6 Modified CAR approach

Table G6 Modified CAR approach

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 Multiple R 099 099 093 098F-test 5753605 (000) 100470(000) 6280421 283281a0 -00091 (000) -00349 (000) 00056 (001) 00015 (073)a1 00083 (000) -00110 (000) 00010 (000) -00031 (000)

Anomaly confirmed confirmed confirmed confirmed1959-1968 Multiple R 099 099 099 099

F-test 3923274 (000) 3005562 (000) 443198 (000) 372583 (000)a0 00096 (000) 00073 (016) -00082 (000) -00095 (004)a1 00116 (001) -00149 (000) 00025 (000) -00047 (000)

Anomaly confirmed confirmed confirmed confirmed1969-1978 Multiple R 099 099 098 099

F-test 4302608 (000) 2723953 (000) 179969 (000) 639745a0 00246 (000) -00002 (000) 00217 (000) -00514 (000)a1 00176 (000) -00182 (000) 00049 (000) -00062 (000)

Anomaly confirmed confirmed confirmed confirmed1979-1988 Multiple R 099 099 099 099

F-test 5872335 (000) 1182609 (000) 1083558 (000) 910089 (000)a0 00136 (000) -01081 (000) -00285 (000) -00101 (000)a1 00131 (000) -00167 (000) 00062 (000) -00048 (000)

Anomaly confirmed confirmed confirmed confirmed1989-1998 Multiple R 09 056 069 016

F-test 46947 (000) 4885 (000) 10131 (000) 263 (011)a0 00102 (002) -00261 (000) -0016 (001) -00237 (000)a1 00015 (000) 00010 (000) 0001 (000) 00002 (011)

Anomaly confirmed confirmed confirmed not confirmed1999-2008 Multiple R 093 087 073 037

F-test 71863 (000) 32530 (000) 13273 (000) 1669 (000)a0 00185 (004) 00311 (000) -00130 (039) -00546 (000)a1 00037 (000) 00032 (000) -00026 (000) -00007 (000)

Anomaly confirmed not confirmed not confirmed confirmed2009-2018 Multiple R 089 001 096 091

F-test 40818 (000) 000 (094) 116744 (000) 53770 (000)a0 01436 (000) -01099 (000) -01036 (000) 00697 (000)a1 00030 (000) 00000 (094) 00024 (000) -00021 (000)

Anomaly confirmed not confirmed confirmed confirmed

33

H Detailed statistical results SampP 500 sub-periods

H1 Average analysis

Table H1 Average analysis

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 Mean return (gapday)

138 -171 004 -014

Mean return(non-gap day)

0 0 0 0

Anomaly confirmed confirmed confirmed confirmed1939-1948 Mean return (gap

day)001 -042 172 -195

Mean return(non-gap day)

003 003 003 003

Anomaly confirmed confirmed confirmed confirmed1949-1958 Mean return (gap

day)165 -18 02 002

Mean return(non-gap day)

006 006 006 006

Anomaly confirmed confirmed confirmed not confirmed1959-1968 Mean return (gap

day)104 -102 015 0

Mean return(non-gap day)

002 002 002 002

Anomaly confirmed confirmed confirmed not confirmed1969-1978 Mean return (gap

day)131 -13 019 -03

Mean return(non-gap day)

0 0 0 0

Anomaly confirmed confirmed confirmed confirmed1979-1988 Mean return (gap

day)058 -042 015 003

Mean return(non-gap day)

005 005 005 005

Anomaly confirmed confirmed confirmed not confirmed1989-1998 Mean return (gap

day)02 -023 -002 01

Mean return(non-gap day)

007 007 007 007

Anomaly confirmed confirmed not confirmed not confirmed1999-2008 Mean return (gap

day)083 -089 -023 -005

Mean return(non-gap day)

001 001 001 001

Anomaly confirmed confirmed not confirmed confirmed2009-2018 Mean return (gap

day)055 -052 001 -015

Mean return(non-gap day)

004 004 004 004

Anomaly confirmed confirmed not confirmed confirmed

34

H2 Parametric tests Students t-test

Table H2 T-test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 t-criterion 101 85 029 048t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

1939-1948 t-criterion 064 479 3074 225t-critical (=095) 196 196 196 196Null hypothesis not rejected rejected rejected rejected

1949-1958 t-criterion 2964 2383 193 041t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

1959-1968 t-criterion 2281 2157 21 023t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected not rejected

1969-1978 t-criterion 1318 2034 187 321t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected rejected

1979-1988 t-criterion 435 535 07 037t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

1989-1998 t-criterion 201 396 132 052t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

1999-2008 t-criterion 362 433 117 022t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

2009-2018 t-criterion 375 382 027 132t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

H3 Parametric tests ANOVA

Table H3 ANOVA

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 F 6281 8032 005 051p-value 0 0 082 047

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

1939-1948 F 056 2603 34854 51034p-value 045 0 0 0

F critical 384 384 384 384Null hypothesis not rejected rejected rejected rejected

1949-1958 F 100174 128997 897 062p-value 0 0 0 043

F critical 384 384 384 384Null hypothesis rejected rejected rejected not rejected

1959-1968 F 36831 32858 617 01p-value 0 0 001 074

F critical 384 384 384 384Null hypothesis rejected rejected rejected not rejected

1969-1978 F 26601 3063 53 152p-value 0 0 002 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1979-1988 F 23 245 076 009p-value 0 0 039 077

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

1989-1998 F 399 1156 118 015p-value 004 0 027 069

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

1999-2008 F 4253 5622 365 024p-value 0 0 006 062

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

2009-2018 F 3064 3656 01 43p-value 0 0 075 004

F critical 384 384 384 384Null hypothesis rejected rejected not rejected rejected

35

H4 Non-parametric tests Kruskal -Wallis test

Table H4 Kruskal-Wallis test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 Adjusted H 9982 5913 332 14df 1 1 1 1

P value 0 0 007 024Null hypothesis rejected rejected not rejected not rejected

1939-1948 Adjusted H 494 1999 23387 24927df 1 1 1 1

P value 003 0 0 0Null hypothesis rejected rejected rejected rejected

1949-1958 Adjusted H 28728 28175 348 15df 1 1 1 1

P value 0 0 006 022Null hypothesis rejected rejected not rejected not rejected

1959-1968 Adjusted H 25729 21437 701 063df 1 1 1 1

P value 0 0 001 043Null hypothesis rejected rejected rejected not rejected

1969-1978 Adjusted H 14407 20078 27 1706df 1 1 1 1

P value 0 0 01 0Null hypothesis rejected rejected not rejected rejected

1979-1988 Adjusted H 1788 2836 027 034df 1 1 1 1

P value 0 0 06 056Null hypothesis rejected rejected not rejected not rejected

1989-1998 Adjusted H 251 1431 111 044df 1 1 1 1

P value 011 0 029 051Null hypothesis not rejected rejected not rejected not rejected

1999-2008 Adjusted H 1812 1788 042 002df 1 1 1 1

P value 0 0 052 089Null hypothesis rejected rejected not rejected not rejected

2009-2018 Adjusted H 1314 1783 074 37df 1 1 1 1

P value 0 0 039 005Null hypothesis rejected rejected not rejected not rejected

36

H5 Regression analysis with dummy variables

Table H5 Regression analysis with dummy variables

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 a0 00000 (097) 00000 (004) 00000 (097) 00000 (097)a1 00138 (000) -00172 (000) 00004 (082) -00014 (047)

Anomaly confirmed confirmed not confirmed not confirmed1939-1948 a0 00003 (015) 00003 (015) 00003 (015) 00003 (015)

a1 00007 (045) -00045 (000) 00170 (000) -00199 (000)Anomaly not confirmed confirmed confirmed confirmed

1949-1958 a0 00006 (000) 00006 (000) 00006 (000) 00006 (000)a1 00160 (000) -00188 (000) 00016 (000) -00004 (043)

Anomaly confirmed confirmed confirmed not confirmed1959-1968 a0 00002 (007) 00002 (004) 00002 (008) 00002 (008)

a1 00103 (000) -00105 (000) 00014 (001) -00002 (074)Anomaly confirmed confirmed confirmed not confirmed

1969-1978 a0 00000 (078) 00000 (078) 00000 (078) 00000 (078)a1 00132 (000) -00132 (000) 00019 (002) -00030 (000)

Anomaly confirmed confirmed confirmed confirmed1979-1988 a0 00006 (001) 00006 (001) 00006 (001) 00006 (000)

a1 00053 (000) -00048 (000) 00009 (040) -00003 (075)Anomaly confirmed confirmed not confirmed not confirmed

1989-1998 a0 00007 (000) 00007 (000) 00007 (000) 00007 (000)a1 00016 (005) -00030 (000) -00009 (026) 00003 (072)

Anomaly confirmed confirmed not confirmed not confirmed1999-2008 a0 00001 (075) 00001 (075) 00001 (075) 00001 (076)

a1 00083 (000) -00091 (000) -00024 (005) -00006 (062)Anomaly confirmed confirmed not confirmed not confirmed

2009-2018 a0 00004 (003) 00004 (000) 00004 (003) 00004 (003)a1 00051 (000) -00059 (000) -00003 (075) -00019 (003)

Anomaly confirmed confirmed not confirmed confirmed

37

H6 Modified CAR approach

Table H6 Modified CAR approach

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 Multiple R 096 095 046 046F-test 175935 (000) 96500 (000) 3534 (000) 2880 (000)a0 -01070 (000) 01958 (000) 00405 (000) 00535 (000)a1 00121 (000) -00160 (000) 00006 (000) -00014 (000)

Anomaly confirmed confirmed confirmed confirmed1939-1948 Multiple R 08 099 099 099

F-test 18777 (000) 755727 (000) 3572830 (000) 2696099 (000)a0 00019 (073) -00346 (000) -00373 (000) 00912 (000)a1 00012 (000) -00044 (000) 00168 (000) -00197 (000)

Anomaly confirmed confirmed confirmed confirmed1949-1958 Multiple R 099 099 094 015

F-test 1021705 (000) 7171257 (000) 75858 (000) 242 (012)a0 -00176 (000) -00191 (000) 00095 (000) -00498 (000)a1 00154 (000) -00181 (000) 00013 (000) -00002 (012)

Anomaly confirmed confirmed confirmed not confirmed1959-1968 Multiple R 099 099 094 078

F-test 1463311 (000) 6002659 (000) 82273 (000) 14352 (000)a0 -00112 (000) 00004 (085) 00151 (000) 00389 (000)a1 00098 (000) -00102 (000) 00011 (000) -00009 (000)

Anomaly confirmed confirmed confirmed confirmed1969-1978 Multiple R 098 099 093 099

F-test 241655 (000) 1451901 (000) 57333 (000) 368160 (000)a0 -00433 (000) 00276 (000) 00099 (002) -00144 (000)a1 00132 (000) -00134 (000) 00020 (000) -00030 (000)

Anomaly confirmed confirmed confirmed confirmed1979-1988 Multiple R 092 078 023 008

F-test 53757 (000) 18707 (000) 487 (003) 085 (036)a0 00813 (000) -02508 (000) 00204 (000) -00235 (000)a1 00036 (000) -00031 (000) -00003 (003) -00001 (036)

Anomaly confirmed confirmed not confirmed not confirmed1989-1998 Multiple R 079 099 074 044

F-test 19705(000) 761967 (000) 14133 (000) 2369 (000)a0 00268 (000) 00023 (021) -00381 (000) 00087 (000)a1 00013 (000) -00028 (000) -00008 (000) 00002 (000)

Anomaly confirmed confirmed not confirmed not confirmed1999-2008 Multiple R 091 093 071 065

F-test 47218 (000) 76564 (000) 9843 (000) 7768 (000)a0 -01493 (000) 01351 (000) 00397 (000) 00007 (093)a1 00081 (000) -00083 (000) -00026 (000) -00011 (000)

Anomaly confirmed confirmed not confirmed confirmed2009-2018 Multiple R 086 087 083 074

F-test 29971 (000) 32484 (000) 23228 (000) 12764 (000)a0 01711 (000) -02250 (000) 00407 (000) -00472 (000)a1 00038 (000) -00044 (000) -00010 (000) -00012 (000)

Anomaly confirmed confirmed not confirmed confirmed

38

Tab

le7

H1minus2statisticalresults

SampP500sub-periods

PeriodM

ethod

Average

analysis

t-test

ANOVA

test

Man

n-

Whitney

test

Regression

analysiswith

dummy

variab

les

Modified

CAR

approach

Overall

Dayofanomaly

1929-1938

++

++

++

61939-1948

++

++

++

61949-1958

++

++

++

61959-1968

++

++

++

61969-1978

++

++

++

61979-1988

++

++

++

61989-1998

++

++

++

61999-2008

++

++

++

62009-2018

++

++

++

6Dayafteranomaly

1929-1938

+-

--

-+

21939-1948

++

++

++

61949-1958

--

--

--

01959-1968

--

--

-+

11969-1978

++

++

++

61979-1988

--

--

--

01989-1998

--

--

--

01999-2008

+-

--

-+

22009-2018

+-

+-

++

4

Note+

indicates

thattheanom

alyis

confirm

edand-indicates

thatan

omaly

isnot

confirm

edThehigher

theoverallrating

the

strongertheeviden

ceofthean

omaly

13

45 Trading simulation

The algorithm of the trading strategy is to buysell at the start of the updown gapday and close this position at the end of this day To test this strategy data for the DJIand SampP 500 are used (for this case the price anomaly still exists based on the day itoccurred) The results for DJI are presented in Table A8 and for the SampP 500 in Table8 For the SampP 500 and DJI the trading strategy built on price gap anomaly is efficientand its results differ from random

Table 8 Trading simulation results of the price gap anomaly for the SampP 500

Period Gaptype

Numberof

tradesunits

Numberof suc-cessfultradesunits

Numberof suc-cessfultrades

Profit

Profit peryear

z-test Result

1929-1938 Up 131 130 992 1816 182 1065 passedDown 110 108 982 1893 189 876 passed

1939-1948 Up 110 67 609 106 11 09 failedDown 122 79 648 518 52 465 passed

1949-1958 Up 106 105 991 1765 176 3191 passedDown 104 103 99 1891 189 2356 passed

1959-1968 Up 108 106 981 1331 113 2441 passedDown 92 91 989 948 95 2214 passed

1969-1978 Up 85 71 835 1128 113 1361 passedDown 96 90 938 1262 126 2118 passed

1979-1988 Up 92 63 685 54 54 495 passedDown 123 81 659 519 52 496 passed

1989-1998 Up 117 72 615 267 27 295 passedDown 99 61 616 228 23 32 passed

1999-2008 Up 99 65 657 828 83 373 passedDown 110 72 655 987 99 438 passed

2009-2018 Up 106 71 67 59 59 416 passedDown 107 65 607 56 56 362 passed

14

Figure 1 Trading simulation results of the price gap anomaly for the SampP 500

Note The primary axis refers to the percentage profit per year and the secondary to thez minus test statistic

One more interesting fact (see Figure 1) is the decrease of trading strategy efficiencyThis is indirect evidence in favour of evolution of the US stock market and its movementfrom less efficient to more efficient state Overall it can be concluded that the price gapanomaly is a real market anomaly The US stock market loses its efficiency after pricegaps This effect is temporary and lasts only for a day Still even this time is enoughto exploit the hole in the market efficiency and generate abnormal profits from trading

5 Conclusion

We analysed price gap anomaly in the US stock market by using information from threestock market indexes(DJI SampP 500 and NASDAQ) We tested three hypotheses of in-terest that is H1 the price gap anomaly exists H1minus1 prices tend to rise after positivegaps H1minus2 prices tend to fall after negative gaps H2 the price gap anomaly evolvesand H3 there is seasonality in price gaps Various statistical methods including para-metric tests (Students t-tests ANOVA) non-parametric tests (Mann-Whitney test)regression analysis with dummy variables MCAR approach and the trading simulationapproach were utilised

We conclude that the US stock market in the main did not exhibit seasonality in pricegaps Therefore H3 is rejected Furthermore no evidence was found that price gaps inthe US stock market were filled within five days of their occurrence However strongevidence in favour of abnormal price movements after the gaps were found confirming

15

H1 and H2 Particularly on the day of the occurrence of the gap and not on the dayafter the price gap In the DJI and the SampP 500 this pattern persists indicating thatthese markets take a day to incorporate new information As the results of the tradingsimulation indicate a day is enough to profit from a price gap anomaly trading strategyin the DJI and the SampP 500

Similar to other studies and other anomalies (see McLean and Pontiff (2016) Ca-jueiro and Tabak (2004) and Tiwari et al (2019) for example) the price gap anomalyevolved It is less prevalent since the 1990s as shown in the SampP 500 and NASDAQThis pattern of evolution is common amongst most stock market anomalies (see Plastunet al (2019b) on calendar anomalies amongst others) Our findings therefore add onto the existing literature Finally in the main our results are against the EMH and aretherefore interesting to both practitioners and academics

16

References

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Akerlof G A and Shiller R J (2009) Animal Spirits How human psychology drivesthe economy and why it matters for global capitalism Princeton University Press

Basu S (1977) Investment performance of common stocks in relation to their price-earnings ratios A test of the efficient market hypothesis The Journal of Finance32(3)663ndash682

Bildik R (2004) Are calendar anomalies still alive Evidence from istanbul stockexchange SSRN Electronic Journal 2004

Cai J Li Y and Qi Y (2006) The day-of-the-week effect New evidence from theChinese stock market Chinese Economy 39(2)71ndash88

Cajueiro D O and Tabak B M (2004) The Hurst exponent over time testing theassertion that emerging markets are becoming more efficient Physica A StatisticalMechanics and its Applications 336(3-4)521ndash537

Caporale G M Gil-Alana L Plastun A and Makarenko I (2016) Intraday anoma-lies and market efficiency A trading robot analysis Computational Economics47(2)275ndash295

Caporale G M and Plastun A (2017) Price gaps Another market anomaly Invest-ment Analysts Journal 46(4)279ndash293

Cross F (1973) The behavior of stock prices on Fridays and Mondays FinancialAnalysts Journal 29(6)67ndash69

Fama E F (1965) The behavior of stock-market prices The Journal of Business38(1)34ndash105

Fama E F (1970) Efficient capital markets A review of theory and empirical workThe Journal of Finance 25(2)383ndash417

Fortune P (1998) Weekends can be rough revisiting the weekend effect in stock pricesTechnical report

Fortune P (1999) Are stock returns different over weekends A jump diffusion analysisof the weekend effect New England Economic Review 103ndash19

French K R (1980) Stock returns and the weekend effect Journal of FinancialEconomics 8(1)55ndash69

Fung A K-W Lam K and Lam K-M (2010) Do the prices of stock index futuresin asia overreact to us market returns Journal of Empirical Finance 17(3)428ndash440

17

Gibbons M R and Hess P (1981) Day of the week effects and asset returns Journalof business pages 579ndash596

Grant J L Wolf A and Yu S (2005) Intraday price reversals in the us stock indexfutures market A 15-year study Journal of Banking amp Finance 29(5)1311ndash1327

Grossman S J and Stiglitz J E (1980) On the impossibility of informationallyefficient markets The American Economic Review 70(3)393ndash408

Jacobsen B Mamun A and Visaltanachoti N (2005) Seasonal size and valueanomalies

Jensen M (1978) Some anomalous evidence regarding market efficiency Journal ofFinancial Economics 6(23 (1978))95ndash101

Lakonishok J and Smidt S (1988) Are seasonal anomalies real A ninety-year per-spective The Review of Financial Studies 1(4)403ndash425

MacKinlay A (1997) Event studies in economics and finance Journal of EconomicLiterature (35)113ndash39

Mandelbrot B B (1997) The variation of certain speculative prices In Fractals andscaling in finance pages 371ndash418 Springer

McLean R D and Pontiff J (2016) Does academic research destroy stock returnpredictability The Journal of Finance 71(1)5ndash32

Plastun A Makarenko I Khomutenko L Shcherbak S and Tryfonova O (2019a)Exploring price gap anomaly in the ukrainian stock market Investment Managementamp Financial Innovations 16(2)150

Plastun A Sibande X Gupta R and Wohar M E (2019b) Rise and fall of calendaranomalies over a century The North American Journal of Economics and Finance49181ndash205

Schwert G W (2003) Chapter 15 anomalies and market efficiency In FinancialMarkets and Asset Pricing volume 1 of Handbook of the Economics of Finance pages939 ndash 974 Elsevier

Shiller R J (2000) Irrational exuberance Princeton University

Tiwari A K Aye G C and Gupta R (2019) Stock market efficiency analysis usinglong spans of data A multifractal detrended fluctuation approach Finance ResearchLetters 28398ndash411

Yuan Y (2015) Market-wide attention trading and stock returns Journal of FinancialEconomics 116(3)548ndash564

18

Appendices

A DJI and NASDAQ Summary Results

A1 Overall Results

Table A1 Gap size used for different sub-periods over the period 1929-2018

Period DJI NASDAQ1929-1938 - -1939-1948 - -1949-1958 - 0711959-1968 - 0951969-1978 - 1351979-1988 - 1101989-1998 040 0681999-2008 007 1502009-2018 020 110Overall data set 030 110

Table A2 Day of the week and gaps

Day of the week DJI NASDAQMonday 024 02Tuesday 02 02Wednesday 017 02Thursday 019 019Friday 021 02

A2 Statistical tests

Table A3 Results of the statistical tests for the overall data sets

PeriodMethod Averageanalysis

t-test ANOVAtest

Mann-Whitney

test

Regressionanalysiswith

dummyvariables

ModifiedCAR

approach

Overall

Dow Jones Index overall data setGap day - - - - - + 1Gap day (Positive gaps) + - - - - - 1Gap day (Negative gaps) + - - - - + 2Day after gap (Positive gaps) + - - - - - 1Day after gap (Negative gaps) + - - + - + 3

NASDAQ overall data setGap day + + + + + + 6Gap day (Positive gaps) + + + + + + 6Gap day (Negative gaps) + + + + + + 6Day after gap (Positive gaps) + + + + + + 6Day after gap (Negative gaps) + + + + + + 6

Note + indicates that the anomaly is confirmed and - indicates that anomaly is not confirmedThe higher the overall rating the stronger the evidence of the anomaly

19

Table A4 Results of the statistical tests for H1minus1 DJI

Period Averageanalysis

t-test ANOVA test Mann-Whitney

test

Regressionanalysis with

dummyvariables

ModifiedCAR

approach

Overall

Day of anomaly1989-1998 + - - - - + 21999-2008 + + + + + + 62009-2018 + + + + + + 6

Day after anomaly1989-1998 + - - - - + 21999-2008 + - - - - + 22009-2018 - - - - - - 0

Note + indicates that the anomaly is confirmed and - indicates that anomaly is not confirmedThe higher the overall rating the stronger the evidence of the anomaly

Table A5 Results of the statistical tests for H1minus2 DJI

Period Averageanalysis

t-test ANOVA test Mann-Whitneytest

Regressionanalysis with

dummyvariables

Modified CARapproach

Overall

Day of anomaly1989-1998 - - - - - - 01999-2008 + + + + + + 62009-2018 + + + + + + 6

Day after anomaly1989-1998 + - - - - + 21999-2008 + - - - - - 12009-2018 + - - - - + 2

Note + indicates that the anomaly is confirmed and - indicates that anomaly is not confirmedThe higher the overall rating the stronger the evidence of the anomaly

Table A6 Results of the statistical tests for H1minus1 NASDAQ

PeriodMethod Averageanalysis

t-test ANOVA test Mann-Whitney

test

Regressionanalysis with

dummyvariables

ModifiedCAR

approach

Overall

Day of anomaly1949-1958 + + + + + + 61959-1968 + + + + + + 61969-1978 + + + + + + 61979-1988 + + + + + + 61989-1998 + - - - - + 21999-2008 + - + + + + 52009-2018 + + + + + + 6

Day after anomaly1949-1958 + + + + + + 61959-1968 + + + + + + 61969-1978 + + + + + + 61979-1988 + + + + + + 61989-1998 + - + - + + 41999-2008 - - - - - - 02009-2018 + - - - - + 2

Note + indicates that the anomaly is confirmed and - indicates that anomaly is not confirmedThe higher the overall rating the stronger the evidence of the anomaly

20

Table A7 Results of the statistical tests for H1minus2 NASDAQ

PeriodMethod Averageanalysis

t-test ANOVA test Mann-Whitney

test

Regressionanalysis with

dummyvariables

ModifiedCAR

approach

Overall

Day of anomaly1949-1958 + + + + + + 61959-1968 + + + + + + 61969-1978 + + + + + + 61979-1988 + + + + + + 61989-1998 - - - - - + 11999-2008 - - + - - - 12009-2018 - - - - - - 0

Day after anomaly1949-1958 + + + + + + 61959-1968 + + + + + + 61969-1978 + + + + + + 61979-1988 + + + + + + 61989-1998 + - - - - - 11999-2008 - - - - - + 12009-2018 + - - + + + 4

Note + indicates that the anomaly is confirmed and - indicates that anomaly is not confirmedThe higher the overall rating the stronger the evidence of the anomaly

A3 Trading Simulation Results

Table A8 Trading simulation results of the price gap anomaly for the DJI 1989-2018

Period Gap type Number oftradesunits

Number ofsuccessfultradesunits

Number ofsuccessfultrades

Profit Profit per year

z-test Result

1989-1998 Up 102 46 451 -11 -01 011 failedDown 116 49 422 -267 -27 242 passed

1999-2008 Up 73 51 699 665 66 37 passedDown 143 81 566 641 64 331 passed

2009-2018 Up 127 88 693 308 31 327 passedDown 81 47 58 196 2 184 passed

21

B Short-term price behavior in DJI SampP 500 and

NASDAQ Price gaps (overall data sets)

Table B1 Momentum effect in the US stock market after the gap

Instrument Parameter Number of days after the gap1 2 3

Dow Jones Index Positive gaps 53 57 61Negative gaps 50 50 47

All gaps 51 54 54SampP 500 Index Positive gaps 40 63 60

Negative gaps 4 52 45All gaps 4 58 53

NASDAQ Positive gaps 32 65 67Negative gaps 24 63 59

All gaps 28 64 63

Table B2 Momentum effect in the US stock market before the gap

Instrument Parameter Number of days before the gap1 2 3

Dow Jones Index Positive gaps 56 49 52Negative gaps 54 49 49

All gaps 55 49 50SampP 500 Index Positive gaps 57 57 52

Negative gaps 60 59 54All gaps 58 58 53

NASDAQ Positive gaps 61 56 54Negative gaps 68 69 70

All gaps 64 63 63

Table B3 Fill gap effect in the US stock market

Instrument Parameter Number of days after the gap1 2 3 4 5

Dow Jones Index Positive gaps 22 28 26 30 28Negative gaps 25 33 36 42 46

All gaps 24 30 31 35 37SampP 500 Index Positive gaps 0 6 11 16 19

Negative gaps 1 10 19 26 27All gaps 1 8 15 20 23

NASDAQ Positive gaps 8 13 18 21 19Negative gaps 7 11 17 21 25

All gaps 8 12 18 21 22

22

C Detailed statistical results DJI overall data

C1 Average analysis

Table C1 Average analysis

Parameter Gap day Gap day(Positive gaps)

Gap day(Negative gaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Mean return (gap day) 003 006 0 005 -003Mean return (non-gap day) 004 004 004 004 004Anomaly not confirmed not confirmed confirmed not confirmed confirmed

C2 Parametric tests Students t-test

Table C2 T-test

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

t-criterion 016 042 053 015 104t-critical (=095) 196 196 196 196 196Null hypothesis not rejected not rejected not rejected not rejected not rejected

C3 Parametric tests ANOVA

Table C3 ANOVA

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

F 0036 018 053 003 14p-value 085 067 047 086 024F critical 384 384 384 384 384Null hypothesis not rejected not rejected not rejected not rejected not rejected

C4 Non-parametric tests Kruskal-Wallis test

Table C4 Kruskal -Wallis test

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Adjusted H 082 012 126 0 455df 1 1 1 1 1P value 037 073 026 095 003Critical value 384 384 384 384 384Null hypothesis not rejected not rejected not rejected not rejected rejected

23

C5 Regression analysis with dummy variables

Table C5 Regression analysis with dummy variables

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

a0 00004 (000) 00004 (000) 00004 (000) 00004 (000) 00004 (000)a1 -00001 (-019) 00002 (067) -00004 (047) 00001 (086) -00007 (024)Anomaly not confirmed not confirmed not confirmed not confirmed not confirmed

C6 Modified CAR approach

Table C6 Modified CAR approach

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Multiple R 049 05 025 0 092F-test 23347 (000) 12913 (000) 2207 (000) 000 (098) 1822 (000)a0 -00041 (060) 00128 (006) -00267 (000) 00354 (000) 00319 (000)a1 -00003 (000) -00003 (000) -00002 (000) 00000 (098) -00008 (000)Anomaly confirmed confirmed confirmed not confirmed confirmed

24

D Detailed statistical results SampP 500 overall data

D1 Average analysis

Table D1 Average analysis

Parameter Gap day Gap day(Positive gaps)

Gap day(Negative gaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Mean return (gap day) 006 115 -129 017 -011Mean return (non-gap day) 002 002 002 002 002Anomaly confirmed confirmed confirmed confirmed confirmed

D2 Parametric tests Students t-test

Table D2 T-test

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

t-criterion 092 4546 3579 485 271t-critical (=095) 196 196 196 196 196Null hypothesis not rejected rejected rejected rejected rejected

D3 Parametric tests ANOVA

Table D3 ANOVA

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

F 155 116211 126952 1866 136p-value 022 0 0 0 0F critical 384 384 384 384 384Null hypothesis not rejected rejected rejected not rejected not rejected

D4 Non-parametric tests Kruskal-Wallis test

Table D4 Kruskal-Wallis test

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Adjusted H 1352 70516 47237 3946 004df 1 1 1 1 1P value 0 0 0 0 084Critical value 384 384 384 384 384Null hypothesis rejected rejected rejected rejected not rejected

25

D5 Regression analysis with dummy variables

Table D5 Regression analysis with dummy variables

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

a0 00002 (000) 00002 (000) 00002 (000) 00002 (000) 00002 (000)a1 00003 (021) 00113 (000) -00132 (000) 00014 (000) -00014 (000)Anomaly not confirmed confirmed confirmed confirmed confirmed

D6 Modified CAR approach

Table D6 Modified CAR approach

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Multiple R 051 099 099 099 096F-test 69486 (000) 325351 (000) 1457582 (000) 6345973 (000) 1213344 (000)a0 -01003(000) 04081 (000) -05444 (000) -01088 (000) 00272 (000)a1 00002 (000) 00106 (000) -00127 (000) 00016 (000) -00016 (000)Anomaly confirmed confirmed confirmed confirmed confirmed

26

E Detailed statistical results NASDAQ overall data

E1 Average analysis

Table E1 Average analysis

Parameter Gap day Gap day(Positive gaps)

Gap day(Negative gaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Mean return (gap day) -009 084 -090 022 -037Mean return (non-gap day) 003 003 003 003 003Anomaly confirmed confirmed confirmed confirmed confirmed

E2 Parametric tests Students t-test

Table E2 T-test

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

t-criterion 230 1257 1341 306 664t-critical (=095) 196 196 196 196 196Null hypothesis rejected rejected rejected rejected rejected

E3 Parametric tests ANOVA

Table E3 ANOVA

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

F 2289 62720 88402 3330 17356p-value 0 0 0 0 0F critical 384 384 384 384 384Null hypothesis rejected rejected rejected rejected rejected

E4 Non-parametric tests Kruskal-Wallis test

Table E4 Kruskal-Wallis test

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Adjusted H 1892 36022 45248 4695 10437df 1 1 1 1 1P value 0 0 0 0 0Critical value 384 384 384 384 384Null hypothesis rejected rejected rejected rejected rejected

27

E5 Regression analysis with dummy variables

Table E5 Regression analysis with dummy variables

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

a0 00003 (000) 00003 (000) 00003 (000) 00003 (000) 00003 (000)a1 -00012 (000) 00081 (000) -00093 (000) 00018 (000) -00040 (000)Anomaly confirmed confirmed confirmed confirmed confirmed

E6 Modified CAR approach

Table E6 Modified CAR approach

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Multiple R 069 092 092 072 097F-test 133255 (000) 361102 (000) 442376 (000) 72903 (000) 1082812 (000)a0 -10646 (000) 11373 (000) -12888 (000) 03928 (000) -02297 (000)a1 -00011 (000) 00073 (000) -00097 (000) 00017 (000) -00039 (000)Anomaly confirmed confirmed confirmed confirmed confirmed

28

F Detailed statistical results DJI sub-periods

F1 Average analysis

Table F1 Average analysis

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 Mean return (gapday)

-001 023 015 -004

Mean return(non-gap day)

007 007 007 007

Anomaly confirmed confirmed confirmed confirmed1999-2008 Mean return (gap

day)090 -045 013 -004

Mean return(non-gap day)

-004 -004 -004 -004

Anomaly confirmed confirmed confirmed confirmed2009-2018 Mean return (gap

day)024 -024 0 -004

Mean return(non-gap day)

004 004 004 004

Anomaly confirmed confirmed not confirmed confirmed

F2 Parametric tests Students t-test

Table F2 T-test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 t-criterion 083 165 087 139t-critical (=095) 196 196 196 196Null hypothesis not rejected not rejected not rejected not rejected

1999-2008 t-criterion 347 351 054 047t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected rejected

2009-2018 t-criterion 265 207 051 058t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

F3 Parametric tests ANOVA

Table F3 ANOVA

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 F 085 409 093 179p-value 035 004 033 018

F critical 384 384 384 384Null hypothesis not rejected rejected not rejected not rejected

1999-2008 F 5405 3196 065 072p-value 0 0 042 039

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

2009-2018 F 554 697 024 058p-value 001 0 062 044

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

29

F4 Non-parametric tests Kruskal-Wallis test

Table F4 Kruskal-Wallis test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 Adjusted H 113 211 113 332df 1 1 1 1

P value 029 015 029 007Null hypothesis not rejected not rejected not rejected not rejected

1999-2008 Adjusted H 1484 1414 003 139df 1 1 1 1

P value 0 0 086 024Null hypothesis rejected rejected not rejected not rejected

2009-2018 Adjusted H 506 68 051 171df 1 1 1 1

P value 002 001 047 019Null hypothesis rejected rejected not rejected not rejected

F5 Regression analysis with dummy variables

Table F5 Regression analysis with dummy variables

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 a0 000068 (000) 00007 (000) 00007 (000) 00007 (000)a1 -000078 (035) 00016 (004) 00008 (033) -00011 (018)

Anomaly not confirmed confirmed not confirmed not confirmed1999-2008 a0 00004 (008) 00004 (008) 00004 (006) 00004 (008)

a1 00087 (000) -00049 (000) 00009 (042) -00008 (039)Anomaly confirmed confirmed not confirmed not confirmed

2009-2018 a0 00004 (006) 00004 (006) 00004 (006) 00004 (006)a1 00021 (001) -00028 (001) -00004 (062) -00008 (047)

Anomaly confirmed confirmed not confirmed not confirmed

F6 Modified CAR approach

Table F6 Modified CAR approach

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 Multiple R 083 088 082 086F-test 22779 (000) 40583 (000) 20401 (000) 3269454 (000)a0 00042 (023) 00017 (073) 00014 (058) -00266 (000)a1 -00009 (000) 00015 (000) 00006 (000) -00009 (000)

Anomaly confirmed confirmed confirmed confirmed1999-2008 Multiple R 095 093 076 019

F-test 62658 (000) 84712 (000) 10056 (000) 492 (003)a0 -00972 (000) 00365 (000) -00198 (000) -00115 (021)a1 00086 (000) -00042 (000) 00014 (000) 00002 (003)

Anomaly confirmed confirmed confirmed not confirmed2009-2018 Multiple R 096 082 08 05

F-test 150452 (000) 16731 (000) 22287 (000) 2620 (000)a0 00548 (000) -00618 (000) 00031 (020) -00112 (000)a1 00013 (000) -00014 (000) -00005 (000) -00004 (000)

Anomaly confirmed confirmed not confirmed confirmed

30

G Detailed statistical results NASDAQ sub-periods

G1 Average analysis

Table G1 Average analysis

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 Mean return (gapday)

094 -111 0189 -029

Mean return(non-gap day)

007 007 007 007

Anomaly confirmed confirmed confirmed confirmed1959-1968 Mean return (gap

day)133 -147 033 -039

Mean return(non-gap day)

006 006 006 006

Anomaly confirmed confirmed confirmed confirmed1969-1978 Mean return (gap

day)19 -186 057 -068

Mean return(non-gap day)

005 005 005 005

Anomaly confirmed confirmed confirmed confirmed1979-1988 Mean return (gap

day)138 -162 066 -04

Mean return(non-gap day)

008 008 008 008

Anomaly confirmed confirmed confirmed confirmed1989-1998 Mean return (gap

day)016 012 018 -009

Mean return(non-gap day)

002 002 002 002

Anomaly confirmed not confirmed confirmed confirmed1999-2008 Mean return (gap

day)38E-3 027 -036 -013

Mean return(non-gap day)

-01 -01 -01 -01

Anomaly confirmed not confirmed not confirmed not confirmed2009-2018 Mean return (gap

day)039 009 013 -025

Mean return(non-gap day)

001 001 001 001

Anomaly confirmed not confirmed confirmed confirmed

G2 Parametric tests Students t-test

Table G2 T-test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 t-criterion 3194 3076 201 559t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected rejected

1959-1968 t-criterion 1399 2246 443 382t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected rejected

1969-1978 t-criterion 261 4358 417 786t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected rejected

1979-1988 t-criterion 1847 1445 709 395t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected rejected

1989-1998 t-criterion 13 066 126 093t-critical (=095) 196 196 196 196Null hypothesis not rejected not rejected not rejected not rejected

1999-2008 t-criterion 192 106 111 009t-critical (=095) 196 196 196 196Null hypothesis not rejected not rejected not rejected not rejected

2009-2018 t-criterion 27 05 089 188t-critical (=095) 196 196 196 196Null hypothesis rejected not rejected not rejected not rejected

31

G3 Parametric tests ANOVA

Table G3 ANOVA

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 F 88153 190609 1272 14521p-value 0 0 0 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1959-1968 F 93974 149771 4715 10418p-value 0 0 0 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1969-1978 F 84546 145429 6295 18241p-value 0 0 0 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1979-1988 F 66952 110482 13138 8626p-value 0 0 0 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1989-1998 F 323 138 43 168p-value 007 024 003 019

F critical 384 384 384 384Null hypothesis not rejected not rejected rejected not rejected

1999-2008 F 106 512 327 003p-value 001 002 007 085

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

2009-2018 F 169 069 175 93p-value 0 04 018 0

F critical 384 384 384 384Null hypothesis rejected not rejected not rejected rejected

G4 Non-parametric tests Kruskal-Wallis test

Table G4 Kruskal-Wallis test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 Adjusted H 26254 32592 1464 3962df 1 1 1 1

P value 0 0 0 0Null hypothesis rejected rejected rejected rejected

1959-1968 Adjusted H 28235 27989 2736 332df 1 1 1 1

P value 0 0 0 0Null hypothesis rejected rejected rejected rejected

1969-1978 Adjusted H 22202 33777 3311 7591df 1 1 1 1

P value 0 0 0 0Null hypothesis rejected rejected rejected rejected

1979-1988 Adjusted H 23282 25292 4812 3964df 1 1 1 1

P value 0 0 0 0Null hypothesis rejected rejected rejected rejected

1989-1998 Adjusted H 381 017 175 132df 1 1 1 1

P value 005 068 019 025Null hypothesis not rejected not rejected not rejected not rejected

1999-2008 Adjusted H 855 023 044 004df 1 1 1 1

P value 0 063 051 084Null hypothesis rejected not rejected not rejected not rejected

2009-2018 Adjusted H 1063 009 257 709df 1 1 1 1

P value 0 077 011 001Null hypothesis rejected not rejected not rejected rejected

32

G5 Regression analysis with dummy variables

Table G5 Regression analysis with dummy variables

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 a0 00007 (000) 00007 (000) 00007 (000) 00007 (000)a1 00088 (000) -00119 (000) 00011 (000) -00036 (000)

Anomaly confirmed confirmed confirmed confirmed1959-1968 a0 00006 (000) 00006 (000) 00006 (000) 00006 (000)

a1 00128 (000) -00153 (000) 00027 (000) -00046 (000)Anomaly confirmed confirmed confirmed confirmed

1969-1978 a0 00005 (000) 00005 (000) 00005 (000) 00005 (000)a1 00185 (000) -00192 (000) 00053 (000) -00073 (000)

Anomaly confirmed confirmed confirmed confirmed1979-1988 a0 00008 (000) 00008 (000) 00008 (000) 00008 (000)

a1 00131 (000) -00172 (000) 00059 (000) -00048 (000)Anomaly confirmed confirmed confirmed confirmed

1989-1998 a0 00002 (027) 00002 (028) 00002 (028) 00002 (027)a1 00014 (007) 00010 (024) 00017 (004) -00011 (019)

Anomaly not confirmed not confirmed confirmed not confirmed1999-2008 a0 00001 (059) 00001 (062) 00001 (059) 00001 (060)

a1 00037 (000) 00026 (002) -00038 (000) -00014 (019)Anomaly confirmed not confirmed not confirmed not confirmed

2009-2018 a0 00001 (049) 00001 (049) 00001 (049) 00001 (049)a1 00038 (000) 00007 (040) 00012 (018) -00027 (000)

Anomaly confirmed not confirmed not confirmed confirmed

G6 Modified CAR approach

Table G6 Modified CAR approach

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 Multiple R 099 099 093 098F-test 5753605 (000) 100470(000) 6280421 283281a0 -00091 (000) -00349 (000) 00056 (001) 00015 (073)a1 00083 (000) -00110 (000) 00010 (000) -00031 (000)

Anomaly confirmed confirmed confirmed confirmed1959-1968 Multiple R 099 099 099 099

F-test 3923274 (000) 3005562 (000) 443198 (000) 372583 (000)a0 00096 (000) 00073 (016) -00082 (000) -00095 (004)a1 00116 (001) -00149 (000) 00025 (000) -00047 (000)

Anomaly confirmed confirmed confirmed confirmed1969-1978 Multiple R 099 099 098 099

F-test 4302608 (000) 2723953 (000) 179969 (000) 639745a0 00246 (000) -00002 (000) 00217 (000) -00514 (000)a1 00176 (000) -00182 (000) 00049 (000) -00062 (000)

Anomaly confirmed confirmed confirmed confirmed1979-1988 Multiple R 099 099 099 099

F-test 5872335 (000) 1182609 (000) 1083558 (000) 910089 (000)a0 00136 (000) -01081 (000) -00285 (000) -00101 (000)a1 00131 (000) -00167 (000) 00062 (000) -00048 (000)

Anomaly confirmed confirmed confirmed confirmed1989-1998 Multiple R 09 056 069 016

F-test 46947 (000) 4885 (000) 10131 (000) 263 (011)a0 00102 (002) -00261 (000) -0016 (001) -00237 (000)a1 00015 (000) 00010 (000) 0001 (000) 00002 (011)

Anomaly confirmed confirmed confirmed not confirmed1999-2008 Multiple R 093 087 073 037

F-test 71863 (000) 32530 (000) 13273 (000) 1669 (000)a0 00185 (004) 00311 (000) -00130 (039) -00546 (000)a1 00037 (000) 00032 (000) -00026 (000) -00007 (000)

Anomaly confirmed not confirmed not confirmed confirmed2009-2018 Multiple R 089 001 096 091

F-test 40818 (000) 000 (094) 116744 (000) 53770 (000)a0 01436 (000) -01099 (000) -01036 (000) 00697 (000)a1 00030 (000) 00000 (094) 00024 (000) -00021 (000)

Anomaly confirmed not confirmed confirmed confirmed

33

H Detailed statistical results SampP 500 sub-periods

H1 Average analysis

Table H1 Average analysis

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 Mean return (gapday)

138 -171 004 -014

Mean return(non-gap day)

0 0 0 0

Anomaly confirmed confirmed confirmed confirmed1939-1948 Mean return (gap

day)001 -042 172 -195

Mean return(non-gap day)

003 003 003 003

Anomaly confirmed confirmed confirmed confirmed1949-1958 Mean return (gap

day)165 -18 02 002

Mean return(non-gap day)

006 006 006 006

Anomaly confirmed confirmed confirmed not confirmed1959-1968 Mean return (gap

day)104 -102 015 0

Mean return(non-gap day)

002 002 002 002

Anomaly confirmed confirmed confirmed not confirmed1969-1978 Mean return (gap

day)131 -13 019 -03

Mean return(non-gap day)

0 0 0 0

Anomaly confirmed confirmed confirmed confirmed1979-1988 Mean return (gap

day)058 -042 015 003

Mean return(non-gap day)

005 005 005 005

Anomaly confirmed confirmed confirmed not confirmed1989-1998 Mean return (gap

day)02 -023 -002 01

Mean return(non-gap day)

007 007 007 007

Anomaly confirmed confirmed not confirmed not confirmed1999-2008 Mean return (gap

day)083 -089 -023 -005

Mean return(non-gap day)

001 001 001 001

Anomaly confirmed confirmed not confirmed confirmed2009-2018 Mean return (gap

day)055 -052 001 -015

Mean return(non-gap day)

004 004 004 004

Anomaly confirmed confirmed not confirmed confirmed

34

H2 Parametric tests Students t-test

Table H2 T-test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 t-criterion 101 85 029 048t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

1939-1948 t-criterion 064 479 3074 225t-critical (=095) 196 196 196 196Null hypothesis not rejected rejected rejected rejected

1949-1958 t-criterion 2964 2383 193 041t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

1959-1968 t-criterion 2281 2157 21 023t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected not rejected

1969-1978 t-criterion 1318 2034 187 321t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected rejected

1979-1988 t-criterion 435 535 07 037t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

1989-1998 t-criterion 201 396 132 052t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

1999-2008 t-criterion 362 433 117 022t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

2009-2018 t-criterion 375 382 027 132t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

H3 Parametric tests ANOVA

Table H3 ANOVA

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 F 6281 8032 005 051p-value 0 0 082 047

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

1939-1948 F 056 2603 34854 51034p-value 045 0 0 0

F critical 384 384 384 384Null hypothesis not rejected rejected rejected rejected

1949-1958 F 100174 128997 897 062p-value 0 0 0 043

F critical 384 384 384 384Null hypothesis rejected rejected rejected not rejected

1959-1968 F 36831 32858 617 01p-value 0 0 001 074

F critical 384 384 384 384Null hypothesis rejected rejected rejected not rejected

1969-1978 F 26601 3063 53 152p-value 0 0 002 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1979-1988 F 23 245 076 009p-value 0 0 039 077

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

1989-1998 F 399 1156 118 015p-value 004 0 027 069

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

1999-2008 F 4253 5622 365 024p-value 0 0 006 062

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

2009-2018 F 3064 3656 01 43p-value 0 0 075 004

F critical 384 384 384 384Null hypothesis rejected rejected not rejected rejected

35

H4 Non-parametric tests Kruskal -Wallis test

Table H4 Kruskal-Wallis test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 Adjusted H 9982 5913 332 14df 1 1 1 1

P value 0 0 007 024Null hypothesis rejected rejected not rejected not rejected

1939-1948 Adjusted H 494 1999 23387 24927df 1 1 1 1

P value 003 0 0 0Null hypothesis rejected rejected rejected rejected

1949-1958 Adjusted H 28728 28175 348 15df 1 1 1 1

P value 0 0 006 022Null hypothesis rejected rejected not rejected not rejected

1959-1968 Adjusted H 25729 21437 701 063df 1 1 1 1

P value 0 0 001 043Null hypothesis rejected rejected rejected not rejected

1969-1978 Adjusted H 14407 20078 27 1706df 1 1 1 1

P value 0 0 01 0Null hypothesis rejected rejected not rejected rejected

1979-1988 Adjusted H 1788 2836 027 034df 1 1 1 1

P value 0 0 06 056Null hypothesis rejected rejected not rejected not rejected

1989-1998 Adjusted H 251 1431 111 044df 1 1 1 1

P value 011 0 029 051Null hypothesis not rejected rejected not rejected not rejected

1999-2008 Adjusted H 1812 1788 042 002df 1 1 1 1

P value 0 0 052 089Null hypothesis rejected rejected not rejected not rejected

2009-2018 Adjusted H 1314 1783 074 37df 1 1 1 1

P value 0 0 039 005Null hypothesis rejected rejected not rejected not rejected

36

H5 Regression analysis with dummy variables

Table H5 Regression analysis with dummy variables

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 a0 00000 (097) 00000 (004) 00000 (097) 00000 (097)a1 00138 (000) -00172 (000) 00004 (082) -00014 (047)

Anomaly confirmed confirmed not confirmed not confirmed1939-1948 a0 00003 (015) 00003 (015) 00003 (015) 00003 (015)

a1 00007 (045) -00045 (000) 00170 (000) -00199 (000)Anomaly not confirmed confirmed confirmed confirmed

1949-1958 a0 00006 (000) 00006 (000) 00006 (000) 00006 (000)a1 00160 (000) -00188 (000) 00016 (000) -00004 (043)

Anomaly confirmed confirmed confirmed not confirmed1959-1968 a0 00002 (007) 00002 (004) 00002 (008) 00002 (008)

a1 00103 (000) -00105 (000) 00014 (001) -00002 (074)Anomaly confirmed confirmed confirmed not confirmed

1969-1978 a0 00000 (078) 00000 (078) 00000 (078) 00000 (078)a1 00132 (000) -00132 (000) 00019 (002) -00030 (000)

Anomaly confirmed confirmed confirmed confirmed1979-1988 a0 00006 (001) 00006 (001) 00006 (001) 00006 (000)

a1 00053 (000) -00048 (000) 00009 (040) -00003 (075)Anomaly confirmed confirmed not confirmed not confirmed

1989-1998 a0 00007 (000) 00007 (000) 00007 (000) 00007 (000)a1 00016 (005) -00030 (000) -00009 (026) 00003 (072)

Anomaly confirmed confirmed not confirmed not confirmed1999-2008 a0 00001 (075) 00001 (075) 00001 (075) 00001 (076)

a1 00083 (000) -00091 (000) -00024 (005) -00006 (062)Anomaly confirmed confirmed not confirmed not confirmed

2009-2018 a0 00004 (003) 00004 (000) 00004 (003) 00004 (003)a1 00051 (000) -00059 (000) -00003 (075) -00019 (003)

Anomaly confirmed confirmed not confirmed confirmed

37

H6 Modified CAR approach

Table H6 Modified CAR approach

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 Multiple R 096 095 046 046F-test 175935 (000) 96500 (000) 3534 (000) 2880 (000)a0 -01070 (000) 01958 (000) 00405 (000) 00535 (000)a1 00121 (000) -00160 (000) 00006 (000) -00014 (000)

Anomaly confirmed confirmed confirmed confirmed1939-1948 Multiple R 08 099 099 099

F-test 18777 (000) 755727 (000) 3572830 (000) 2696099 (000)a0 00019 (073) -00346 (000) -00373 (000) 00912 (000)a1 00012 (000) -00044 (000) 00168 (000) -00197 (000)

Anomaly confirmed confirmed confirmed confirmed1949-1958 Multiple R 099 099 094 015

F-test 1021705 (000) 7171257 (000) 75858 (000) 242 (012)a0 -00176 (000) -00191 (000) 00095 (000) -00498 (000)a1 00154 (000) -00181 (000) 00013 (000) -00002 (012)

Anomaly confirmed confirmed confirmed not confirmed1959-1968 Multiple R 099 099 094 078

F-test 1463311 (000) 6002659 (000) 82273 (000) 14352 (000)a0 -00112 (000) 00004 (085) 00151 (000) 00389 (000)a1 00098 (000) -00102 (000) 00011 (000) -00009 (000)

Anomaly confirmed confirmed confirmed confirmed1969-1978 Multiple R 098 099 093 099

F-test 241655 (000) 1451901 (000) 57333 (000) 368160 (000)a0 -00433 (000) 00276 (000) 00099 (002) -00144 (000)a1 00132 (000) -00134 (000) 00020 (000) -00030 (000)

Anomaly confirmed confirmed confirmed confirmed1979-1988 Multiple R 092 078 023 008

F-test 53757 (000) 18707 (000) 487 (003) 085 (036)a0 00813 (000) -02508 (000) 00204 (000) -00235 (000)a1 00036 (000) -00031 (000) -00003 (003) -00001 (036)

Anomaly confirmed confirmed not confirmed not confirmed1989-1998 Multiple R 079 099 074 044

F-test 19705(000) 761967 (000) 14133 (000) 2369 (000)a0 00268 (000) 00023 (021) -00381 (000) 00087 (000)a1 00013 (000) -00028 (000) -00008 (000) 00002 (000)

Anomaly confirmed confirmed not confirmed not confirmed1999-2008 Multiple R 091 093 071 065

F-test 47218 (000) 76564 (000) 9843 (000) 7768 (000)a0 -01493 (000) 01351 (000) 00397 (000) 00007 (093)a1 00081 (000) -00083 (000) -00026 (000) -00011 (000)

Anomaly confirmed confirmed not confirmed confirmed2009-2018 Multiple R 086 087 083 074

F-test 29971 (000) 32484 (000) 23228 (000) 12764 (000)a0 01711 (000) -02250 (000) 00407 (000) -00472 (000)a1 00038 (000) -00044 (000) -00010 (000) -00012 (000)

Anomaly confirmed confirmed not confirmed confirmed

38

45 Trading simulation

The algorithm of the trading strategy is to buysell at the start of the updown gapday and close this position at the end of this day To test this strategy data for the DJIand SampP 500 are used (for this case the price anomaly still exists based on the day itoccurred) The results for DJI are presented in Table A8 and for the SampP 500 in Table8 For the SampP 500 and DJI the trading strategy built on price gap anomaly is efficientand its results differ from random

Table 8 Trading simulation results of the price gap anomaly for the SampP 500

Period Gaptype

Numberof

tradesunits

Numberof suc-cessfultradesunits

Numberof suc-cessfultrades

Profit

Profit peryear

z-test Result

1929-1938 Up 131 130 992 1816 182 1065 passedDown 110 108 982 1893 189 876 passed

1939-1948 Up 110 67 609 106 11 09 failedDown 122 79 648 518 52 465 passed

1949-1958 Up 106 105 991 1765 176 3191 passedDown 104 103 99 1891 189 2356 passed

1959-1968 Up 108 106 981 1331 113 2441 passedDown 92 91 989 948 95 2214 passed

1969-1978 Up 85 71 835 1128 113 1361 passedDown 96 90 938 1262 126 2118 passed

1979-1988 Up 92 63 685 54 54 495 passedDown 123 81 659 519 52 496 passed

1989-1998 Up 117 72 615 267 27 295 passedDown 99 61 616 228 23 32 passed

1999-2008 Up 99 65 657 828 83 373 passedDown 110 72 655 987 99 438 passed

2009-2018 Up 106 71 67 59 59 416 passedDown 107 65 607 56 56 362 passed

14

Figure 1 Trading simulation results of the price gap anomaly for the SampP 500

Note The primary axis refers to the percentage profit per year and the secondary to thez minus test statistic

One more interesting fact (see Figure 1) is the decrease of trading strategy efficiencyThis is indirect evidence in favour of evolution of the US stock market and its movementfrom less efficient to more efficient state Overall it can be concluded that the price gapanomaly is a real market anomaly The US stock market loses its efficiency after pricegaps This effect is temporary and lasts only for a day Still even this time is enoughto exploit the hole in the market efficiency and generate abnormal profits from trading

5 Conclusion

We analysed price gap anomaly in the US stock market by using information from threestock market indexes(DJI SampP 500 and NASDAQ) We tested three hypotheses of in-terest that is H1 the price gap anomaly exists H1minus1 prices tend to rise after positivegaps H1minus2 prices tend to fall after negative gaps H2 the price gap anomaly evolvesand H3 there is seasonality in price gaps Various statistical methods including para-metric tests (Students t-tests ANOVA) non-parametric tests (Mann-Whitney test)regression analysis with dummy variables MCAR approach and the trading simulationapproach were utilised

We conclude that the US stock market in the main did not exhibit seasonality in pricegaps Therefore H3 is rejected Furthermore no evidence was found that price gaps inthe US stock market were filled within five days of their occurrence However strongevidence in favour of abnormal price movements after the gaps were found confirming

15

H1 and H2 Particularly on the day of the occurrence of the gap and not on the dayafter the price gap In the DJI and the SampP 500 this pattern persists indicating thatthese markets take a day to incorporate new information As the results of the tradingsimulation indicate a day is enough to profit from a price gap anomaly trading strategyin the DJI and the SampP 500

Similar to other studies and other anomalies (see McLean and Pontiff (2016) Ca-jueiro and Tabak (2004) and Tiwari et al (2019) for example) the price gap anomalyevolved It is less prevalent since the 1990s as shown in the SampP 500 and NASDAQThis pattern of evolution is common amongst most stock market anomalies (see Plastunet al (2019b) on calendar anomalies amongst others) Our findings therefore add onto the existing literature Finally in the main our results are against the EMH and aretherefore interesting to both practitioners and academics

16

References

Agrawal A and Tandon K (1994) Anomalies or illusions evidence from stock marketsin eighteen countries Journal of international Money and Finance 13(1)83ndash106

Akerlof G A and Shiller R J (2009) Animal Spirits How human psychology drivesthe economy and why it matters for global capitalism Princeton University Press

Basu S (1977) Investment performance of common stocks in relation to their price-earnings ratios A test of the efficient market hypothesis The Journal of Finance32(3)663ndash682

Bildik R (2004) Are calendar anomalies still alive Evidence from istanbul stockexchange SSRN Electronic Journal 2004

Cai J Li Y and Qi Y (2006) The day-of-the-week effect New evidence from theChinese stock market Chinese Economy 39(2)71ndash88

Cajueiro D O and Tabak B M (2004) The Hurst exponent over time testing theassertion that emerging markets are becoming more efficient Physica A StatisticalMechanics and its Applications 336(3-4)521ndash537

Caporale G M Gil-Alana L Plastun A and Makarenko I (2016) Intraday anoma-lies and market efficiency A trading robot analysis Computational Economics47(2)275ndash295

Caporale G M and Plastun A (2017) Price gaps Another market anomaly Invest-ment Analysts Journal 46(4)279ndash293

Cross F (1973) The behavior of stock prices on Fridays and Mondays FinancialAnalysts Journal 29(6)67ndash69

Fama E F (1965) The behavior of stock-market prices The Journal of Business38(1)34ndash105

Fama E F (1970) Efficient capital markets A review of theory and empirical workThe Journal of Finance 25(2)383ndash417

Fortune P (1998) Weekends can be rough revisiting the weekend effect in stock pricesTechnical report

Fortune P (1999) Are stock returns different over weekends A jump diffusion analysisof the weekend effect New England Economic Review 103ndash19

French K R (1980) Stock returns and the weekend effect Journal of FinancialEconomics 8(1)55ndash69

Fung A K-W Lam K and Lam K-M (2010) Do the prices of stock index futuresin asia overreact to us market returns Journal of Empirical Finance 17(3)428ndash440

17

Gibbons M R and Hess P (1981) Day of the week effects and asset returns Journalof business pages 579ndash596

Grant J L Wolf A and Yu S (2005) Intraday price reversals in the us stock indexfutures market A 15-year study Journal of Banking amp Finance 29(5)1311ndash1327

Grossman S J and Stiglitz J E (1980) On the impossibility of informationallyefficient markets The American Economic Review 70(3)393ndash408

Jacobsen B Mamun A and Visaltanachoti N (2005) Seasonal size and valueanomalies

Jensen M (1978) Some anomalous evidence regarding market efficiency Journal ofFinancial Economics 6(23 (1978))95ndash101

Lakonishok J and Smidt S (1988) Are seasonal anomalies real A ninety-year per-spective The Review of Financial Studies 1(4)403ndash425

MacKinlay A (1997) Event studies in economics and finance Journal of EconomicLiterature (35)113ndash39

Mandelbrot B B (1997) The variation of certain speculative prices In Fractals andscaling in finance pages 371ndash418 Springer

McLean R D and Pontiff J (2016) Does academic research destroy stock returnpredictability The Journal of Finance 71(1)5ndash32

Plastun A Makarenko I Khomutenko L Shcherbak S and Tryfonova O (2019a)Exploring price gap anomaly in the ukrainian stock market Investment Managementamp Financial Innovations 16(2)150

Plastun A Sibande X Gupta R and Wohar M E (2019b) Rise and fall of calendaranomalies over a century The North American Journal of Economics and Finance49181ndash205

Schwert G W (2003) Chapter 15 anomalies and market efficiency In FinancialMarkets and Asset Pricing volume 1 of Handbook of the Economics of Finance pages939 ndash 974 Elsevier

Shiller R J (2000) Irrational exuberance Princeton University

Tiwari A K Aye G C and Gupta R (2019) Stock market efficiency analysis usinglong spans of data A multifractal detrended fluctuation approach Finance ResearchLetters 28398ndash411

Yuan Y (2015) Market-wide attention trading and stock returns Journal of FinancialEconomics 116(3)548ndash564

18

Appendices

A DJI and NASDAQ Summary Results

A1 Overall Results

Table A1 Gap size used for different sub-periods over the period 1929-2018

Period DJI NASDAQ1929-1938 - -1939-1948 - -1949-1958 - 0711959-1968 - 0951969-1978 - 1351979-1988 - 1101989-1998 040 0681999-2008 007 1502009-2018 020 110Overall data set 030 110

Table A2 Day of the week and gaps

Day of the week DJI NASDAQMonday 024 02Tuesday 02 02Wednesday 017 02Thursday 019 019Friday 021 02

A2 Statistical tests

Table A3 Results of the statistical tests for the overall data sets

PeriodMethod Averageanalysis

t-test ANOVAtest

Mann-Whitney

test

Regressionanalysiswith

dummyvariables

ModifiedCAR

approach

Overall

Dow Jones Index overall data setGap day - - - - - + 1Gap day (Positive gaps) + - - - - - 1Gap day (Negative gaps) + - - - - + 2Day after gap (Positive gaps) + - - - - - 1Day after gap (Negative gaps) + - - + - + 3

NASDAQ overall data setGap day + + + + + + 6Gap day (Positive gaps) + + + + + + 6Gap day (Negative gaps) + + + + + + 6Day after gap (Positive gaps) + + + + + + 6Day after gap (Negative gaps) + + + + + + 6

Note + indicates that the anomaly is confirmed and - indicates that anomaly is not confirmedThe higher the overall rating the stronger the evidence of the anomaly

19

Table A4 Results of the statistical tests for H1minus1 DJI

Period Averageanalysis

t-test ANOVA test Mann-Whitney

test

Regressionanalysis with

dummyvariables

ModifiedCAR

approach

Overall

Day of anomaly1989-1998 + - - - - + 21999-2008 + + + + + + 62009-2018 + + + + + + 6

Day after anomaly1989-1998 + - - - - + 21999-2008 + - - - - + 22009-2018 - - - - - - 0

Note + indicates that the anomaly is confirmed and - indicates that anomaly is not confirmedThe higher the overall rating the stronger the evidence of the anomaly

Table A5 Results of the statistical tests for H1minus2 DJI

Period Averageanalysis

t-test ANOVA test Mann-Whitneytest

Regressionanalysis with

dummyvariables

Modified CARapproach

Overall

Day of anomaly1989-1998 - - - - - - 01999-2008 + + + + + + 62009-2018 + + + + + + 6

Day after anomaly1989-1998 + - - - - + 21999-2008 + - - - - - 12009-2018 + - - - - + 2

Note + indicates that the anomaly is confirmed and - indicates that anomaly is not confirmedThe higher the overall rating the stronger the evidence of the anomaly

Table A6 Results of the statistical tests for H1minus1 NASDAQ

PeriodMethod Averageanalysis

t-test ANOVA test Mann-Whitney

test

Regressionanalysis with

dummyvariables

ModifiedCAR

approach

Overall

Day of anomaly1949-1958 + + + + + + 61959-1968 + + + + + + 61969-1978 + + + + + + 61979-1988 + + + + + + 61989-1998 + - - - - + 21999-2008 + - + + + + 52009-2018 + + + + + + 6

Day after anomaly1949-1958 + + + + + + 61959-1968 + + + + + + 61969-1978 + + + + + + 61979-1988 + + + + + + 61989-1998 + - + - + + 41999-2008 - - - - - - 02009-2018 + - - - - + 2

Note + indicates that the anomaly is confirmed and - indicates that anomaly is not confirmedThe higher the overall rating the stronger the evidence of the anomaly

20

Table A7 Results of the statistical tests for H1minus2 NASDAQ

PeriodMethod Averageanalysis

t-test ANOVA test Mann-Whitney

test

Regressionanalysis with

dummyvariables

ModifiedCAR

approach

Overall

Day of anomaly1949-1958 + + + + + + 61959-1968 + + + + + + 61969-1978 + + + + + + 61979-1988 + + + + + + 61989-1998 - - - - - + 11999-2008 - - + - - - 12009-2018 - - - - - - 0

Day after anomaly1949-1958 + + + + + + 61959-1968 + + + + + + 61969-1978 + + + + + + 61979-1988 + + + + + + 61989-1998 + - - - - - 11999-2008 - - - - - + 12009-2018 + - - + + + 4

Note + indicates that the anomaly is confirmed and - indicates that anomaly is not confirmedThe higher the overall rating the stronger the evidence of the anomaly

A3 Trading Simulation Results

Table A8 Trading simulation results of the price gap anomaly for the DJI 1989-2018

Period Gap type Number oftradesunits

Number ofsuccessfultradesunits

Number ofsuccessfultrades

Profit Profit per year

z-test Result

1989-1998 Up 102 46 451 -11 -01 011 failedDown 116 49 422 -267 -27 242 passed

1999-2008 Up 73 51 699 665 66 37 passedDown 143 81 566 641 64 331 passed

2009-2018 Up 127 88 693 308 31 327 passedDown 81 47 58 196 2 184 passed

21

B Short-term price behavior in DJI SampP 500 and

NASDAQ Price gaps (overall data sets)

Table B1 Momentum effect in the US stock market after the gap

Instrument Parameter Number of days after the gap1 2 3

Dow Jones Index Positive gaps 53 57 61Negative gaps 50 50 47

All gaps 51 54 54SampP 500 Index Positive gaps 40 63 60

Negative gaps 4 52 45All gaps 4 58 53

NASDAQ Positive gaps 32 65 67Negative gaps 24 63 59

All gaps 28 64 63

Table B2 Momentum effect in the US stock market before the gap

Instrument Parameter Number of days before the gap1 2 3

Dow Jones Index Positive gaps 56 49 52Negative gaps 54 49 49

All gaps 55 49 50SampP 500 Index Positive gaps 57 57 52

Negative gaps 60 59 54All gaps 58 58 53

NASDAQ Positive gaps 61 56 54Negative gaps 68 69 70

All gaps 64 63 63

Table B3 Fill gap effect in the US stock market

Instrument Parameter Number of days after the gap1 2 3 4 5

Dow Jones Index Positive gaps 22 28 26 30 28Negative gaps 25 33 36 42 46

All gaps 24 30 31 35 37SampP 500 Index Positive gaps 0 6 11 16 19

Negative gaps 1 10 19 26 27All gaps 1 8 15 20 23

NASDAQ Positive gaps 8 13 18 21 19Negative gaps 7 11 17 21 25

All gaps 8 12 18 21 22

22

C Detailed statistical results DJI overall data

C1 Average analysis

Table C1 Average analysis

Parameter Gap day Gap day(Positive gaps)

Gap day(Negative gaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Mean return (gap day) 003 006 0 005 -003Mean return (non-gap day) 004 004 004 004 004Anomaly not confirmed not confirmed confirmed not confirmed confirmed

C2 Parametric tests Students t-test

Table C2 T-test

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

t-criterion 016 042 053 015 104t-critical (=095) 196 196 196 196 196Null hypothesis not rejected not rejected not rejected not rejected not rejected

C3 Parametric tests ANOVA

Table C3 ANOVA

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

F 0036 018 053 003 14p-value 085 067 047 086 024F critical 384 384 384 384 384Null hypothesis not rejected not rejected not rejected not rejected not rejected

C4 Non-parametric tests Kruskal-Wallis test

Table C4 Kruskal -Wallis test

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Adjusted H 082 012 126 0 455df 1 1 1 1 1P value 037 073 026 095 003Critical value 384 384 384 384 384Null hypothesis not rejected not rejected not rejected not rejected rejected

23

C5 Regression analysis with dummy variables

Table C5 Regression analysis with dummy variables

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

a0 00004 (000) 00004 (000) 00004 (000) 00004 (000) 00004 (000)a1 -00001 (-019) 00002 (067) -00004 (047) 00001 (086) -00007 (024)Anomaly not confirmed not confirmed not confirmed not confirmed not confirmed

C6 Modified CAR approach

Table C6 Modified CAR approach

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Multiple R 049 05 025 0 092F-test 23347 (000) 12913 (000) 2207 (000) 000 (098) 1822 (000)a0 -00041 (060) 00128 (006) -00267 (000) 00354 (000) 00319 (000)a1 -00003 (000) -00003 (000) -00002 (000) 00000 (098) -00008 (000)Anomaly confirmed confirmed confirmed not confirmed confirmed

24

D Detailed statistical results SampP 500 overall data

D1 Average analysis

Table D1 Average analysis

Parameter Gap day Gap day(Positive gaps)

Gap day(Negative gaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Mean return (gap day) 006 115 -129 017 -011Mean return (non-gap day) 002 002 002 002 002Anomaly confirmed confirmed confirmed confirmed confirmed

D2 Parametric tests Students t-test

Table D2 T-test

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

t-criterion 092 4546 3579 485 271t-critical (=095) 196 196 196 196 196Null hypothesis not rejected rejected rejected rejected rejected

D3 Parametric tests ANOVA

Table D3 ANOVA

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

F 155 116211 126952 1866 136p-value 022 0 0 0 0F critical 384 384 384 384 384Null hypothesis not rejected rejected rejected not rejected not rejected

D4 Non-parametric tests Kruskal-Wallis test

Table D4 Kruskal-Wallis test

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Adjusted H 1352 70516 47237 3946 004df 1 1 1 1 1P value 0 0 0 0 084Critical value 384 384 384 384 384Null hypothesis rejected rejected rejected rejected not rejected

25

D5 Regression analysis with dummy variables

Table D5 Regression analysis with dummy variables

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

a0 00002 (000) 00002 (000) 00002 (000) 00002 (000) 00002 (000)a1 00003 (021) 00113 (000) -00132 (000) 00014 (000) -00014 (000)Anomaly not confirmed confirmed confirmed confirmed confirmed

D6 Modified CAR approach

Table D6 Modified CAR approach

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Multiple R 051 099 099 099 096F-test 69486 (000) 325351 (000) 1457582 (000) 6345973 (000) 1213344 (000)a0 -01003(000) 04081 (000) -05444 (000) -01088 (000) 00272 (000)a1 00002 (000) 00106 (000) -00127 (000) 00016 (000) -00016 (000)Anomaly confirmed confirmed confirmed confirmed confirmed

26

E Detailed statistical results NASDAQ overall data

E1 Average analysis

Table E1 Average analysis

Parameter Gap day Gap day(Positive gaps)

Gap day(Negative gaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Mean return (gap day) -009 084 -090 022 -037Mean return (non-gap day) 003 003 003 003 003Anomaly confirmed confirmed confirmed confirmed confirmed

E2 Parametric tests Students t-test

Table E2 T-test

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

t-criterion 230 1257 1341 306 664t-critical (=095) 196 196 196 196 196Null hypothesis rejected rejected rejected rejected rejected

E3 Parametric tests ANOVA

Table E3 ANOVA

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

F 2289 62720 88402 3330 17356p-value 0 0 0 0 0F critical 384 384 384 384 384Null hypothesis rejected rejected rejected rejected rejected

E4 Non-parametric tests Kruskal-Wallis test

Table E4 Kruskal-Wallis test

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Adjusted H 1892 36022 45248 4695 10437df 1 1 1 1 1P value 0 0 0 0 0Critical value 384 384 384 384 384Null hypothesis rejected rejected rejected rejected rejected

27

E5 Regression analysis with dummy variables

Table E5 Regression analysis with dummy variables

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

a0 00003 (000) 00003 (000) 00003 (000) 00003 (000) 00003 (000)a1 -00012 (000) 00081 (000) -00093 (000) 00018 (000) -00040 (000)Anomaly confirmed confirmed confirmed confirmed confirmed

E6 Modified CAR approach

Table E6 Modified CAR approach

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Multiple R 069 092 092 072 097F-test 133255 (000) 361102 (000) 442376 (000) 72903 (000) 1082812 (000)a0 -10646 (000) 11373 (000) -12888 (000) 03928 (000) -02297 (000)a1 -00011 (000) 00073 (000) -00097 (000) 00017 (000) -00039 (000)Anomaly confirmed confirmed confirmed confirmed confirmed

28

F Detailed statistical results DJI sub-periods

F1 Average analysis

Table F1 Average analysis

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 Mean return (gapday)

-001 023 015 -004

Mean return(non-gap day)

007 007 007 007

Anomaly confirmed confirmed confirmed confirmed1999-2008 Mean return (gap

day)090 -045 013 -004

Mean return(non-gap day)

-004 -004 -004 -004

Anomaly confirmed confirmed confirmed confirmed2009-2018 Mean return (gap

day)024 -024 0 -004

Mean return(non-gap day)

004 004 004 004

Anomaly confirmed confirmed not confirmed confirmed

F2 Parametric tests Students t-test

Table F2 T-test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 t-criterion 083 165 087 139t-critical (=095) 196 196 196 196Null hypothesis not rejected not rejected not rejected not rejected

1999-2008 t-criterion 347 351 054 047t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected rejected

2009-2018 t-criterion 265 207 051 058t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

F3 Parametric tests ANOVA

Table F3 ANOVA

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 F 085 409 093 179p-value 035 004 033 018

F critical 384 384 384 384Null hypothesis not rejected rejected not rejected not rejected

1999-2008 F 5405 3196 065 072p-value 0 0 042 039

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

2009-2018 F 554 697 024 058p-value 001 0 062 044

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

29

F4 Non-parametric tests Kruskal-Wallis test

Table F4 Kruskal-Wallis test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 Adjusted H 113 211 113 332df 1 1 1 1

P value 029 015 029 007Null hypothesis not rejected not rejected not rejected not rejected

1999-2008 Adjusted H 1484 1414 003 139df 1 1 1 1

P value 0 0 086 024Null hypothesis rejected rejected not rejected not rejected

2009-2018 Adjusted H 506 68 051 171df 1 1 1 1

P value 002 001 047 019Null hypothesis rejected rejected not rejected not rejected

F5 Regression analysis with dummy variables

Table F5 Regression analysis with dummy variables

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 a0 000068 (000) 00007 (000) 00007 (000) 00007 (000)a1 -000078 (035) 00016 (004) 00008 (033) -00011 (018)

Anomaly not confirmed confirmed not confirmed not confirmed1999-2008 a0 00004 (008) 00004 (008) 00004 (006) 00004 (008)

a1 00087 (000) -00049 (000) 00009 (042) -00008 (039)Anomaly confirmed confirmed not confirmed not confirmed

2009-2018 a0 00004 (006) 00004 (006) 00004 (006) 00004 (006)a1 00021 (001) -00028 (001) -00004 (062) -00008 (047)

Anomaly confirmed confirmed not confirmed not confirmed

F6 Modified CAR approach

Table F6 Modified CAR approach

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 Multiple R 083 088 082 086F-test 22779 (000) 40583 (000) 20401 (000) 3269454 (000)a0 00042 (023) 00017 (073) 00014 (058) -00266 (000)a1 -00009 (000) 00015 (000) 00006 (000) -00009 (000)

Anomaly confirmed confirmed confirmed confirmed1999-2008 Multiple R 095 093 076 019

F-test 62658 (000) 84712 (000) 10056 (000) 492 (003)a0 -00972 (000) 00365 (000) -00198 (000) -00115 (021)a1 00086 (000) -00042 (000) 00014 (000) 00002 (003)

Anomaly confirmed confirmed confirmed not confirmed2009-2018 Multiple R 096 082 08 05

F-test 150452 (000) 16731 (000) 22287 (000) 2620 (000)a0 00548 (000) -00618 (000) 00031 (020) -00112 (000)a1 00013 (000) -00014 (000) -00005 (000) -00004 (000)

Anomaly confirmed confirmed not confirmed confirmed

30

G Detailed statistical results NASDAQ sub-periods

G1 Average analysis

Table G1 Average analysis

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 Mean return (gapday)

094 -111 0189 -029

Mean return(non-gap day)

007 007 007 007

Anomaly confirmed confirmed confirmed confirmed1959-1968 Mean return (gap

day)133 -147 033 -039

Mean return(non-gap day)

006 006 006 006

Anomaly confirmed confirmed confirmed confirmed1969-1978 Mean return (gap

day)19 -186 057 -068

Mean return(non-gap day)

005 005 005 005

Anomaly confirmed confirmed confirmed confirmed1979-1988 Mean return (gap

day)138 -162 066 -04

Mean return(non-gap day)

008 008 008 008

Anomaly confirmed confirmed confirmed confirmed1989-1998 Mean return (gap

day)016 012 018 -009

Mean return(non-gap day)

002 002 002 002

Anomaly confirmed not confirmed confirmed confirmed1999-2008 Mean return (gap

day)38E-3 027 -036 -013

Mean return(non-gap day)

-01 -01 -01 -01

Anomaly confirmed not confirmed not confirmed not confirmed2009-2018 Mean return (gap

day)039 009 013 -025

Mean return(non-gap day)

001 001 001 001

Anomaly confirmed not confirmed confirmed confirmed

G2 Parametric tests Students t-test

Table G2 T-test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 t-criterion 3194 3076 201 559t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected rejected

1959-1968 t-criterion 1399 2246 443 382t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected rejected

1969-1978 t-criterion 261 4358 417 786t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected rejected

1979-1988 t-criterion 1847 1445 709 395t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected rejected

1989-1998 t-criterion 13 066 126 093t-critical (=095) 196 196 196 196Null hypothesis not rejected not rejected not rejected not rejected

1999-2008 t-criterion 192 106 111 009t-critical (=095) 196 196 196 196Null hypothesis not rejected not rejected not rejected not rejected

2009-2018 t-criterion 27 05 089 188t-critical (=095) 196 196 196 196Null hypothesis rejected not rejected not rejected not rejected

31

G3 Parametric tests ANOVA

Table G3 ANOVA

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 F 88153 190609 1272 14521p-value 0 0 0 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1959-1968 F 93974 149771 4715 10418p-value 0 0 0 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1969-1978 F 84546 145429 6295 18241p-value 0 0 0 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1979-1988 F 66952 110482 13138 8626p-value 0 0 0 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1989-1998 F 323 138 43 168p-value 007 024 003 019

F critical 384 384 384 384Null hypothesis not rejected not rejected rejected not rejected

1999-2008 F 106 512 327 003p-value 001 002 007 085

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

2009-2018 F 169 069 175 93p-value 0 04 018 0

F critical 384 384 384 384Null hypothesis rejected not rejected not rejected rejected

G4 Non-parametric tests Kruskal-Wallis test

Table G4 Kruskal-Wallis test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 Adjusted H 26254 32592 1464 3962df 1 1 1 1

P value 0 0 0 0Null hypothesis rejected rejected rejected rejected

1959-1968 Adjusted H 28235 27989 2736 332df 1 1 1 1

P value 0 0 0 0Null hypothesis rejected rejected rejected rejected

1969-1978 Adjusted H 22202 33777 3311 7591df 1 1 1 1

P value 0 0 0 0Null hypothesis rejected rejected rejected rejected

1979-1988 Adjusted H 23282 25292 4812 3964df 1 1 1 1

P value 0 0 0 0Null hypothesis rejected rejected rejected rejected

1989-1998 Adjusted H 381 017 175 132df 1 1 1 1

P value 005 068 019 025Null hypothesis not rejected not rejected not rejected not rejected

1999-2008 Adjusted H 855 023 044 004df 1 1 1 1

P value 0 063 051 084Null hypothesis rejected not rejected not rejected not rejected

2009-2018 Adjusted H 1063 009 257 709df 1 1 1 1

P value 0 077 011 001Null hypothesis rejected not rejected not rejected rejected

32

G5 Regression analysis with dummy variables

Table G5 Regression analysis with dummy variables

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 a0 00007 (000) 00007 (000) 00007 (000) 00007 (000)a1 00088 (000) -00119 (000) 00011 (000) -00036 (000)

Anomaly confirmed confirmed confirmed confirmed1959-1968 a0 00006 (000) 00006 (000) 00006 (000) 00006 (000)

a1 00128 (000) -00153 (000) 00027 (000) -00046 (000)Anomaly confirmed confirmed confirmed confirmed

1969-1978 a0 00005 (000) 00005 (000) 00005 (000) 00005 (000)a1 00185 (000) -00192 (000) 00053 (000) -00073 (000)

Anomaly confirmed confirmed confirmed confirmed1979-1988 a0 00008 (000) 00008 (000) 00008 (000) 00008 (000)

a1 00131 (000) -00172 (000) 00059 (000) -00048 (000)Anomaly confirmed confirmed confirmed confirmed

1989-1998 a0 00002 (027) 00002 (028) 00002 (028) 00002 (027)a1 00014 (007) 00010 (024) 00017 (004) -00011 (019)

Anomaly not confirmed not confirmed confirmed not confirmed1999-2008 a0 00001 (059) 00001 (062) 00001 (059) 00001 (060)

a1 00037 (000) 00026 (002) -00038 (000) -00014 (019)Anomaly confirmed not confirmed not confirmed not confirmed

2009-2018 a0 00001 (049) 00001 (049) 00001 (049) 00001 (049)a1 00038 (000) 00007 (040) 00012 (018) -00027 (000)

Anomaly confirmed not confirmed not confirmed confirmed

G6 Modified CAR approach

Table G6 Modified CAR approach

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 Multiple R 099 099 093 098F-test 5753605 (000) 100470(000) 6280421 283281a0 -00091 (000) -00349 (000) 00056 (001) 00015 (073)a1 00083 (000) -00110 (000) 00010 (000) -00031 (000)

Anomaly confirmed confirmed confirmed confirmed1959-1968 Multiple R 099 099 099 099

F-test 3923274 (000) 3005562 (000) 443198 (000) 372583 (000)a0 00096 (000) 00073 (016) -00082 (000) -00095 (004)a1 00116 (001) -00149 (000) 00025 (000) -00047 (000)

Anomaly confirmed confirmed confirmed confirmed1969-1978 Multiple R 099 099 098 099

F-test 4302608 (000) 2723953 (000) 179969 (000) 639745a0 00246 (000) -00002 (000) 00217 (000) -00514 (000)a1 00176 (000) -00182 (000) 00049 (000) -00062 (000)

Anomaly confirmed confirmed confirmed confirmed1979-1988 Multiple R 099 099 099 099

F-test 5872335 (000) 1182609 (000) 1083558 (000) 910089 (000)a0 00136 (000) -01081 (000) -00285 (000) -00101 (000)a1 00131 (000) -00167 (000) 00062 (000) -00048 (000)

Anomaly confirmed confirmed confirmed confirmed1989-1998 Multiple R 09 056 069 016

F-test 46947 (000) 4885 (000) 10131 (000) 263 (011)a0 00102 (002) -00261 (000) -0016 (001) -00237 (000)a1 00015 (000) 00010 (000) 0001 (000) 00002 (011)

Anomaly confirmed confirmed confirmed not confirmed1999-2008 Multiple R 093 087 073 037

F-test 71863 (000) 32530 (000) 13273 (000) 1669 (000)a0 00185 (004) 00311 (000) -00130 (039) -00546 (000)a1 00037 (000) 00032 (000) -00026 (000) -00007 (000)

Anomaly confirmed not confirmed not confirmed confirmed2009-2018 Multiple R 089 001 096 091

F-test 40818 (000) 000 (094) 116744 (000) 53770 (000)a0 01436 (000) -01099 (000) -01036 (000) 00697 (000)a1 00030 (000) 00000 (094) 00024 (000) -00021 (000)

Anomaly confirmed not confirmed confirmed confirmed

33

H Detailed statistical results SampP 500 sub-periods

H1 Average analysis

Table H1 Average analysis

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 Mean return (gapday)

138 -171 004 -014

Mean return(non-gap day)

0 0 0 0

Anomaly confirmed confirmed confirmed confirmed1939-1948 Mean return (gap

day)001 -042 172 -195

Mean return(non-gap day)

003 003 003 003

Anomaly confirmed confirmed confirmed confirmed1949-1958 Mean return (gap

day)165 -18 02 002

Mean return(non-gap day)

006 006 006 006

Anomaly confirmed confirmed confirmed not confirmed1959-1968 Mean return (gap

day)104 -102 015 0

Mean return(non-gap day)

002 002 002 002

Anomaly confirmed confirmed confirmed not confirmed1969-1978 Mean return (gap

day)131 -13 019 -03

Mean return(non-gap day)

0 0 0 0

Anomaly confirmed confirmed confirmed confirmed1979-1988 Mean return (gap

day)058 -042 015 003

Mean return(non-gap day)

005 005 005 005

Anomaly confirmed confirmed confirmed not confirmed1989-1998 Mean return (gap

day)02 -023 -002 01

Mean return(non-gap day)

007 007 007 007

Anomaly confirmed confirmed not confirmed not confirmed1999-2008 Mean return (gap

day)083 -089 -023 -005

Mean return(non-gap day)

001 001 001 001

Anomaly confirmed confirmed not confirmed confirmed2009-2018 Mean return (gap

day)055 -052 001 -015

Mean return(non-gap day)

004 004 004 004

Anomaly confirmed confirmed not confirmed confirmed

34

H2 Parametric tests Students t-test

Table H2 T-test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 t-criterion 101 85 029 048t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

1939-1948 t-criterion 064 479 3074 225t-critical (=095) 196 196 196 196Null hypothesis not rejected rejected rejected rejected

1949-1958 t-criterion 2964 2383 193 041t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

1959-1968 t-criterion 2281 2157 21 023t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected not rejected

1969-1978 t-criterion 1318 2034 187 321t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected rejected

1979-1988 t-criterion 435 535 07 037t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

1989-1998 t-criterion 201 396 132 052t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

1999-2008 t-criterion 362 433 117 022t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

2009-2018 t-criterion 375 382 027 132t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

H3 Parametric tests ANOVA

Table H3 ANOVA

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 F 6281 8032 005 051p-value 0 0 082 047

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

1939-1948 F 056 2603 34854 51034p-value 045 0 0 0

F critical 384 384 384 384Null hypothesis not rejected rejected rejected rejected

1949-1958 F 100174 128997 897 062p-value 0 0 0 043

F critical 384 384 384 384Null hypothesis rejected rejected rejected not rejected

1959-1968 F 36831 32858 617 01p-value 0 0 001 074

F critical 384 384 384 384Null hypothesis rejected rejected rejected not rejected

1969-1978 F 26601 3063 53 152p-value 0 0 002 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1979-1988 F 23 245 076 009p-value 0 0 039 077

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

1989-1998 F 399 1156 118 015p-value 004 0 027 069

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

1999-2008 F 4253 5622 365 024p-value 0 0 006 062

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

2009-2018 F 3064 3656 01 43p-value 0 0 075 004

F critical 384 384 384 384Null hypothesis rejected rejected not rejected rejected

35

H4 Non-parametric tests Kruskal -Wallis test

Table H4 Kruskal-Wallis test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 Adjusted H 9982 5913 332 14df 1 1 1 1

P value 0 0 007 024Null hypothesis rejected rejected not rejected not rejected

1939-1948 Adjusted H 494 1999 23387 24927df 1 1 1 1

P value 003 0 0 0Null hypothesis rejected rejected rejected rejected

1949-1958 Adjusted H 28728 28175 348 15df 1 1 1 1

P value 0 0 006 022Null hypothesis rejected rejected not rejected not rejected

1959-1968 Adjusted H 25729 21437 701 063df 1 1 1 1

P value 0 0 001 043Null hypothesis rejected rejected rejected not rejected

1969-1978 Adjusted H 14407 20078 27 1706df 1 1 1 1

P value 0 0 01 0Null hypothesis rejected rejected not rejected rejected

1979-1988 Adjusted H 1788 2836 027 034df 1 1 1 1

P value 0 0 06 056Null hypothesis rejected rejected not rejected not rejected

1989-1998 Adjusted H 251 1431 111 044df 1 1 1 1

P value 011 0 029 051Null hypothesis not rejected rejected not rejected not rejected

1999-2008 Adjusted H 1812 1788 042 002df 1 1 1 1

P value 0 0 052 089Null hypothesis rejected rejected not rejected not rejected

2009-2018 Adjusted H 1314 1783 074 37df 1 1 1 1

P value 0 0 039 005Null hypothesis rejected rejected not rejected not rejected

36

H5 Regression analysis with dummy variables

Table H5 Regression analysis with dummy variables

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 a0 00000 (097) 00000 (004) 00000 (097) 00000 (097)a1 00138 (000) -00172 (000) 00004 (082) -00014 (047)

Anomaly confirmed confirmed not confirmed not confirmed1939-1948 a0 00003 (015) 00003 (015) 00003 (015) 00003 (015)

a1 00007 (045) -00045 (000) 00170 (000) -00199 (000)Anomaly not confirmed confirmed confirmed confirmed

1949-1958 a0 00006 (000) 00006 (000) 00006 (000) 00006 (000)a1 00160 (000) -00188 (000) 00016 (000) -00004 (043)

Anomaly confirmed confirmed confirmed not confirmed1959-1968 a0 00002 (007) 00002 (004) 00002 (008) 00002 (008)

a1 00103 (000) -00105 (000) 00014 (001) -00002 (074)Anomaly confirmed confirmed confirmed not confirmed

1969-1978 a0 00000 (078) 00000 (078) 00000 (078) 00000 (078)a1 00132 (000) -00132 (000) 00019 (002) -00030 (000)

Anomaly confirmed confirmed confirmed confirmed1979-1988 a0 00006 (001) 00006 (001) 00006 (001) 00006 (000)

a1 00053 (000) -00048 (000) 00009 (040) -00003 (075)Anomaly confirmed confirmed not confirmed not confirmed

1989-1998 a0 00007 (000) 00007 (000) 00007 (000) 00007 (000)a1 00016 (005) -00030 (000) -00009 (026) 00003 (072)

Anomaly confirmed confirmed not confirmed not confirmed1999-2008 a0 00001 (075) 00001 (075) 00001 (075) 00001 (076)

a1 00083 (000) -00091 (000) -00024 (005) -00006 (062)Anomaly confirmed confirmed not confirmed not confirmed

2009-2018 a0 00004 (003) 00004 (000) 00004 (003) 00004 (003)a1 00051 (000) -00059 (000) -00003 (075) -00019 (003)

Anomaly confirmed confirmed not confirmed confirmed

37

H6 Modified CAR approach

Table H6 Modified CAR approach

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 Multiple R 096 095 046 046F-test 175935 (000) 96500 (000) 3534 (000) 2880 (000)a0 -01070 (000) 01958 (000) 00405 (000) 00535 (000)a1 00121 (000) -00160 (000) 00006 (000) -00014 (000)

Anomaly confirmed confirmed confirmed confirmed1939-1948 Multiple R 08 099 099 099

F-test 18777 (000) 755727 (000) 3572830 (000) 2696099 (000)a0 00019 (073) -00346 (000) -00373 (000) 00912 (000)a1 00012 (000) -00044 (000) 00168 (000) -00197 (000)

Anomaly confirmed confirmed confirmed confirmed1949-1958 Multiple R 099 099 094 015

F-test 1021705 (000) 7171257 (000) 75858 (000) 242 (012)a0 -00176 (000) -00191 (000) 00095 (000) -00498 (000)a1 00154 (000) -00181 (000) 00013 (000) -00002 (012)

Anomaly confirmed confirmed confirmed not confirmed1959-1968 Multiple R 099 099 094 078

F-test 1463311 (000) 6002659 (000) 82273 (000) 14352 (000)a0 -00112 (000) 00004 (085) 00151 (000) 00389 (000)a1 00098 (000) -00102 (000) 00011 (000) -00009 (000)

Anomaly confirmed confirmed confirmed confirmed1969-1978 Multiple R 098 099 093 099

F-test 241655 (000) 1451901 (000) 57333 (000) 368160 (000)a0 -00433 (000) 00276 (000) 00099 (002) -00144 (000)a1 00132 (000) -00134 (000) 00020 (000) -00030 (000)

Anomaly confirmed confirmed confirmed confirmed1979-1988 Multiple R 092 078 023 008

F-test 53757 (000) 18707 (000) 487 (003) 085 (036)a0 00813 (000) -02508 (000) 00204 (000) -00235 (000)a1 00036 (000) -00031 (000) -00003 (003) -00001 (036)

Anomaly confirmed confirmed not confirmed not confirmed1989-1998 Multiple R 079 099 074 044

F-test 19705(000) 761967 (000) 14133 (000) 2369 (000)a0 00268 (000) 00023 (021) -00381 (000) 00087 (000)a1 00013 (000) -00028 (000) -00008 (000) 00002 (000)

Anomaly confirmed confirmed not confirmed not confirmed1999-2008 Multiple R 091 093 071 065

F-test 47218 (000) 76564 (000) 9843 (000) 7768 (000)a0 -01493 (000) 01351 (000) 00397 (000) 00007 (093)a1 00081 (000) -00083 (000) -00026 (000) -00011 (000)

Anomaly confirmed confirmed not confirmed confirmed2009-2018 Multiple R 086 087 083 074

F-test 29971 (000) 32484 (000) 23228 (000) 12764 (000)a0 01711 (000) -02250 (000) 00407 (000) -00472 (000)a1 00038 (000) -00044 (000) -00010 (000) -00012 (000)

Anomaly confirmed confirmed not confirmed confirmed

38

Figure 1 Trading simulation results of the price gap anomaly for the SampP 500

Note The primary axis refers to the percentage profit per year and the secondary to thez minus test statistic

One more interesting fact (see Figure 1) is the decrease of trading strategy efficiencyThis is indirect evidence in favour of evolution of the US stock market and its movementfrom less efficient to more efficient state Overall it can be concluded that the price gapanomaly is a real market anomaly The US stock market loses its efficiency after pricegaps This effect is temporary and lasts only for a day Still even this time is enoughto exploit the hole in the market efficiency and generate abnormal profits from trading

5 Conclusion

We analysed price gap anomaly in the US stock market by using information from threestock market indexes(DJI SampP 500 and NASDAQ) We tested three hypotheses of in-terest that is H1 the price gap anomaly exists H1minus1 prices tend to rise after positivegaps H1minus2 prices tend to fall after negative gaps H2 the price gap anomaly evolvesand H3 there is seasonality in price gaps Various statistical methods including para-metric tests (Students t-tests ANOVA) non-parametric tests (Mann-Whitney test)regression analysis with dummy variables MCAR approach and the trading simulationapproach were utilised

We conclude that the US stock market in the main did not exhibit seasonality in pricegaps Therefore H3 is rejected Furthermore no evidence was found that price gaps inthe US stock market were filled within five days of their occurrence However strongevidence in favour of abnormal price movements after the gaps were found confirming

15

H1 and H2 Particularly on the day of the occurrence of the gap and not on the dayafter the price gap In the DJI and the SampP 500 this pattern persists indicating thatthese markets take a day to incorporate new information As the results of the tradingsimulation indicate a day is enough to profit from a price gap anomaly trading strategyin the DJI and the SampP 500

Similar to other studies and other anomalies (see McLean and Pontiff (2016) Ca-jueiro and Tabak (2004) and Tiwari et al (2019) for example) the price gap anomalyevolved It is less prevalent since the 1990s as shown in the SampP 500 and NASDAQThis pattern of evolution is common amongst most stock market anomalies (see Plastunet al (2019b) on calendar anomalies amongst others) Our findings therefore add onto the existing literature Finally in the main our results are against the EMH and aretherefore interesting to both practitioners and academics

16

References

Agrawal A and Tandon K (1994) Anomalies or illusions evidence from stock marketsin eighteen countries Journal of international Money and Finance 13(1)83ndash106

Akerlof G A and Shiller R J (2009) Animal Spirits How human psychology drivesthe economy and why it matters for global capitalism Princeton University Press

Basu S (1977) Investment performance of common stocks in relation to their price-earnings ratios A test of the efficient market hypothesis The Journal of Finance32(3)663ndash682

Bildik R (2004) Are calendar anomalies still alive Evidence from istanbul stockexchange SSRN Electronic Journal 2004

Cai J Li Y and Qi Y (2006) The day-of-the-week effect New evidence from theChinese stock market Chinese Economy 39(2)71ndash88

Cajueiro D O and Tabak B M (2004) The Hurst exponent over time testing theassertion that emerging markets are becoming more efficient Physica A StatisticalMechanics and its Applications 336(3-4)521ndash537

Caporale G M Gil-Alana L Plastun A and Makarenko I (2016) Intraday anoma-lies and market efficiency A trading robot analysis Computational Economics47(2)275ndash295

Caporale G M and Plastun A (2017) Price gaps Another market anomaly Invest-ment Analysts Journal 46(4)279ndash293

Cross F (1973) The behavior of stock prices on Fridays and Mondays FinancialAnalysts Journal 29(6)67ndash69

Fama E F (1965) The behavior of stock-market prices The Journal of Business38(1)34ndash105

Fama E F (1970) Efficient capital markets A review of theory and empirical workThe Journal of Finance 25(2)383ndash417

Fortune P (1998) Weekends can be rough revisiting the weekend effect in stock pricesTechnical report

Fortune P (1999) Are stock returns different over weekends A jump diffusion analysisof the weekend effect New England Economic Review 103ndash19

French K R (1980) Stock returns and the weekend effect Journal of FinancialEconomics 8(1)55ndash69

Fung A K-W Lam K and Lam K-M (2010) Do the prices of stock index futuresin asia overreact to us market returns Journal of Empirical Finance 17(3)428ndash440

17

Gibbons M R and Hess P (1981) Day of the week effects and asset returns Journalof business pages 579ndash596

Grant J L Wolf A and Yu S (2005) Intraday price reversals in the us stock indexfutures market A 15-year study Journal of Banking amp Finance 29(5)1311ndash1327

Grossman S J and Stiglitz J E (1980) On the impossibility of informationallyefficient markets The American Economic Review 70(3)393ndash408

Jacobsen B Mamun A and Visaltanachoti N (2005) Seasonal size and valueanomalies

Jensen M (1978) Some anomalous evidence regarding market efficiency Journal ofFinancial Economics 6(23 (1978))95ndash101

Lakonishok J and Smidt S (1988) Are seasonal anomalies real A ninety-year per-spective The Review of Financial Studies 1(4)403ndash425

MacKinlay A (1997) Event studies in economics and finance Journal of EconomicLiterature (35)113ndash39

Mandelbrot B B (1997) The variation of certain speculative prices In Fractals andscaling in finance pages 371ndash418 Springer

McLean R D and Pontiff J (2016) Does academic research destroy stock returnpredictability The Journal of Finance 71(1)5ndash32

Plastun A Makarenko I Khomutenko L Shcherbak S and Tryfonova O (2019a)Exploring price gap anomaly in the ukrainian stock market Investment Managementamp Financial Innovations 16(2)150

Plastun A Sibande X Gupta R and Wohar M E (2019b) Rise and fall of calendaranomalies over a century The North American Journal of Economics and Finance49181ndash205

Schwert G W (2003) Chapter 15 anomalies and market efficiency In FinancialMarkets and Asset Pricing volume 1 of Handbook of the Economics of Finance pages939 ndash 974 Elsevier

Shiller R J (2000) Irrational exuberance Princeton University

Tiwari A K Aye G C and Gupta R (2019) Stock market efficiency analysis usinglong spans of data A multifractal detrended fluctuation approach Finance ResearchLetters 28398ndash411

Yuan Y (2015) Market-wide attention trading and stock returns Journal of FinancialEconomics 116(3)548ndash564

18

Appendices

A DJI and NASDAQ Summary Results

A1 Overall Results

Table A1 Gap size used for different sub-periods over the period 1929-2018

Period DJI NASDAQ1929-1938 - -1939-1948 - -1949-1958 - 0711959-1968 - 0951969-1978 - 1351979-1988 - 1101989-1998 040 0681999-2008 007 1502009-2018 020 110Overall data set 030 110

Table A2 Day of the week and gaps

Day of the week DJI NASDAQMonday 024 02Tuesday 02 02Wednesday 017 02Thursday 019 019Friday 021 02

A2 Statistical tests

Table A3 Results of the statistical tests for the overall data sets

PeriodMethod Averageanalysis

t-test ANOVAtest

Mann-Whitney

test

Regressionanalysiswith

dummyvariables

ModifiedCAR

approach

Overall

Dow Jones Index overall data setGap day - - - - - + 1Gap day (Positive gaps) + - - - - - 1Gap day (Negative gaps) + - - - - + 2Day after gap (Positive gaps) + - - - - - 1Day after gap (Negative gaps) + - - + - + 3

NASDAQ overall data setGap day + + + + + + 6Gap day (Positive gaps) + + + + + + 6Gap day (Negative gaps) + + + + + + 6Day after gap (Positive gaps) + + + + + + 6Day after gap (Negative gaps) + + + + + + 6

Note + indicates that the anomaly is confirmed and - indicates that anomaly is not confirmedThe higher the overall rating the stronger the evidence of the anomaly

19

Table A4 Results of the statistical tests for H1minus1 DJI

Period Averageanalysis

t-test ANOVA test Mann-Whitney

test

Regressionanalysis with

dummyvariables

ModifiedCAR

approach

Overall

Day of anomaly1989-1998 + - - - - + 21999-2008 + + + + + + 62009-2018 + + + + + + 6

Day after anomaly1989-1998 + - - - - + 21999-2008 + - - - - + 22009-2018 - - - - - - 0

Note + indicates that the anomaly is confirmed and - indicates that anomaly is not confirmedThe higher the overall rating the stronger the evidence of the anomaly

Table A5 Results of the statistical tests for H1minus2 DJI

Period Averageanalysis

t-test ANOVA test Mann-Whitneytest

Regressionanalysis with

dummyvariables

Modified CARapproach

Overall

Day of anomaly1989-1998 - - - - - - 01999-2008 + + + + + + 62009-2018 + + + + + + 6

Day after anomaly1989-1998 + - - - - + 21999-2008 + - - - - - 12009-2018 + - - - - + 2

Note + indicates that the anomaly is confirmed and - indicates that anomaly is not confirmedThe higher the overall rating the stronger the evidence of the anomaly

Table A6 Results of the statistical tests for H1minus1 NASDAQ

PeriodMethod Averageanalysis

t-test ANOVA test Mann-Whitney

test

Regressionanalysis with

dummyvariables

ModifiedCAR

approach

Overall

Day of anomaly1949-1958 + + + + + + 61959-1968 + + + + + + 61969-1978 + + + + + + 61979-1988 + + + + + + 61989-1998 + - - - - + 21999-2008 + - + + + + 52009-2018 + + + + + + 6

Day after anomaly1949-1958 + + + + + + 61959-1968 + + + + + + 61969-1978 + + + + + + 61979-1988 + + + + + + 61989-1998 + - + - + + 41999-2008 - - - - - - 02009-2018 + - - - - + 2

Note + indicates that the anomaly is confirmed and - indicates that anomaly is not confirmedThe higher the overall rating the stronger the evidence of the anomaly

20

Table A7 Results of the statistical tests for H1minus2 NASDAQ

PeriodMethod Averageanalysis

t-test ANOVA test Mann-Whitney

test

Regressionanalysis with

dummyvariables

ModifiedCAR

approach

Overall

Day of anomaly1949-1958 + + + + + + 61959-1968 + + + + + + 61969-1978 + + + + + + 61979-1988 + + + + + + 61989-1998 - - - - - + 11999-2008 - - + - - - 12009-2018 - - - - - - 0

Day after anomaly1949-1958 + + + + + + 61959-1968 + + + + + + 61969-1978 + + + + + + 61979-1988 + + + + + + 61989-1998 + - - - - - 11999-2008 - - - - - + 12009-2018 + - - + + + 4

Note + indicates that the anomaly is confirmed and - indicates that anomaly is not confirmedThe higher the overall rating the stronger the evidence of the anomaly

A3 Trading Simulation Results

Table A8 Trading simulation results of the price gap anomaly for the DJI 1989-2018

Period Gap type Number oftradesunits

Number ofsuccessfultradesunits

Number ofsuccessfultrades

Profit Profit per year

z-test Result

1989-1998 Up 102 46 451 -11 -01 011 failedDown 116 49 422 -267 -27 242 passed

1999-2008 Up 73 51 699 665 66 37 passedDown 143 81 566 641 64 331 passed

2009-2018 Up 127 88 693 308 31 327 passedDown 81 47 58 196 2 184 passed

21

B Short-term price behavior in DJI SampP 500 and

NASDAQ Price gaps (overall data sets)

Table B1 Momentum effect in the US stock market after the gap

Instrument Parameter Number of days after the gap1 2 3

Dow Jones Index Positive gaps 53 57 61Negative gaps 50 50 47

All gaps 51 54 54SampP 500 Index Positive gaps 40 63 60

Negative gaps 4 52 45All gaps 4 58 53

NASDAQ Positive gaps 32 65 67Negative gaps 24 63 59

All gaps 28 64 63

Table B2 Momentum effect in the US stock market before the gap

Instrument Parameter Number of days before the gap1 2 3

Dow Jones Index Positive gaps 56 49 52Negative gaps 54 49 49

All gaps 55 49 50SampP 500 Index Positive gaps 57 57 52

Negative gaps 60 59 54All gaps 58 58 53

NASDAQ Positive gaps 61 56 54Negative gaps 68 69 70

All gaps 64 63 63

Table B3 Fill gap effect in the US stock market

Instrument Parameter Number of days after the gap1 2 3 4 5

Dow Jones Index Positive gaps 22 28 26 30 28Negative gaps 25 33 36 42 46

All gaps 24 30 31 35 37SampP 500 Index Positive gaps 0 6 11 16 19

Negative gaps 1 10 19 26 27All gaps 1 8 15 20 23

NASDAQ Positive gaps 8 13 18 21 19Negative gaps 7 11 17 21 25

All gaps 8 12 18 21 22

22

C Detailed statistical results DJI overall data

C1 Average analysis

Table C1 Average analysis

Parameter Gap day Gap day(Positive gaps)

Gap day(Negative gaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Mean return (gap day) 003 006 0 005 -003Mean return (non-gap day) 004 004 004 004 004Anomaly not confirmed not confirmed confirmed not confirmed confirmed

C2 Parametric tests Students t-test

Table C2 T-test

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

t-criterion 016 042 053 015 104t-critical (=095) 196 196 196 196 196Null hypothesis not rejected not rejected not rejected not rejected not rejected

C3 Parametric tests ANOVA

Table C3 ANOVA

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

F 0036 018 053 003 14p-value 085 067 047 086 024F critical 384 384 384 384 384Null hypothesis not rejected not rejected not rejected not rejected not rejected

C4 Non-parametric tests Kruskal-Wallis test

Table C4 Kruskal -Wallis test

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Adjusted H 082 012 126 0 455df 1 1 1 1 1P value 037 073 026 095 003Critical value 384 384 384 384 384Null hypothesis not rejected not rejected not rejected not rejected rejected

23

C5 Regression analysis with dummy variables

Table C5 Regression analysis with dummy variables

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

a0 00004 (000) 00004 (000) 00004 (000) 00004 (000) 00004 (000)a1 -00001 (-019) 00002 (067) -00004 (047) 00001 (086) -00007 (024)Anomaly not confirmed not confirmed not confirmed not confirmed not confirmed

C6 Modified CAR approach

Table C6 Modified CAR approach

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Multiple R 049 05 025 0 092F-test 23347 (000) 12913 (000) 2207 (000) 000 (098) 1822 (000)a0 -00041 (060) 00128 (006) -00267 (000) 00354 (000) 00319 (000)a1 -00003 (000) -00003 (000) -00002 (000) 00000 (098) -00008 (000)Anomaly confirmed confirmed confirmed not confirmed confirmed

24

D Detailed statistical results SampP 500 overall data

D1 Average analysis

Table D1 Average analysis

Parameter Gap day Gap day(Positive gaps)

Gap day(Negative gaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Mean return (gap day) 006 115 -129 017 -011Mean return (non-gap day) 002 002 002 002 002Anomaly confirmed confirmed confirmed confirmed confirmed

D2 Parametric tests Students t-test

Table D2 T-test

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

t-criterion 092 4546 3579 485 271t-critical (=095) 196 196 196 196 196Null hypothesis not rejected rejected rejected rejected rejected

D3 Parametric tests ANOVA

Table D3 ANOVA

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

F 155 116211 126952 1866 136p-value 022 0 0 0 0F critical 384 384 384 384 384Null hypothesis not rejected rejected rejected not rejected not rejected

D4 Non-parametric tests Kruskal-Wallis test

Table D4 Kruskal-Wallis test

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Adjusted H 1352 70516 47237 3946 004df 1 1 1 1 1P value 0 0 0 0 084Critical value 384 384 384 384 384Null hypothesis rejected rejected rejected rejected not rejected

25

D5 Regression analysis with dummy variables

Table D5 Regression analysis with dummy variables

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

a0 00002 (000) 00002 (000) 00002 (000) 00002 (000) 00002 (000)a1 00003 (021) 00113 (000) -00132 (000) 00014 (000) -00014 (000)Anomaly not confirmed confirmed confirmed confirmed confirmed

D6 Modified CAR approach

Table D6 Modified CAR approach

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Multiple R 051 099 099 099 096F-test 69486 (000) 325351 (000) 1457582 (000) 6345973 (000) 1213344 (000)a0 -01003(000) 04081 (000) -05444 (000) -01088 (000) 00272 (000)a1 00002 (000) 00106 (000) -00127 (000) 00016 (000) -00016 (000)Anomaly confirmed confirmed confirmed confirmed confirmed

26

E Detailed statistical results NASDAQ overall data

E1 Average analysis

Table E1 Average analysis

Parameter Gap day Gap day(Positive gaps)

Gap day(Negative gaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Mean return (gap day) -009 084 -090 022 -037Mean return (non-gap day) 003 003 003 003 003Anomaly confirmed confirmed confirmed confirmed confirmed

E2 Parametric tests Students t-test

Table E2 T-test

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

t-criterion 230 1257 1341 306 664t-critical (=095) 196 196 196 196 196Null hypothesis rejected rejected rejected rejected rejected

E3 Parametric tests ANOVA

Table E3 ANOVA

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

F 2289 62720 88402 3330 17356p-value 0 0 0 0 0F critical 384 384 384 384 384Null hypothesis rejected rejected rejected rejected rejected

E4 Non-parametric tests Kruskal-Wallis test

Table E4 Kruskal-Wallis test

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Adjusted H 1892 36022 45248 4695 10437df 1 1 1 1 1P value 0 0 0 0 0Critical value 384 384 384 384 384Null hypothesis rejected rejected rejected rejected rejected

27

E5 Regression analysis with dummy variables

Table E5 Regression analysis with dummy variables

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

a0 00003 (000) 00003 (000) 00003 (000) 00003 (000) 00003 (000)a1 -00012 (000) 00081 (000) -00093 (000) 00018 (000) -00040 (000)Anomaly confirmed confirmed confirmed confirmed confirmed

E6 Modified CAR approach

Table E6 Modified CAR approach

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Multiple R 069 092 092 072 097F-test 133255 (000) 361102 (000) 442376 (000) 72903 (000) 1082812 (000)a0 -10646 (000) 11373 (000) -12888 (000) 03928 (000) -02297 (000)a1 -00011 (000) 00073 (000) -00097 (000) 00017 (000) -00039 (000)Anomaly confirmed confirmed confirmed confirmed confirmed

28

F Detailed statistical results DJI sub-periods

F1 Average analysis

Table F1 Average analysis

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 Mean return (gapday)

-001 023 015 -004

Mean return(non-gap day)

007 007 007 007

Anomaly confirmed confirmed confirmed confirmed1999-2008 Mean return (gap

day)090 -045 013 -004

Mean return(non-gap day)

-004 -004 -004 -004

Anomaly confirmed confirmed confirmed confirmed2009-2018 Mean return (gap

day)024 -024 0 -004

Mean return(non-gap day)

004 004 004 004

Anomaly confirmed confirmed not confirmed confirmed

F2 Parametric tests Students t-test

Table F2 T-test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 t-criterion 083 165 087 139t-critical (=095) 196 196 196 196Null hypothesis not rejected not rejected not rejected not rejected

1999-2008 t-criterion 347 351 054 047t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected rejected

2009-2018 t-criterion 265 207 051 058t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

F3 Parametric tests ANOVA

Table F3 ANOVA

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 F 085 409 093 179p-value 035 004 033 018

F critical 384 384 384 384Null hypothesis not rejected rejected not rejected not rejected

1999-2008 F 5405 3196 065 072p-value 0 0 042 039

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

2009-2018 F 554 697 024 058p-value 001 0 062 044

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

29

F4 Non-parametric tests Kruskal-Wallis test

Table F4 Kruskal-Wallis test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 Adjusted H 113 211 113 332df 1 1 1 1

P value 029 015 029 007Null hypothesis not rejected not rejected not rejected not rejected

1999-2008 Adjusted H 1484 1414 003 139df 1 1 1 1

P value 0 0 086 024Null hypothesis rejected rejected not rejected not rejected

2009-2018 Adjusted H 506 68 051 171df 1 1 1 1

P value 002 001 047 019Null hypothesis rejected rejected not rejected not rejected

F5 Regression analysis with dummy variables

Table F5 Regression analysis with dummy variables

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 a0 000068 (000) 00007 (000) 00007 (000) 00007 (000)a1 -000078 (035) 00016 (004) 00008 (033) -00011 (018)

Anomaly not confirmed confirmed not confirmed not confirmed1999-2008 a0 00004 (008) 00004 (008) 00004 (006) 00004 (008)

a1 00087 (000) -00049 (000) 00009 (042) -00008 (039)Anomaly confirmed confirmed not confirmed not confirmed

2009-2018 a0 00004 (006) 00004 (006) 00004 (006) 00004 (006)a1 00021 (001) -00028 (001) -00004 (062) -00008 (047)

Anomaly confirmed confirmed not confirmed not confirmed

F6 Modified CAR approach

Table F6 Modified CAR approach

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 Multiple R 083 088 082 086F-test 22779 (000) 40583 (000) 20401 (000) 3269454 (000)a0 00042 (023) 00017 (073) 00014 (058) -00266 (000)a1 -00009 (000) 00015 (000) 00006 (000) -00009 (000)

Anomaly confirmed confirmed confirmed confirmed1999-2008 Multiple R 095 093 076 019

F-test 62658 (000) 84712 (000) 10056 (000) 492 (003)a0 -00972 (000) 00365 (000) -00198 (000) -00115 (021)a1 00086 (000) -00042 (000) 00014 (000) 00002 (003)

Anomaly confirmed confirmed confirmed not confirmed2009-2018 Multiple R 096 082 08 05

F-test 150452 (000) 16731 (000) 22287 (000) 2620 (000)a0 00548 (000) -00618 (000) 00031 (020) -00112 (000)a1 00013 (000) -00014 (000) -00005 (000) -00004 (000)

Anomaly confirmed confirmed not confirmed confirmed

30

G Detailed statistical results NASDAQ sub-periods

G1 Average analysis

Table G1 Average analysis

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 Mean return (gapday)

094 -111 0189 -029

Mean return(non-gap day)

007 007 007 007

Anomaly confirmed confirmed confirmed confirmed1959-1968 Mean return (gap

day)133 -147 033 -039

Mean return(non-gap day)

006 006 006 006

Anomaly confirmed confirmed confirmed confirmed1969-1978 Mean return (gap

day)19 -186 057 -068

Mean return(non-gap day)

005 005 005 005

Anomaly confirmed confirmed confirmed confirmed1979-1988 Mean return (gap

day)138 -162 066 -04

Mean return(non-gap day)

008 008 008 008

Anomaly confirmed confirmed confirmed confirmed1989-1998 Mean return (gap

day)016 012 018 -009

Mean return(non-gap day)

002 002 002 002

Anomaly confirmed not confirmed confirmed confirmed1999-2008 Mean return (gap

day)38E-3 027 -036 -013

Mean return(non-gap day)

-01 -01 -01 -01

Anomaly confirmed not confirmed not confirmed not confirmed2009-2018 Mean return (gap

day)039 009 013 -025

Mean return(non-gap day)

001 001 001 001

Anomaly confirmed not confirmed confirmed confirmed

G2 Parametric tests Students t-test

Table G2 T-test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 t-criterion 3194 3076 201 559t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected rejected

1959-1968 t-criterion 1399 2246 443 382t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected rejected

1969-1978 t-criterion 261 4358 417 786t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected rejected

1979-1988 t-criterion 1847 1445 709 395t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected rejected

1989-1998 t-criterion 13 066 126 093t-critical (=095) 196 196 196 196Null hypothesis not rejected not rejected not rejected not rejected

1999-2008 t-criterion 192 106 111 009t-critical (=095) 196 196 196 196Null hypothesis not rejected not rejected not rejected not rejected

2009-2018 t-criterion 27 05 089 188t-critical (=095) 196 196 196 196Null hypothesis rejected not rejected not rejected not rejected

31

G3 Parametric tests ANOVA

Table G3 ANOVA

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 F 88153 190609 1272 14521p-value 0 0 0 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1959-1968 F 93974 149771 4715 10418p-value 0 0 0 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1969-1978 F 84546 145429 6295 18241p-value 0 0 0 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1979-1988 F 66952 110482 13138 8626p-value 0 0 0 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1989-1998 F 323 138 43 168p-value 007 024 003 019

F critical 384 384 384 384Null hypothesis not rejected not rejected rejected not rejected

1999-2008 F 106 512 327 003p-value 001 002 007 085

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

2009-2018 F 169 069 175 93p-value 0 04 018 0

F critical 384 384 384 384Null hypothesis rejected not rejected not rejected rejected

G4 Non-parametric tests Kruskal-Wallis test

Table G4 Kruskal-Wallis test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 Adjusted H 26254 32592 1464 3962df 1 1 1 1

P value 0 0 0 0Null hypothesis rejected rejected rejected rejected

1959-1968 Adjusted H 28235 27989 2736 332df 1 1 1 1

P value 0 0 0 0Null hypothesis rejected rejected rejected rejected

1969-1978 Adjusted H 22202 33777 3311 7591df 1 1 1 1

P value 0 0 0 0Null hypothesis rejected rejected rejected rejected

1979-1988 Adjusted H 23282 25292 4812 3964df 1 1 1 1

P value 0 0 0 0Null hypothesis rejected rejected rejected rejected

1989-1998 Adjusted H 381 017 175 132df 1 1 1 1

P value 005 068 019 025Null hypothesis not rejected not rejected not rejected not rejected

1999-2008 Adjusted H 855 023 044 004df 1 1 1 1

P value 0 063 051 084Null hypothesis rejected not rejected not rejected not rejected

2009-2018 Adjusted H 1063 009 257 709df 1 1 1 1

P value 0 077 011 001Null hypothesis rejected not rejected not rejected rejected

32

G5 Regression analysis with dummy variables

Table G5 Regression analysis with dummy variables

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 a0 00007 (000) 00007 (000) 00007 (000) 00007 (000)a1 00088 (000) -00119 (000) 00011 (000) -00036 (000)

Anomaly confirmed confirmed confirmed confirmed1959-1968 a0 00006 (000) 00006 (000) 00006 (000) 00006 (000)

a1 00128 (000) -00153 (000) 00027 (000) -00046 (000)Anomaly confirmed confirmed confirmed confirmed

1969-1978 a0 00005 (000) 00005 (000) 00005 (000) 00005 (000)a1 00185 (000) -00192 (000) 00053 (000) -00073 (000)

Anomaly confirmed confirmed confirmed confirmed1979-1988 a0 00008 (000) 00008 (000) 00008 (000) 00008 (000)

a1 00131 (000) -00172 (000) 00059 (000) -00048 (000)Anomaly confirmed confirmed confirmed confirmed

1989-1998 a0 00002 (027) 00002 (028) 00002 (028) 00002 (027)a1 00014 (007) 00010 (024) 00017 (004) -00011 (019)

Anomaly not confirmed not confirmed confirmed not confirmed1999-2008 a0 00001 (059) 00001 (062) 00001 (059) 00001 (060)

a1 00037 (000) 00026 (002) -00038 (000) -00014 (019)Anomaly confirmed not confirmed not confirmed not confirmed

2009-2018 a0 00001 (049) 00001 (049) 00001 (049) 00001 (049)a1 00038 (000) 00007 (040) 00012 (018) -00027 (000)

Anomaly confirmed not confirmed not confirmed confirmed

G6 Modified CAR approach

Table G6 Modified CAR approach

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 Multiple R 099 099 093 098F-test 5753605 (000) 100470(000) 6280421 283281a0 -00091 (000) -00349 (000) 00056 (001) 00015 (073)a1 00083 (000) -00110 (000) 00010 (000) -00031 (000)

Anomaly confirmed confirmed confirmed confirmed1959-1968 Multiple R 099 099 099 099

F-test 3923274 (000) 3005562 (000) 443198 (000) 372583 (000)a0 00096 (000) 00073 (016) -00082 (000) -00095 (004)a1 00116 (001) -00149 (000) 00025 (000) -00047 (000)

Anomaly confirmed confirmed confirmed confirmed1969-1978 Multiple R 099 099 098 099

F-test 4302608 (000) 2723953 (000) 179969 (000) 639745a0 00246 (000) -00002 (000) 00217 (000) -00514 (000)a1 00176 (000) -00182 (000) 00049 (000) -00062 (000)

Anomaly confirmed confirmed confirmed confirmed1979-1988 Multiple R 099 099 099 099

F-test 5872335 (000) 1182609 (000) 1083558 (000) 910089 (000)a0 00136 (000) -01081 (000) -00285 (000) -00101 (000)a1 00131 (000) -00167 (000) 00062 (000) -00048 (000)

Anomaly confirmed confirmed confirmed confirmed1989-1998 Multiple R 09 056 069 016

F-test 46947 (000) 4885 (000) 10131 (000) 263 (011)a0 00102 (002) -00261 (000) -0016 (001) -00237 (000)a1 00015 (000) 00010 (000) 0001 (000) 00002 (011)

Anomaly confirmed confirmed confirmed not confirmed1999-2008 Multiple R 093 087 073 037

F-test 71863 (000) 32530 (000) 13273 (000) 1669 (000)a0 00185 (004) 00311 (000) -00130 (039) -00546 (000)a1 00037 (000) 00032 (000) -00026 (000) -00007 (000)

Anomaly confirmed not confirmed not confirmed confirmed2009-2018 Multiple R 089 001 096 091

F-test 40818 (000) 000 (094) 116744 (000) 53770 (000)a0 01436 (000) -01099 (000) -01036 (000) 00697 (000)a1 00030 (000) 00000 (094) 00024 (000) -00021 (000)

Anomaly confirmed not confirmed confirmed confirmed

33

H Detailed statistical results SampP 500 sub-periods

H1 Average analysis

Table H1 Average analysis

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 Mean return (gapday)

138 -171 004 -014

Mean return(non-gap day)

0 0 0 0

Anomaly confirmed confirmed confirmed confirmed1939-1948 Mean return (gap

day)001 -042 172 -195

Mean return(non-gap day)

003 003 003 003

Anomaly confirmed confirmed confirmed confirmed1949-1958 Mean return (gap

day)165 -18 02 002

Mean return(non-gap day)

006 006 006 006

Anomaly confirmed confirmed confirmed not confirmed1959-1968 Mean return (gap

day)104 -102 015 0

Mean return(non-gap day)

002 002 002 002

Anomaly confirmed confirmed confirmed not confirmed1969-1978 Mean return (gap

day)131 -13 019 -03

Mean return(non-gap day)

0 0 0 0

Anomaly confirmed confirmed confirmed confirmed1979-1988 Mean return (gap

day)058 -042 015 003

Mean return(non-gap day)

005 005 005 005

Anomaly confirmed confirmed confirmed not confirmed1989-1998 Mean return (gap

day)02 -023 -002 01

Mean return(non-gap day)

007 007 007 007

Anomaly confirmed confirmed not confirmed not confirmed1999-2008 Mean return (gap

day)083 -089 -023 -005

Mean return(non-gap day)

001 001 001 001

Anomaly confirmed confirmed not confirmed confirmed2009-2018 Mean return (gap

day)055 -052 001 -015

Mean return(non-gap day)

004 004 004 004

Anomaly confirmed confirmed not confirmed confirmed

34

H2 Parametric tests Students t-test

Table H2 T-test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 t-criterion 101 85 029 048t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

1939-1948 t-criterion 064 479 3074 225t-critical (=095) 196 196 196 196Null hypothesis not rejected rejected rejected rejected

1949-1958 t-criterion 2964 2383 193 041t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

1959-1968 t-criterion 2281 2157 21 023t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected not rejected

1969-1978 t-criterion 1318 2034 187 321t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected rejected

1979-1988 t-criterion 435 535 07 037t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

1989-1998 t-criterion 201 396 132 052t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

1999-2008 t-criterion 362 433 117 022t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

2009-2018 t-criterion 375 382 027 132t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

H3 Parametric tests ANOVA

Table H3 ANOVA

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 F 6281 8032 005 051p-value 0 0 082 047

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

1939-1948 F 056 2603 34854 51034p-value 045 0 0 0

F critical 384 384 384 384Null hypothesis not rejected rejected rejected rejected

1949-1958 F 100174 128997 897 062p-value 0 0 0 043

F critical 384 384 384 384Null hypothesis rejected rejected rejected not rejected

1959-1968 F 36831 32858 617 01p-value 0 0 001 074

F critical 384 384 384 384Null hypothesis rejected rejected rejected not rejected

1969-1978 F 26601 3063 53 152p-value 0 0 002 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1979-1988 F 23 245 076 009p-value 0 0 039 077

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

1989-1998 F 399 1156 118 015p-value 004 0 027 069

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

1999-2008 F 4253 5622 365 024p-value 0 0 006 062

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

2009-2018 F 3064 3656 01 43p-value 0 0 075 004

F critical 384 384 384 384Null hypothesis rejected rejected not rejected rejected

35

H4 Non-parametric tests Kruskal -Wallis test

Table H4 Kruskal-Wallis test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 Adjusted H 9982 5913 332 14df 1 1 1 1

P value 0 0 007 024Null hypothesis rejected rejected not rejected not rejected

1939-1948 Adjusted H 494 1999 23387 24927df 1 1 1 1

P value 003 0 0 0Null hypothesis rejected rejected rejected rejected

1949-1958 Adjusted H 28728 28175 348 15df 1 1 1 1

P value 0 0 006 022Null hypothesis rejected rejected not rejected not rejected

1959-1968 Adjusted H 25729 21437 701 063df 1 1 1 1

P value 0 0 001 043Null hypothesis rejected rejected rejected not rejected

1969-1978 Adjusted H 14407 20078 27 1706df 1 1 1 1

P value 0 0 01 0Null hypothesis rejected rejected not rejected rejected

1979-1988 Adjusted H 1788 2836 027 034df 1 1 1 1

P value 0 0 06 056Null hypothesis rejected rejected not rejected not rejected

1989-1998 Adjusted H 251 1431 111 044df 1 1 1 1

P value 011 0 029 051Null hypothesis not rejected rejected not rejected not rejected

1999-2008 Adjusted H 1812 1788 042 002df 1 1 1 1

P value 0 0 052 089Null hypothesis rejected rejected not rejected not rejected

2009-2018 Adjusted H 1314 1783 074 37df 1 1 1 1

P value 0 0 039 005Null hypothesis rejected rejected not rejected not rejected

36

H5 Regression analysis with dummy variables

Table H5 Regression analysis with dummy variables

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 a0 00000 (097) 00000 (004) 00000 (097) 00000 (097)a1 00138 (000) -00172 (000) 00004 (082) -00014 (047)

Anomaly confirmed confirmed not confirmed not confirmed1939-1948 a0 00003 (015) 00003 (015) 00003 (015) 00003 (015)

a1 00007 (045) -00045 (000) 00170 (000) -00199 (000)Anomaly not confirmed confirmed confirmed confirmed

1949-1958 a0 00006 (000) 00006 (000) 00006 (000) 00006 (000)a1 00160 (000) -00188 (000) 00016 (000) -00004 (043)

Anomaly confirmed confirmed confirmed not confirmed1959-1968 a0 00002 (007) 00002 (004) 00002 (008) 00002 (008)

a1 00103 (000) -00105 (000) 00014 (001) -00002 (074)Anomaly confirmed confirmed confirmed not confirmed

1969-1978 a0 00000 (078) 00000 (078) 00000 (078) 00000 (078)a1 00132 (000) -00132 (000) 00019 (002) -00030 (000)

Anomaly confirmed confirmed confirmed confirmed1979-1988 a0 00006 (001) 00006 (001) 00006 (001) 00006 (000)

a1 00053 (000) -00048 (000) 00009 (040) -00003 (075)Anomaly confirmed confirmed not confirmed not confirmed

1989-1998 a0 00007 (000) 00007 (000) 00007 (000) 00007 (000)a1 00016 (005) -00030 (000) -00009 (026) 00003 (072)

Anomaly confirmed confirmed not confirmed not confirmed1999-2008 a0 00001 (075) 00001 (075) 00001 (075) 00001 (076)

a1 00083 (000) -00091 (000) -00024 (005) -00006 (062)Anomaly confirmed confirmed not confirmed not confirmed

2009-2018 a0 00004 (003) 00004 (000) 00004 (003) 00004 (003)a1 00051 (000) -00059 (000) -00003 (075) -00019 (003)

Anomaly confirmed confirmed not confirmed confirmed

37

H6 Modified CAR approach

Table H6 Modified CAR approach

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 Multiple R 096 095 046 046F-test 175935 (000) 96500 (000) 3534 (000) 2880 (000)a0 -01070 (000) 01958 (000) 00405 (000) 00535 (000)a1 00121 (000) -00160 (000) 00006 (000) -00014 (000)

Anomaly confirmed confirmed confirmed confirmed1939-1948 Multiple R 08 099 099 099

F-test 18777 (000) 755727 (000) 3572830 (000) 2696099 (000)a0 00019 (073) -00346 (000) -00373 (000) 00912 (000)a1 00012 (000) -00044 (000) 00168 (000) -00197 (000)

Anomaly confirmed confirmed confirmed confirmed1949-1958 Multiple R 099 099 094 015

F-test 1021705 (000) 7171257 (000) 75858 (000) 242 (012)a0 -00176 (000) -00191 (000) 00095 (000) -00498 (000)a1 00154 (000) -00181 (000) 00013 (000) -00002 (012)

Anomaly confirmed confirmed confirmed not confirmed1959-1968 Multiple R 099 099 094 078

F-test 1463311 (000) 6002659 (000) 82273 (000) 14352 (000)a0 -00112 (000) 00004 (085) 00151 (000) 00389 (000)a1 00098 (000) -00102 (000) 00011 (000) -00009 (000)

Anomaly confirmed confirmed confirmed confirmed1969-1978 Multiple R 098 099 093 099

F-test 241655 (000) 1451901 (000) 57333 (000) 368160 (000)a0 -00433 (000) 00276 (000) 00099 (002) -00144 (000)a1 00132 (000) -00134 (000) 00020 (000) -00030 (000)

Anomaly confirmed confirmed confirmed confirmed1979-1988 Multiple R 092 078 023 008

F-test 53757 (000) 18707 (000) 487 (003) 085 (036)a0 00813 (000) -02508 (000) 00204 (000) -00235 (000)a1 00036 (000) -00031 (000) -00003 (003) -00001 (036)

Anomaly confirmed confirmed not confirmed not confirmed1989-1998 Multiple R 079 099 074 044

F-test 19705(000) 761967 (000) 14133 (000) 2369 (000)a0 00268 (000) 00023 (021) -00381 (000) 00087 (000)a1 00013 (000) -00028 (000) -00008 (000) 00002 (000)

Anomaly confirmed confirmed not confirmed not confirmed1999-2008 Multiple R 091 093 071 065

F-test 47218 (000) 76564 (000) 9843 (000) 7768 (000)a0 -01493 (000) 01351 (000) 00397 (000) 00007 (093)a1 00081 (000) -00083 (000) -00026 (000) -00011 (000)

Anomaly confirmed confirmed not confirmed confirmed2009-2018 Multiple R 086 087 083 074

F-test 29971 (000) 32484 (000) 23228 (000) 12764 (000)a0 01711 (000) -02250 (000) 00407 (000) -00472 (000)a1 00038 (000) -00044 (000) -00010 (000) -00012 (000)

Anomaly confirmed confirmed not confirmed confirmed

38

H1 and H2 Particularly on the day of the occurrence of the gap and not on the dayafter the price gap In the DJI and the SampP 500 this pattern persists indicating thatthese markets take a day to incorporate new information As the results of the tradingsimulation indicate a day is enough to profit from a price gap anomaly trading strategyin the DJI and the SampP 500

Similar to other studies and other anomalies (see McLean and Pontiff (2016) Ca-jueiro and Tabak (2004) and Tiwari et al (2019) for example) the price gap anomalyevolved It is less prevalent since the 1990s as shown in the SampP 500 and NASDAQThis pattern of evolution is common amongst most stock market anomalies (see Plastunet al (2019b) on calendar anomalies amongst others) Our findings therefore add onto the existing literature Finally in the main our results are against the EMH and aretherefore interesting to both practitioners and academics

16

References

Agrawal A and Tandon K (1994) Anomalies or illusions evidence from stock marketsin eighteen countries Journal of international Money and Finance 13(1)83ndash106

Akerlof G A and Shiller R J (2009) Animal Spirits How human psychology drivesthe economy and why it matters for global capitalism Princeton University Press

Basu S (1977) Investment performance of common stocks in relation to their price-earnings ratios A test of the efficient market hypothesis The Journal of Finance32(3)663ndash682

Bildik R (2004) Are calendar anomalies still alive Evidence from istanbul stockexchange SSRN Electronic Journal 2004

Cai J Li Y and Qi Y (2006) The day-of-the-week effect New evidence from theChinese stock market Chinese Economy 39(2)71ndash88

Cajueiro D O and Tabak B M (2004) The Hurst exponent over time testing theassertion that emerging markets are becoming more efficient Physica A StatisticalMechanics and its Applications 336(3-4)521ndash537

Caporale G M Gil-Alana L Plastun A and Makarenko I (2016) Intraday anoma-lies and market efficiency A trading robot analysis Computational Economics47(2)275ndash295

Caporale G M and Plastun A (2017) Price gaps Another market anomaly Invest-ment Analysts Journal 46(4)279ndash293

Cross F (1973) The behavior of stock prices on Fridays and Mondays FinancialAnalysts Journal 29(6)67ndash69

Fama E F (1965) The behavior of stock-market prices The Journal of Business38(1)34ndash105

Fama E F (1970) Efficient capital markets A review of theory and empirical workThe Journal of Finance 25(2)383ndash417

Fortune P (1998) Weekends can be rough revisiting the weekend effect in stock pricesTechnical report

Fortune P (1999) Are stock returns different over weekends A jump diffusion analysisof the weekend effect New England Economic Review 103ndash19

French K R (1980) Stock returns and the weekend effect Journal of FinancialEconomics 8(1)55ndash69

Fung A K-W Lam K and Lam K-M (2010) Do the prices of stock index futuresin asia overreact to us market returns Journal of Empirical Finance 17(3)428ndash440

17

Gibbons M R and Hess P (1981) Day of the week effects and asset returns Journalof business pages 579ndash596

Grant J L Wolf A and Yu S (2005) Intraday price reversals in the us stock indexfutures market A 15-year study Journal of Banking amp Finance 29(5)1311ndash1327

Grossman S J and Stiglitz J E (1980) On the impossibility of informationallyefficient markets The American Economic Review 70(3)393ndash408

Jacobsen B Mamun A and Visaltanachoti N (2005) Seasonal size and valueanomalies

Jensen M (1978) Some anomalous evidence regarding market efficiency Journal ofFinancial Economics 6(23 (1978))95ndash101

Lakonishok J and Smidt S (1988) Are seasonal anomalies real A ninety-year per-spective The Review of Financial Studies 1(4)403ndash425

MacKinlay A (1997) Event studies in economics and finance Journal of EconomicLiterature (35)113ndash39

Mandelbrot B B (1997) The variation of certain speculative prices In Fractals andscaling in finance pages 371ndash418 Springer

McLean R D and Pontiff J (2016) Does academic research destroy stock returnpredictability The Journal of Finance 71(1)5ndash32

Plastun A Makarenko I Khomutenko L Shcherbak S and Tryfonova O (2019a)Exploring price gap anomaly in the ukrainian stock market Investment Managementamp Financial Innovations 16(2)150

Plastun A Sibande X Gupta R and Wohar M E (2019b) Rise and fall of calendaranomalies over a century The North American Journal of Economics and Finance49181ndash205

Schwert G W (2003) Chapter 15 anomalies and market efficiency In FinancialMarkets and Asset Pricing volume 1 of Handbook of the Economics of Finance pages939 ndash 974 Elsevier

Shiller R J (2000) Irrational exuberance Princeton University

Tiwari A K Aye G C and Gupta R (2019) Stock market efficiency analysis usinglong spans of data A multifractal detrended fluctuation approach Finance ResearchLetters 28398ndash411

Yuan Y (2015) Market-wide attention trading and stock returns Journal of FinancialEconomics 116(3)548ndash564

18

Appendices

A DJI and NASDAQ Summary Results

A1 Overall Results

Table A1 Gap size used for different sub-periods over the period 1929-2018

Period DJI NASDAQ1929-1938 - -1939-1948 - -1949-1958 - 0711959-1968 - 0951969-1978 - 1351979-1988 - 1101989-1998 040 0681999-2008 007 1502009-2018 020 110Overall data set 030 110

Table A2 Day of the week and gaps

Day of the week DJI NASDAQMonday 024 02Tuesday 02 02Wednesday 017 02Thursday 019 019Friday 021 02

A2 Statistical tests

Table A3 Results of the statistical tests for the overall data sets

PeriodMethod Averageanalysis

t-test ANOVAtest

Mann-Whitney

test

Regressionanalysiswith

dummyvariables

ModifiedCAR

approach

Overall

Dow Jones Index overall data setGap day - - - - - + 1Gap day (Positive gaps) + - - - - - 1Gap day (Negative gaps) + - - - - + 2Day after gap (Positive gaps) + - - - - - 1Day after gap (Negative gaps) + - - + - + 3

NASDAQ overall data setGap day + + + + + + 6Gap day (Positive gaps) + + + + + + 6Gap day (Negative gaps) + + + + + + 6Day after gap (Positive gaps) + + + + + + 6Day after gap (Negative gaps) + + + + + + 6

Note + indicates that the anomaly is confirmed and - indicates that anomaly is not confirmedThe higher the overall rating the stronger the evidence of the anomaly

19

Table A4 Results of the statistical tests for H1minus1 DJI

Period Averageanalysis

t-test ANOVA test Mann-Whitney

test

Regressionanalysis with

dummyvariables

ModifiedCAR

approach

Overall

Day of anomaly1989-1998 + - - - - + 21999-2008 + + + + + + 62009-2018 + + + + + + 6

Day after anomaly1989-1998 + - - - - + 21999-2008 + - - - - + 22009-2018 - - - - - - 0

Note + indicates that the anomaly is confirmed and - indicates that anomaly is not confirmedThe higher the overall rating the stronger the evidence of the anomaly

Table A5 Results of the statistical tests for H1minus2 DJI

Period Averageanalysis

t-test ANOVA test Mann-Whitneytest

Regressionanalysis with

dummyvariables

Modified CARapproach

Overall

Day of anomaly1989-1998 - - - - - - 01999-2008 + + + + + + 62009-2018 + + + + + + 6

Day after anomaly1989-1998 + - - - - + 21999-2008 + - - - - - 12009-2018 + - - - - + 2

Note + indicates that the anomaly is confirmed and - indicates that anomaly is not confirmedThe higher the overall rating the stronger the evidence of the anomaly

Table A6 Results of the statistical tests for H1minus1 NASDAQ

PeriodMethod Averageanalysis

t-test ANOVA test Mann-Whitney

test

Regressionanalysis with

dummyvariables

ModifiedCAR

approach

Overall

Day of anomaly1949-1958 + + + + + + 61959-1968 + + + + + + 61969-1978 + + + + + + 61979-1988 + + + + + + 61989-1998 + - - - - + 21999-2008 + - + + + + 52009-2018 + + + + + + 6

Day after anomaly1949-1958 + + + + + + 61959-1968 + + + + + + 61969-1978 + + + + + + 61979-1988 + + + + + + 61989-1998 + - + - + + 41999-2008 - - - - - - 02009-2018 + - - - - + 2

Note + indicates that the anomaly is confirmed and - indicates that anomaly is not confirmedThe higher the overall rating the stronger the evidence of the anomaly

20

Table A7 Results of the statistical tests for H1minus2 NASDAQ

PeriodMethod Averageanalysis

t-test ANOVA test Mann-Whitney

test

Regressionanalysis with

dummyvariables

ModifiedCAR

approach

Overall

Day of anomaly1949-1958 + + + + + + 61959-1968 + + + + + + 61969-1978 + + + + + + 61979-1988 + + + + + + 61989-1998 - - - - - + 11999-2008 - - + - - - 12009-2018 - - - - - - 0

Day after anomaly1949-1958 + + + + + + 61959-1968 + + + + + + 61969-1978 + + + + + + 61979-1988 + + + + + + 61989-1998 + - - - - - 11999-2008 - - - - - + 12009-2018 + - - + + + 4

Note + indicates that the anomaly is confirmed and - indicates that anomaly is not confirmedThe higher the overall rating the stronger the evidence of the anomaly

A3 Trading Simulation Results

Table A8 Trading simulation results of the price gap anomaly for the DJI 1989-2018

Period Gap type Number oftradesunits

Number ofsuccessfultradesunits

Number ofsuccessfultrades

Profit Profit per year

z-test Result

1989-1998 Up 102 46 451 -11 -01 011 failedDown 116 49 422 -267 -27 242 passed

1999-2008 Up 73 51 699 665 66 37 passedDown 143 81 566 641 64 331 passed

2009-2018 Up 127 88 693 308 31 327 passedDown 81 47 58 196 2 184 passed

21

B Short-term price behavior in DJI SampP 500 and

NASDAQ Price gaps (overall data sets)

Table B1 Momentum effect in the US stock market after the gap

Instrument Parameter Number of days after the gap1 2 3

Dow Jones Index Positive gaps 53 57 61Negative gaps 50 50 47

All gaps 51 54 54SampP 500 Index Positive gaps 40 63 60

Negative gaps 4 52 45All gaps 4 58 53

NASDAQ Positive gaps 32 65 67Negative gaps 24 63 59

All gaps 28 64 63

Table B2 Momentum effect in the US stock market before the gap

Instrument Parameter Number of days before the gap1 2 3

Dow Jones Index Positive gaps 56 49 52Negative gaps 54 49 49

All gaps 55 49 50SampP 500 Index Positive gaps 57 57 52

Negative gaps 60 59 54All gaps 58 58 53

NASDAQ Positive gaps 61 56 54Negative gaps 68 69 70

All gaps 64 63 63

Table B3 Fill gap effect in the US stock market

Instrument Parameter Number of days after the gap1 2 3 4 5

Dow Jones Index Positive gaps 22 28 26 30 28Negative gaps 25 33 36 42 46

All gaps 24 30 31 35 37SampP 500 Index Positive gaps 0 6 11 16 19

Negative gaps 1 10 19 26 27All gaps 1 8 15 20 23

NASDAQ Positive gaps 8 13 18 21 19Negative gaps 7 11 17 21 25

All gaps 8 12 18 21 22

22

C Detailed statistical results DJI overall data

C1 Average analysis

Table C1 Average analysis

Parameter Gap day Gap day(Positive gaps)

Gap day(Negative gaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Mean return (gap day) 003 006 0 005 -003Mean return (non-gap day) 004 004 004 004 004Anomaly not confirmed not confirmed confirmed not confirmed confirmed

C2 Parametric tests Students t-test

Table C2 T-test

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

t-criterion 016 042 053 015 104t-critical (=095) 196 196 196 196 196Null hypothesis not rejected not rejected not rejected not rejected not rejected

C3 Parametric tests ANOVA

Table C3 ANOVA

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

F 0036 018 053 003 14p-value 085 067 047 086 024F critical 384 384 384 384 384Null hypothesis not rejected not rejected not rejected not rejected not rejected

C4 Non-parametric tests Kruskal-Wallis test

Table C4 Kruskal -Wallis test

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Adjusted H 082 012 126 0 455df 1 1 1 1 1P value 037 073 026 095 003Critical value 384 384 384 384 384Null hypothesis not rejected not rejected not rejected not rejected rejected

23

C5 Regression analysis with dummy variables

Table C5 Regression analysis with dummy variables

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

a0 00004 (000) 00004 (000) 00004 (000) 00004 (000) 00004 (000)a1 -00001 (-019) 00002 (067) -00004 (047) 00001 (086) -00007 (024)Anomaly not confirmed not confirmed not confirmed not confirmed not confirmed

C6 Modified CAR approach

Table C6 Modified CAR approach

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Multiple R 049 05 025 0 092F-test 23347 (000) 12913 (000) 2207 (000) 000 (098) 1822 (000)a0 -00041 (060) 00128 (006) -00267 (000) 00354 (000) 00319 (000)a1 -00003 (000) -00003 (000) -00002 (000) 00000 (098) -00008 (000)Anomaly confirmed confirmed confirmed not confirmed confirmed

24

D Detailed statistical results SampP 500 overall data

D1 Average analysis

Table D1 Average analysis

Parameter Gap day Gap day(Positive gaps)

Gap day(Negative gaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Mean return (gap day) 006 115 -129 017 -011Mean return (non-gap day) 002 002 002 002 002Anomaly confirmed confirmed confirmed confirmed confirmed

D2 Parametric tests Students t-test

Table D2 T-test

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

t-criterion 092 4546 3579 485 271t-critical (=095) 196 196 196 196 196Null hypothesis not rejected rejected rejected rejected rejected

D3 Parametric tests ANOVA

Table D3 ANOVA

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

F 155 116211 126952 1866 136p-value 022 0 0 0 0F critical 384 384 384 384 384Null hypothesis not rejected rejected rejected not rejected not rejected

D4 Non-parametric tests Kruskal-Wallis test

Table D4 Kruskal-Wallis test

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Adjusted H 1352 70516 47237 3946 004df 1 1 1 1 1P value 0 0 0 0 084Critical value 384 384 384 384 384Null hypothesis rejected rejected rejected rejected not rejected

25

D5 Regression analysis with dummy variables

Table D5 Regression analysis with dummy variables

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

a0 00002 (000) 00002 (000) 00002 (000) 00002 (000) 00002 (000)a1 00003 (021) 00113 (000) -00132 (000) 00014 (000) -00014 (000)Anomaly not confirmed confirmed confirmed confirmed confirmed

D6 Modified CAR approach

Table D6 Modified CAR approach

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Multiple R 051 099 099 099 096F-test 69486 (000) 325351 (000) 1457582 (000) 6345973 (000) 1213344 (000)a0 -01003(000) 04081 (000) -05444 (000) -01088 (000) 00272 (000)a1 00002 (000) 00106 (000) -00127 (000) 00016 (000) -00016 (000)Anomaly confirmed confirmed confirmed confirmed confirmed

26

E Detailed statistical results NASDAQ overall data

E1 Average analysis

Table E1 Average analysis

Parameter Gap day Gap day(Positive gaps)

Gap day(Negative gaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Mean return (gap day) -009 084 -090 022 -037Mean return (non-gap day) 003 003 003 003 003Anomaly confirmed confirmed confirmed confirmed confirmed

E2 Parametric tests Students t-test

Table E2 T-test

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

t-criterion 230 1257 1341 306 664t-critical (=095) 196 196 196 196 196Null hypothesis rejected rejected rejected rejected rejected

E3 Parametric tests ANOVA

Table E3 ANOVA

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

F 2289 62720 88402 3330 17356p-value 0 0 0 0 0F critical 384 384 384 384 384Null hypothesis rejected rejected rejected rejected rejected

E4 Non-parametric tests Kruskal-Wallis test

Table E4 Kruskal-Wallis test

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Adjusted H 1892 36022 45248 4695 10437df 1 1 1 1 1P value 0 0 0 0 0Critical value 384 384 384 384 384Null hypothesis rejected rejected rejected rejected rejected

27

E5 Regression analysis with dummy variables

Table E5 Regression analysis with dummy variables

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

a0 00003 (000) 00003 (000) 00003 (000) 00003 (000) 00003 (000)a1 -00012 (000) 00081 (000) -00093 (000) 00018 (000) -00040 (000)Anomaly confirmed confirmed confirmed confirmed confirmed

E6 Modified CAR approach

Table E6 Modified CAR approach

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Multiple R 069 092 092 072 097F-test 133255 (000) 361102 (000) 442376 (000) 72903 (000) 1082812 (000)a0 -10646 (000) 11373 (000) -12888 (000) 03928 (000) -02297 (000)a1 -00011 (000) 00073 (000) -00097 (000) 00017 (000) -00039 (000)Anomaly confirmed confirmed confirmed confirmed confirmed

28

F Detailed statistical results DJI sub-periods

F1 Average analysis

Table F1 Average analysis

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 Mean return (gapday)

-001 023 015 -004

Mean return(non-gap day)

007 007 007 007

Anomaly confirmed confirmed confirmed confirmed1999-2008 Mean return (gap

day)090 -045 013 -004

Mean return(non-gap day)

-004 -004 -004 -004

Anomaly confirmed confirmed confirmed confirmed2009-2018 Mean return (gap

day)024 -024 0 -004

Mean return(non-gap day)

004 004 004 004

Anomaly confirmed confirmed not confirmed confirmed

F2 Parametric tests Students t-test

Table F2 T-test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 t-criterion 083 165 087 139t-critical (=095) 196 196 196 196Null hypothesis not rejected not rejected not rejected not rejected

1999-2008 t-criterion 347 351 054 047t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected rejected

2009-2018 t-criterion 265 207 051 058t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

F3 Parametric tests ANOVA

Table F3 ANOVA

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 F 085 409 093 179p-value 035 004 033 018

F critical 384 384 384 384Null hypothesis not rejected rejected not rejected not rejected

1999-2008 F 5405 3196 065 072p-value 0 0 042 039

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

2009-2018 F 554 697 024 058p-value 001 0 062 044

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

29

F4 Non-parametric tests Kruskal-Wallis test

Table F4 Kruskal-Wallis test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 Adjusted H 113 211 113 332df 1 1 1 1

P value 029 015 029 007Null hypothesis not rejected not rejected not rejected not rejected

1999-2008 Adjusted H 1484 1414 003 139df 1 1 1 1

P value 0 0 086 024Null hypothesis rejected rejected not rejected not rejected

2009-2018 Adjusted H 506 68 051 171df 1 1 1 1

P value 002 001 047 019Null hypothesis rejected rejected not rejected not rejected

F5 Regression analysis with dummy variables

Table F5 Regression analysis with dummy variables

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 a0 000068 (000) 00007 (000) 00007 (000) 00007 (000)a1 -000078 (035) 00016 (004) 00008 (033) -00011 (018)

Anomaly not confirmed confirmed not confirmed not confirmed1999-2008 a0 00004 (008) 00004 (008) 00004 (006) 00004 (008)

a1 00087 (000) -00049 (000) 00009 (042) -00008 (039)Anomaly confirmed confirmed not confirmed not confirmed

2009-2018 a0 00004 (006) 00004 (006) 00004 (006) 00004 (006)a1 00021 (001) -00028 (001) -00004 (062) -00008 (047)

Anomaly confirmed confirmed not confirmed not confirmed

F6 Modified CAR approach

Table F6 Modified CAR approach

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 Multiple R 083 088 082 086F-test 22779 (000) 40583 (000) 20401 (000) 3269454 (000)a0 00042 (023) 00017 (073) 00014 (058) -00266 (000)a1 -00009 (000) 00015 (000) 00006 (000) -00009 (000)

Anomaly confirmed confirmed confirmed confirmed1999-2008 Multiple R 095 093 076 019

F-test 62658 (000) 84712 (000) 10056 (000) 492 (003)a0 -00972 (000) 00365 (000) -00198 (000) -00115 (021)a1 00086 (000) -00042 (000) 00014 (000) 00002 (003)

Anomaly confirmed confirmed confirmed not confirmed2009-2018 Multiple R 096 082 08 05

F-test 150452 (000) 16731 (000) 22287 (000) 2620 (000)a0 00548 (000) -00618 (000) 00031 (020) -00112 (000)a1 00013 (000) -00014 (000) -00005 (000) -00004 (000)

Anomaly confirmed confirmed not confirmed confirmed

30

G Detailed statistical results NASDAQ sub-periods

G1 Average analysis

Table G1 Average analysis

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 Mean return (gapday)

094 -111 0189 -029

Mean return(non-gap day)

007 007 007 007

Anomaly confirmed confirmed confirmed confirmed1959-1968 Mean return (gap

day)133 -147 033 -039

Mean return(non-gap day)

006 006 006 006

Anomaly confirmed confirmed confirmed confirmed1969-1978 Mean return (gap

day)19 -186 057 -068

Mean return(non-gap day)

005 005 005 005

Anomaly confirmed confirmed confirmed confirmed1979-1988 Mean return (gap

day)138 -162 066 -04

Mean return(non-gap day)

008 008 008 008

Anomaly confirmed confirmed confirmed confirmed1989-1998 Mean return (gap

day)016 012 018 -009

Mean return(non-gap day)

002 002 002 002

Anomaly confirmed not confirmed confirmed confirmed1999-2008 Mean return (gap

day)38E-3 027 -036 -013

Mean return(non-gap day)

-01 -01 -01 -01

Anomaly confirmed not confirmed not confirmed not confirmed2009-2018 Mean return (gap

day)039 009 013 -025

Mean return(non-gap day)

001 001 001 001

Anomaly confirmed not confirmed confirmed confirmed

G2 Parametric tests Students t-test

Table G2 T-test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 t-criterion 3194 3076 201 559t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected rejected

1959-1968 t-criterion 1399 2246 443 382t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected rejected

1969-1978 t-criterion 261 4358 417 786t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected rejected

1979-1988 t-criterion 1847 1445 709 395t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected rejected

1989-1998 t-criterion 13 066 126 093t-critical (=095) 196 196 196 196Null hypothesis not rejected not rejected not rejected not rejected

1999-2008 t-criterion 192 106 111 009t-critical (=095) 196 196 196 196Null hypothesis not rejected not rejected not rejected not rejected

2009-2018 t-criterion 27 05 089 188t-critical (=095) 196 196 196 196Null hypothesis rejected not rejected not rejected not rejected

31

G3 Parametric tests ANOVA

Table G3 ANOVA

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 F 88153 190609 1272 14521p-value 0 0 0 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1959-1968 F 93974 149771 4715 10418p-value 0 0 0 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1969-1978 F 84546 145429 6295 18241p-value 0 0 0 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1979-1988 F 66952 110482 13138 8626p-value 0 0 0 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1989-1998 F 323 138 43 168p-value 007 024 003 019

F critical 384 384 384 384Null hypothesis not rejected not rejected rejected not rejected

1999-2008 F 106 512 327 003p-value 001 002 007 085

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

2009-2018 F 169 069 175 93p-value 0 04 018 0

F critical 384 384 384 384Null hypothesis rejected not rejected not rejected rejected

G4 Non-parametric tests Kruskal-Wallis test

Table G4 Kruskal-Wallis test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 Adjusted H 26254 32592 1464 3962df 1 1 1 1

P value 0 0 0 0Null hypothesis rejected rejected rejected rejected

1959-1968 Adjusted H 28235 27989 2736 332df 1 1 1 1

P value 0 0 0 0Null hypothesis rejected rejected rejected rejected

1969-1978 Adjusted H 22202 33777 3311 7591df 1 1 1 1

P value 0 0 0 0Null hypothesis rejected rejected rejected rejected

1979-1988 Adjusted H 23282 25292 4812 3964df 1 1 1 1

P value 0 0 0 0Null hypothesis rejected rejected rejected rejected

1989-1998 Adjusted H 381 017 175 132df 1 1 1 1

P value 005 068 019 025Null hypothesis not rejected not rejected not rejected not rejected

1999-2008 Adjusted H 855 023 044 004df 1 1 1 1

P value 0 063 051 084Null hypothesis rejected not rejected not rejected not rejected

2009-2018 Adjusted H 1063 009 257 709df 1 1 1 1

P value 0 077 011 001Null hypothesis rejected not rejected not rejected rejected

32

G5 Regression analysis with dummy variables

Table G5 Regression analysis with dummy variables

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 a0 00007 (000) 00007 (000) 00007 (000) 00007 (000)a1 00088 (000) -00119 (000) 00011 (000) -00036 (000)

Anomaly confirmed confirmed confirmed confirmed1959-1968 a0 00006 (000) 00006 (000) 00006 (000) 00006 (000)

a1 00128 (000) -00153 (000) 00027 (000) -00046 (000)Anomaly confirmed confirmed confirmed confirmed

1969-1978 a0 00005 (000) 00005 (000) 00005 (000) 00005 (000)a1 00185 (000) -00192 (000) 00053 (000) -00073 (000)

Anomaly confirmed confirmed confirmed confirmed1979-1988 a0 00008 (000) 00008 (000) 00008 (000) 00008 (000)

a1 00131 (000) -00172 (000) 00059 (000) -00048 (000)Anomaly confirmed confirmed confirmed confirmed

1989-1998 a0 00002 (027) 00002 (028) 00002 (028) 00002 (027)a1 00014 (007) 00010 (024) 00017 (004) -00011 (019)

Anomaly not confirmed not confirmed confirmed not confirmed1999-2008 a0 00001 (059) 00001 (062) 00001 (059) 00001 (060)

a1 00037 (000) 00026 (002) -00038 (000) -00014 (019)Anomaly confirmed not confirmed not confirmed not confirmed

2009-2018 a0 00001 (049) 00001 (049) 00001 (049) 00001 (049)a1 00038 (000) 00007 (040) 00012 (018) -00027 (000)

Anomaly confirmed not confirmed not confirmed confirmed

G6 Modified CAR approach

Table G6 Modified CAR approach

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 Multiple R 099 099 093 098F-test 5753605 (000) 100470(000) 6280421 283281a0 -00091 (000) -00349 (000) 00056 (001) 00015 (073)a1 00083 (000) -00110 (000) 00010 (000) -00031 (000)

Anomaly confirmed confirmed confirmed confirmed1959-1968 Multiple R 099 099 099 099

F-test 3923274 (000) 3005562 (000) 443198 (000) 372583 (000)a0 00096 (000) 00073 (016) -00082 (000) -00095 (004)a1 00116 (001) -00149 (000) 00025 (000) -00047 (000)

Anomaly confirmed confirmed confirmed confirmed1969-1978 Multiple R 099 099 098 099

F-test 4302608 (000) 2723953 (000) 179969 (000) 639745a0 00246 (000) -00002 (000) 00217 (000) -00514 (000)a1 00176 (000) -00182 (000) 00049 (000) -00062 (000)

Anomaly confirmed confirmed confirmed confirmed1979-1988 Multiple R 099 099 099 099

F-test 5872335 (000) 1182609 (000) 1083558 (000) 910089 (000)a0 00136 (000) -01081 (000) -00285 (000) -00101 (000)a1 00131 (000) -00167 (000) 00062 (000) -00048 (000)

Anomaly confirmed confirmed confirmed confirmed1989-1998 Multiple R 09 056 069 016

F-test 46947 (000) 4885 (000) 10131 (000) 263 (011)a0 00102 (002) -00261 (000) -0016 (001) -00237 (000)a1 00015 (000) 00010 (000) 0001 (000) 00002 (011)

Anomaly confirmed confirmed confirmed not confirmed1999-2008 Multiple R 093 087 073 037

F-test 71863 (000) 32530 (000) 13273 (000) 1669 (000)a0 00185 (004) 00311 (000) -00130 (039) -00546 (000)a1 00037 (000) 00032 (000) -00026 (000) -00007 (000)

Anomaly confirmed not confirmed not confirmed confirmed2009-2018 Multiple R 089 001 096 091

F-test 40818 (000) 000 (094) 116744 (000) 53770 (000)a0 01436 (000) -01099 (000) -01036 (000) 00697 (000)a1 00030 (000) 00000 (094) 00024 (000) -00021 (000)

Anomaly confirmed not confirmed confirmed confirmed

33

H Detailed statistical results SampP 500 sub-periods

H1 Average analysis

Table H1 Average analysis

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 Mean return (gapday)

138 -171 004 -014

Mean return(non-gap day)

0 0 0 0

Anomaly confirmed confirmed confirmed confirmed1939-1948 Mean return (gap

day)001 -042 172 -195

Mean return(non-gap day)

003 003 003 003

Anomaly confirmed confirmed confirmed confirmed1949-1958 Mean return (gap

day)165 -18 02 002

Mean return(non-gap day)

006 006 006 006

Anomaly confirmed confirmed confirmed not confirmed1959-1968 Mean return (gap

day)104 -102 015 0

Mean return(non-gap day)

002 002 002 002

Anomaly confirmed confirmed confirmed not confirmed1969-1978 Mean return (gap

day)131 -13 019 -03

Mean return(non-gap day)

0 0 0 0

Anomaly confirmed confirmed confirmed confirmed1979-1988 Mean return (gap

day)058 -042 015 003

Mean return(non-gap day)

005 005 005 005

Anomaly confirmed confirmed confirmed not confirmed1989-1998 Mean return (gap

day)02 -023 -002 01

Mean return(non-gap day)

007 007 007 007

Anomaly confirmed confirmed not confirmed not confirmed1999-2008 Mean return (gap

day)083 -089 -023 -005

Mean return(non-gap day)

001 001 001 001

Anomaly confirmed confirmed not confirmed confirmed2009-2018 Mean return (gap

day)055 -052 001 -015

Mean return(non-gap day)

004 004 004 004

Anomaly confirmed confirmed not confirmed confirmed

34

H2 Parametric tests Students t-test

Table H2 T-test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 t-criterion 101 85 029 048t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

1939-1948 t-criterion 064 479 3074 225t-critical (=095) 196 196 196 196Null hypothesis not rejected rejected rejected rejected

1949-1958 t-criterion 2964 2383 193 041t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

1959-1968 t-criterion 2281 2157 21 023t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected not rejected

1969-1978 t-criterion 1318 2034 187 321t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected rejected

1979-1988 t-criterion 435 535 07 037t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

1989-1998 t-criterion 201 396 132 052t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

1999-2008 t-criterion 362 433 117 022t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

2009-2018 t-criterion 375 382 027 132t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

H3 Parametric tests ANOVA

Table H3 ANOVA

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 F 6281 8032 005 051p-value 0 0 082 047

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

1939-1948 F 056 2603 34854 51034p-value 045 0 0 0

F critical 384 384 384 384Null hypothesis not rejected rejected rejected rejected

1949-1958 F 100174 128997 897 062p-value 0 0 0 043

F critical 384 384 384 384Null hypothesis rejected rejected rejected not rejected

1959-1968 F 36831 32858 617 01p-value 0 0 001 074

F critical 384 384 384 384Null hypothesis rejected rejected rejected not rejected

1969-1978 F 26601 3063 53 152p-value 0 0 002 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1979-1988 F 23 245 076 009p-value 0 0 039 077

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

1989-1998 F 399 1156 118 015p-value 004 0 027 069

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

1999-2008 F 4253 5622 365 024p-value 0 0 006 062

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

2009-2018 F 3064 3656 01 43p-value 0 0 075 004

F critical 384 384 384 384Null hypothesis rejected rejected not rejected rejected

35

H4 Non-parametric tests Kruskal -Wallis test

Table H4 Kruskal-Wallis test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 Adjusted H 9982 5913 332 14df 1 1 1 1

P value 0 0 007 024Null hypothesis rejected rejected not rejected not rejected

1939-1948 Adjusted H 494 1999 23387 24927df 1 1 1 1

P value 003 0 0 0Null hypothesis rejected rejected rejected rejected

1949-1958 Adjusted H 28728 28175 348 15df 1 1 1 1

P value 0 0 006 022Null hypothesis rejected rejected not rejected not rejected

1959-1968 Adjusted H 25729 21437 701 063df 1 1 1 1

P value 0 0 001 043Null hypothesis rejected rejected rejected not rejected

1969-1978 Adjusted H 14407 20078 27 1706df 1 1 1 1

P value 0 0 01 0Null hypothesis rejected rejected not rejected rejected

1979-1988 Adjusted H 1788 2836 027 034df 1 1 1 1

P value 0 0 06 056Null hypothesis rejected rejected not rejected not rejected

1989-1998 Adjusted H 251 1431 111 044df 1 1 1 1

P value 011 0 029 051Null hypothesis not rejected rejected not rejected not rejected

1999-2008 Adjusted H 1812 1788 042 002df 1 1 1 1

P value 0 0 052 089Null hypothesis rejected rejected not rejected not rejected

2009-2018 Adjusted H 1314 1783 074 37df 1 1 1 1

P value 0 0 039 005Null hypothesis rejected rejected not rejected not rejected

36

H5 Regression analysis with dummy variables

Table H5 Regression analysis with dummy variables

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 a0 00000 (097) 00000 (004) 00000 (097) 00000 (097)a1 00138 (000) -00172 (000) 00004 (082) -00014 (047)

Anomaly confirmed confirmed not confirmed not confirmed1939-1948 a0 00003 (015) 00003 (015) 00003 (015) 00003 (015)

a1 00007 (045) -00045 (000) 00170 (000) -00199 (000)Anomaly not confirmed confirmed confirmed confirmed

1949-1958 a0 00006 (000) 00006 (000) 00006 (000) 00006 (000)a1 00160 (000) -00188 (000) 00016 (000) -00004 (043)

Anomaly confirmed confirmed confirmed not confirmed1959-1968 a0 00002 (007) 00002 (004) 00002 (008) 00002 (008)

a1 00103 (000) -00105 (000) 00014 (001) -00002 (074)Anomaly confirmed confirmed confirmed not confirmed

1969-1978 a0 00000 (078) 00000 (078) 00000 (078) 00000 (078)a1 00132 (000) -00132 (000) 00019 (002) -00030 (000)

Anomaly confirmed confirmed confirmed confirmed1979-1988 a0 00006 (001) 00006 (001) 00006 (001) 00006 (000)

a1 00053 (000) -00048 (000) 00009 (040) -00003 (075)Anomaly confirmed confirmed not confirmed not confirmed

1989-1998 a0 00007 (000) 00007 (000) 00007 (000) 00007 (000)a1 00016 (005) -00030 (000) -00009 (026) 00003 (072)

Anomaly confirmed confirmed not confirmed not confirmed1999-2008 a0 00001 (075) 00001 (075) 00001 (075) 00001 (076)

a1 00083 (000) -00091 (000) -00024 (005) -00006 (062)Anomaly confirmed confirmed not confirmed not confirmed

2009-2018 a0 00004 (003) 00004 (000) 00004 (003) 00004 (003)a1 00051 (000) -00059 (000) -00003 (075) -00019 (003)

Anomaly confirmed confirmed not confirmed confirmed

37

H6 Modified CAR approach

Table H6 Modified CAR approach

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 Multiple R 096 095 046 046F-test 175935 (000) 96500 (000) 3534 (000) 2880 (000)a0 -01070 (000) 01958 (000) 00405 (000) 00535 (000)a1 00121 (000) -00160 (000) 00006 (000) -00014 (000)

Anomaly confirmed confirmed confirmed confirmed1939-1948 Multiple R 08 099 099 099

F-test 18777 (000) 755727 (000) 3572830 (000) 2696099 (000)a0 00019 (073) -00346 (000) -00373 (000) 00912 (000)a1 00012 (000) -00044 (000) 00168 (000) -00197 (000)

Anomaly confirmed confirmed confirmed confirmed1949-1958 Multiple R 099 099 094 015

F-test 1021705 (000) 7171257 (000) 75858 (000) 242 (012)a0 -00176 (000) -00191 (000) 00095 (000) -00498 (000)a1 00154 (000) -00181 (000) 00013 (000) -00002 (012)

Anomaly confirmed confirmed confirmed not confirmed1959-1968 Multiple R 099 099 094 078

F-test 1463311 (000) 6002659 (000) 82273 (000) 14352 (000)a0 -00112 (000) 00004 (085) 00151 (000) 00389 (000)a1 00098 (000) -00102 (000) 00011 (000) -00009 (000)

Anomaly confirmed confirmed confirmed confirmed1969-1978 Multiple R 098 099 093 099

F-test 241655 (000) 1451901 (000) 57333 (000) 368160 (000)a0 -00433 (000) 00276 (000) 00099 (002) -00144 (000)a1 00132 (000) -00134 (000) 00020 (000) -00030 (000)

Anomaly confirmed confirmed confirmed confirmed1979-1988 Multiple R 092 078 023 008

F-test 53757 (000) 18707 (000) 487 (003) 085 (036)a0 00813 (000) -02508 (000) 00204 (000) -00235 (000)a1 00036 (000) -00031 (000) -00003 (003) -00001 (036)

Anomaly confirmed confirmed not confirmed not confirmed1989-1998 Multiple R 079 099 074 044

F-test 19705(000) 761967 (000) 14133 (000) 2369 (000)a0 00268 (000) 00023 (021) -00381 (000) 00087 (000)a1 00013 (000) -00028 (000) -00008 (000) 00002 (000)

Anomaly confirmed confirmed not confirmed not confirmed1999-2008 Multiple R 091 093 071 065

F-test 47218 (000) 76564 (000) 9843 (000) 7768 (000)a0 -01493 (000) 01351 (000) 00397 (000) 00007 (093)a1 00081 (000) -00083 (000) -00026 (000) -00011 (000)

Anomaly confirmed confirmed not confirmed confirmed2009-2018 Multiple R 086 087 083 074

F-test 29971 (000) 32484 (000) 23228 (000) 12764 (000)a0 01711 (000) -02250 (000) 00407 (000) -00472 (000)a1 00038 (000) -00044 (000) -00010 (000) -00012 (000)

Anomaly confirmed confirmed not confirmed confirmed

38

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Akerlof G A and Shiller R J (2009) Animal Spirits How human psychology drivesthe economy and why it matters for global capitalism Princeton University Press

Basu S (1977) Investment performance of common stocks in relation to their price-earnings ratios A test of the efficient market hypothesis The Journal of Finance32(3)663ndash682

Bildik R (2004) Are calendar anomalies still alive Evidence from istanbul stockexchange SSRN Electronic Journal 2004

Cai J Li Y and Qi Y (2006) The day-of-the-week effect New evidence from theChinese stock market Chinese Economy 39(2)71ndash88

Cajueiro D O and Tabak B M (2004) The Hurst exponent over time testing theassertion that emerging markets are becoming more efficient Physica A StatisticalMechanics and its Applications 336(3-4)521ndash537

Caporale G M Gil-Alana L Plastun A and Makarenko I (2016) Intraday anoma-lies and market efficiency A trading robot analysis Computational Economics47(2)275ndash295

Caporale G M and Plastun A (2017) Price gaps Another market anomaly Invest-ment Analysts Journal 46(4)279ndash293

Cross F (1973) The behavior of stock prices on Fridays and Mondays FinancialAnalysts Journal 29(6)67ndash69

Fama E F (1965) The behavior of stock-market prices The Journal of Business38(1)34ndash105

Fama E F (1970) Efficient capital markets A review of theory and empirical workThe Journal of Finance 25(2)383ndash417

Fortune P (1998) Weekends can be rough revisiting the weekend effect in stock pricesTechnical report

Fortune P (1999) Are stock returns different over weekends A jump diffusion analysisof the weekend effect New England Economic Review 103ndash19

French K R (1980) Stock returns and the weekend effect Journal of FinancialEconomics 8(1)55ndash69

Fung A K-W Lam K and Lam K-M (2010) Do the prices of stock index futuresin asia overreact to us market returns Journal of Empirical Finance 17(3)428ndash440

17

Gibbons M R and Hess P (1981) Day of the week effects and asset returns Journalof business pages 579ndash596

Grant J L Wolf A and Yu S (2005) Intraday price reversals in the us stock indexfutures market A 15-year study Journal of Banking amp Finance 29(5)1311ndash1327

Grossman S J and Stiglitz J E (1980) On the impossibility of informationallyefficient markets The American Economic Review 70(3)393ndash408

Jacobsen B Mamun A and Visaltanachoti N (2005) Seasonal size and valueanomalies

Jensen M (1978) Some anomalous evidence regarding market efficiency Journal ofFinancial Economics 6(23 (1978))95ndash101

Lakonishok J and Smidt S (1988) Are seasonal anomalies real A ninety-year per-spective The Review of Financial Studies 1(4)403ndash425

MacKinlay A (1997) Event studies in economics and finance Journal of EconomicLiterature (35)113ndash39

Mandelbrot B B (1997) The variation of certain speculative prices In Fractals andscaling in finance pages 371ndash418 Springer

McLean R D and Pontiff J (2016) Does academic research destroy stock returnpredictability The Journal of Finance 71(1)5ndash32

Plastun A Makarenko I Khomutenko L Shcherbak S and Tryfonova O (2019a)Exploring price gap anomaly in the ukrainian stock market Investment Managementamp Financial Innovations 16(2)150

Plastun A Sibande X Gupta R and Wohar M E (2019b) Rise and fall of calendaranomalies over a century The North American Journal of Economics and Finance49181ndash205

Schwert G W (2003) Chapter 15 anomalies and market efficiency In FinancialMarkets and Asset Pricing volume 1 of Handbook of the Economics of Finance pages939 ndash 974 Elsevier

Shiller R J (2000) Irrational exuberance Princeton University

Tiwari A K Aye G C and Gupta R (2019) Stock market efficiency analysis usinglong spans of data A multifractal detrended fluctuation approach Finance ResearchLetters 28398ndash411

Yuan Y (2015) Market-wide attention trading and stock returns Journal of FinancialEconomics 116(3)548ndash564

18

Appendices

A DJI and NASDAQ Summary Results

A1 Overall Results

Table A1 Gap size used for different sub-periods over the period 1929-2018

Period DJI NASDAQ1929-1938 - -1939-1948 - -1949-1958 - 0711959-1968 - 0951969-1978 - 1351979-1988 - 1101989-1998 040 0681999-2008 007 1502009-2018 020 110Overall data set 030 110

Table A2 Day of the week and gaps

Day of the week DJI NASDAQMonday 024 02Tuesday 02 02Wednesday 017 02Thursday 019 019Friday 021 02

A2 Statistical tests

Table A3 Results of the statistical tests for the overall data sets

PeriodMethod Averageanalysis

t-test ANOVAtest

Mann-Whitney

test

Regressionanalysiswith

dummyvariables

ModifiedCAR

approach

Overall

Dow Jones Index overall data setGap day - - - - - + 1Gap day (Positive gaps) + - - - - - 1Gap day (Negative gaps) + - - - - + 2Day after gap (Positive gaps) + - - - - - 1Day after gap (Negative gaps) + - - + - + 3

NASDAQ overall data setGap day + + + + + + 6Gap day (Positive gaps) + + + + + + 6Gap day (Negative gaps) + + + + + + 6Day after gap (Positive gaps) + + + + + + 6Day after gap (Negative gaps) + + + + + + 6

Note + indicates that the anomaly is confirmed and - indicates that anomaly is not confirmedThe higher the overall rating the stronger the evidence of the anomaly

19

Table A4 Results of the statistical tests for H1minus1 DJI

Period Averageanalysis

t-test ANOVA test Mann-Whitney

test

Regressionanalysis with

dummyvariables

ModifiedCAR

approach

Overall

Day of anomaly1989-1998 + - - - - + 21999-2008 + + + + + + 62009-2018 + + + + + + 6

Day after anomaly1989-1998 + - - - - + 21999-2008 + - - - - + 22009-2018 - - - - - - 0

Note + indicates that the anomaly is confirmed and - indicates that anomaly is not confirmedThe higher the overall rating the stronger the evidence of the anomaly

Table A5 Results of the statistical tests for H1minus2 DJI

Period Averageanalysis

t-test ANOVA test Mann-Whitneytest

Regressionanalysis with

dummyvariables

Modified CARapproach

Overall

Day of anomaly1989-1998 - - - - - - 01999-2008 + + + + + + 62009-2018 + + + + + + 6

Day after anomaly1989-1998 + - - - - + 21999-2008 + - - - - - 12009-2018 + - - - - + 2

Note + indicates that the anomaly is confirmed and - indicates that anomaly is not confirmedThe higher the overall rating the stronger the evidence of the anomaly

Table A6 Results of the statistical tests for H1minus1 NASDAQ

PeriodMethod Averageanalysis

t-test ANOVA test Mann-Whitney

test

Regressionanalysis with

dummyvariables

ModifiedCAR

approach

Overall

Day of anomaly1949-1958 + + + + + + 61959-1968 + + + + + + 61969-1978 + + + + + + 61979-1988 + + + + + + 61989-1998 + - - - - + 21999-2008 + - + + + + 52009-2018 + + + + + + 6

Day after anomaly1949-1958 + + + + + + 61959-1968 + + + + + + 61969-1978 + + + + + + 61979-1988 + + + + + + 61989-1998 + - + - + + 41999-2008 - - - - - - 02009-2018 + - - - - + 2

Note + indicates that the anomaly is confirmed and - indicates that anomaly is not confirmedThe higher the overall rating the stronger the evidence of the anomaly

20

Table A7 Results of the statistical tests for H1minus2 NASDAQ

PeriodMethod Averageanalysis

t-test ANOVA test Mann-Whitney

test

Regressionanalysis with

dummyvariables

ModifiedCAR

approach

Overall

Day of anomaly1949-1958 + + + + + + 61959-1968 + + + + + + 61969-1978 + + + + + + 61979-1988 + + + + + + 61989-1998 - - - - - + 11999-2008 - - + - - - 12009-2018 - - - - - - 0

Day after anomaly1949-1958 + + + + + + 61959-1968 + + + + + + 61969-1978 + + + + + + 61979-1988 + + + + + + 61989-1998 + - - - - - 11999-2008 - - - - - + 12009-2018 + - - + + + 4

Note + indicates that the anomaly is confirmed and - indicates that anomaly is not confirmedThe higher the overall rating the stronger the evidence of the anomaly

A3 Trading Simulation Results

Table A8 Trading simulation results of the price gap anomaly for the DJI 1989-2018

Period Gap type Number oftradesunits

Number ofsuccessfultradesunits

Number ofsuccessfultrades

Profit Profit per year

z-test Result

1989-1998 Up 102 46 451 -11 -01 011 failedDown 116 49 422 -267 -27 242 passed

1999-2008 Up 73 51 699 665 66 37 passedDown 143 81 566 641 64 331 passed

2009-2018 Up 127 88 693 308 31 327 passedDown 81 47 58 196 2 184 passed

21

B Short-term price behavior in DJI SampP 500 and

NASDAQ Price gaps (overall data sets)

Table B1 Momentum effect in the US stock market after the gap

Instrument Parameter Number of days after the gap1 2 3

Dow Jones Index Positive gaps 53 57 61Negative gaps 50 50 47

All gaps 51 54 54SampP 500 Index Positive gaps 40 63 60

Negative gaps 4 52 45All gaps 4 58 53

NASDAQ Positive gaps 32 65 67Negative gaps 24 63 59

All gaps 28 64 63

Table B2 Momentum effect in the US stock market before the gap

Instrument Parameter Number of days before the gap1 2 3

Dow Jones Index Positive gaps 56 49 52Negative gaps 54 49 49

All gaps 55 49 50SampP 500 Index Positive gaps 57 57 52

Negative gaps 60 59 54All gaps 58 58 53

NASDAQ Positive gaps 61 56 54Negative gaps 68 69 70

All gaps 64 63 63

Table B3 Fill gap effect in the US stock market

Instrument Parameter Number of days after the gap1 2 3 4 5

Dow Jones Index Positive gaps 22 28 26 30 28Negative gaps 25 33 36 42 46

All gaps 24 30 31 35 37SampP 500 Index Positive gaps 0 6 11 16 19

Negative gaps 1 10 19 26 27All gaps 1 8 15 20 23

NASDAQ Positive gaps 8 13 18 21 19Negative gaps 7 11 17 21 25

All gaps 8 12 18 21 22

22

C Detailed statistical results DJI overall data

C1 Average analysis

Table C1 Average analysis

Parameter Gap day Gap day(Positive gaps)

Gap day(Negative gaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Mean return (gap day) 003 006 0 005 -003Mean return (non-gap day) 004 004 004 004 004Anomaly not confirmed not confirmed confirmed not confirmed confirmed

C2 Parametric tests Students t-test

Table C2 T-test

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

t-criterion 016 042 053 015 104t-critical (=095) 196 196 196 196 196Null hypothesis not rejected not rejected not rejected not rejected not rejected

C3 Parametric tests ANOVA

Table C3 ANOVA

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

F 0036 018 053 003 14p-value 085 067 047 086 024F critical 384 384 384 384 384Null hypothesis not rejected not rejected not rejected not rejected not rejected

C4 Non-parametric tests Kruskal-Wallis test

Table C4 Kruskal -Wallis test

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Adjusted H 082 012 126 0 455df 1 1 1 1 1P value 037 073 026 095 003Critical value 384 384 384 384 384Null hypothesis not rejected not rejected not rejected not rejected rejected

23

C5 Regression analysis with dummy variables

Table C5 Regression analysis with dummy variables

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

a0 00004 (000) 00004 (000) 00004 (000) 00004 (000) 00004 (000)a1 -00001 (-019) 00002 (067) -00004 (047) 00001 (086) -00007 (024)Anomaly not confirmed not confirmed not confirmed not confirmed not confirmed

C6 Modified CAR approach

Table C6 Modified CAR approach

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Multiple R 049 05 025 0 092F-test 23347 (000) 12913 (000) 2207 (000) 000 (098) 1822 (000)a0 -00041 (060) 00128 (006) -00267 (000) 00354 (000) 00319 (000)a1 -00003 (000) -00003 (000) -00002 (000) 00000 (098) -00008 (000)Anomaly confirmed confirmed confirmed not confirmed confirmed

24

D Detailed statistical results SampP 500 overall data

D1 Average analysis

Table D1 Average analysis

Parameter Gap day Gap day(Positive gaps)

Gap day(Negative gaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Mean return (gap day) 006 115 -129 017 -011Mean return (non-gap day) 002 002 002 002 002Anomaly confirmed confirmed confirmed confirmed confirmed

D2 Parametric tests Students t-test

Table D2 T-test

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

t-criterion 092 4546 3579 485 271t-critical (=095) 196 196 196 196 196Null hypothesis not rejected rejected rejected rejected rejected

D3 Parametric tests ANOVA

Table D3 ANOVA

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

F 155 116211 126952 1866 136p-value 022 0 0 0 0F critical 384 384 384 384 384Null hypothesis not rejected rejected rejected not rejected not rejected

D4 Non-parametric tests Kruskal-Wallis test

Table D4 Kruskal-Wallis test

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Adjusted H 1352 70516 47237 3946 004df 1 1 1 1 1P value 0 0 0 0 084Critical value 384 384 384 384 384Null hypothesis rejected rejected rejected rejected not rejected

25

D5 Regression analysis with dummy variables

Table D5 Regression analysis with dummy variables

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

a0 00002 (000) 00002 (000) 00002 (000) 00002 (000) 00002 (000)a1 00003 (021) 00113 (000) -00132 (000) 00014 (000) -00014 (000)Anomaly not confirmed confirmed confirmed confirmed confirmed

D6 Modified CAR approach

Table D6 Modified CAR approach

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Multiple R 051 099 099 099 096F-test 69486 (000) 325351 (000) 1457582 (000) 6345973 (000) 1213344 (000)a0 -01003(000) 04081 (000) -05444 (000) -01088 (000) 00272 (000)a1 00002 (000) 00106 (000) -00127 (000) 00016 (000) -00016 (000)Anomaly confirmed confirmed confirmed confirmed confirmed

26

E Detailed statistical results NASDAQ overall data

E1 Average analysis

Table E1 Average analysis

Parameter Gap day Gap day(Positive gaps)

Gap day(Negative gaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Mean return (gap day) -009 084 -090 022 -037Mean return (non-gap day) 003 003 003 003 003Anomaly confirmed confirmed confirmed confirmed confirmed

E2 Parametric tests Students t-test

Table E2 T-test

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

t-criterion 230 1257 1341 306 664t-critical (=095) 196 196 196 196 196Null hypothesis rejected rejected rejected rejected rejected

E3 Parametric tests ANOVA

Table E3 ANOVA

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

F 2289 62720 88402 3330 17356p-value 0 0 0 0 0F critical 384 384 384 384 384Null hypothesis rejected rejected rejected rejected rejected

E4 Non-parametric tests Kruskal-Wallis test

Table E4 Kruskal-Wallis test

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Adjusted H 1892 36022 45248 4695 10437df 1 1 1 1 1P value 0 0 0 0 0Critical value 384 384 384 384 384Null hypothesis rejected rejected rejected rejected rejected

27

E5 Regression analysis with dummy variables

Table E5 Regression analysis with dummy variables

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

a0 00003 (000) 00003 (000) 00003 (000) 00003 (000) 00003 (000)a1 -00012 (000) 00081 (000) -00093 (000) 00018 (000) -00040 (000)Anomaly confirmed confirmed confirmed confirmed confirmed

E6 Modified CAR approach

Table E6 Modified CAR approach

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Multiple R 069 092 092 072 097F-test 133255 (000) 361102 (000) 442376 (000) 72903 (000) 1082812 (000)a0 -10646 (000) 11373 (000) -12888 (000) 03928 (000) -02297 (000)a1 -00011 (000) 00073 (000) -00097 (000) 00017 (000) -00039 (000)Anomaly confirmed confirmed confirmed confirmed confirmed

28

F Detailed statistical results DJI sub-periods

F1 Average analysis

Table F1 Average analysis

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 Mean return (gapday)

-001 023 015 -004

Mean return(non-gap day)

007 007 007 007

Anomaly confirmed confirmed confirmed confirmed1999-2008 Mean return (gap

day)090 -045 013 -004

Mean return(non-gap day)

-004 -004 -004 -004

Anomaly confirmed confirmed confirmed confirmed2009-2018 Mean return (gap

day)024 -024 0 -004

Mean return(non-gap day)

004 004 004 004

Anomaly confirmed confirmed not confirmed confirmed

F2 Parametric tests Students t-test

Table F2 T-test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 t-criterion 083 165 087 139t-critical (=095) 196 196 196 196Null hypothesis not rejected not rejected not rejected not rejected

1999-2008 t-criterion 347 351 054 047t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected rejected

2009-2018 t-criterion 265 207 051 058t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

F3 Parametric tests ANOVA

Table F3 ANOVA

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 F 085 409 093 179p-value 035 004 033 018

F critical 384 384 384 384Null hypothesis not rejected rejected not rejected not rejected

1999-2008 F 5405 3196 065 072p-value 0 0 042 039

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

2009-2018 F 554 697 024 058p-value 001 0 062 044

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

29

F4 Non-parametric tests Kruskal-Wallis test

Table F4 Kruskal-Wallis test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 Adjusted H 113 211 113 332df 1 1 1 1

P value 029 015 029 007Null hypothesis not rejected not rejected not rejected not rejected

1999-2008 Adjusted H 1484 1414 003 139df 1 1 1 1

P value 0 0 086 024Null hypothesis rejected rejected not rejected not rejected

2009-2018 Adjusted H 506 68 051 171df 1 1 1 1

P value 002 001 047 019Null hypothesis rejected rejected not rejected not rejected

F5 Regression analysis with dummy variables

Table F5 Regression analysis with dummy variables

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 a0 000068 (000) 00007 (000) 00007 (000) 00007 (000)a1 -000078 (035) 00016 (004) 00008 (033) -00011 (018)

Anomaly not confirmed confirmed not confirmed not confirmed1999-2008 a0 00004 (008) 00004 (008) 00004 (006) 00004 (008)

a1 00087 (000) -00049 (000) 00009 (042) -00008 (039)Anomaly confirmed confirmed not confirmed not confirmed

2009-2018 a0 00004 (006) 00004 (006) 00004 (006) 00004 (006)a1 00021 (001) -00028 (001) -00004 (062) -00008 (047)

Anomaly confirmed confirmed not confirmed not confirmed

F6 Modified CAR approach

Table F6 Modified CAR approach

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 Multiple R 083 088 082 086F-test 22779 (000) 40583 (000) 20401 (000) 3269454 (000)a0 00042 (023) 00017 (073) 00014 (058) -00266 (000)a1 -00009 (000) 00015 (000) 00006 (000) -00009 (000)

Anomaly confirmed confirmed confirmed confirmed1999-2008 Multiple R 095 093 076 019

F-test 62658 (000) 84712 (000) 10056 (000) 492 (003)a0 -00972 (000) 00365 (000) -00198 (000) -00115 (021)a1 00086 (000) -00042 (000) 00014 (000) 00002 (003)

Anomaly confirmed confirmed confirmed not confirmed2009-2018 Multiple R 096 082 08 05

F-test 150452 (000) 16731 (000) 22287 (000) 2620 (000)a0 00548 (000) -00618 (000) 00031 (020) -00112 (000)a1 00013 (000) -00014 (000) -00005 (000) -00004 (000)

Anomaly confirmed confirmed not confirmed confirmed

30

G Detailed statistical results NASDAQ sub-periods

G1 Average analysis

Table G1 Average analysis

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 Mean return (gapday)

094 -111 0189 -029

Mean return(non-gap day)

007 007 007 007

Anomaly confirmed confirmed confirmed confirmed1959-1968 Mean return (gap

day)133 -147 033 -039

Mean return(non-gap day)

006 006 006 006

Anomaly confirmed confirmed confirmed confirmed1969-1978 Mean return (gap

day)19 -186 057 -068

Mean return(non-gap day)

005 005 005 005

Anomaly confirmed confirmed confirmed confirmed1979-1988 Mean return (gap

day)138 -162 066 -04

Mean return(non-gap day)

008 008 008 008

Anomaly confirmed confirmed confirmed confirmed1989-1998 Mean return (gap

day)016 012 018 -009

Mean return(non-gap day)

002 002 002 002

Anomaly confirmed not confirmed confirmed confirmed1999-2008 Mean return (gap

day)38E-3 027 -036 -013

Mean return(non-gap day)

-01 -01 -01 -01

Anomaly confirmed not confirmed not confirmed not confirmed2009-2018 Mean return (gap

day)039 009 013 -025

Mean return(non-gap day)

001 001 001 001

Anomaly confirmed not confirmed confirmed confirmed

G2 Parametric tests Students t-test

Table G2 T-test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 t-criterion 3194 3076 201 559t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected rejected

1959-1968 t-criterion 1399 2246 443 382t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected rejected

1969-1978 t-criterion 261 4358 417 786t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected rejected

1979-1988 t-criterion 1847 1445 709 395t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected rejected

1989-1998 t-criterion 13 066 126 093t-critical (=095) 196 196 196 196Null hypothesis not rejected not rejected not rejected not rejected

1999-2008 t-criterion 192 106 111 009t-critical (=095) 196 196 196 196Null hypothesis not rejected not rejected not rejected not rejected

2009-2018 t-criterion 27 05 089 188t-critical (=095) 196 196 196 196Null hypothesis rejected not rejected not rejected not rejected

31

G3 Parametric tests ANOVA

Table G3 ANOVA

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 F 88153 190609 1272 14521p-value 0 0 0 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1959-1968 F 93974 149771 4715 10418p-value 0 0 0 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1969-1978 F 84546 145429 6295 18241p-value 0 0 0 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1979-1988 F 66952 110482 13138 8626p-value 0 0 0 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1989-1998 F 323 138 43 168p-value 007 024 003 019

F critical 384 384 384 384Null hypothesis not rejected not rejected rejected not rejected

1999-2008 F 106 512 327 003p-value 001 002 007 085

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

2009-2018 F 169 069 175 93p-value 0 04 018 0

F critical 384 384 384 384Null hypothesis rejected not rejected not rejected rejected

G4 Non-parametric tests Kruskal-Wallis test

Table G4 Kruskal-Wallis test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 Adjusted H 26254 32592 1464 3962df 1 1 1 1

P value 0 0 0 0Null hypothesis rejected rejected rejected rejected

1959-1968 Adjusted H 28235 27989 2736 332df 1 1 1 1

P value 0 0 0 0Null hypothesis rejected rejected rejected rejected

1969-1978 Adjusted H 22202 33777 3311 7591df 1 1 1 1

P value 0 0 0 0Null hypothesis rejected rejected rejected rejected

1979-1988 Adjusted H 23282 25292 4812 3964df 1 1 1 1

P value 0 0 0 0Null hypothesis rejected rejected rejected rejected

1989-1998 Adjusted H 381 017 175 132df 1 1 1 1

P value 005 068 019 025Null hypothesis not rejected not rejected not rejected not rejected

1999-2008 Adjusted H 855 023 044 004df 1 1 1 1

P value 0 063 051 084Null hypothesis rejected not rejected not rejected not rejected

2009-2018 Adjusted H 1063 009 257 709df 1 1 1 1

P value 0 077 011 001Null hypothesis rejected not rejected not rejected rejected

32

G5 Regression analysis with dummy variables

Table G5 Regression analysis with dummy variables

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 a0 00007 (000) 00007 (000) 00007 (000) 00007 (000)a1 00088 (000) -00119 (000) 00011 (000) -00036 (000)

Anomaly confirmed confirmed confirmed confirmed1959-1968 a0 00006 (000) 00006 (000) 00006 (000) 00006 (000)

a1 00128 (000) -00153 (000) 00027 (000) -00046 (000)Anomaly confirmed confirmed confirmed confirmed

1969-1978 a0 00005 (000) 00005 (000) 00005 (000) 00005 (000)a1 00185 (000) -00192 (000) 00053 (000) -00073 (000)

Anomaly confirmed confirmed confirmed confirmed1979-1988 a0 00008 (000) 00008 (000) 00008 (000) 00008 (000)

a1 00131 (000) -00172 (000) 00059 (000) -00048 (000)Anomaly confirmed confirmed confirmed confirmed

1989-1998 a0 00002 (027) 00002 (028) 00002 (028) 00002 (027)a1 00014 (007) 00010 (024) 00017 (004) -00011 (019)

Anomaly not confirmed not confirmed confirmed not confirmed1999-2008 a0 00001 (059) 00001 (062) 00001 (059) 00001 (060)

a1 00037 (000) 00026 (002) -00038 (000) -00014 (019)Anomaly confirmed not confirmed not confirmed not confirmed

2009-2018 a0 00001 (049) 00001 (049) 00001 (049) 00001 (049)a1 00038 (000) 00007 (040) 00012 (018) -00027 (000)

Anomaly confirmed not confirmed not confirmed confirmed

G6 Modified CAR approach

Table G6 Modified CAR approach

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 Multiple R 099 099 093 098F-test 5753605 (000) 100470(000) 6280421 283281a0 -00091 (000) -00349 (000) 00056 (001) 00015 (073)a1 00083 (000) -00110 (000) 00010 (000) -00031 (000)

Anomaly confirmed confirmed confirmed confirmed1959-1968 Multiple R 099 099 099 099

F-test 3923274 (000) 3005562 (000) 443198 (000) 372583 (000)a0 00096 (000) 00073 (016) -00082 (000) -00095 (004)a1 00116 (001) -00149 (000) 00025 (000) -00047 (000)

Anomaly confirmed confirmed confirmed confirmed1969-1978 Multiple R 099 099 098 099

F-test 4302608 (000) 2723953 (000) 179969 (000) 639745a0 00246 (000) -00002 (000) 00217 (000) -00514 (000)a1 00176 (000) -00182 (000) 00049 (000) -00062 (000)

Anomaly confirmed confirmed confirmed confirmed1979-1988 Multiple R 099 099 099 099

F-test 5872335 (000) 1182609 (000) 1083558 (000) 910089 (000)a0 00136 (000) -01081 (000) -00285 (000) -00101 (000)a1 00131 (000) -00167 (000) 00062 (000) -00048 (000)

Anomaly confirmed confirmed confirmed confirmed1989-1998 Multiple R 09 056 069 016

F-test 46947 (000) 4885 (000) 10131 (000) 263 (011)a0 00102 (002) -00261 (000) -0016 (001) -00237 (000)a1 00015 (000) 00010 (000) 0001 (000) 00002 (011)

Anomaly confirmed confirmed confirmed not confirmed1999-2008 Multiple R 093 087 073 037

F-test 71863 (000) 32530 (000) 13273 (000) 1669 (000)a0 00185 (004) 00311 (000) -00130 (039) -00546 (000)a1 00037 (000) 00032 (000) -00026 (000) -00007 (000)

Anomaly confirmed not confirmed not confirmed confirmed2009-2018 Multiple R 089 001 096 091

F-test 40818 (000) 000 (094) 116744 (000) 53770 (000)a0 01436 (000) -01099 (000) -01036 (000) 00697 (000)a1 00030 (000) 00000 (094) 00024 (000) -00021 (000)

Anomaly confirmed not confirmed confirmed confirmed

33

H Detailed statistical results SampP 500 sub-periods

H1 Average analysis

Table H1 Average analysis

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 Mean return (gapday)

138 -171 004 -014

Mean return(non-gap day)

0 0 0 0

Anomaly confirmed confirmed confirmed confirmed1939-1948 Mean return (gap

day)001 -042 172 -195

Mean return(non-gap day)

003 003 003 003

Anomaly confirmed confirmed confirmed confirmed1949-1958 Mean return (gap

day)165 -18 02 002

Mean return(non-gap day)

006 006 006 006

Anomaly confirmed confirmed confirmed not confirmed1959-1968 Mean return (gap

day)104 -102 015 0

Mean return(non-gap day)

002 002 002 002

Anomaly confirmed confirmed confirmed not confirmed1969-1978 Mean return (gap

day)131 -13 019 -03

Mean return(non-gap day)

0 0 0 0

Anomaly confirmed confirmed confirmed confirmed1979-1988 Mean return (gap

day)058 -042 015 003

Mean return(non-gap day)

005 005 005 005

Anomaly confirmed confirmed confirmed not confirmed1989-1998 Mean return (gap

day)02 -023 -002 01

Mean return(non-gap day)

007 007 007 007

Anomaly confirmed confirmed not confirmed not confirmed1999-2008 Mean return (gap

day)083 -089 -023 -005

Mean return(non-gap day)

001 001 001 001

Anomaly confirmed confirmed not confirmed confirmed2009-2018 Mean return (gap

day)055 -052 001 -015

Mean return(non-gap day)

004 004 004 004

Anomaly confirmed confirmed not confirmed confirmed

34

H2 Parametric tests Students t-test

Table H2 T-test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 t-criterion 101 85 029 048t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

1939-1948 t-criterion 064 479 3074 225t-critical (=095) 196 196 196 196Null hypothesis not rejected rejected rejected rejected

1949-1958 t-criterion 2964 2383 193 041t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

1959-1968 t-criterion 2281 2157 21 023t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected not rejected

1969-1978 t-criterion 1318 2034 187 321t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected rejected

1979-1988 t-criterion 435 535 07 037t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

1989-1998 t-criterion 201 396 132 052t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

1999-2008 t-criterion 362 433 117 022t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

2009-2018 t-criterion 375 382 027 132t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

H3 Parametric tests ANOVA

Table H3 ANOVA

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 F 6281 8032 005 051p-value 0 0 082 047

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

1939-1948 F 056 2603 34854 51034p-value 045 0 0 0

F critical 384 384 384 384Null hypothesis not rejected rejected rejected rejected

1949-1958 F 100174 128997 897 062p-value 0 0 0 043

F critical 384 384 384 384Null hypothesis rejected rejected rejected not rejected

1959-1968 F 36831 32858 617 01p-value 0 0 001 074

F critical 384 384 384 384Null hypothesis rejected rejected rejected not rejected

1969-1978 F 26601 3063 53 152p-value 0 0 002 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1979-1988 F 23 245 076 009p-value 0 0 039 077

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

1989-1998 F 399 1156 118 015p-value 004 0 027 069

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

1999-2008 F 4253 5622 365 024p-value 0 0 006 062

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

2009-2018 F 3064 3656 01 43p-value 0 0 075 004

F critical 384 384 384 384Null hypothesis rejected rejected not rejected rejected

35

H4 Non-parametric tests Kruskal -Wallis test

Table H4 Kruskal-Wallis test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 Adjusted H 9982 5913 332 14df 1 1 1 1

P value 0 0 007 024Null hypothesis rejected rejected not rejected not rejected

1939-1948 Adjusted H 494 1999 23387 24927df 1 1 1 1

P value 003 0 0 0Null hypothesis rejected rejected rejected rejected

1949-1958 Adjusted H 28728 28175 348 15df 1 1 1 1

P value 0 0 006 022Null hypothesis rejected rejected not rejected not rejected

1959-1968 Adjusted H 25729 21437 701 063df 1 1 1 1

P value 0 0 001 043Null hypothesis rejected rejected rejected not rejected

1969-1978 Adjusted H 14407 20078 27 1706df 1 1 1 1

P value 0 0 01 0Null hypothesis rejected rejected not rejected rejected

1979-1988 Adjusted H 1788 2836 027 034df 1 1 1 1

P value 0 0 06 056Null hypothesis rejected rejected not rejected not rejected

1989-1998 Adjusted H 251 1431 111 044df 1 1 1 1

P value 011 0 029 051Null hypothesis not rejected rejected not rejected not rejected

1999-2008 Adjusted H 1812 1788 042 002df 1 1 1 1

P value 0 0 052 089Null hypothesis rejected rejected not rejected not rejected

2009-2018 Adjusted H 1314 1783 074 37df 1 1 1 1

P value 0 0 039 005Null hypothesis rejected rejected not rejected not rejected

36

H5 Regression analysis with dummy variables

Table H5 Regression analysis with dummy variables

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 a0 00000 (097) 00000 (004) 00000 (097) 00000 (097)a1 00138 (000) -00172 (000) 00004 (082) -00014 (047)

Anomaly confirmed confirmed not confirmed not confirmed1939-1948 a0 00003 (015) 00003 (015) 00003 (015) 00003 (015)

a1 00007 (045) -00045 (000) 00170 (000) -00199 (000)Anomaly not confirmed confirmed confirmed confirmed

1949-1958 a0 00006 (000) 00006 (000) 00006 (000) 00006 (000)a1 00160 (000) -00188 (000) 00016 (000) -00004 (043)

Anomaly confirmed confirmed confirmed not confirmed1959-1968 a0 00002 (007) 00002 (004) 00002 (008) 00002 (008)

a1 00103 (000) -00105 (000) 00014 (001) -00002 (074)Anomaly confirmed confirmed confirmed not confirmed

1969-1978 a0 00000 (078) 00000 (078) 00000 (078) 00000 (078)a1 00132 (000) -00132 (000) 00019 (002) -00030 (000)

Anomaly confirmed confirmed confirmed confirmed1979-1988 a0 00006 (001) 00006 (001) 00006 (001) 00006 (000)

a1 00053 (000) -00048 (000) 00009 (040) -00003 (075)Anomaly confirmed confirmed not confirmed not confirmed

1989-1998 a0 00007 (000) 00007 (000) 00007 (000) 00007 (000)a1 00016 (005) -00030 (000) -00009 (026) 00003 (072)

Anomaly confirmed confirmed not confirmed not confirmed1999-2008 a0 00001 (075) 00001 (075) 00001 (075) 00001 (076)

a1 00083 (000) -00091 (000) -00024 (005) -00006 (062)Anomaly confirmed confirmed not confirmed not confirmed

2009-2018 a0 00004 (003) 00004 (000) 00004 (003) 00004 (003)a1 00051 (000) -00059 (000) -00003 (075) -00019 (003)

Anomaly confirmed confirmed not confirmed confirmed

37

H6 Modified CAR approach

Table H6 Modified CAR approach

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 Multiple R 096 095 046 046F-test 175935 (000) 96500 (000) 3534 (000) 2880 (000)a0 -01070 (000) 01958 (000) 00405 (000) 00535 (000)a1 00121 (000) -00160 (000) 00006 (000) -00014 (000)

Anomaly confirmed confirmed confirmed confirmed1939-1948 Multiple R 08 099 099 099

F-test 18777 (000) 755727 (000) 3572830 (000) 2696099 (000)a0 00019 (073) -00346 (000) -00373 (000) 00912 (000)a1 00012 (000) -00044 (000) 00168 (000) -00197 (000)

Anomaly confirmed confirmed confirmed confirmed1949-1958 Multiple R 099 099 094 015

F-test 1021705 (000) 7171257 (000) 75858 (000) 242 (012)a0 -00176 (000) -00191 (000) 00095 (000) -00498 (000)a1 00154 (000) -00181 (000) 00013 (000) -00002 (012)

Anomaly confirmed confirmed confirmed not confirmed1959-1968 Multiple R 099 099 094 078

F-test 1463311 (000) 6002659 (000) 82273 (000) 14352 (000)a0 -00112 (000) 00004 (085) 00151 (000) 00389 (000)a1 00098 (000) -00102 (000) 00011 (000) -00009 (000)

Anomaly confirmed confirmed confirmed confirmed1969-1978 Multiple R 098 099 093 099

F-test 241655 (000) 1451901 (000) 57333 (000) 368160 (000)a0 -00433 (000) 00276 (000) 00099 (002) -00144 (000)a1 00132 (000) -00134 (000) 00020 (000) -00030 (000)

Anomaly confirmed confirmed confirmed confirmed1979-1988 Multiple R 092 078 023 008

F-test 53757 (000) 18707 (000) 487 (003) 085 (036)a0 00813 (000) -02508 (000) 00204 (000) -00235 (000)a1 00036 (000) -00031 (000) -00003 (003) -00001 (036)

Anomaly confirmed confirmed not confirmed not confirmed1989-1998 Multiple R 079 099 074 044

F-test 19705(000) 761967 (000) 14133 (000) 2369 (000)a0 00268 (000) 00023 (021) -00381 (000) 00087 (000)a1 00013 (000) -00028 (000) -00008 (000) 00002 (000)

Anomaly confirmed confirmed not confirmed not confirmed1999-2008 Multiple R 091 093 071 065

F-test 47218 (000) 76564 (000) 9843 (000) 7768 (000)a0 -01493 (000) 01351 (000) 00397 (000) 00007 (093)a1 00081 (000) -00083 (000) -00026 (000) -00011 (000)

Anomaly confirmed confirmed not confirmed confirmed2009-2018 Multiple R 086 087 083 074

F-test 29971 (000) 32484 (000) 23228 (000) 12764 (000)a0 01711 (000) -02250 (000) 00407 (000) -00472 (000)a1 00038 (000) -00044 (000) -00010 (000) -00012 (000)

Anomaly confirmed confirmed not confirmed confirmed

38

Gibbons M R and Hess P (1981) Day of the week effects and asset returns Journalof business pages 579ndash596

Grant J L Wolf A and Yu S (2005) Intraday price reversals in the us stock indexfutures market A 15-year study Journal of Banking amp Finance 29(5)1311ndash1327

Grossman S J and Stiglitz J E (1980) On the impossibility of informationallyefficient markets The American Economic Review 70(3)393ndash408

Jacobsen B Mamun A and Visaltanachoti N (2005) Seasonal size and valueanomalies

Jensen M (1978) Some anomalous evidence regarding market efficiency Journal ofFinancial Economics 6(23 (1978))95ndash101

Lakonishok J and Smidt S (1988) Are seasonal anomalies real A ninety-year per-spective The Review of Financial Studies 1(4)403ndash425

MacKinlay A (1997) Event studies in economics and finance Journal of EconomicLiterature (35)113ndash39

Mandelbrot B B (1997) The variation of certain speculative prices In Fractals andscaling in finance pages 371ndash418 Springer

McLean R D and Pontiff J (2016) Does academic research destroy stock returnpredictability The Journal of Finance 71(1)5ndash32

Plastun A Makarenko I Khomutenko L Shcherbak S and Tryfonova O (2019a)Exploring price gap anomaly in the ukrainian stock market Investment Managementamp Financial Innovations 16(2)150

Plastun A Sibande X Gupta R and Wohar M E (2019b) Rise and fall of calendaranomalies over a century The North American Journal of Economics and Finance49181ndash205

Schwert G W (2003) Chapter 15 anomalies and market efficiency In FinancialMarkets and Asset Pricing volume 1 of Handbook of the Economics of Finance pages939 ndash 974 Elsevier

Shiller R J (2000) Irrational exuberance Princeton University

Tiwari A K Aye G C and Gupta R (2019) Stock market efficiency analysis usinglong spans of data A multifractal detrended fluctuation approach Finance ResearchLetters 28398ndash411

Yuan Y (2015) Market-wide attention trading and stock returns Journal of FinancialEconomics 116(3)548ndash564

18

Appendices

A DJI and NASDAQ Summary Results

A1 Overall Results

Table A1 Gap size used for different sub-periods over the period 1929-2018

Period DJI NASDAQ1929-1938 - -1939-1948 - -1949-1958 - 0711959-1968 - 0951969-1978 - 1351979-1988 - 1101989-1998 040 0681999-2008 007 1502009-2018 020 110Overall data set 030 110

Table A2 Day of the week and gaps

Day of the week DJI NASDAQMonday 024 02Tuesday 02 02Wednesday 017 02Thursday 019 019Friday 021 02

A2 Statistical tests

Table A3 Results of the statistical tests for the overall data sets

PeriodMethod Averageanalysis

t-test ANOVAtest

Mann-Whitney

test

Regressionanalysiswith

dummyvariables

ModifiedCAR

approach

Overall

Dow Jones Index overall data setGap day - - - - - + 1Gap day (Positive gaps) + - - - - - 1Gap day (Negative gaps) + - - - - + 2Day after gap (Positive gaps) + - - - - - 1Day after gap (Negative gaps) + - - + - + 3

NASDAQ overall data setGap day + + + + + + 6Gap day (Positive gaps) + + + + + + 6Gap day (Negative gaps) + + + + + + 6Day after gap (Positive gaps) + + + + + + 6Day after gap (Negative gaps) + + + + + + 6

Note + indicates that the anomaly is confirmed and - indicates that anomaly is not confirmedThe higher the overall rating the stronger the evidence of the anomaly

19

Table A4 Results of the statistical tests for H1minus1 DJI

Period Averageanalysis

t-test ANOVA test Mann-Whitney

test

Regressionanalysis with

dummyvariables

ModifiedCAR

approach

Overall

Day of anomaly1989-1998 + - - - - + 21999-2008 + + + + + + 62009-2018 + + + + + + 6

Day after anomaly1989-1998 + - - - - + 21999-2008 + - - - - + 22009-2018 - - - - - - 0

Note + indicates that the anomaly is confirmed and - indicates that anomaly is not confirmedThe higher the overall rating the stronger the evidence of the anomaly

Table A5 Results of the statistical tests for H1minus2 DJI

Period Averageanalysis

t-test ANOVA test Mann-Whitneytest

Regressionanalysis with

dummyvariables

Modified CARapproach

Overall

Day of anomaly1989-1998 - - - - - - 01999-2008 + + + + + + 62009-2018 + + + + + + 6

Day after anomaly1989-1998 + - - - - + 21999-2008 + - - - - - 12009-2018 + - - - - + 2

Note + indicates that the anomaly is confirmed and - indicates that anomaly is not confirmedThe higher the overall rating the stronger the evidence of the anomaly

Table A6 Results of the statistical tests for H1minus1 NASDAQ

PeriodMethod Averageanalysis

t-test ANOVA test Mann-Whitney

test

Regressionanalysis with

dummyvariables

ModifiedCAR

approach

Overall

Day of anomaly1949-1958 + + + + + + 61959-1968 + + + + + + 61969-1978 + + + + + + 61979-1988 + + + + + + 61989-1998 + - - - - + 21999-2008 + - + + + + 52009-2018 + + + + + + 6

Day after anomaly1949-1958 + + + + + + 61959-1968 + + + + + + 61969-1978 + + + + + + 61979-1988 + + + + + + 61989-1998 + - + - + + 41999-2008 - - - - - - 02009-2018 + - - - - + 2

Note + indicates that the anomaly is confirmed and - indicates that anomaly is not confirmedThe higher the overall rating the stronger the evidence of the anomaly

20

Table A7 Results of the statistical tests for H1minus2 NASDAQ

PeriodMethod Averageanalysis

t-test ANOVA test Mann-Whitney

test

Regressionanalysis with

dummyvariables

ModifiedCAR

approach

Overall

Day of anomaly1949-1958 + + + + + + 61959-1968 + + + + + + 61969-1978 + + + + + + 61979-1988 + + + + + + 61989-1998 - - - - - + 11999-2008 - - + - - - 12009-2018 - - - - - - 0

Day after anomaly1949-1958 + + + + + + 61959-1968 + + + + + + 61969-1978 + + + + + + 61979-1988 + + + + + + 61989-1998 + - - - - - 11999-2008 - - - - - + 12009-2018 + - - + + + 4

Note + indicates that the anomaly is confirmed and - indicates that anomaly is not confirmedThe higher the overall rating the stronger the evidence of the anomaly

A3 Trading Simulation Results

Table A8 Trading simulation results of the price gap anomaly for the DJI 1989-2018

Period Gap type Number oftradesunits

Number ofsuccessfultradesunits

Number ofsuccessfultrades

Profit Profit per year

z-test Result

1989-1998 Up 102 46 451 -11 -01 011 failedDown 116 49 422 -267 -27 242 passed

1999-2008 Up 73 51 699 665 66 37 passedDown 143 81 566 641 64 331 passed

2009-2018 Up 127 88 693 308 31 327 passedDown 81 47 58 196 2 184 passed

21

B Short-term price behavior in DJI SampP 500 and

NASDAQ Price gaps (overall data sets)

Table B1 Momentum effect in the US stock market after the gap

Instrument Parameter Number of days after the gap1 2 3

Dow Jones Index Positive gaps 53 57 61Negative gaps 50 50 47

All gaps 51 54 54SampP 500 Index Positive gaps 40 63 60

Negative gaps 4 52 45All gaps 4 58 53

NASDAQ Positive gaps 32 65 67Negative gaps 24 63 59

All gaps 28 64 63

Table B2 Momentum effect in the US stock market before the gap

Instrument Parameter Number of days before the gap1 2 3

Dow Jones Index Positive gaps 56 49 52Negative gaps 54 49 49

All gaps 55 49 50SampP 500 Index Positive gaps 57 57 52

Negative gaps 60 59 54All gaps 58 58 53

NASDAQ Positive gaps 61 56 54Negative gaps 68 69 70

All gaps 64 63 63

Table B3 Fill gap effect in the US stock market

Instrument Parameter Number of days after the gap1 2 3 4 5

Dow Jones Index Positive gaps 22 28 26 30 28Negative gaps 25 33 36 42 46

All gaps 24 30 31 35 37SampP 500 Index Positive gaps 0 6 11 16 19

Negative gaps 1 10 19 26 27All gaps 1 8 15 20 23

NASDAQ Positive gaps 8 13 18 21 19Negative gaps 7 11 17 21 25

All gaps 8 12 18 21 22

22

C Detailed statistical results DJI overall data

C1 Average analysis

Table C1 Average analysis

Parameter Gap day Gap day(Positive gaps)

Gap day(Negative gaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Mean return (gap day) 003 006 0 005 -003Mean return (non-gap day) 004 004 004 004 004Anomaly not confirmed not confirmed confirmed not confirmed confirmed

C2 Parametric tests Students t-test

Table C2 T-test

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

t-criterion 016 042 053 015 104t-critical (=095) 196 196 196 196 196Null hypothesis not rejected not rejected not rejected not rejected not rejected

C3 Parametric tests ANOVA

Table C3 ANOVA

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

F 0036 018 053 003 14p-value 085 067 047 086 024F critical 384 384 384 384 384Null hypothesis not rejected not rejected not rejected not rejected not rejected

C4 Non-parametric tests Kruskal-Wallis test

Table C4 Kruskal -Wallis test

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Adjusted H 082 012 126 0 455df 1 1 1 1 1P value 037 073 026 095 003Critical value 384 384 384 384 384Null hypothesis not rejected not rejected not rejected not rejected rejected

23

C5 Regression analysis with dummy variables

Table C5 Regression analysis with dummy variables

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

a0 00004 (000) 00004 (000) 00004 (000) 00004 (000) 00004 (000)a1 -00001 (-019) 00002 (067) -00004 (047) 00001 (086) -00007 (024)Anomaly not confirmed not confirmed not confirmed not confirmed not confirmed

C6 Modified CAR approach

Table C6 Modified CAR approach

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Multiple R 049 05 025 0 092F-test 23347 (000) 12913 (000) 2207 (000) 000 (098) 1822 (000)a0 -00041 (060) 00128 (006) -00267 (000) 00354 (000) 00319 (000)a1 -00003 (000) -00003 (000) -00002 (000) 00000 (098) -00008 (000)Anomaly confirmed confirmed confirmed not confirmed confirmed

24

D Detailed statistical results SampP 500 overall data

D1 Average analysis

Table D1 Average analysis

Parameter Gap day Gap day(Positive gaps)

Gap day(Negative gaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Mean return (gap day) 006 115 -129 017 -011Mean return (non-gap day) 002 002 002 002 002Anomaly confirmed confirmed confirmed confirmed confirmed

D2 Parametric tests Students t-test

Table D2 T-test

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

t-criterion 092 4546 3579 485 271t-critical (=095) 196 196 196 196 196Null hypothesis not rejected rejected rejected rejected rejected

D3 Parametric tests ANOVA

Table D3 ANOVA

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

F 155 116211 126952 1866 136p-value 022 0 0 0 0F critical 384 384 384 384 384Null hypothesis not rejected rejected rejected not rejected not rejected

D4 Non-parametric tests Kruskal-Wallis test

Table D4 Kruskal-Wallis test

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Adjusted H 1352 70516 47237 3946 004df 1 1 1 1 1P value 0 0 0 0 084Critical value 384 384 384 384 384Null hypothesis rejected rejected rejected rejected not rejected

25

D5 Regression analysis with dummy variables

Table D5 Regression analysis with dummy variables

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

a0 00002 (000) 00002 (000) 00002 (000) 00002 (000) 00002 (000)a1 00003 (021) 00113 (000) -00132 (000) 00014 (000) -00014 (000)Anomaly not confirmed confirmed confirmed confirmed confirmed

D6 Modified CAR approach

Table D6 Modified CAR approach

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Multiple R 051 099 099 099 096F-test 69486 (000) 325351 (000) 1457582 (000) 6345973 (000) 1213344 (000)a0 -01003(000) 04081 (000) -05444 (000) -01088 (000) 00272 (000)a1 00002 (000) 00106 (000) -00127 (000) 00016 (000) -00016 (000)Anomaly confirmed confirmed confirmed confirmed confirmed

26

E Detailed statistical results NASDAQ overall data

E1 Average analysis

Table E1 Average analysis

Parameter Gap day Gap day(Positive gaps)

Gap day(Negative gaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Mean return (gap day) -009 084 -090 022 -037Mean return (non-gap day) 003 003 003 003 003Anomaly confirmed confirmed confirmed confirmed confirmed

E2 Parametric tests Students t-test

Table E2 T-test

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

t-criterion 230 1257 1341 306 664t-critical (=095) 196 196 196 196 196Null hypothesis rejected rejected rejected rejected rejected

E3 Parametric tests ANOVA

Table E3 ANOVA

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

F 2289 62720 88402 3330 17356p-value 0 0 0 0 0F critical 384 384 384 384 384Null hypothesis rejected rejected rejected rejected rejected

E4 Non-parametric tests Kruskal-Wallis test

Table E4 Kruskal-Wallis test

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Adjusted H 1892 36022 45248 4695 10437df 1 1 1 1 1P value 0 0 0 0 0Critical value 384 384 384 384 384Null hypothesis rejected rejected rejected rejected rejected

27

E5 Regression analysis with dummy variables

Table E5 Regression analysis with dummy variables

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

a0 00003 (000) 00003 (000) 00003 (000) 00003 (000) 00003 (000)a1 -00012 (000) 00081 (000) -00093 (000) 00018 (000) -00040 (000)Anomaly confirmed confirmed confirmed confirmed confirmed

E6 Modified CAR approach

Table E6 Modified CAR approach

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Multiple R 069 092 092 072 097F-test 133255 (000) 361102 (000) 442376 (000) 72903 (000) 1082812 (000)a0 -10646 (000) 11373 (000) -12888 (000) 03928 (000) -02297 (000)a1 -00011 (000) 00073 (000) -00097 (000) 00017 (000) -00039 (000)Anomaly confirmed confirmed confirmed confirmed confirmed

28

F Detailed statistical results DJI sub-periods

F1 Average analysis

Table F1 Average analysis

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 Mean return (gapday)

-001 023 015 -004

Mean return(non-gap day)

007 007 007 007

Anomaly confirmed confirmed confirmed confirmed1999-2008 Mean return (gap

day)090 -045 013 -004

Mean return(non-gap day)

-004 -004 -004 -004

Anomaly confirmed confirmed confirmed confirmed2009-2018 Mean return (gap

day)024 -024 0 -004

Mean return(non-gap day)

004 004 004 004

Anomaly confirmed confirmed not confirmed confirmed

F2 Parametric tests Students t-test

Table F2 T-test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 t-criterion 083 165 087 139t-critical (=095) 196 196 196 196Null hypothesis not rejected not rejected not rejected not rejected

1999-2008 t-criterion 347 351 054 047t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected rejected

2009-2018 t-criterion 265 207 051 058t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

F3 Parametric tests ANOVA

Table F3 ANOVA

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 F 085 409 093 179p-value 035 004 033 018

F critical 384 384 384 384Null hypothesis not rejected rejected not rejected not rejected

1999-2008 F 5405 3196 065 072p-value 0 0 042 039

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

2009-2018 F 554 697 024 058p-value 001 0 062 044

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

29

F4 Non-parametric tests Kruskal-Wallis test

Table F4 Kruskal-Wallis test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 Adjusted H 113 211 113 332df 1 1 1 1

P value 029 015 029 007Null hypothesis not rejected not rejected not rejected not rejected

1999-2008 Adjusted H 1484 1414 003 139df 1 1 1 1

P value 0 0 086 024Null hypothesis rejected rejected not rejected not rejected

2009-2018 Adjusted H 506 68 051 171df 1 1 1 1

P value 002 001 047 019Null hypothesis rejected rejected not rejected not rejected

F5 Regression analysis with dummy variables

Table F5 Regression analysis with dummy variables

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 a0 000068 (000) 00007 (000) 00007 (000) 00007 (000)a1 -000078 (035) 00016 (004) 00008 (033) -00011 (018)

Anomaly not confirmed confirmed not confirmed not confirmed1999-2008 a0 00004 (008) 00004 (008) 00004 (006) 00004 (008)

a1 00087 (000) -00049 (000) 00009 (042) -00008 (039)Anomaly confirmed confirmed not confirmed not confirmed

2009-2018 a0 00004 (006) 00004 (006) 00004 (006) 00004 (006)a1 00021 (001) -00028 (001) -00004 (062) -00008 (047)

Anomaly confirmed confirmed not confirmed not confirmed

F6 Modified CAR approach

Table F6 Modified CAR approach

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 Multiple R 083 088 082 086F-test 22779 (000) 40583 (000) 20401 (000) 3269454 (000)a0 00042 (023) 00017 (073) 00014 (058) -00266 (000)a1 -00009 (000) 00015 (000) 00006 (000) -00009 (000)

Anomaly confirmed confirmed confirmed confirmed1999-2008 Multiple R 095 093 076 019

F-test 62658 (000) 84712 (000) 10056 (000) 492 (003)a0 -00972 (000) 00365 (000) -00198 (000) -00115 (021)a1 00086 (000) -00042 (000) 00014 (000) 00002 (003)

Anomaly confirmed confirmed confirmed not confirmed2009-2018 Multiple R 096 082 08 05

F-test 150452 (000) 16731 (000) 22287 (000) 2620 (000)a0 00548 (000) -00618 (000) 00031 (020) -00112 (000)a1 00013 (000) -00014 (000) -00005 (000) -00004 (000)

Anomaly confirmed confirmed not confirmed confirmed

30

G Detailed statistical results NASDAQ sub-periods

G1 Average analysis

Table G1 Average analysis

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 Mean return (gapday)

094 -111 0189 -029

Mean return(non-gap day)

007 007 007 007

Anomaly confirmed confirmed confirmed confirmed1959-1968 Mean return (gap

day)133 -147 033 -039

Mean return(non-gap day)

006 006 006 006

Anomaly confirmed confirmed confirmed confirmed1969-1978 Mean return (gap

day)19 -186 057 -068

Mean return(non-gap day)

005 005 005 005

Anomaly confirmed confirmed confirmed confirmed1979-1988 Mean return (gap

day)138 -162 066 -04

Mean return(non-gap day)

008 008 008 008

Anomaly confirmed confirmed confirmed confirmed1989-1998 Mean return (gap

day)016 012 018 -009

Mean return(non-gap day)

002 002 002 002

Anomaly confirmed not confirmed confirmed confirmed1999-2008 Mean return (gap

day)38E-3 027 -036 -013

Mean return(non-gap day)

-01 -01 -01 -01

Anomaly confirmed not confirmed not confirmed not confirmed2009-2018 Mean return (gap

day)039 009 013 -025

Mean return(non-gap day)

001 001 001 001

Anomaly confirmed not confirmed confirmed confirmed

G2 Parametric tests Students t-test

Table G2 T-test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 t-criterion 3194 3076 201 559t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected rejected

1959-1968 t-criterion 1399 2246 443 382t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected rejected

1969-1978 t-criterion 261 4358 417 786t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected rejected

1979-1988 t-criterion 1847 1445 709 395t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected rejected

1989-1998 t-criterion 13 066 126 093t-critical (=095) 196 196 196 196Null hypothesis not rejected not rejected not rejected not rejected

1999-2008 t-criterion 192 106 111 009t-critical (=095) 196 196 196 196Null hypothesis not rejected not rejected not rejected not rejected

2009-2018 t-criterion 27 05 089 188t-critical (=095) 196 196 196 196Null hypothesis rejected not rejected not rejected not rejected

31

G3 Parametric tests ANOVA

Table G3 ANOVA

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 F 88153 190609 1272 14521p-value 0 0 0 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1959-1968 F 93974 149771 4715 10418p-value 0 0 0 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1969-1978 F 84546 145429 6295 18241p-value 0 0 0 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1979-1988 F 66952 110482 13138 8626p-value 0 0 0 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1989-1998 F 323 138 43 168p-value 007 024 003 019

F critical 384 384 384 384Null hypothesis not rejected not rejected rejected not rejected

1999-2008 F 106 512 327 003p-value 001 002 007 085

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

2009-2018 F 169 069 175 93p-value 0 04 018 0

F critical 384 384 384 384Null hypothesis rejected not rejected not rejected rejected

G4 Non-parametric tests Kruskal-Wallis test

Table G4 Kruskal-Wallis test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 Adjusted H 26254 32592 1464 3962df 1 1 1 1

P value 0 0 0 0Null hypothesis rejected rejected rejected rejected

1959-1968 Adjusted H 28235 27989 2736 332df 1 1 1 1

P value 0 0 0 0Null hypothesis rejected rejected rejected rejected

1969-1978 Adjusted H 22202 33777 3311 7591df 1 1 1 1

P value 0 0 0 0Null hypothesis rejected rejected rejected rejected

1979-1988 Adjusted H 23282 25292 4812 3964df 1 1 1 1

P value 0 0 0 0Null hypothesis rejected rejected rejected rejected

1989-1998 Adjusted H 381 017 175 132df 1 1 1 1

P value 005 068 019 025Null hypothesis not rejected not rejected not rejected not rejected

1999-2008 Adjusted H 855 023 044 004df 1 1 1 1

P value 0 063 051 084Null hypothesis rejected not rejected not rejected not rejected

2009-2018 Adjusted H 1063 009 257 709df 1 1 1 1

P value 0 077 011 001Null hypothesis rejected not rejected not rejected rejected

32

G5 Regression analysis with dummy variables

Table G5 Regression analysis with dummy variables

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 a0 00007 (000) 00007 (000) 00007 (000) 00007 (000)a1 00088 (000) -00119 (000) 00011 (000) -00036 (000)

Anomaly confirmed confirmed confirmed confirmed1959-1968 a0 00006 (000) 00006 (000) 00006 (000) 00006 (000)

a1 00128 (000) -00153 (000) 00027 (000) -00046 (000)Anomaly confirmed confirmed confirmed confirmed

1969-1978 a0 00005 (000) 00005 (000) 00005 (000) 00005 (000)a1 00185 (000) -00192 (000) 00053 (000) -00073 (000)

Anomaly confirmed confirmed confirmed confirmed1979-1988 a0 00008 (000) 00008 (000) 00008 (000) 00008 (000)

a1 00131 (000) -00172 (000) 00059 (000) -00048 (000)Anomaly confirmed confirmed confirmed confirmed

1989-1998 a0 00002 (027) 00002 (028) 00002 (028) 00002 (027)a1 00014 (007) 00010 (024) 00017 (004) -00011 (019)

Anomaly not confirmed not confirmed confirmed not confirmed1999-2008 a0 00001 (059) 00001 (062) 00001 (059) 00001 (060)

a1 00037 (000) 00026 (002) -00038 (000) -00014 (019)Anomaly confirmed not confirmed not confirmed not confirmed

2009-2018 a0 00001 (049) 00001 (049) 00001 (049) 00001 (049)a1 00038 (000) 00007 (040) 00012 (018) -00027 (000)

Anomaly confirmed not confirmed not confirmed confirmed

G6 Modified CAR approach

Table G6 Modified CAR approach

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 Multiple R 099 099 093 098F-test 5753605 (000) 100470(000) 6280421 283281a0 -00091 (000) -00349 (000) 00056 (001) 00015 (073)a1 00083 (000) -00110 (000) 00010 (000) -00031 (000)

Anomaly confirmed confirmed confirmed confirmed1959-1968 Multiple R 099 099 099 099

F-test 3923274 (000) 3005562 (000) 443198 (000) 372583 (000)a0 00096 (000) 00073 (016) -00082 (000) -00095 (004)a1 00116 (001) -00149 (000) 00025 (000) -00047 (000)

Anomaly confirmed confirmed confirmed confirmed1969-1978 Multiple R 099 099 098 099

F-test 4302608 (000) 2723953 (000) 179969 (000) 639745a0 00246 (000) -00002 (000) 00217 (000) -00514 (000)a1 00176 (000) -00182 (000) 00049 (000) -00062 (000)

Anomaly confirmed confirmed confirmed confirmed1979-1988 Multiple R 099 099 099 099

F-test 5872335 (000) 1182609 (000) 1083558 (000) 910089 (000)a0 00136 (000) -01081 (000) -00285 (000) -00101 (000)a1 00131 (000) -00167 (000) 00062 (000) -00048 (000)

Anomaly confirmed confirmed confirmed confirmed1989-1998 Multiple R 09 056 069 016

F-test 46947 (000) 4885 (000) 10131 (000) 263 (011)a0 00102 (002) -00261 (000) -0016 (001) -00237 (000)a1 00015 (000) 00010 (000) 0001 (000) 00002 (011)

Anomaly confirmed confirmed confirmed not confirmed1999-2008 Multiple R 093 087 073 037

F-test 71863 (000) 32530 (000) 13273 (000) 1669 (000)a0 00185 (004) 00311 (000) -00130 (039) -00546 (000)a1 00037 (000) 00032 (000) -00026 (000) -00007 (000)

Anomaly confirmed not confirmed not confirmed confirmed2009-2018 Multiple R 089 001 096 091

F-test 40818 (000) 000 (094) 116744 (000) 53770 (000)a0 01436 (000) -01099 (000) -01036 (000) 00697 (000)a1 00030 (000) 00000 (094) 00024 (000) -00021 (000)

Anomaly confirmed not confirmed confirmed confirmed

33

H Detailed statistical results SampP 500 sub-periods

H1 Average analysis

Table H1 Average analysis

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 Mean return (gapday)

138 -171 004 -014

Mean return(non-gap day)

0 0 0 0

Anomaly confirmed confirmed confirmed confirmed1939-1948 Mean return (gap

day)001 -042 172 -195

Mean return(non-gap day)

003 003 003 003

Anomaly confirmed confirmed confirmed confirmed1949-1958 Mean return (gap

day)165 -18 02 002

Mean return(non-gap day)

006 006 006 006

Anomaly confirmed confirmed confirmed not confirmed1959-1968 Mean return (gap

day)104 -102 015 0

Mean return(non-gap day)

002 002 002 002

Anomaly confirmed confirmed confirmed not confirmed1969-1978 Mean return (gap

day)131 -13 019 -03

Mean return(non-gap day)

0 0 0 0

Anomaly confirmed confirmed confirmed confirmed1979-1988 Mean return (gap

day)058 -042 015 003

Mean return(non-gap day)

005 005 005 005

Anomaly confirmed confirmed confirmed not confirmed1989-1998 Mean return (gap

day)02 -023 -002 01

Mean return(non-gap day)

007 007 007 007

Anomaly confirmed confirmed not confirmed not confirmed1999-2008 Mean return (gap

day)083 -089 -023 -005

Mean return(non-gap day)

001 001 001 001

Anomaly confirmed confirmed not confirmed confirmed2009-2018 Mean return (gap

day)055 -052 001 -015

Mean return(non-gap day)

004 004 004 004

Anomaly confirmed confirmed not confirmed confirmed

34

H2 Parametric tests Students t-test

Table H2 T-test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 t-criterion 101 85 029 048t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

1939-1948 t-criterion 064 479 3074 225t-critical (=095) 196 196 196 196Null hypothesis not rejected rejected rejected rejected

1949-1958 t-criterion 2964 2383 193 041t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

1959-1968 t-criterion 2281 2157 21 023t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected not rejected

1969-1978 t-criterion 1318 2034 187 321t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected rejected

1979-1988 t-criterion 435 535 07 037t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

1989-1998 t-criterion 201 396 132 052t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

1999-2008 t-criterion 362 433 117 022t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

2009-2018 t-criterion 375 382 027 132t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

H3 Parametric tests ANOVA

Table H3 ANOVA

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 F 6281 8032 005 051p-value 0 0 082 047

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

1939-1948 F 056 2603 34854 51034p-value 045 0 0 0

F critical 384 384 384 384Null hypothesis not rejected rejected rejected rejected

1949-1958 F 100174 128997 897 062p-value 0 0 0 043

F critical 384 384 384 384Null hypothesis rejected rejected rejected not rejected

1959-1968 F 36831 32858 617 01p-value 0 0 001 074

F critical 384 384 384 384Null hypothesis rejected rejected rejected not rejected

1969-1978 F 26601 3063 53 152p-value 0 0 002 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1979-1988 F 23 245 076 009p-value 0 0 039 077

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

1989-1998 F 399 1156 118 015p-value 004 0 027 069

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

1999-2008 F 4253 5622 365 024p-value 0 0 006 062

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

2009-2018 F 3064 3656 01 43p-value 0 0 075 004

F critical 384 384 384 384Null hypothesis rejected rejected not rejected rejected

35

H4 Non-parametric tests Kruskal -Wallis test

Table H4 Kruskal-Wallis test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 Adjusted H 9982 5913 332 14df 1 1 1 1

P value 0 0 007 024Null hypothesis rejected rejected not rejected not rejected

1939-1948 Adjusted H 494 1999 23387 24927df 1 1 1 1

P value 003 0 0 0Null hypothesis rejected rejected rejected rejected

1949-1958 Adjusted H 28728 28175 348 15df 1 1 1 1

P value 0 0 006 022Null hypothesis rejected rejected not rejected not rejected

1959-1968 Adjusted H 25729 21437 701 063df 1 1 1 1

P value 0 0 001 043Null hypothesis rejected rejected rejected not rejected

1969-1978 Adjusted H 14407 20078 27 1706df 1 1 1 1

P value 0 0 01 0Null hypothesis rejected rejected not rejected rejected

1979-1988 Adjusted H 1788 2836 027 034df 1 1 1 1

P value 0 0 06 056Null hypothesis rejected rejected not rejected not rejected

1989-1998 Adjusted H 251 1431 111 044df 1 1 1 1

P value 011 0 029 051Null hypothesis not rejected rejected not rejected not rejected

1999-2008 Adjusted H 1812 1788 042 002df 1 1 1 1

P value 0 0 052 089Null hypothesis rejected rejected not rejected not rejected

2009-2018 Adjusted H 1314 1783 074 37df 1 1 1 1

P value 0 0 039 005Null hypothesis rejected rejected not rejected not rejected

36

H5 Regression analysis with dummy variables

Table H5 Regression analysis with dummy variables

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 a0 00000 (097) 00000 (004) 00000 (097) 00000 (097)a1 00138 (000) -00172 (000) 00004 (082) -00014 (047)

Anomaly confirmed confirmed not confirmed not confirmed1939-1948 a0 00003 (015) 00003 (015) 00003 (015) 00003 (015)

a1 00007 (045) -00045 (000) 00170 (000) -00199 (000)Anomaly not confirmed confirmed confirmed confirmed

1949-1958 a0 00006 (000) 00006 (000) 00006 (000) 00006 (000)a1 00160 (000) -00188 (000) 00016 (000) -00004 (043)

Anomaly confirmed confirmed confirmed not confirmed1959-1968 a0 00002 (007) 00002 (004) 00002 (008) 00002 (008)

a1 00103 (000) -00105 (000) 00014 (001) -00002 (074)Anomaly confirmed confirmed confirmed not confirmed

1969-1978 a0 00000 (078) 00000 (078) 00000 (078) 00000 (078)a1 00132 (000) -00132 (000) 00019 (002) -00030 (000)

Anomaly confirmed confirmed confirmed confirmed1979-1988 a0 00006 (001) 00006 (001) 00006 (001) 00006 (000)

a1 00053 (000) -00048 (000) 00009 (040) -00003 (075)Anomaly confirmed confirmed not confirmed not confirmed

1989-1998 a0 00007 (000) 00007 (000) 00007 (000) 00007 (000)a1 00016 (005) -00030 (000) -00009 (026) 00003 (072)

Anomaly confirmed confirmed not confirmed not confirmed1999-2008 a0 00001 (075) 00001 (075) 00001 (075) 00001 (076)

a1 00083 (000) -00091 (000) -00024 (005) -00006 (062)Anomaly confirmed confirmed not confirmed not confirmed

2009-2018 a0 00004 (003) 00004 (000) 00004 (003) 00004 (003)a1 00051 (000) -00059 (000) -00003 (075) -00019 (003)

Anomaly confirmed confirmed not confirmed confirmed

37

H6 Modified CAR approach

Table H6 Modified CAR approach

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 Multiple R 096 095 046 046F-test 175935 (000) 96500 (000) 3534 (000) 2880 (000)a0 -01070 (000) 01958 (000) 00405 (000) 00535 (000)a1 00121 (000) -00160 (000) 00006 (000) -00014 (000)

Anomaly confirmed confirmed confirmed confirmed1939-1948 Multiple R 08 099 099 099

F-test 18777 (000) 755727 (000) 3572830 (000) 2696099 (000)a0 00019 (073) -00346 (000) -00373 (000) 00912 (000)a1 00012 (000) -00044 (000) 00168 (000) -00197 (000)

Anomaly confirmed confirmed confirmed confirmed1949-1958 Multiple R 099 099 094 015

F-test 1021705 (000) 7171257 (000) 75858 (000) 242 (012)a0 -00176 (000) -00191 (000) 00095 (000) -00498 (000)a1 00154 (000) -00181 (000) 00013 (000) -00002 (012)

Anomaly confirmed confirmed confirmed not confirmed1959-1968 Multiple R 099 099 094 078

F-test 1463311 (000) 6002659 (000) 82273 (000) 14352 (000)a0 -00112 (000) 00004 (085) 00151 (000) 00389 (000)a1 00098 (000) -00102 (000) 00011 (000) -00009 (000)

Anomaly confirmed confirmed confirmed confirmed1969-1978 Multiple R 098 099 093 099

F-test 241655 (000) 1451901 (000) 57333 (000) 368160 (000)a0 -00433 (000) 00276 (000) 00099 (002) -00144 (000)a1 00132 (000) -00134 (000) 00020 (000) -00030 (000)

Anomaly confirmed confirmed confirmed confirmed1979-1988 Multiple R 092 078 023 008

F-test 53757 (000) 18707 (000) 487 (003) 085 (036)a0 00813 (000) -02508 (000) 00204 (000) -00235 (000)a1 00036 (000) -00031 (000) -00003 (003) -00001 (036)

Anomaly confirmed confirmed not confirmed not confirmed1989-1998 Multiple R 079 099 074 044

F-test 19705(000) 761967 (000) 14133 (000) 2369 (000)a0 00268 (000) 00023 (021) -00381 (000) 00087 (000)a1 00013 (000) -00028 (000) -00008 (000) 00002 (000)

Anomaly confirmed confirmed not confirmed not confirmed1999-2008 Multiple R 091 093 071 065

F-test 47218 (000) 76564 (000) 9843 (000) 7768 (000)a0 -01493 (000) 01351 (000) 00397 (000) 00007 (093)a1 00081 (000) -00083 (000) -00026 (000) -00011 (000)

Anomaly confirmed confirmed not confirmed confirmed2009-2018 Multiple R 086 087 083 074

F-test 29971 (000) 32484 (000) 23228 (000) 12764 (000)a0 01711 (000) -02250 (000) 00407 (000) -00472 (000)a1 00038 (000) -00044 (000) -00010 (000) -00012 (000)

Anomaly confirmed confirmed not confirmed confirmed

38

Appendices

A DJI and NASDAQ Summary Results

A1 Overall Results

Table A1 Gap size used for different sub-periods over the period 1929-2018

Period DJI NASDAQ1929-1938 - -1939-1948 - -1949-1958 - 0711959-1968 - 0951969-1978 - 1351979-1988 - 1101989-1998 040 0681999-2008 007 1502009-2018 020 110Overall data set 030 110

Table A2 Day of the week and gaps

Day of the week DJI NASDAQMonday 024 02Tuesday 02 02Wednesday 017 02Thursday 019 019Friday 021 02

A2 Statistical tests

Table A3 Results of the statistical tests for the overall data sets

PeriodMethod Averageanalysis

t-test ANOVAtest

Mann-Whitney

test

Regressionanalysiswith

dummyvariables

ModifiedCAR

approach

Overall

Dow Jones Index overall data setGap day - - - - - + 1Gap day (Positive gaps) + - - - - - 1Gap day (Negative gaps) + - - - - + 2Day after gap (Positive gaps) + - - - - - 1Day after gap (Negative gaps) + - - + - + 3

NASDAQ overall data setGap day + + + + + + 6Gap day (Positive gaps) + + + + + + 6Gap day (Negative gaps) + + + + + + 6Day after gap (Positive gaps) + + + + + + 6Day after gap (Negative gaps) + + + + + + 6

Note + indicates that the anomaly is confirmed and - indicates that anomaly is not confirmedThe higher the overall rating the stronger the evidence of the anomaly

19

Table A4 Results of the statistical tests for H1minus1 DJI

Period Averageanalysis

t-test ANOVA test Mann-Whitney

test

Regressionanalysis with

dummyvariables

ModifiedCAR

approach

Overall

Day of anomaly1989-1998 + - - - - + 21999-2008 + + + + + + 62009-2018 + + + + + + 6

Day after anomaly1989-1998 + - - - - + 21999-2008 + - - - - + 22009-2018 - - - - - - 0

Note + indicates that the anomaly is confirmed and - indicates that anomaly is not confirmedThe higher the overall rating the stronger the evidence of the anomaly

Table A5 Results of the statistical tests for H1minus2 DJI

Period Averageanalysis

t-test ANOVA test Mann-Whitneytest

Regressionanalysis with

dummyvariables

Modified CARapproach

Overall

Day of anomaly1989-1998 - - - - - - 01999-2008 + + + + + + 62009-2018 + + + + + + 6

Day after anomaly1989-1998 + - - - - + 21999-2008 + - - - - - 12009-2018 + - - - - + 2

Note + indicates that the anomaly is confirmed and - indicates that anomaly is not confirmedThe higher the overall rating the stronger the evidence of the anomaly

Table A6 Results of the statistical tests for H1minus1 NASDAQ

PeriodMethod Averageanalysis

t-test ANOVA test Mann-Whitney

test

Regressionanalysis with

dummyvariables

ModifiedCAR

approach

Overall

Day of anomaly1949-1958 + + + + + + 61959-1968 + + + + + + 61969-1978 + + + + + + 61979-1988 + + + + + + 61989-1998 + - - - - + 21999-2008 + - + + + + 52009-2018 + + + + + + 6

Day after anomaly1949-1958 + + + + + + 61959-1968 + + + + + + 61969-1978 + + + + + + 61979-1988 + + + + + + 61989-1998 + - + - + + 41999-2008 - - - - - - 02009-2018 + - - - - + 2

Note + indicates that the anomaly is confirmed and - indicates that anomaly is not confirmedThe higher the overall rating the stronger the evidence of the anomaly

20

Table A7 Results of the statistical tests for H1minus2 NASDAQ

PeriodMethod Averageanalysis

t-test ANOVA test Mann-Whitney

test

Regressionanalysis with

dummyvariables

ModifiedCAR

approach

Overall

Day of anomaly1949-1958 + + + + + + 61959-1968 + + + + + + 61969-1978 + + + + + + 61979-1988 + + + + + + 61989-1998 - - - - - + 11999-2008 - - + - - - 12009-2018 - - - - - - 0

Day after anomaly1949-1958 + + + + + + 61959-1968 + + + + + + 61969-1978 + + + + + + 61979-1988 + + + + + + 61989-1998 + - - - - - 11999-2008 - - - - - + 12009-2018 + - - + + + 4

Note + indicates that the anomaly is confirmed and - indicates that anomaly is not confirmedThe higher the overall rating the stronger the evidence of the anomaly

A3 Trading Simulation Results

Table A8 Trading simulation results of the price gap anomaly for the DJI 1989-2018

Period Gap type Number oftradesunits

Number ofsuccessfultradesunits

Number ofsuccessfultrades

Profit Profit per year

z-test Result

1989-1998 Up 102 46 451 -11 -01 011 failedDown 116 49 422 -267 -27 242 passed

1999-2008 Up 73 51 699 665 66 37 passedDown 143 81 566 641 64 331 passed

2009-2018 Up 127 88 693 308 31 327 passedDown 81 47 58 196 2 184 passed

21

B Short-term price behavior in DJI SampP 500 and

NASDAQ Price gaps (overall data sets)

Table B1 Momentum effect in the US stock market after the gap

Instrument Parameter Number of days after the gap1 2 3

Dow Jones Index Positive gaps 53 57 61Negative gaps 50 50 47

All gaps 51 54 54SampP 500 Index Positive gaps 40 63 60

Negative gaps 4 52 45All gaps 4 58 53

NASDAQ Positive gaps 32 65 67Negative gaps 24 63 59

All gaps 28 64 63

Table B2 Momentum effect in the US stock market before the gap

Instrument Parameter Number of days before the gap1 2 3

Dow Jones Index Positive gaps 56 49 52Negative gaps 54 49 49

All gaps 55 49 50SampP 500 Index Positive gaps 57 57 52

Negative gaps 60 59 54All gaps 58 58 53

NASDAQ Positive gaps 61 56 54Negative gaps 68 69 70

All gaps 64 63 63

Table B3 Fill gap effect in the US stock market

Instrument Parameter Number of days after the gap1 2 3 4 5

Dow Jones Index Positive gaps 22 28 26 30 28Negative gaps 25 33 36 42 46

All gaps 24 30 31 35 37SampP 500 Index Positive gaps 0 6 11 16 19

Negative gaps 1 10 19 26 27All gaps 1 8 15 20 23

NASDAQ Positive gaps 8 13 18 21 19Negative gaps 7 11 17 21 25

All gaps 8 12 18 21 22

22

C Detailed statistical results DJI overall data

C1 Average analysis

Table C1 Average analysis

Parameter Gap day Gap day(Positive gaps)

Gap day(Negative gaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Mean return (gap day) 003 006 0 005 -003Mean return (non-gap day) 004 004 004 004 004Anomaly not confirmed not confirmed confirmed not confirmed confirmed

C2 Parametric tests Students t-test

Table C2 T-test

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

t-criterion 016 042 053 015 104t-critical (=095) 196 196 196 196 196Null hypothesis not rejected not rejected not rejected not rejected not rejected

C3 Parametric tests ANOVA

Table C3 ANOVA

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

F 0036 018 053 003 14p-value 085 067 047 086 024F critical 384 384 384 384 384Null hypothesis not rejected not rejected not rejected not rejected not rejected

C4 Non-parametric tests Kruskal-Wallis test

Table C4 Kruskal -Wallis test

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Adjusted H 082 012 126 0 455df 1 1 1 1 1P value 037 073 026 095 003Critical value 384 384 384 384 384Null hypothesis not rejected not rejected not rejected not rejected rejected

23

C5 Regression analysis with dummy variables

Table C5 Regression analysis with dummy variables

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

a0 00004 (000) 00004 (000) 00004 (000) 00004 (000) 00004 (000)a1 -00001 (-019) 00002 (067) -00004 (047) 00001 (086) -00007 (024)Anomaly not confirmed not confirmed not confirmed not confirmed not confirmed

C6 Modified CAR approach

Table C6 Modified CAR approach

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Multiple R 049 05 025 0 092F-test 23347 (000) 12913 (000) 2207 (000) 000 (098) 1822 (000)a0 -00041 (060) 00128 (006) -00267 (000) 00354 (000) 00319 (000)a1 -00003 (000) -00003 (000) -00002 (000) 00000 (098) -00008 (000)Anomaly confirmed confirmed confirmed not confirmed confirmed

24

D Detailed statistical results SampP 500 overall data

D1 Average analysis

Table D1 Average analysis

Parameter Gap day Gap day(Positive gaps)

Gap day(Negative gaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Mean return (gap day) 006 115 -129 017 -011Mean return (non-gap day) 002 002 002 002 002Anomaly confirmed confirmed confirmed confirmed confirmed

D2 Parametric tests Students t-test

Table D2 T-test

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

t-criterion 092 4546 3579 485 271t-critical (=095) 196 196 196 196 196Null hypothesis not rejected rejected rejected rejected rejected

D3 Parametric tests ANOVA

Table D3 ANOVA

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

F 155 116211 126952 1866 136p-value 022 0 0 0 0F critical 384 384 384 384 384Null hypothesis not rejected rejected rejected not rejected not rejected

D4 Non-parametric tests Kruskal-Wallis test

Table D4 Kruskal-Wallis test

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Adjusted H 1352 70516 47237 3946 004df 1 1 1 1 1P value 0 0 0 0 084Critical value 384 384 384 384 384Null hypothesis rejected rejected rejected rejected not rejected

25

D5 Regression analysis with dummy variables

Table D5 Regression analysis with dummy variables

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

a0 00002 (000) 00002 (000) 00002 (000) 00002 (000) 00002 (000)a1 00003 (021) 00113 (000) -00132 (000) 00014 (000) -00014 (000)Anomaly not confirmed confirmed confirmed confirmed confirmed

D6 Modified CAR approach

Table D6 Modified CAR approach

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Multiple R 051 099 099 099 096F-test 69486 (000) 325351 (000) 1457582 (000) 6345973 (000) 1213344 (000)a0 -01003(000) 04081 (000) -05444 (000) -01088 (000) 00272 (000)a1 00002 (000) 00106 (000) -00127 (000) 00016 (000) -00016 (000)Anomaly confirmed confirmed confirmed confirmed confirmed

26

E Detailed statistical results NASDAQ overall data

E1 Average analysis

Table E1 Average analysis

Parameter Gap day Gap day(Positive gaps)

Gap day(Negative gaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Mean return (gap day) -009 084 -090 022 -037Mean return (non-gap day) 003 003 003 003 003Anomaly confirmed confirmed confirmed confirmed confirmed

E2 Parametric tests Students t-test

Table E2 T-test

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

t-criterion 230 1257 1341 306 664t-critical (=095) 196 196 196 196 196Null hypothesis rejected rejected rejected rejected rejected

E3 Parametric tests ANOVA

Table E3 ANOVA

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

F 2289 62720 88402 3330 17356p-value 0 0 0 0 0F critical 384 384 384 384 384Null hypothesis rejected rejected rejected rejected rejected

E4 Non-parametric tests Kruskal-Wallis test

Table E4 Kruskal-Wallis test

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Adjusted H 1892 36022 45248 4695 10437df 1 1 1 1 1P value 0 0 0 0 0Critical value 384 384 384 384 384Null hypothesis rejected rejected rejected rejected rejected

27

E5 Regression analysis with dummy variables

Table E5 Regression analysis with dummy variables

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

a0 00003 (000) 00003 (000) 00003 (000) 00003 (000) 00003 (000)a1 -00012 (000) 00081 (000) -00093 (000) 00018 (000) -00040 (000)Anomaly confirmed confirmed confirmed confirmed confirmed

E6 Modified CAR approach

Table E6 Modified CAR approach

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Multiple R 069 092 092 072 097F-test 133255 (000) 361102 (000) 442376 (000) 72903 (000) 1082812 (000)a0 -10646 (000) 11373 (000) -12888 (000) 03928 (000) -02297 (000)a1 -00011 (000) 00073 (000) -00097 (000) 00017 (000) -00039 (000)Anomaly confirmed confirmed confirmed confirmed confirmed

28

F Detailed statistical results DJI sub-periods

F1 Average analysis

Table F1 Average analysis

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 Mean return (gapday)

-001 023 015 -004

Mean return(non-gap day)

007 007 007 007

Anomaly confirmed confirmed confirmed confirmed1999-2008 Mean return (gap

day)090 -045 013 -004

Mean return(non-gap day)

-004 -004 -004 -004

Anomaly confirmed confirmed confirmed confirmed2009-2018 Mean return (gap

day)024 -024 0 -004

Mean return(non-gap day)

004 004 004 004

Anomaly confirmed confirmed not confirmed confirmed

F2 Parametric tests Students t-test

Table F2 T-test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 t-criterion 083 165 087 139t-critical (=095) 196 196 196 196Null hypothesis not rejected not rejected not rejected not rejected

1999-2008 t-criterion 347 351 054 047t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected rejected

2009-2018 t-criterion 265 207 051 058t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

F3 Parametric tests ANOVA

Table F3 ANOVA

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 F 085 409 093 179p-value 035 004 033 018

F critical 384 384 384 384Null hypothesis not rejected rejected not rejected not rejected

1999-2008 F 5405 3196 065 072p-value 0 0 042 039

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

2009-2018 F 554 697 024 058p-value 001 0 062 044

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

29

F4 Non-parametric tests Kruskal-Wallis test

Table F4 Kruskal-Wallis test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 Adjusted H 113 211 113 332df 1 1 1 1

P value 029 015 029 007Null hypothesis not rejected not rejected not rejected not rejected

1999-2008 Adjusted H 1484 1414 003 139df 1 1 1 1

P value 0 0 086 024Null hypothesis rejected rejected not rejected not rejected

2009-2018 Adjusted H 506 68 051 171df 1 1 1 1

P value 002 001 047 019Null hypothesis rejected rejected not rejected not rejected

F5 Regression analysis with dummy variables

Table F5 Regression analysis with dummy variables

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 a0 000068 (000) 00007 (000) 00007 (000) 00007 (000)a1 -000078 (035) 00016 (004) 00008 (033) -00011 (018)

Anomaly not confirmed confirmed not confirmed not confirmed1999-2008 a0 00004 (008) 00004 (008) 00004 (006) 00004 (008)

a1 00087 (000) -00049 (000) 00009 (042) -00008 (039)Anomaly confirmed confirmed not confirmed not confirmed

2009-2018 a0 00004 (006) 00004 (006) 00004 (006) 00004 (006)a1 00021 (001) -00028 (001) -00004 (062) -00008 (047)

Anomaly confirmed confirmed not confirmed not confirmed

F6 Modified CAR approach

Table F6 Modified CAR approach

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 Multiple R 083 088 082 086F-test 22779 (000) 40583 (000) 20401 (000) 3269454 (000)a0 00042 (023) 00017 (073) 00014 (058) -00266 (000)a1 -00009 (000) 00015 (000) 00006 (000) -00009 (000)

Anomaly confirmed confirmed confirmed confirmed1999-2008 Multiple R 095 093 076 019

F-test 62658 (000) 84712 (000) 10056 (000) 492 (003)a0 -00972 (000) 00365 (000) -00198 (000) -00115 (021)a1 00086 (000) -00042 (000) 00014 (000) 00002 (003)

Anomaly confirmed confirmed confirmed not confirmed2009-2018 Multiple R 096 082 08 05

F-test 150452 (000) 16731 (000) 22287 (000) 2620 (000)a0 00548 (000) -00618 (000) 00031 (020) -00112 (000)a1 00013 (000) -00014 (000) -00005 (000) -00004 (000)

Anomaly confirmed confirmed not confirmed confirmed

30

G Detailed statistical results NASDAQ sub-periods

G1 Average analysis

Table G1 Average analysis

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 Mean return (gapday)

094 -111 0189 -029

Mean return(non-gap day)

007 007 007 007

Anomaly confirmed confirmed confirmed confirmed1959-1968 Mean return (gap

day)133 -147 033 -039

Mean return(non-gap day)

006 006 006 006

Anomaly confirmed confirmed confirmed confirmed1969-1978 Mean return (gap

day)19 -186 057 -068

Mean return(non-gap day)

005 005 005 005

Anomaly confirmed confirmed confirmed confirmed1979-1988 Mean return (gap

day)138 -162 066 -04

Mean return(non-gap day)

008 008 008 008

Anomaly confirmed confirmed confirmed confirmed1989-1998 Mean return (gap

day)016 012 018 -009

Mean return(non-gap day)

002 002 002 002

Anomaly confirmed not confirmed confirmed confirmed1999-2008 Mean return (gap

day)38E-3 027 -036 -013

Mean return(non-gap day)

-01 -01 -01 -01

Anomaly confirmed not confirmed not confirmed not confirmed2009-2018 Mean return (gap

day)039 009 013 -025

Mean return(non-gap day)

001 001 001 001

Anomaly confirmed not confirmed confirmed confirmed

G2 Parametric tests Students t-test

Table G2 T-test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 t-criterion 3194 3076 201 559t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected rejected

1959-1968 t-criterion 1399 2246 443 382t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected rejected

1969-1978 t-criterion 261 4358 417 786t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected rejected

1979-1988 t-criterion 1847 1445 709 395t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected rejected

1989-1998 t-criterion 13 066 126 093t-critical (=095) 196 196 196 196Null hypothesis not rejected not rejected not rejected not rejected

1999-2008 t-criterion 192 106 111 009t-critical (=095) 196 196 196 196Null hypothesis not rejected not rejected not rejected not rejected

2009-2018 t-criterion 27 05 089 188t-critical (=095) 196 196 196 196Null hypothesis rejected not rejected not rejected not rejected

31

G3 Parametric tests ANOVA

Table G3 ANOVA

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 F 88153 190609 1272 14521p-value 0 0 0 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1959-1968 F 93974 149771 4715 10418p-value 0 0 0 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1969-1978 F 84546 145429 6295 18241p-value 0 0 0 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1979-1988 F 66952 110482 13138 8626p-value 0 0 0 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1989-1998 F 323 138 43 168p-value 007 024 003 019

F critical 384 384 384 384Null hypothesis not rejected not rejected rejected not rejected

1999-2008 F 106 512 327 003p-value 001 002 007 085

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

2009-2018 F 169 069 175 93p-value 0 04 018 0

F critical 384 384 384 384Null hypothesis rejected not rejected not rejected rejected

G4 Non-parametric tests Kruskal-Wallis test

Table G4 Kruskal-Wallis test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 Adjusted H 26254 32592 1464 3962df 1 1 1 1

P value 0 0 0 0Null hypothesis rejected rejected rejected rejected

1959-1968 Adjusted H 28235 27989 2736 332df 1 1 1 1

P value 0 0 0 0Null hypothesis rejected rejected rejected rejected

1969-1978 Adjusted H 22202 33777 3311 7591df 1 1 1 1

P value 0 0 0 0Null hypothesis rejected rejected rejected rejected

1979-1988 Adjusted H 23282 25292 4812 3964df 1 1 1 1

P value 0 0 0 0Null hypothesis rejected rejected rejected rejected

1989-1998 Adjusted H 381 017 175 132df 1 1 1 1

P value 005 068 019 025Null hypothesis not rejected not rejected not rejected not rejected

1999-2008 Adjusted H 855 023 044 004df 1 1 1 1

P value 0 063 051 084Null hypothesis rejected not rejected not rejected not rejected

2009-2018 Adjusted H 1063 009 257 709df 1 1 1 1

P value 0 077 011 001Null hypothesis rejected not rejected not rejected rejected

32

G5 Regression analysis with dummy variables

Table G5 Regression analysis with dummy variables

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 a0 00007 (000) 00007 (000) 00007 (000) 00007 (000)a1 00088 (000) -00119 (000) 00011 (000) -00036 (000)

Anomaly confirmed confirmed confirmed confirmed1959-1968 a0 00006 (000) 00006 (000) 00006 (000) 00006 (000)

a1 00128 (000) -00153 (000) 00027 (000) -00046 (000)Anomaly confirmed confirmed confirmed confirmed

1969-1978 a0 00005 (000) 00005 (000) 00005 (000) 00005 (000)a1 00185 (000) -00192 (000) 00053 (000) -00073 (000)

Anomaly confirmed confirmed confirmed confirmed1979-1988 a0 00008 (000) 00008 (000) 00008 (000) 00008 (000)

a1 00131 (000) -00172 (000) 00059 (000) -00048 (000)Anomaly confirmed confirmed confirmed confirmed

1989-1998 a0 00002 (027) 00002 (028) 00002 (028) 00002 (027)a1 00014 (007) 00010 (024) 00017 (004) -00011 (019)

Anomaly not confirmed not confirmed confirmed not confirmed1999-2008 a0 00001 (059) 00001 (062) 00001 (059) 00001 (060)

a1 00037 (000) 00026 (002) -00038 (000) -00014 (019)Anomaly confirmed not confirmed not confirmed not confirmed

2009-2018 a0 00001 (049) 00001 (049) 00001 (049) 00001 (049)a1 00038 (000) 00007 (040) 00012 (018) -00027 (000)

Anomaly confirmed not confirmed not confirmed confirmed

G6 Modified CAR approach

Table G6 Modified CAR approach

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 Multiple R 099 099 093 098F-test 5753605 (000) 100470(000) 6280421 283281a0 -00091 (000) -00349 (000) 00056 (001) 00015 (073)a1 00083 (000) -00110 (000) 00010 (000) -00031 (000)

Anomaly confirmed confirmed confirmed confirmed1959-1968 Multiple R 099 099 099 099

F-test 3923274 (000) 3005562 (000) 443198 (000) 372583 (000)a0 00096 (000) 00073 (016) -00082 (000) -00095 (004)a1 00116 (001) -00149 (000) 00025 (000) -00047 (000)

Anomaly confirmed confirmed confirmed confirmed1969-1978 Multiple R 099 099 098 099

F-test 4302608 (000) 2723953 (000) 179969 (000) 639745a0 00246 (000) -00002 (000) 00217 (000) -00514 (000)a1 00176 (000) -00182 (000) 00049 (000) -00062 (000)

Anomaly confirmed confirmed confirmed confirmed1979-1988 Multiple R 099 099 099 099

F-test 5872335 (000) 1182609 (000) 1083558 (000) 910089 (000)a0 00136 (000) -01081 (000) -00285 (000) -00101 (000)a1 00131 (000) -00167 (000) 00062 (000) -00048 (000)

Anomaly confirmed confirmed confirmed confirmed1989-1998 Multiple R 09 056 069 016

F-test 46947 (000) 4885 (000) 10131 (000) 263 (011)a0 00102 (002) -00261 (000) -0016 (001) -00237 (000)a1 00015 (000) 00010 (000) 0001 (000) 00002 (011)

Anomaly confirmed confirmed confirmed not confirmed1999-2008 Multiple R 093 087 073 037

F-test 71863 (000) 32530 (000) 13273 (000) 1669 (000)a0 00185 (004) 00311 (000) -00130 (039) -00546 (000)a1 00037 (000) 00032 (000) -00026 (000) -00007 (000)

Anomaly confirmed not confirmed not confirmed confirmed2009-2018 Multiple R 089 001 096 091

F-test 40818 (000) 000 (094) 116744 (000) 53770 (000)a0 01436 (000) -01099 (000) -01036 (000) 00697 (000)a1 00030 (000) 00000 (094) 00024 (000) -00021 (000)

Anomaly confirmed not confirmed confirmed confirmed

33

H Detailed statistical results SampP 500 sub-periods

H1 Average analysis

Table H1 Average analysis

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 Mean return (gapday)

138 -171 004 -014

Mean return(non-gap day)

0 0 0 0

Anomaly confirmed confirmed confirmed confirmed1939-1948 Mean return (gap

day)001 -042 172 -195

Mean return(non-gap day)

003 003 003 003

Anomaly confirmed confirmed confirmed confirmed1949-1958 Mean return (gap

day)165 -18 02 002

Mean return(non-gap day)

006 006 006 006

Anomaly confirmed confirmed confirmed not confirmed1959-1968 Mean return (gap

day)104 -102 015 0

Mean return(non-gap day)

002 002 002 002

Anomaly confirmed confirmed confirmed not confirmed1969-1978 Mean return (gap

day)131 -13 019 -03

Mean return(non-gap day)

0 0 0 0

Anomaly confirmed confirmed confirmed confirmed1979-1988 Mean return (gap

day)058 -042 015 003

Mean return(non-gap day)

005 005 005 005

Anomaly confirmed confirmed confirmed not confirmed1989-1998 Mean return (gap

day)02 -023 -002 01

Mean return(non-gap day)

007 007 007 007

Anomaly confirmed confirmed not confirmed not confirmed1999-2008 Mean return (gap

day)083 -089 -023 -005

Mean return(non-gap day)

001 001 001 001

Anomaly confirmed confirmed not confirmed confirmed2009-2018 Mean return (gap

day)055 -052 001 -015

Mean return(non-gap day)

004 004 004 004

Anomaly confirmed confirmed not confirmed confirmed

34

H2 Parametric tests Students t-test

Table H2 T-test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 t-criterion 101 85 029 048t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

1939-1948 t-criterion 064 479 3074 225t-critical (=095) 196 196 196 196Null hypothesis not rejected rejected rejected rejected

1949-1958 t-criterion 2964 2383 193 041t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

1959-1968 t-criterion 2281 2157 21 023t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected not rejected

1969-1978 t-criterion 1318 2034 187 321t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected rejected

1979-1988 t-criterion 435 535 07 037t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

1989-1998 t-criterion 201 396 132 052t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

1999-2008 t-criterion 362 433 117 022t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

2009-2018 t-criterion 375 382 027 132t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

H3 Parametric tests ANOVA

Table H3 ANOVA

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 F 6281 8032 005 051p-value 0 0 082 047

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

1939-1948 F 056 2603 34854 51034p-value 045 0 0 0

F critical 384 384 384 384Null hypothesis not rejected rejected rejected rejected

1949-1958 F 100174 128997 897 062p-value 0 0 0 043

F critical 384 384 384 384Null hypothesis rejected rejected rejected not rejected

1959-1968 F 36831 32858 617 01p-value 0 0 001 074

F critical 384 384 384 384Null hypothesis rejected rejected rejected not rejected

1969-1978 F 26601 3063 53 152p-value 0 0 002 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1979-1988 F 23 245 076 009p-value 0 0 039 077

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

1989-1998 F 399 1156 118 015p-value 004 0 027 069

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

1999-2008 F 4253 5622 365 024p-value 0 0 006 062

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

2009-2018 F 3064 3656 01 43p-value 0 0 075 004

F critical 384 384 384 384Null hypothesis rejected rejected not rejected rejected

35

H4 Non-parametric tests Kruskal -Wallis test

Table H4 Kruskal-Wallis test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 Adjusted H 9982 5913 332 14df 1 1 1 1

P value 0 0 007 024Null hypothesis rejected rejected not rejected not rejected

1939-1948 Adjusted H 494 1999 23387 24927df 1 1 1 1

P value 003 0 0 0Null hypothesis rejected rejected rejected rejected

1949-1958 Adjusted H 28728 28175 348 15df 1 1 1 1

P value 0 0 006 022Null hypothesis rejected rejected not rejected not rejected

1959-1968 Adjusted H 25729 21437 701 063df 1 1 1 1

P value 0 0 001 043Null hypothesis rejected rejected rejected not rejected

1969-1978 Adjusted H 14407 20078 27 1706df 1 1 1 1

P value 0 0 01 0Null hypothesis rejected rejected not rejected rejected

1979-1988 Adjusted H 1788 2836 027 034df 1 1 1 1

P value 0 0 06 056Null hypothesis rejected rejected not rejected not rejected

1989-1998 Adjusted H 251 1431 111 044df 1 1 1 1

P value 011 0 029 051Null hypothesis not rejected rejected not rejected not rejected

1999-2008 Adjusted H 1812 1788 042 002df 1 1 1 1

P value 0 0 052 089Null hypothesis rejected rejected not rejected not rejected

2009-2018 Adjusted H 1314 1783 074 37df 1 1 1 1

P value 0 0 039 005Null hypothesis rejected rejected not rejected not rejected

36

H5 Regression analysis with dummy variables

Table H5 Regression analysis with dummy variables

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 a0 00000 (097) 00000 (004) 00000 (097) 00000 (097)a1 00138 (000) -00172 (000) 00004 (082) -00014 (047)

Anomaly confirmed confirmed not confirmed not confirmed1939-1948 a0 00003 (015) 00003 (015) 00003 (015) 00003 (015)

a1 00007 (045) -00045 (000) 00170 (000) -00199 (000)Anomaly not confirmed confirmed confirmed confirmed

1949-1958 a0 00006 (000) 00006 (000) 00006 (000) 00006 (000)a1 00160 (000) -00188 (000) 00016 (000) -00004 (043)

Anomaly confirmed confirmed confirmed not confirmed1959-1968 a0 00002 (007) 00002 (004) 00002 (008) 00002 (008)

a1 00103 (000) -00105 (000) 00014 (001) -00002 (074)Anomaly confirmed confirmed confirmed not confirmed

1969-1978 a0 00000 (078) 00000 (078) 00000 (078) 00000 (078)a1 00132 (000) -00132 (000) 00019 (002) -00030 (000)

Anomaly confirmed confirmed confirmed confirmed1979-1988 a0 00006 (001) 00006 (001) 00006 (001) 00006 (000)

a1 00053 (000) -00048 (000) 00009 (040) -00003 (075)Anomaly confirmed confirmed not confirmed not confirmed

1989-1998 a0 00007 (000) 00007 (000) 00007 (000) 00007 (000)a1 00016 (005) -00030 (000) -00009 (026) 00003 (072)

Anomaly confirmed confirmed not confirmed not confirmed1999-2008 a0 00001 (075) 00001 (075) 00001 (075) 00001 (076)

a1 00083 (000) -00091 (000) -00024 (005) -00006 (062)Anomaly confirmed confirmed not confirmed not confirmed

2009-2018 a0 00004 (003) 00004 (000) 00004 (003) 00004 (003)a1 00051 (000) -00059 (000) -00003 (075) -00019 (003)

Anomaly confirmed confirmed not confirmed confirmed

37

H6 Modified CAR approach

Table H6 Modified CAR approach

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 Multiple R 096 095 046 046F-test 175935 (000) 96500 (000) 3534 (000) 2880 (000)a0 -01070 (000) 01958 (000) 00405 (000) 00535 (000)a1 00121 (000) -00160 (000) 00006 (000) -00014 (000)

Anomaly confirmed confirmed confirmed confirmed1939-1948 Multiple R 08 099 099 099

F-test 18777 (000) 755727 (000) 3572830 (000) 2696099 (000)a0 00019 (073) -00346 (000) -00373 (000) 00912 (000)a1 00012 (000) -00044 (000) 00168 (000) -00197 (000)

Anomaly confirmed confirmed confirmed confirmed1949-1958 Multiple R 099 099 094 015

F-test 1021705 (000) 7171257 (000) 75858 (000) 242 (012)a0 -00176 (000) -00191 (000) 00095 (000) -00498 (000)a1 00154 (000) -00181 (000) 00013 (000) -00002 (012)

Anomaly confirmed confirmed confirmed not confirmed1959-1968 Multiple R 099 099 094 078

F-test 1463311 (000) 6002659 (000) 82273 (000) 14352 (000)a0 -00112 (000) 00004 (085) 00151 (000) 00389 (000)a1 00098 (000) -00102 (000) 00011 (000) -00009 (000)

Anomaly confirmed confirmed confirmed confirmed1969-1978 Multiple R 098 099 093 099

F-test 241655 (000) 1451901 (000) 57333 (000) 368160 (000)a0 -00433 (000) 00276 (000) 00099 (002) -00144 (000)a1 00132 (000) -00134 (000) 00020 (000) -00030 (000)

Anomaly confirmed confirmed confirmed confirmed1979-1988 Multiple R 092 078 023 008

F-test 53757 (000) 18707 (000) 487 (003) 085 (036)a0 00813 (000) -02508 (000) 00204 (000) -00235 (000)a1 00036 (000) -00031 (000) -00003 (003) -00001 (036)

Anomaly confirmed confirmed not confirmed not confirmed1989-1998 Multiple R 079 099 074 044

F-test 19705(000) 761967 (000) 14133 (000) 2369 (000)a0 00268 (000) 00023 (021) -00381 (000) 00087 (000)a1 00013 (000) -00028 (000) -00008 (000) 00002 (000)

Anomaly confirmed confirmed not confirmed not confirmed1999-2008 Multiple R 091 093 071 065

F-test 47218 (000) 76564 (000) 9843 (000) 7768 (000)a0 -01493 (000) 01351 (000) 00397 (000) 00007 (093)a1 00081 (000) -00083 (000) -00026 (000) -00011 (000)

Anomaly confirmed confirmed not confirmed confirmed2009-2018 Multiple R 086 087 083 074

F-test 29971 (000) 32484 (000) 23228 (000) 12764 (000)a0 01711 (000) -02250 (000) 00407 (000) -00472 (000)a1 00038 (000) -00044 (000) -00010 (000) -00012 (000)

Anomaly confirmed confirmed not confirmed confirmed

38

Table A4 Results of the statistical tests for H1minus1 DJI

Period Averageanalysis

t-test ANOVA test Mann-Whitney

test

Regressionanalysis with

dummyvariables

ModifiedCAR

approach

Overall

Day of anomaly1989-1998 + - - - - + 21999-2008 + + + + + + 62009-2018 + + + + + + 6

Day after anomaly1989-1998 + - - - - + 21999-2008 + - - - - + 22009-2018 - - - - - - 0

Note + indicates that the anomaly is confirmed and - indicates that anomaly is not confirmedThe higher the overall rating the stronger the evidence of the anomaly

Table A5 Results of the statistical tests for H1minus2 DJI

Period Averageanalysis

t-test ANOVA test Mann-Whitneytest

Regressionanalysis with

dummyvariables

Modified CARapproach

Overall

Day of anomaly1989-1998 - - - - - - 01999-2008 + + + + + + 62009-2018 + + + + + + 6

Day after anomaly1989-1998 + - - - - + 21999-2008 + - - - - - 12009-2018 + - - - - + 2

Note + indicates that the anomaly is confirmed and - indicates that anomaly is not confirmedThe higher the overall rating the stronger the evidence of the anomaly

Table A6 Results of the statistical tests for H1minus1 NASDAQ

PeriodMethod Averageanalysis

t-test ANOVA test Mann-Whitney

test

Regressionanalysis with

dummyvariables

ModifiedCAR

approach

Overall

Day of anomaly1949-1958 + + + + + + 61959-1968 + + + + + + 61969-1978 + + + + + + 61979-1988 + + + + + + 61989-1998 + - - - - + 21999-2008 + - + + + + 52009-2018 + + + + + + 6

Day after anomaly1949-1958 + + + + + + 61959-1968 + + + + + + 61969-1978 + + + + + + 61979-1988 + + + + + + 61989-1998 + - + - + + 41999-2008 - - - - - - 02009-2018 + - - - - + 2

Note + indicates that the anomaly is confirmed and - indicates that anomaly is not confirmedThe higher the overall rating the stronger the evidence of the anomaly

20

Table A7 Results of the statistical tests for H1minus2 NASDAQ

PeriodMethod Averageanalysis

t-test ANOVA test Mann-Whitney

test

Regressionanalysis with

dummyvariables

ModifiedCAR

approach

Overall

Day of anomaly1949-1958 + + + + + + 61959-1968 + + + + + + 61969-1978 + + + + + + 61979-1988 + + + + + + 61989-1998 - - - - - + 11999-2008 - - + - - - 12009-2018 - - - - - - 0

Day after anomaly1949-1958 + + + + + + 61959-1968 + + + + + + 61969-1978 + + + + + + 61979-1988 + + + + + + 61989-1998 + - - - - - 11999-2008 - - - - - + 12009-2018 + - - + + + 4

Note + indicates that the anomaly is confirmed and - indicates that anomaly is not confirmedThe higher the overall rating the stronger the evidence of the anomaly

A3 Trading Simulation Results

Table A8 Trading simulation results of the price gap anomaly for the DJI 1989-2018

Period Gap type Number oftradesunits

Number ofsuccessfultradesunits

Number ofsuccessfultrades

Profit Profit per year

z-test Result

1989-1998 Up 102 46 451 -11 -01 011 failedDown 116 49 422 -267 -27 242 passed

1999-2008 Up 73 51 699 665 66 37 passedDown 143 81 566 641 64 331 passed

2009-2018 Up 127 88 693 308 31 327 passedDown 81 47 58 196 2 184 passed

21

B Short-term price behavior in DJI SampP 500 and

NASDAQ Price gaps (overall data sets)

Table B1 Momentum effect in the US stock market after the gap

Instrument Parameter Number of days after the gap1 2 3

Dow Jones Index Positive gaps 53 57 61Negative gaps 50 50 47

All gaps 51 54 54SampP 500 Index Positive gaps 40 63 60

Negative gaps 4 52 45All gaps 4 58 53

NASDAQ Positive gaps 32 65 67Negative gaps 24 63 59

All gaps 28 64 63

Table B2 Momentum effect in the US stock market before the gap

Instrument Parameter Number of days before the gap1 2 3

Dow Jones Index Positive gaps 56 49 52Negative gaps 54 49 49

All gaps 55 49 50SampP 500 Index Positive gaps 57 57 52

Negative gaps 60 59 54All gaps 58 58 53

NASDAQ Positive gaps 61 56 54Negative gaps 68 69 70

All gaps 64 63 63

Table B3 Fill gap effect in the US stock market

Instrument Parameter Number of days after the gap1 2 3 4 5

Dow Jones Index Positive gaps 22 28 26 30 28Negative gaps 25 33 36 42 46

All gaps 24 30 31 35 37SampP 500 Index Positive gaps 0 6 11 16 19

Negative gaps 1 10 19 26 27All gaps 1 8 15 20 23

NASDAQ Positive gaps 8 13 18 21 19Negative gaps 7 11 17 21 25

All gaps 8 12 18 21 22

22

C Detailed statistical results DJI overall data

C1 Average analysis

Table C1 Average analysis

Parameter Gap day Gap day(Positive gaps)

Gap day(Negative gaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Mean return (gap day) 003 006 0 005 -003Mean return (non-gap day) 004 004 004 004 004Anomaly not confirmed not confirmed confirmed not confirmed confirmed

C2 Parametric tests Students t-test

Table C2 T-test

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

t-criterion 016 042 053 015 104t-critical (=095) 196 196 196 196 196Null hypothesis not rejected not rejected not rejected not rejected not rejected

C3 Parametric tests ANOVA

Table C3 ANOVA

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

F 0036 018 053 003 14p-value 085 067 047 086 024F critical 384 384 384 384 384Null hypothesis not rejected not rejected not rejected not rejected not rejected

C4 Non-parametric tests Kruskal-Wallis test

Table C4 Kruskal -Wallis test

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Adjusted H 082 012 126 0 455df 1 1 1 1 1P value 037 073 026 095 003Critical value 384 384 384 384 384Null hypothesis not rejected not rejected not rejected not rejected rejected

23

C5 Regression analysis with dummy variables

Table C5 Regression analysis with dummy variables

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

a0 00004 (000) 00004 (000) 00004 (000) 00004 (000) 00004 (000)a1 -00001 (-019) 00002 (067) -00004 (047) 00001 (086) -00007 (024)Anomaly not confirmed not confirmed not confirmed not confirmed not confirmed

C6 Modified CAR approach

Table C6 Modified CAR approach

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Multiple R 049 05 025 0 092F-test 23347 (000) 12913 (000) 2207 (000) 000 (098) 1822 (000)a0 -00041 (060) 00128 (006) -00267 (000) 00354 (000) 00319 (000)a1 -00003 (000) -00003 (000) -00002 (000) 00000 (098) -00008 (000)Anomaly confirmed confirmed confirmed not confirmed confirmed

24

D Detailed statistical results SampP 500 overall data

D1 Average analysis

Table D1 Average analysis

Parameter Gap day Gap day(Positive gaps)

Gap day(Negative gaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Mean return (gap day) 006 115 -129 017 -011Mean return (non-gap day) 002 002 002 002 002Anomaly confirmed confirmed confirmed confirmed confirmed

D2 Parametric tests Students t-test

Table D2 T-test

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

t-criterion 092 4546 3579 485 271t-critical (=095) 196 196 196 196 196Null hypothesis not rejected rejected rejected rejected rejected

D3 Parametric tests ANOVA

Table D3 ANOVA

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

F 155 116211 126952 1866 136p-value 022 0 0 0 0F critical 384 384 384 384 384Null hypothesis not rejected rejected rejected not rejected not rejected

D4 Non-parametric tests Kruskal-Wallis test

Table D4 Kruskal-Wallis test

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Adjusted H 1352 70516 47237 3946 004df 1 1 1 1 1P value 0 0 0 0 084Critical value 384 384 384 384 384Null hypothesis rejected rejected rejected rejected not rejected

25

D5 Regression analysis with dummy variables

Table D5 Regression analysis with dummy variables

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

a0 00002 (000) 00002 (000) 00002 (000) 00002 (000) 00002 (000)a1 00003 (021) 00113 (000) -00132 (000) 00014 (000) -00014 (000)Anomaly not confirmed confirmed confirmed confirmed confirmed

D6 Modified CAR approach

Table D6 Modified CAR approach

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Multiple R 051 099 099 099 096F-test 69486 (000) 325351 (000) 1457582 (000) 6345973 (000) 1213344 (000)a0 -01003(000) 04081 (000) -05444 (000) -01088 (000) 00272 (000)a1 00002 (000) 00106 (000) -00127 (000) 00016 (000) -00016 (000)Anomaly confirmed confirmed confirmed confirmed confirmed

26

E Detailed statistical results NASDAQ overall data

E1 Average analysis

Table E1 Average analysis

Parameter Gap day Gap day(Positive gaps)

Gap day(Negative gaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Mean return (gap day) -009 084 -090 022 -037Mean return (non-gap day) 003 003 003 003 003Anomaly confirmed confirmed confirmed confirmed confirmed

E2 Parametric tests Students t-test

Table E2 T-test

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

t-criterion 230 1257 1341 306 664t-critical (=095) 196 196 196 196 196Null hypothesis rejected rejected rejected rejected rejected

E3 Parametric tests ANOVA

Table E3 ANOVA

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

F 2289 62720 88402 3330 17356p-value 0 0 0 0 0F critical 384 384 384 384 384Null hypothesis rejected rejected rejected rejected rejected

E4 Non-parametric tests Kruskal-Wallis test

Table E4 Kruskal-Wallis test

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Adjusted H 1892 36022 45248 4695 10437df 1 1 1 1 1P value 0 0 0 0 0Critical value 384 384 384 384 384Null hypothesis rejected rejected rejected rejected rejected

27

E5 Regression analysis with dummy variables

Table E5 Regression analysis with dummy variables

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

a0 00003 (000) 00003 (000) 00003 (000) 00003 (000) 00003 (000)a1 -00012 (000) 00081 (000) -00093 (000) 00018 (000) -00040 (000)Anomaly confirmed confirmed confirmed confirmed confirmed

E6 Modified CAR approach

Table E6 Modified CAR approach

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Multiple R 069 092 092 072 097F-test 133255 (000) 361102 (000) 442376 (000) 72903 (000) 1082812 (000)a0 -10646 (000) 11373 (000) -12888 (000) 03928 (000) -02297 (000)a1 -00011 (000) 00073 (000) -00097 (000) 00017 (000) -00039 (000)Anomaly confirmed confirmed confirmed confirmed confirmed

28

F Detailed statistical results DJI sub-periods

F1 Average analysis

Table F1 Average analysis

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 Mean return (gapday)

-001 023 015 -004

Mean return(non-gap day)

007 007 007 007

Anomaly confirmed confirmed confirmed confirmed1999-2008 Mean return (gap

day)090 -045 013 -004

Mean return(non-gap day)

-004 -004 -004 -004

Anomaly confirmed confirmed confirmed confirmed2009-2018 Mean return (gap

day)024 -024 0 -004

Mean return(non-gap day)

004 004 004 004

Anomaly confirmed confirmed not confirmed confirmed

F2 Parametric tests Students t-test

Table F2 T-test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 t-criterion 083 165 087 139t-critical (=095) 196 196 196 196Null hypothesis not rejected not rejected not rejected not rejected

1999-2008 t-criterion 347 351 054 047t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected rejected

2009-2018 t-criterion 265 207 051 058t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

F3 Parametric tests ANOVA

Table F3 ANOVA

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 F 085 409 093 179p-value 035 004 033 018

F critical 384 384 384 384Null hypothesis not rejected rejected not rejected not rejected

1999-2008 F 5405 3196 065 072p-value 0 0 042 039

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

2009-2018 F 554 697 024 058p-value 001 0 062 044

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

29

F4 Non-parametric tests Kruskal-Wallis test

Table F4 Kruskal-Wallis test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 Adjusted H 113 211 113 332df 1 1 1 1

P value 029 015 029 007Null hypothesis not rejected not rejected not rejected not rejected

1999-2008 Adjusted H 1484 1414 003 139df 1 1 1 1

P value 0 0 086 024Null hypothesis rejected rejected not rejected not rejected

2009-2018 Adjusted H 506 68 051 171df 1 1 1 1

P value 002 001 047 019Null hypothesis rejected rejected not rejected not rejected

F5 Regression analysis with dummy variables

Table F5 Regression analysis with dummy variables

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 a0 000068 (000) 00007 (000) 00007 (000) 00007 (000)a1 -000078 (035) 00016 (004) 00008 (033) -00011 (018)

Anomaly not confirmed confirmed not confirmed not confirmed1999-2008 a0 00004 (008) 00004 (008) 00004 (006) 00004 (008)

a1 00087 (000) -00049 (000) 00009 (042) -00008 (039)Anomaly confirmed confirmed not confirmed not confirmed

2009-2018 a0 00004 (006) 00004 (006) 00004 (006) 00004 (006)a1 00021 (001) -00028 (001) -00004 (062) -00008 (047)

Anomaly confirmed confirmed not confirmed not confirmed

F6 Modified CAR approach

Table F6 Modified CAR approach

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 Multiple R 083 088 082 086F-test 22779 (000) 40583 (000) 20401 (000) 3269454 (000)a0 00042 (023) 00017 (073) 00014 (058) -00266 (000)a1 -00009 (000) 00015 (000) 00006 (000) -00009 (000)

Anomaly confirmed confirmed confirmed confirmed1999-2008 Multiple R 095 093 076 019

F-test 62658 (000) 84712 (000) 10056 (000) 492 (003)a0 -00972 (000) 00365 (000) -00198 (000) -00115 (021)a1 00086 (000) -00042 (000) 00014 (000) 00002 (003)

Anomaly confirmed confirmed confirmed not confirmed2009-2018 Multiple R 096 082 08 05

F-test 150452 (000) 16731 (000) 22287 (000) 2620 (000)a0 00548 (000) -00618 (000) 00031 (020) -00112 (000)a1 00013 (000) -00014 (000) -00005 (000) -00004 (000)

Anomaly confirmed confirmed not confirmed confirmed

30

G Detailed statistical results NASDAQ sub-periods

G1 Average analysis

Table G1 Average analysis

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 Mean return (gapday)

094 -111 0189 -029

Mean return(non-gap day)

007 007 007 007

Anomaly confirmed confirmed confirmed confirmed1959-1968 Mean return (gap

day)133 -147 033 -039

Mean return(non-gap day)

006 006 006 006

Anomaly confirmed confirmed confirmed confirmed1969-1978 Mean return (gap

day)19 -186 057 -068

Mean return(non-gap day)

005 005 005 005

Anomaly confirmed confirmed confirmed confirmed1979-1988 Mean return (gap

day)138 -162 066 -04

Mean return(non-gap day)

008 008 008 008

Anomaly confirmed confirmed confirmed confirmed1989-1998 Mean return (gap

day)016 012 018 -009

Mean return(non-gap day)

002 002 002 002

Anomaly confirmed not confirmed confirmed confirmed1999-2008 Mean return (gap

day)38E-3 027 -036 -013

Mean return(non-gap day)

-01 -01 -01 -01

Anomaly confirmed not confirmed not confirmed not confirmed2009-2018 Mean return (gap

day)039 009 013 -025

Mean return(non-gap day)

001 001 001 001

Anomaly confirmed not confirmed confirmed confirmed

G2 Parametric tests Students t-test

Table G2 T-test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 t-criterion 3194 3076 201 559t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected rejected

1959-1968 t-criterion 1399 2246 443 382t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected rejected

1969-1978 t-criterion 261 4358 417 786t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected rejected

1979-1988 t-criterion 1847 1445 709 395t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected rejected

1989-1998 t-criterion 13 066 126 093t-critical (=095) 196 196 196 196Null hypothesis not rejected not rejected not rejected not rejected

1999-2008 t-criterion 192 106 111 009t-critical (=095) 196 196 196 196Null hypothesis not rejected not rejected not rejected not rejected

2009-2018 t-criterion 27 05 089 188t-critical (=095) 196 196 196 196Null hypothesis rejected not rejected not rejected not rejected

31

G3 Parametric tests ANOVA

Table G3 ANOVA

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 F 88153 190609 1272 14521p-value 0 0 0 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1959-1968 F 93974 149771 4715 10418p-value 0 0 0 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1969-1978 F 84546 145429 6295 18241p-value 0 0 0 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1979-1988 F 66952 110482 13138 8626p-value 0 0 0 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1989-1998 F 323 138 43 168p-value 007 024 003 019

F critical 384 384 384 384Null hypothesis not rejected not rejected rejected not rejected

1999-2008 F 106 512 327 003p-value 001 002 007 085

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

2009-2018 F 169 069 175 93p-value 0 04 018 0

F critical 384 384 384 384Null hypothesis rejected not rejected not rejected rejected

G4 Non-parametric tests Kruskal-Wallis test

Table G4 Kruskal-Wallis test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 Adjusted H 26254 32592 1464 3962df 1 1 1 1

P value 0 0 0 0Null hypothesis rejected rejected rejected rejected

1959-1968 Adjusted H 28235 27989 2736 332df 1 1 1 1

P value 0 0 0 0Null hypothesis rejected rejected rejected rejected

1969-1978 Adjusted H 22202 33777 3311 7591df 1 1 1 1

P value 0 0 0 0Null hypothesis rejected rejected rejected rejected

1979-1988 Adjusted H 23282 25292 4812 3964df 1 1 1 1

P value 0 0 0 0Null hypothesis rejected rejected rejected rejected

1989-1998 Adjusted H 381 017 175 132df 1 1 1 1

P value 005 068 019 025Null hypothesis not rejected not rejected not rejected not rejected

1999-2008 Adjusted H 855 023 044 004df 1 1 1 1

P value 0 063 051 084Null hypothesis rejected not rejected not rejected not rejected

2009-2018 Adjusted H 1063 009 257 709df 1 1 1 1

P value 0 077 011 001Null hypothesis rejected not rejected not rejected rejected

32

G5 Regression analysis with dummy variables

Table G5 Regression analysis with dummy variables

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 a0 00007 (000) 00007 (000) 00007 (000) 00007 (000)a1 00088 (000) -00119 (000) 00011 (000) -00036 (000)

Anomaly confirmed confirmed confirmed confirmed1959-1968 a0 00006 (000) 00006 (000) 00006 (000) 00006 (000)

a1 00128 (000) -00153 (000) 00027 (000) -00046 (000)Anomaly confirmed confirmed confirmed confirmed

1969-1978 a0 00005 (000) 00005 (000) 00005 (000) 00005 (000)a1 00185 (000) -00192 (000) 00053 (000) -00073 (000)

Anomaly confirmed confirmed confirmed confirmed1979-1988 a0 00008 (000) 00008 (000) 00008 (000) 00008 (000)

a1 00131 (000) -00172 (000) 00059 (000) -00048 (000)Anomaly confirmed confirmed confirmed confirmed

1989-1998 a0 00002 (027) 00002 (028) 00002 (028) 00002 (027)a1 00014 (007) 00010 (024) 00017 (004) -00011 (019)

Anomaly not confirmed not confirmed confirmed not confirmed1999-2008 a0 00001 (059) 00001 (062) 00001 (059) 00001 (060)

a1 00037 (000) 00026 (002) -00038 (000) -00014 (019)Anomaly confirmed not confirmed not confirmed not confirmed

2009-2018 a0 00001 (049) 00001 (049) 00001 (049) 00001 (049)a1 00038 (000) 00007 (040) 00012 (018) -00027 (000)

Anomaly confirmed not confirmed not confirmed confirmed

G6 Modified CAR approach

Table G6 Modified CAR approach

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 Multiple R 099 099 093 098F-test 5753605 (000) 100470(000) 6280421 283281a0 -00091 (000) -00349 (000) 00056 (001) 00015 (073)a1 00083 (000) -00110 (000) 00010 (000) -00031 (000)

Anomaly confirmed confirmed confirmed confirmed1959-1968 Multiple R 099 099 099 099

F-test 3923274 (000) 3005562 (000) 443198 (000) 372583 (000)a0 00096 (000) 00073 (016) -00082 (000) -00095 (004)a1 00116 (001) -00149 (000) 00025 (000) -00047 (000)

Anomaly confirmed confirmed confirmed confirmed1969-1978 Multiple R 099 099 098 099

F-test 4302608 (000) 2723953 (000) 179969 (000) 639745a0 00246 (000) -00002 (000) 00217 (000) -00514 (000)a1 00176 (000) -00182 (000) 00049 (000) -00062 (000)

Anomaly confirmed confirmed confirmed confirmed1979-1988 Multiple R 099 099 099 099

F-test 5872335 (000) 1182609 (000) 1083558 (000) 910089 (000)a0 00136 (000) -01081 (000) -00285 (000) -00101 (000)a1 00131 (000) -00167 (000) 00062 (000) -00048 (000)

Anomaly confirmed confirmed confirmed confirmed1989-1998 Multiple R 09 056 069 016

F-test 46947 (000) 4885 (000) 10131 (000) 263 (011)a0 00102 (002) -00261 (000) -0016 (001) -00237 (000)a1 00015 (000) 00010 (000) 0001 (000) 00002 (011)

Anomaly confirmed confirmed confirmed not confirmed1999-2008 Multiple R 093 087 073 037

F-test 71863 (000) 32530 (000) 13273 (000) 1669 (000)a0 00185 (004) 00311 (000) -00130 (039) -00546 (000)a1 00037 (000) 00032 (000) -00026 (000) -00007 (000)

Anomaly confirmed not confirmed not confirmed confirmed2009-2018 Multiple R 089 001 096 091

F-test 40818 (000) 000 (094) 116744 (000) 53770 (000)a0 01436 (000) -01099 (000) -01036 (000) 00697 (000)a1 00030 (000) 00000 (094) 00024 (000) -00021 (000)

Anomaly confirmed not confirmed confirmed confirmed

33

H Detailed statistical results SampP 500 sub-periods

H1 Average analysis

Table H1 Average analysis

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 Mean return (gapday)

138 -171 004 -014

Mean return(non-gap day)

0 0 0 0

Anomaly confirmed confirmed confirmed confirmed1939-1948 Mean return (gap

day)001 -042 172 -195

Mean return(non-gap day)

003 003 003 003

Anomaly confirmed confirmed confirmed confirmed1949-1958 Mean return (gap

day)165 -18 02 002

Mean return(non-gap day)

006 006 006 006

Anomaly confirmed confirmed confirmed not confirmed1959-1968 Mean return (gap

day)104 -102 015 0

Mean return(non-gap day)

002 002 002 002

Anomaly confirmed confirmed confirmed not confirmed1969-1978 Mean return (gap

day)131 -13 019 -03

Mean return(non-gap day)

0 0 0 0

Anomaly confirmed confirmed confirmed confirmed1979-1988 Mean return (gap

day)058 -042 015 003

Mean return(non-gap day)

005 005 005 005

Anomaly confirmed confirmed confirmed not confirmed1989-1998 Mean return (gap

day)02 -023 -002 01

Mean return(non-gap day)

007 007 007 007

Anomaly confirmed confirmed not confirmed not confirmed1999-2008 Mean return (gap

day)083 -089 -023 -005

Mean return(non-gap day)

001 001 001 001

Anomaly confirmed confirmed not confirmed confirmed2009-2018 Mean return (gap

day)055 -052 001 -015

Mean return(non-gap day)

004 004 004 004

Anomaly confirmed confirmed not confirmed confirmed

34

H2 Parametric tests Students t-test

Table H2 T-test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 t-criterion 101 85 029 048t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

1939-1948 t-criterion 064 479 3074 225t-critical (=095) 196 196 196 196Null hypothesis not rejected rejected rejected rejected

1949-1958 t-criterion 2964 2383 193 041t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

1959-1968 t-criterion 2281 2157 21 023t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected not rejected

1969-1978 t-criterion 1318 2034 187 321t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected rejected

1979-1988 t-criterion 435 535 07 037t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

1989-1998 t-criterion 201 396 132 052t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

1999-2008 t-criterion 362 433 117 022t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

2009-2018 t-criterion 375 382 027 132t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

H3 Parametric tests ANOVA

Table H3 ANOVA

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 F 6281 8032 005 051p-value 0 0 082 047

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

1939-1948 F 056 2603 34854 51034p-value 045 0 0 0

F critical 384 384 384 384Null hypothesis not rejected rejected rejected rejected

1949-1958 F 100174 128997 897 062p-value 0 0 0 043

F critical 384 384 384 384Null hypothesis rejected rejected rejected not rejected

1959-1968 F 36831 32858 617 01p-value 0 0 001 074

F critical 384 384 384 384Null hypothesis rejected rejected rejected not rejected

1969-1978 F 26601 3063 53 152p-value 0 0 002 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1979-1988 F 23 245 076 009p-value 0 0 039 077

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

1989-1998 F 399 1156 118 015p-value 004 0 027 069

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

1999-2008 F 4253 5622 365 024p-value 0 0 006 062

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

2009-2018 F 3064 3656 01 43p-value 0 0 075 004

F critical 384 384 384 384Null hypothesis rejected rejected not rejected rejected

35

H4 Non-parametric tests Kruskal -Wallis test

Table H4 Kruskal-Wallis test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 Adjusted H 9982 5913 332 14df 1 1 1 1

P value 0 0 007 024Null hypothesis rejected rejected not rejected not rejected

1939-1948 Adjusted H 494 1999 23387 24927df 1 1 1 1

P value 003 0 0 0Null hypothesis rejected rejected rejected rejected

1949-1958 Adjusted H 28728 28175 348 15df 1 1 1 1

P value 0 0 006 022Null hypothesis rejected rejected not rejected not rejected

1959-1968 Adjusted H 25729 21437 701 063df 1 1 1 1

P value 0 0 001 043Null hypothesis rejected rejected rejected not rejected

1969-1978 Adjusted H 14407 20078 27 1706df 1 1 1 1

P value 0 0 01 0Null hypothesis rejected rejected not rejected rejected

1979-1988 Adjusted H 1788 2836 027 034df 1 1 1 1

P value 0 0 06 056Null hypothesis rejected rejected not rejected not rejected

1989-1998 Adjusted H 251 1431 111 044df 1 1 1 1

P value 011 0 029 051Null hypothesis not rejected rejected not rejected not rejected

1999-2008 Adjusted H 1812 1788 042 002df 1 1 1 1

P value 0 0 052 089Null hypothesis rejected rejected not rejected not rejected

2009-2018 Adjusted H 1314 1783 074 37df 1 1 1 1

P value 0 0 039 005Null hypothesis rejected rejected not rejected not rejected

36

H5 Regression analysis with dummy variables

Table H5 Regression analysis with dummy variables

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 a0 00000 (097) 00000 (004) 00000 (097) 00000 (097)a1 00138 (000) -00172 (000) 00004 (082) -00014 (047)

Anomaly confirmed confirmed not confirmed not confirmed1939-1948 a0 00003 (015) 00003 (015) 00003 (015) 00003 (015)

a1 00007 (045) -00045 (000) 00170 (000) -00199 (000)Anomaly not confirmed confirmed confirmed confirmed

1949-1958 a0 00006 (000) 00006 (000) 00006 (000) 00006 (000)a1 00160 (000) -00188 (000) 00016 (000) -00004 (043)

Anomaly confirmed confirmed confirmed not confirmed1959-1968 a0 00002 (007) 00002 (004) 00002 (008) 00002 (008)

a1 00103 (000) -00105 (000) 00014 (001) -00002 (074)Anomaly confirmed confirmed confirmed not confirmed

1969-1978 a0 00000 (078) 00000 (078) 00000 (078) 00000 (078)a1 00132 (000) -00132 (000) 00019 (002) -00030 (000)

Anomaly confirmed confirmed confirmed confirmed1979-1988 a0 00006 (001) 00006 (001) 00006 (001) 00006 (000)

a1 00053 (000) -00048 (000) 00009 (040) -00003 (075)Anomaly confirmed confirmed not confirmed not confirmed

1989-1998 a0 00007 (000) 00007 (000) 00007 (000) 00007 (000)a1 00016 (005) -00030 (000) -00009 (026) 00003 (072)

Anomaly confirmed confirmed not confirmed not confirmed1999-2008 a0 00001 (075) 00001 (075) 00001 (075) 00001 (076)

a1 00083 (000) -00091 (000) -00024 (005) -00006 (062)Anomaly confirmed confirmed not confirmed not confirmed

2009-2018 a0 00004 (003) 00004 (000) 00004 (003) 00004 (003)a1 00051 (000) -00059 (000) -00003 (075) -00019 (003)

Anomaly confirmed confirmed not confirmed confirmed

37

H6 Modified CAR approach

Table H6 Modified CAR approach

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 Multiple R 096 095 046 046F-test 175935 (000) 96500 (000) 3534 (000) 2880 (000)a0 -01070 (000) 01958 (000) 00405 (000) 00535 (000)a1 00121 (000) -00160 (000) 00006 (000) -00014 (000)

Anomaly confirmed confirmed confirmed confirmed1939-1948 Multiple R 08 099 099 099

F-test 18777 (000) 755727 (000) 3572830 (000) 2696099 (000)a0 00019 (073) -00346 (000) -00373 (000) 00912 (000)a1 00012 (000) -00044 (000) 00168 (000) -00197 (000)

Anomaly confirmed confirmed confirmed confirmed1949-1958 Multiple R 099 099 094 015

F-test 1021705 (000) 7171257 (000) 75858 (000) 242 (012)a0 -00176 (000) -00191 (000) 00095 (000) -00498 (000)a1 00154 (000) -00181 (000) 00013 (000) -00002 (012)

Anomaly confirmed confirmed confirmed not confirmed1959-1968 Multiple R 099 099 094 078

F-test 1463311 (000) 6002659 (000) 82273 (000) 14352 (000)a0 -00112 (000) 00004 (085) 00151 (000) 00389 (000)a1 00098 (000) -00102 (000) 00011 (000) -00009 (000)

Anomaly confirmed confirmed confirmed confirmed1969-1978 Multiple R 098 099 093 099

F-test 241655 (000) 1451901 (000) 57333 (000) 368160 (000)a0 -00433 (000) 00276 (000) 00099 (002) -00144 (000)a1 00132 (000) -00134 (000) 00020 (000) -00030 (000)

Anomaly confirmed confirmed confirmed confirmed1979-1988 Multiple R 092 078 023 008

F-test 53757 (000) 18707 (000) 487 (003) 085 (036)a0 00813 (000) -02508 (000) 00204 (000) -00235 (000)a1 00036 (000) -00031 (000) -00003 (003) -00001 (036)

Anomaly confirmed confirmed not confirmed not confirmed1989-1998 Multiple R 079 099 074 044

F-test 19705(000) 761967 (000) 14133 (000) 2369 (000)a0 00268 (000) 00023 (021) -00381 (000) 00087 (000)a1 00013 (000) -00028 (000) -00008 (000) 00002 (000)

Anomaly confirmed confirmed not confirmed not confirmed1999-2008 Multiple R 091 093 071 065

F-test 47218 (000) 76564 (000) 9843 (000) 7768 (000)a0 -01493 (000) 01351 (000) 00397 (000) 00007 (093)a1 00081 (000) -00083 (000) -00026 (000) -00011 (000)

Anomaly confirmed confirmed not confirmed confirmed2009-2018 Multiple R 086 087 083 074

F-test 29971 (000) 32484 (000) 23228 (000) 12764 (000)a0 01711 (000) -02250 (000) 00407 (000) -00472 (000)a1 00038 (000) -00044 (000) -00010 (000) -00012 (000)

Anomaly confirmed confirmed not confirmed confirmed

38

Table A7 Results of the statistical tests for H1minus2 NASDAQ

PeriodMethod Averageanalysis

t-test ANOVA test Mann-Whitney

test

Regressionanalysis with

dummyvariables

ModifiedCAR

approach

Overall

Day of anomaly1949-1958 + + + + + + 61959-1968 + + + + + + 61969-1978 + + + + + + 61979-1988 + + + + + + 61989-1998 - - - - - + 11999-2008 - - + - - - 12009-2018 - - - - - - 0

Day after anomaly1949-1958 + + + + + + 61959-1968 + + + + + + 61969-1978 + + + + + + 61979-1988 + + + + + + 61989-1998 + - - - - - 11999-2008 - - - - - + 12009-2018 + - - + + + 4

Note + indicates that the anomaly is confirmed and - indicates that anomaly is not confirmedThe higher the overall rating the stronger the evidence of the anomaly

A3 Trading Simulation Results

Table A8 Trading simulation results of the price gap anomaly for the DJI 1989-2018

Period Gap type Number oftradesunits

Number ofsuccessfultradesunits

Number ofsuccessfultrades

Profit Profit per year

z-test Result

1989-1998 Up 102 46 451 -11 -01 011 failedDown 116 49 422 -267 -27 242 passed

1999-2008 Up 73 51 699 665 66 37 passedDown 143 81 566 641 64 331 passed

2009-2018 Up 127 88 693 308 31 327 passedDown 81 47 58 196 2 184 passed

21

B Short-term price behavior in DJI SampP 500 and

NASDAQ Price gaps (overall data sets)

Table B1 Momentum effect in the US stock market after the gap

Instrument Parameter Number of days after the gap1 2 3

Dow Jones Index Positive gaps 53 57 61Negative gaps 50 50 47

All gaps 51 54 54SampP 500 Index Positive gaps 40 63 60

Negative gaps 4 52 45All gaps 4 58 53

NASDAQ Positive gaps 32 65 67Negative gaps 24 63 59

All gaps 28 64 63

Table B2 Momentum effect in the US stock market before the gap

Instrument Parameter Number of days before the gap1 2 3

Dow Jones Index Positive gaps 56 49 52Negative gaps 54 49 49

All gaps 55 49 50SampP 500 Index Positive gaps 57 57 52

Negative gaps 60 59 54All gaps 58 58 53

NASDAQ Positive gaps 61 56 54Negative gaps 68 69 70

All gaps 64 63 63

Table B3 Fill gap effect in the US stock market

Instrument Parameter Number of days after the gap1 2 3 4 5

Dow Jones Index Positive gaps 22 28 26 30 28Negative gaps 25 33 36 42 46

All gaps 24 30 31 35 37SampP 500 Index Positive gaps 0 6 11 16 19

Negative gaps 1 10 19 26 27All gaps 1 8 15 20 23

NASDAQ Positive gaps 8 13 18 21 19Negative gaps 7 11 17 21 25

All gaps 8 12 18 21 22

22

C Detailed statistical results DJI overall data

C1 Average analysis

Table C1 Average analysis

Parameter Gap day Gap day(Positive gaps)

Gap day(Negative gaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Mean return (gap day) 003 006 0 005 -003Mean return (non-gap day) 004 004 004 004 004Anomaly not confirmed not confirmed confirmed not confirmed confirmed

C2 Parametric tests Students t-test

Table C2 T-test

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

t-criterion 016 042 053 015 104t-critical (=095) 196 196 196 196 196Null hypothesis not rejected not rejected not rejected not rejected not rejected

C3 Parametric tests ANOVA

Table C3 ANOVA

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

F 0036 018 053 003 14p-value 085 067 047 086 024F critical 384 384 384 384 384Null hypothesis not rejected not rejected not rejected not rejected not rejected

C4 Non-parametric tests Kruskal-Wallis test

Table C4 Kruskal -Wallis test

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Adjusted H 082 012 126 0 455df 1 1 1 1 1P value 037 073 026 095 003Critical value 384 384 384 384 384Null hypothesis not rejected not rejected not rejected not rejected rejected

23

C5 Regression analysis with dummy variables

Table C5 Regression analysis with dummy variables

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

a0 00004 (000) 00004 (000) 00004 (000) 00004 (000) 00004 (000)a1 -00001 (-019) 00002 (067) -00004 (047) 00001 (086) -00007 (024)Anomaly not confirmed not confirmed not confirmed not confirmed not confirmed

C6 Modified CAR approach

Table C6 Modified CAR approach

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Multiple R 049 05 025 0 092F-test 23347 (000) 12913 (000) 2207 (000) 000 (098) 1822 (000)a0 -00041 (060) 00128 (006) -00267 (000) 00354 (000) 00319 (000)a1 -00003 (000) -00003 (000) -00002 (000) 00000 (098) -00008 (000)Anomaly confirmed confirmed confirmed not confirmed confirmed

24

D Detailed statistical results SampP 500 overall data

D1 Average analysis

Table D1 Average analysis

Parameter Gap day Gap day(Positive gaps)

Gap day(Negative gaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Mean return (gap day) 006 115 -129 017 -011Mean return (non-gap day) 002 002 002 002 002Anomaly confirmed confirmed confirmed confirmed confirmed

D2 Parametric tests Students t-test

Table D2 T-test

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

t-criterion 092 4546 3579 485 271t-critical (=095) 196 196 196 196 196Null hypothesis not rejected rejected rejected rejected rejected

D3 Parametric tests ANOVA

Table D3 ANOVA

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

F 155 116211 126952 1866 136p-value 022 0 0 0 0F critical 384 384 384 384 384Null hypothesis not rejected rejected rejected not rejected not rejected

D4 Non-parametric tests Kruskal-Wallis test

Table D4 Kruskal-Wallis test

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Adjusted H 1352 70516 47237 3946 004df 1 1 1 1 1P value 0 0 0 0 084Critical value 384 384 384 384 384Null hypothesis rejected rejected rejected rejected not rejected

25

D5 Regression analysis with dummy variables

Table D5 Regression analysis with dummy variables

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

a0 00002 (000) 00002 (000) 00002 (000) 00002 (000) 00002 (000)a1 00003 (021) 00113 (000) -00132 (000) 00014 (000) -00014 (000)Anomaly not confirmed confirmed confirmed confirmed confirmed

D6 Modified CAR approach

Table D6 Modified CAR approach

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Multiple R 051 099 099 099 096F-test 69486 (000) 325351 (000) 1457582 (000) 6345973 (000) 1213344 (000)a0 -01003(000) 04081 (000) -05444 (000) -01088 (000) 00272 (000)a1 00002 (000) 00106 (000) -00127 (000) 00016 (000) -00016 (000)Anomaly confirmed confirmed confirmed confirmed confirmed

26

E Detailed statistical results NASDAQ overall data

E1 Average analysis

Table E1 Average analysis

Parameter Gap day Gap day(Positive gaps)

Gap day(Negative gaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Mean return (gap day) -009 084 -090 022 -037Mean return (non-gap day) 003 003 003 003 003Anomaly confirmed confirmed confirmed confirmed confirmed

E2 Parametric tests Students t-test

Table E2 T-test

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

t-criterion 230 1257 1341 306 664t-critical (=095) 196 196 196 196 196Null hypothesis rejected rejected rejected rejected rejected

E3 Parametric tests ANOVA

Table E3 ANOVA

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

F 2289 62720 88402 3330 17356p-value 0 0 0 0 0F critical 384 384 384 384 384Null hypothesis rejected rejected rejected rejected rejected

E4 Non-parametric tests Kruskal-Wallis test

Table E4 Kruskal-Wallis test

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Adjusted H 1892 36022 45248 4695 10437df 1 1 1 1 1P value 0 0 0 0 0Critical value 384 384 384 384 384Null hypothesis rejected rejected rejected rejected rejected

27

E5 Regression analysis with dummy variables

Table E5 Regression analysis with dummy variables

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

a0 00003 (000) 00003 (000) 00003 (000) 00003 (000) 00003 (000)a1 -00012 (000) 00081 (000) -00093 (000) 00018 (000) -00040 (000)Anomaly confirmed confirmed confirmed confirmed confirmed

E6 Modified CAR approach

Table E6 Modified CAR approach

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Multiple R 069 092 092 072 097F-test 133255 (000) 361102 (000) 442376 (000) 72903 (000) 1082812 (000)a0 -10646 (000) 11373 (000) -12888 (000) 03928 (000) -02297 (000)a1 -00011 (000) 00073 (000) -00097 (000) 00017 (000) -00039 (000)Anomaly confirmed confirmed confirmed confirmed confirmed

28

F Detailed statistical results DJI sub-periods

F1 Average analysis

Table F1 Average analysis

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 Mean return (gapday)

-001 023 015 -004

Mean return(non-gap day)

007 007 007 007

Anomaly confirmed confirmed confirmed confirmed1999-2008 Mean return (gap

day)090 -045 013 -004

Mean return(non-gap day)

-004 -004 -004 -004

Anomaly confirmed confirmed confirmed confirmed2009-2018 Mean return (gap

day)024 -024 0 -004

Mean return(non-gap day)

004 004 004 004

Anomaly confirmed confirmed not confirmed confirmed

F2 Parametric tests Students t-test

Table F2 T-test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 t-criterion 083 165 087 139t-critical (=095) 196 196 196 196Null hypothesis not rejected not rejected not rejected not rejected

1999-2008 t-criterion 347 351 054 047t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected rejected

2009-2018 t-criterion 265 207 051 058t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

F3 Parametric tests ANOVA

Table F3 ANOVA

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 F 085 409 093 179p-value 035 004 033 018

F critical 384 384 384 384Null hypothesis not rejected rejected not rejected not rejected

1999-2008 F 5405 3196 065 072p-value 0 0 042 039

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

2009-2018 F 554 697 024 058p-value 001 0 062 044

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

29

F4 Non-parametric tests Kruskal-Wallis test

Table F4 Kruskal-Wallis test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 Adjusted H 113 211 113 332df 1 1 1 1

P value 029 015 029 007Null hypothesis not rejected not rejected not rejected not rejected

1999-2008 Adjusted H 1484 1414 003 139df 1 1 1 1

P value 0 0 086 024Null hypothesis rejected rejected not rejected not rejected

2009-2018 Adjusted H 506 68 051 171df 1 1 1 1

P value 002 001 047 019Null hypothesis rejected rejected not rejected not rejected

F5 Regression analysis with dummy variables

Table F5 Regression analysis with dummy variables

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 a0 000068 (000) 00007 (000) 00007 (000) 00007 (000)a1 -000078 (035) 00016 (004) 00008 (033) -00011 (018)

Anomaly not confirmed confirmed not confirmed not confirmed1999-2008 a0 00004 (008) 00004 (008) 00004 (006) 00004 (008)

a1 00087 (000) -00049 (000) 00009 (042) -00008 (039)Anomaly confirmed confirmed not confirmed not confirmed

2009-2018 a0 00004 (006) 00004 (006) 00004 (006) 00004 (006)a1 00021 (001) -00028 (001) -00004 (062) -00008 (047)

Anomaly confirmed confirmed not confirmed not confirmed

F6 Modified CAR approach

Table F6 Modified CAR approach

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 Multiple R 083 088 082 086F-test 22779 (000) 40583 (000) 20401 (000) 3269454 (000)a0 00042 (023) 00017 (073) 00014 (058) -00266 (000)a1 -00009 (000) 00015 (000) 00006 (000) -00009 (000)

Anomaly confirmed confirmed confirmed confirmed1999-2008 Multiple R 095 093 076 019

F-test 62658 (000) 84712 (000) 10056 (000) 492 (003)a0 -00972 (000) 00365 (000) -00198 (000) -00115 (021)a1 00086 (000) -00042 (000) 00014 (000) 00002 (003)

Anomaly confirmed confirmed confirmed not confirmed2009-2018 Multiple R 096 082 08 05

F-test 150452 (000) 16731 (000) 22287 (000) 2620 (000)a0 00548 (000) -00618 (000) 00031 (020) -00112 (000)a1 00013 (000) -00014 (000) -00005 (000) -00004 (000)

Anomaly confirmed confirmed not confirmed confirmed

30

G Detailed statistical results NASDAQ sub-periods

G1 Average analysis

Table G1 Average analysis

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 Mean return (gapday)

094 -111 0189 -029

Mean return(non-gap day)

007 007 007 007

Anomaly confirmed confirmed confirmed confirmed1959-1968 Mean return (gap

day)133 -147 033 -039

Mean return(non-gap day)

006 006 006 006

Anomaly confirmed confirmed confirmed confirmed1969-1978 Mean return (gap

day)19 -186 057 -068

Mean return(non-gap day)

005 005 005 005

Anomaly confirmed confirmed confirmed confirmed1979-1988 Mean return (gap

day)138 -162 066 -04

Mean return(non-gap day)

008 008 008 008

Anomaly confirmed confirmed confirmed confirmed1989-1998 Mean return (gap

day)016 012 018 -009

Mean return(non-gap day)

002 002 002 002

Anomaly confirmed not confirmed confirmed confirmed1999-2008 Mean return (gap

day)38E-3 027 -036 -013

Mean return(non-gap day)

-01 -01 -01 -01

Anomaly confirmed not confirmed not confirmed not confirmed2009-2018 Mean return (gap

day)039 009 013 -025

Mean return(non-gap day)

001 001 001 001

Anomaly confirmed not confirmed confirmed confirmed

G2 Parametric tests Students t-test

Table G2 T-test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 t-criterion 3194 3076 201 559t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected rejected

1959-1968 t-criterion 1399 2246 443 382t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected rejected

1969-1978 t-criterion 261 4358 417 786t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected rejected

1979-1988 t-criterion 1847 1445 709 395t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected rejected

1989-1998 t-criterion 13 066 126 093t-critical (=095) 196 196 196 196Null hypothesis not rejected not rejected not rejected not rejected

1999-2008 t-criterion 192 106 111 009t-critical (=095) 196 196 196 196Null hypothesis not rejected not rejected not rejected not rejected

2009-2018 t-criterion 27 05 089 188t-critical (=095) 196 196 196 196Null hypothesis rejected not rejected not rejected not rejected

31

G3 Parametric tests ANOVA

Table G3 ANOVA

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 F 88153 190609 1272 14521p-value 0 0 0 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1959-1968 F 93974 149771 4715 10418p-value 0 0 0 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1969-1978 F 84546 145429 6295 18241p-value 0 0 0 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1979-1988 F 66952 110482 13138 8626p-value 0 0 0 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1989-1998 F 323 138 43 168p-value 007 024 003 019

F critical 384 384 384 384Null hypothesis not rejected not rejected rejected not rejected

1999-2008 F 106 512 327 003p-value 001 002 007 085

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

2009-2018 F 169 069 175 93p-value 0 04 018 0

F critical 384 384 384 384Null hypothesis rejected not rejected not rejected rejected

G4 Non-parametric tests Kruskal-Wallis test

Table G4 Kruskal-Wallis test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 Adjusted H 26254 32592 1464 3962df 1 1 1 1

P value 0 0 0 0Null hypothesis rejected rejected rejected rejected

1959-1968 Adjusted H 28235 27989 2736 332df 1 1 1 1

P value 0 0 0 0Null hypothesis rejected rejected rejected rejected

1969-1978 Adjusted H 22202 33777 3311 7591df 1 1 1 1

P value 0 0 0 0Null hypothesis rejected rejected rejected rejected

1979-1988 Adjusted H 23282 25292 4812 3964df 1 1 1 1

P value 0 0 0 0Null hypothesis rejected rejected rejected rejected

1989-1998 Adjusted H 381 017 175 132df 1 1 1 1

P value 005 068 019 025Null hypothesis not rejected not rejected not rejected not rejected

1999-2008 Adjusted H 855 023 044 004df 1 1 1 1

P value 0 063 051 084Null hypothesis rejected not rejected not rejected not rejected

2009-2018 Adjusted H 1063 009 257 709df 1 1 1 1

P value 0 077 011 001Null hypothesis rejected not rejected not rejected rejected

32

G5 Regression analysis with dummy variables

Table G5 Regression analysis with dummy variables

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 a0 00007 (000) 00007 (000) 00007 (000) 00007 (000)a1 00088 (000) -00119 (000) 00011 (000) -00036 (000)

Anomaly confirmed confirmed confirmed confirmed1959-1968 a0 00006 (000) 00006 (000) 00006 (000) 00006 (000)

a1 00128 (000) -00153 (000) 00027 (000) -00046 (000)Anomaly confirmed confirmed confirmed confirmed

1969-1978 a0 00005 (000) 00005 (000) 00005 (000) 00005 (000)a1 00185 (000) -00192 (000) 00053 (000) -00073 (000)

Anomaly confirmed confirmed confirmed confirmed1979-1988 a0 00008 (000) 00008 (000) 00008 (000) 00008 (000)

a1 00131 (000) -00172 (000) 00059 (000) -00048 (000)Anomaly confirmed confirmed confirmed confirmed

1989-1998 a0 00002 (027) 00002 (028) 00002 (028) 00002 (027)a1 00014 (007) 00010 (024) 00017 (004) -00011 (019)

Anomaly not confirmed not confirmed confirmed not confirmed1999-2008 a0 00001 (059) 00001 (062) 00001 (059) 00001 (060)

a1 00037 (000) 00026 (002) -00038 (000) -00014 (019)Anomaly confirmed not confirmed not confirmed not confirmed

2009-2018 a0 00001 (049) 00001 (049) 00001 (049) 00001 (049)a1 00038 (000) 00007 (040) 00012 (018) -00027 (000)

Anomaly confirmed not confirmed not confirmed confirmed

G6 Modified CAR approach

Table G6 Modified CAR approach

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 Multiple R 099 099 093 098F-test 5753605 (000) 100470(000) 6280421 283281a0 -00091 (000) -00349 (000) 00056 (001) 00015 (073)a1 00083 (000) -00110 (000) 00010 (000) -00031 (000)

Anomaly confirmed confirmed confirmed confirmed1959-1968 Multiple R 099 099 099 099

F-test 3923274 (000) 3005562 (000) 443198 (000) 372583 (000)a0 00096 (000) 00073 (016) -00082 (000) -00095 (004)a1 00116 (001) -00149 (000) 00025 (000) -00047 (000)

Anomaly confirmed confirmed confirmed confirmed1969-1978 Multiple R 099 099 098 099

F-test 4302608 (000) 2723953 (000) 179969 (000) 639745a0 00246 (000) -00002 (000) 00217 (000) -00514 (000)a1 00176 (000) -00182 (000) 00049 (000) -00062 (000)

Anomaly confirmed confirmed confirmed confirmed1979-1988 Multiple R 099 099 099 099

F-test 5872335 (000) 1182609 (000) 1083558 (000) 910089 (000)a0 00136 (000) -01081 (000) -00285 (000) -00101 (000)a1 00131 (000) -00167 (000) 00062 (000) -00048 (000)

Anomaly confirmed confirmed confirmed confirmed1989-1998 Multiple R 09 056 069 016

F-test 46947 (000) 4885 (000) 10131 (000) 263 (011)a0 00102 (002) -00261 (000) -0016 (001) -00237 (000)a1 00015 (000) 00010 (000) 0001 (000) 00002 (011)

Anomaly confirmed confirmed confirmed not confirmed1999-2008 Multiple R 093 087 073 037

F-test 71863 (000) 32530 (000) 13273 (000) 1669 (000)a0 00185 (004) 00311 (000) -00130 (039) -00546 (000)a1 00037 (000) 00032 (000) -00026 (000) -00007 (000)

Anomaly confirmed not confirmed not confirmed confirmed2009-2018 Multiple R 089 001 096 091

F-test 40818 (000) 000 (094) 116744 (000) 53770 (000)a0 01436 (000) -01099 (000) -01036 (000) 00697 (000)a1 00030 (000) 00000 (094) 00024 (000) -00021 (000)

Anomaly confirmed not confirmed confirmed confirmed

33

H Detailed statistical results SampP 500 sub-periods

H1 Average analysis

Table H1 Average analysis

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 Mean return (gapday)

138 -171 004 -014

Mean return(non-gap day)

0 0 0 0

Anomaly confirmed confirmed confirmed confirmed1939-1948 Mean return (gap

day)001 -042 172 -195

Mean return(non-gap day)

003 003 003 003

Anomaly confirmed confirmed confirmed confirmed1949-1958 Mean return (gap

day)165 -18 02 002

Mean return(non-gap day)

006 006 006 006

Anomaly confirmed confirmed confirmed not confirmed1959-1968 Mean return (gap

day)104 -102 015 0

Mean return(non-gap day)

002 002 002 002

Anomaly confirmed confirmed confirmed not confirmed1969-1978 Mean return (gap

day)131 -13 019 -03

Mean return(non-gap day)

0 0 0 0

Anomaly confirmed confirmed confirmed confirmed1979-1988 Mean return (gap

day)058 -042 015 003

Mean return(non-gap day)

005 005 005 005

Anomaly confirmed confirmed confirmed not confirmed1989-1998 Mean return (gap

day)02 -023 -002 01

Mean return(non-gap day)

007 007 007 007

Anomaly confirmed confirmed not confirmed not confirmed1999-2008 Mean return (gap

day)083 -089 -023 -005

Mean return(non-gap day)

001 001 001 001

Anomaly confirmed confirmed not confirmed confirmed2009-2018 Mean return (gap

day)055 -052 001 -015

Mean return(non-gap day)

004 004 004 004

Anomaly confirmed confirmed not confirmed confirmed

34

H2 Parametric tests Students t-test

Table H2 T-test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 t-criterion 101 85 029 048t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

1939-1948 t-criterion 064 479 3074 225t-critical (=095) 196 196 196 196Null hypothesis not rejected rejected rejected rejected

1949-1958 t-criterion 2964 2383 193 041t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

1959-1968 t-criterion 2281 2157 21 023t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected not rejected

1969-1978 t-criterion 1318 2034 187 321t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected rejected

1979-1988 t-criterion 435 535 07 037t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

1989-1998 t-criterion 201 396 132 052t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

1999-2008 t-criterion 362 433 117 022t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

2009-2018 t-criterion 375 382 027 132t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

H3 Parametric tests ANOVA

Table H3 ANOVA

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 F 6281 8032 005 051p-value 0 0 082 047

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

1939-1948 F 056 2603 34854 51034p-value 045 0 0 0

F critical 384 384 384 384Null hypothesis not rejected rejected rejected rejected

1949-1958 F 100174 128997 897 062p-value 0 0 0 043

F critical 384 384 384 384Null hypothesis rejected rejected rejected not rejected

1959-1968 F 36831 32858 617 01p-value 0 0 001 074

F critical 384 384 384 384Null hypothesis rejected rejected rejected not rejected

1969-1978 F 26601 3063 53 152p-value 0 0 002 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1979-1988 F 23 245 076 009p-value 0 0 039 077

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

1989-1998 F 399 1156 118 015p-value 004 0 027 069

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

1999-2008 F 4253 5622 365 024p-value 0 0 006 062

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

2009-2018 F 3064 3656 01 43p-value 0 0 075 004

F critical 384 384 384 384Null hypothesis rejected rejected not rejected rejected

35

H4 Non-parametric tests Kruskal -Wallis test

Table H4 Kruskal-Wallis test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 Adjusted H 9982 5913 332 14df 1 1 1 1

P value 0 0 007 024Null hypothesis rejected rejected not rejected not rejected

1939-1948 Adjusted H 494 1999 23387 24927df 1 1 1 1

P value 003 0 0 0Null hypothesis rejected rejected rejected rejected

1949-1958 Adjusted H 28728 28175 348 15df 1 1 1 1

P value 0 0 006 022Null hypothesis rejected rejected not rejected not rejected

1959-1968 Adjusted H 25729 21437 701 063df 1 1 1 1

P value 0 0 001 043Null hypothesis rejected rejected rejected not rejected

1969-1978 Adjusted H 14407 20078 27 1706df 1 1 1 1

P value 0 0 01 0Null hypothesis rejected rejected not rejected rejected

1979-1988 Adjusted H 1788 2836 027 034df 1 1 1 1

P value 0 0 06 056Null hypothesis rejected rejected not rejected not rejected

1989-1998 Adjusted H 251 1431 111 044df 1 1 1 1

P value 011 0 029 051Null hypothesis not rejected rejected not rejected not rejected

1999-2008 Adjusted H 1812 1788 042 002df 1 1 1 1

P value 0 0 052 089Null hypothesis rejected rejected not rejected not rejected

2009-2018 Adjusted H 1314 1783 074 37df 1 1 1 1

P value 0 0 039 005Null hypothesis rejected rejected not rejected not rejected

36

H5 Regression analysis with dummy variables

Table H5 Regression analysis with dummy variables

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 a0 00000 (097) 00000 (004) 00000 (097) 00000 (097)a1 00138 (000) -00172 (000) 00004 (082) -00014 (047)

Anomaly confirmed confirmed not confirmed not confirmed1939-1948 a0 00003 (015) 00003 (015) 00003 (015) 00003 (015)

a1 00007 (045) -00045 (000) 00170 (000) -00199 (000)Anomaly not confirmed confirmed confirmed confirmed

1949-1958 a0 00006 (000) 00006 (000) 00006 (000) 00006 (000)a1 00160 (000) -00188 (000) 00016 (000) -00004 (043)

Anomaly confirmed confirmed confirmed not confirmed1959-1968 a0 00002 (007) 00002 (004) 00002 (008) 00002 (008)

a1 00103 (000) -00105 (000) 00014 (001) -00002 (074)Anomaly confirmed confirmed confirmed not confirmed

1969-1978 a0 00000 (078) 00000 (078) 00000 (078) 00000 (078)a1 00132 (000) -00132 (000) 00019 (002) -00030 (000)

Anomaly confirmed confirmed confirmed confirmed1979-1988 a0 00006 (001) 00006 (001) 00006 (001) 00006 (000)

a1 00053 (000) -00048 (000) 00009 (040) -00003 (075)Anomaly confirmed confirmed not confirmed not confirmed

1989-1998 a0 00007 (000) 00007 (000) 00007 (000) 00007 (000)a1 00016 (005) -00030 (000) -00009 (026) 00003 (072)

Anomaly confirmed confirmed not confirmed not confirmed1999-2008 a0 00001 (075) 00001 (075) 00001 (075) 00001 (076)

a1 00083 (000) -00091 (000) -00024 (005) -00006 (062)Anomaly confirmed confirmed not confirmed not confirmed

2009-2018 a0 00004 (003) 00004 (000) 00004 (003) 00004 (003)a1 00051 (000) -00059 (000) -00003 (075) -00019 (003)

Anomaly confirmed confirmed not confirmed confirmed

37

H6 Modified CAR approach

Table H6 Modified CAR approach

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 Multiple R 096 095 046 046F-test 175935 (000) 96500 (000) 3534 (000) 2880 (000)a0 -01070 (000) 01958 (000) 00405 (000) 00535 (000)a1 00121 (000) -00160 (000) 00006 (000) -00014 (000)

Anomaly confirmed confirmed confirmed confirmed1939-1948 Multiple R 08 099 099 099

F-test 18777 (000) 755727 (000) 3572830 (000) 2696099 (000)a0 00019 (073) -00346 (000) -00373 (000) 00912 (000)a1 00012 (000) -00044 (000) 00168 (000) -00197 (000)

Anomaly confirmed confirmed confirmed confirmed1949-1958 Multiple R 099 099 094 015

F-test 1021705 (000) 7171257 (000) 75858 (000) 242 (012)a0 -00176 (000) -00191 (000) 00095 (000) -00498 (000)a1 00154 (000) -00181 (000) 00013 (000) -00002 (012)

Anomaly confirmed confirmed confirmed not confirmed1959-1968 Multiple R 099 099 094 078

F-test 1463311 (000) 6002659 (000) 82273 (000) 14352 (000)a0 -00112 (000) 00004 (085) 00151 (000) 00389 (000)a1 00098 (000) -00102 (000) 00011 (000) -00009 (000)

Anomaly confirmed confirmed confirmed confirmed1969-1978 Multiple R 098 099 093 099

F-test 241655 (000) 1451901 (000) 57333 (000) 368160 (000)a0 -00433 (000) 00276 (000) 00099 (002) -00144 (000)a1 00132 (000) -00134 (000) 00020 (000) -00030 (000)

Anomaly confirmed confirmed confirmed confirmed1979-1988 Multiple R 092 078 023 008

F-test 53757 (000) 18707 (000) 487 (003) 085 (036)a0 00813 (000) -02508 (000) 00204 (000) -00235 (000)a1 00036 (000) -00031 (000) -00003 (003) -00001 (036)

Anomaly confirmed confirmed not confirmed not confirmed1989-1998 Multiple R 079 099 074 044

F-test 19705(000) 761967 (000) 14133 (000) 2369 (000)a0 00268 (000) 00023 (021) -00381 (000) 00087 (000)a1 00013 (000) -00028 (000) -00008 (000) 00002 (000)

Anomaly confirmed confirmed not confirmed not confirmed1999-2008 Multiple R 091 093 071 065

F-test 47218 (000) 76564 (000) 9843 (000) 7768 (000)a0 -01493 (000) 01351 (000) 00397 (000) 00007 (093)a1 00081 (000) -00083 (000) -00026 (000) -00011 (000)

Anomaly confirmed confirmed not confirmed confirmed2009-2018 Multiple R 086 087 083 074

F-test 29971 (000) 32484 (000) 23228 (000) 12764 (000)a0 01711 (000) -02250 (000) 00407 (000) -00472 (000)a1 00038 (000) -00044 (000) -00010 (000) -00012 (000)

Anomaly confirmed confirmed not confirmed confirmed

38

B Short-term price behavior in DJI SampP 500 and

NASDAQ Price gaps (overall data sets)

Table B1 Momentum effect in the US stock market after the gap

Instrument Parameter Number of days after the gap1 2 3

Dow Jones Index Positive gaps 53 57 61Negative gaps 50 50 47

All gaps 51 54 54SampP 500 Index Positive gaps 40 63 60

Negative gaps 4 52 45All gaps 4 58 53

NASDAQ Positive gaps 32 65 67Negative gaps 24 63 59

All gaps 28 64 63

Table B2 Momentum effect in the US stock market before the gap

Instrument Parameter Number of days before the gap1 2 3

Dow Jones Index Positive gaps 56 49 52Negative gaps 54 49 49

All gaps 55 49 50SampP 500 Index Positive gaps 57 57 52

Negative gaps 60 59 54All gaps 58 58 53

NASDAQ Positive gaps 61 56 54Negative gaps 68 69 70

All gaps 64 63 63

Table B3 Fill gap effect in the US stock market

Instrument Parameter Number of days after the gap1 2 3 4 5

Dow Jones Index Positive gaps 22 28 26 30 28Negative gaps 25 33 36 42 46

All gaps 24 30 31 35 37SampP 500 Index Positive gaps 0 6 11 16 19

Negative gaps 1 10 19 26 27All gaps 1 8 15 20 23

NASDAQ Positive gaps 8 13 18 21 19Negative gaps 7 11 17 21 25

All gaps 8 12 18 21 22

22

C Detailed statistical results DJI overall data

C1 Average analysis

Table C1 Average analysis

Parameter Gap day Gap day(Positive gaps)

Gap day(Negative gaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Mean return (gap day) 003 006 0 005 -003Mean return (non-gap day) 004 004 004 004 004Anomaly not confirmed not confirmed confirmed not confirmed confirmed

C2 Parametric tests Students t-test

Table C2 T-test

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

t-criterion 016 042 053 015 104t-critical (=095) 196 196 196 196 196Null hypothesis not rejected not rejected not rejected not rejected not rejected

C3 Parametric tests ANOVA

Table C3 ANOVA

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

F 0036 018 053 003 14p-value 085 067 047 086 024F critical 384 384 384 384 384Null hypothesis not rejected not rejected not rejected not rejected not rejected

C4 Non-parametric tests Kruskal-Wallis test

Table C4 Kruskal -Wallis test

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Adjusted H 082 012 126 0 455df 1 1 1 1 1P value 037 073 026 095 003Critical value 384 384 384 384 384Null hypothesis not rejected not rejected not rejected not rejected rejected

23

C5 Regression analysis with dummy variables

Table C5 Regression analysis with dummy variables

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

a0 00004 (000) 00004 (000) 00004 (000) 00004 (000) 00004 (000)a1 -00001 (-019) 00002 (067) -00004 (047) 00001 (086) -00007 (024)Anomaly not confirmed not confirmed not confirmed not confirmed not confirmed

C6 Modified CAR approach

Table C6 Modified CAR approach

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Multiple R 049 05 025 0 092F-test 23347 (000) 12913 (000) 2207 (000) 000 (098) 1822 (000)a0 -00041 (060) 00128 (006) -00267 (000) 00354 (000) 00319 (000)a1 -00003 (000) -00003 (000) -00002 (000) 00000 (098) -00008 (000)Anomaly confirmed confirmed confirmed not confirmed confirmed

24

D Detailed statistical results SampP 500 overall data

D1 Average analysis

Table D1 Average analysis

Parameter Gap day Gap day(Positive gaps)

Gap day(Negative gaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Mean return (gap day) 006 115 -129 017 -011Mean return (non-gap day) 002 002 002 002 002Anomaly confirmed confirmed confirmed confirmed confirmed

D2 Parametric tests Students t-test

Table D2 T-test

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

t-criterion 092 4546 3579 485 271t-critical (=095) 196 196 196 196 196Null hypothesis not rejected rejected rejected rejected rejected

D3 Parametric tests ANOVA

Table D3 ANOVA

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

F 155 116211 126952 1866 136p-value 022 0 0 0 0F critical 384 384 384 384 384Null hypothesis not rejected rejected rejected not rejected not rejected

D4 Non-parametric tests Kruskal-Wallis test

Table D4 Kruskal-Wallis test

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Adjusted H 1352 70516 47237 3946 004df 1 1 1 1 1P value 0 0 0 0 084Critical value 384 384 384 384 384Null hypothesis rejected rejected rejected rejected not rejected

25

D5 Regression analysis with dummy variables

Table D5 Regression analysis with dummy variables

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

a0 00002 (000) 00002 (000) 00002 (000) 00002 (000) 00002 (000)a1 00003 (021) 00113 (000) -00132 (000) 00014 (000) -00014 (000)Anomaly not confirmed confirmed confirmed confirmed confirmed

D6 Modified CAR approach

Table D6 Modified CAR approach

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Multiple R 051 099 099 099 096F-test 69486 (000) 325351 (000) 1457582 (000) 6345973 (000) 1213344 (000)a0 -01003(000) 04081 (000) -05444 (000) -01088 (000) 00272 (000)a1 00002 (000) 00106 (000) -00127 (000) 00016 (000) -00016 (000)Anomaly confirmed confirmed confirmed confirmed confirmed

26

E Detailed statistical results NASDAQ overall data

E1 Average analysis

Table E1 Average analysis

Parameter Gap day Gap day(Positive gaps)

Gap day(Negative gaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Mean return (gap day) -009 084 -090 022 -037Mean return (non-gap day) 003 003 003 003 003Anomaly confirmed confirmed confirmed confirmed confirmed

E2 Parametric tests Students t-test

Table E2 T-test

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

t-criterion 230 1257 1341 306 664t-critical (=095) 196 196 196 196 196Null hypothesis rejected rejected rejected rejected rejected

E3 Parametric tests ANOVA

Table E3 ANOVA

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

F 2289 62720 88402 3330 17356p-value 0 0 0 0 0F critical 384 384 384 384 384Null hypothesis rejected rejected rejected rejected rejected

E4 Non-parametric tests Kruskal-Wallis test

Table E4 Kruskal-Wallis test

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Adjusted H 1892 36022 45248 4695 10437df 1 1 1 1 1P value 0 0 0 0 0Critical value 384 384 384 384 384Null hypothesis rejected rejected rejected rejected rejected

27

E5 Regression analysis with dummy variables

Table E5 Regression analysis with dummy variables

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

a0 00003 (000) 00003 (000) 00003 (000) 00003 (000) 00003 (000)a1 -00012 (000) 00081 (000) -00093 (000) 00018 (000) -00040 (000)Anomaly confirmed confirmed confirmed confirmed confirmed

E6 Modified CAR approach

Table E6 Modified CAR approach

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Multiple R 069 092 092 072 097F-test 133255 (000) 361102 (000) 442376 (000) 72903 (000) 1082812 (000)a0 -10646 (000) 11373 (000) -12888 (000) 03928 (000) -02297 (000)a1 -00011 (000) 00073 (000) -00097 (000) 00017 (000) -00039 (000)Anomaly confirmed confirmed confirmed confirmed confirmed

28

F Detailed statistical results DJI sub-periods

F1 Average analysis

Table F1 Average analysis

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 Mean return (gapday)

-001 023 015 -004

Mean return(non-gap day)

007 007 007 007

Anomaly confirmed confirmed confirmed confirmed1999-2008 Mean return (gap

day)090 -045 013 -004

Mean return(non-gap day)

-004 -004 -004 -004

Anomaly confirmed confirmed confirmed confirmed2009-2018 Mean return (gap

day)024 -024 0 -004

Mean return(non-gap day)

004 004 004 004

Anomaly confirmed confirmed not confirmed confirmed

F2 Parametric tests Students t-test

Table F2 T-test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 t-criterion 083 165 087 139t-critical (=095) 196 196 196 196Null hypothesis not rejected not rejected not rejected not rejected

1999-2008 t-criterion 347 351 054 047t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected rejected

2009-2018 t-criterion 265 207 051 058t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

F3 Parametric tests ANOVA

Table F3 ANOVA

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 F 085 409 093 179p-value 035 004 033 018

F critical 384 384 384 384Null hypothesis not rejected rejected not rejected not rejected

1999-2008 F 5405 3196 065 072p-value 0 0 042 039

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

2009-2018 F 554 697 024 058p-value 001 0 062 044

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

29

F4 Non-parametric tests Kruskal-Wallis test

Table F4 Kruskal-Wallis test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 Adjusted H 113 211 113 332df 1 1 1 1

P value 029 015 029 007Null hypothesis not rejected not rejected not rejected not rejected

1999-2008 Adjusted H 1484 1414 003 139df 1 1 1 1

P value 0 0 086 024Null hypothesis rejected rejected not rejected not rejected

2009-2018 Adjusted H 506 68 051 171df 1 1 1 1

P value 002 001 047 019Null hypothesis rejected rejected not rejected not rejected

F5 Regression analysis with dummy variables

Table F5 Regression analysis with dummy variables

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 a0 000068 (000) 00007 (000) 00007 (000) 00007 (000)a1 -000078 (035) 00016 (004) 00008 (033) -00011 (018)

Anomaly not confirmed confirmed not confirmed not confirmed1999-2008 a0 00004 (008) 00004 (008) 00004 (006) 00004 (008)

a1 00087 (000) -00049 (000) 00009 (042) -00008 (039)Anomaly confirmed confirmed not confirmed not confirmed

2009-2018 a0 00004 (006) 00004 (006) 00004 (006) 00004 (006)a1 00021 (001) -00028 (001) -00004 (062) -00008 (047)

Anomaly confirmed confirmed not confirmed not confirmed

F6 Modified CAR approach

Table F6 Modified CAR approach

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 Multiple R 083 088 082 086F-test 22779 (000) 40583 (000) 20401 (000) 3269454 (000)a0 00042 (023) 00017 (073) 00014 (058) -00266 (000)a1 -00009 (000) 00015 (000) 00006 (000) -00009 (000)

Anomaly confirmed confirmed confirmed confirmed1999-2008 Multiple R 095 093 076 019

F-test 62658 (000) 84712 (000) 10056 (000) 492 (003)a0 -00972 (000) 00365 (000) -00198 (000) -00115 (021)a1 00086 (000) -00042 (000) 00014 (000) 00002 (003)

Anomaly confirmed confirmed confirmed not confirmed2009-2018 Multiple R 096 082 08 05

F-test 150452 (000) 16731 (000) 22287 (000) 2620 (000)a0 00548 (000) -00618 (000) 00031 (020) -00112 (000)a1 00013 (000) -00014 (000) -00005 (000) -00004 (000)

Anomaly confirmed confirmed not confirmed confirmed

30

G Detailed statistical results NASDAQ sub-periods

G1 Average analysis

Table G1 Average analysis

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 Mean return (gapday)

094 -111 0189 -029

Mean return(non-gap day)

007 007 007 007

Anomaly confirmed confirmed confirmed confirmed1959-1968 Mean return (gap

day)133 -147 033 -039

Mean return(non-gap day)

006 006 006 006

Anomaly confirmed confirmed confirmed confirmed1969-1978 Mean return (gap

day)19 -186 057 -068

Mean return(non-gap day)

005 005 005 005

Anomaly confirmed confirmed confirmed confirmed1979-1988 Mean return (gap

day)138 -162 066 -04

Mean return(non-gap day)

008 008 008 008

Anomaly confirmed confirmed confirmed confirmed1989-1998 Mean return (gap

day)016 012 018 -009

Mean return(non-gap day)

002 002 002 002

Anomaly confirmed not confirmed confirmed confirmed1999-2008 Mean return (gap

day)38E-3 027 -036 -013

Mean return(non-gap day)

-01 -01 -01 -01

Anomaly confirmed not confirmed not confirmed not confirmed2009-2018 Mean return (gap

day)039 009 013 -025

Mean return(non-gap day)

001 001 001 001

Anomaly confirmed not confirmed confirmed confirmed

G2 Parametric tests Students t-test

Table G2 T-test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 t-criterion 3194 3076 201 559t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected rejected

1959-1968 t-criterion 1399 2246 443 382t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected rejected

1969-1978 t-criterion 261 4358 417 786t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected rejected

1979-1988 t-criterion 1847 1445 709 395t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected rejected

1989-1998 t-criterion 13 066 126 093t-critical (=095) 196 196 196 196Null hypothesis not rejected not rejected not rejected not rejected

1999-2008 t-criterion 192 106 111 009t-critical (=095) 196 196 196 196Null hypothesis not rejected not rejected not rejected not rejected

2009-2018 t-criterion 27 05 089 188t-critical (=095) 196 196 196 196Null hypothesis rejected not rejected not rejected not rejected

31

G3 Parametric tests ANOVA

Table G3 ANOVA

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 F 88153 190609 1272 14521p-value 0 0 0 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1959-1968 F 93974 149771 4715 10418p-value 0 0 0 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1969-1978 F 84546 145429 6295 18241p-value 0 0 0 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1979-1988 F 66952 110482 13138 8626p-value 0 0 0 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1989-1998 F 323 138 43 168p-value 007 024 003 019

F critical 384 384 384 384Null hypothesis not rejected not rejected rejected not rejected

1999-2008 F 106 512 327 003p-value 001 002 007 085

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

2009-2018 F 169 069 175 93p-value 0 04 018 0

F critical 384 384 384 384Null hypothesis rejected not rejected not rejected rejected

G4 Non-parametric tests Kruskal-Wallis test

Table G4 Kruskal-Wallis test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 Adjusted H 26254 32592 1464 3962df 1 1 1 1

P value 0 0 0 0Null hypothesis rejected rejected rejected rejected

1959-1968 Adjusted H 28235 27989 2736 332df 1 1 1 1

P value 0 0 0 0Null hypothesis rejected rejected rejected rejected

1969-1978 Adjusted H 22202 33777 3311 7591df 1 1 1 1

P value 0 0 0 0Null hypothesis rejected rejected rejected rejected

1979-1988 Adjusted H 23282 25292 4812 3964df 1 1 1 1

P value 0 0 0 0Null hypothesis rejected rejected rejected rejected

1989-1998 Adjusted H 381 017 175 132df 1 1 1 1

P value 005 068 019 025Null hypothesis not rejected not rejected not rejected not rejected

1999-2008 Adjusted H 855 023 044 004df 1 1 1 1

P value 0 063 051 084Null hypothesis rejected not rejected not rejected not rejected

2009-2018 Adjusted H 1063 009 257 709df 1 1 1 1

P value 0 077 011 001Null hypothesis rejected not rejected not rejected rejected

32

G5 Regression analysis with dummy variables

Table G5 Regression analysis with dummy variables

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 a0 00007 (000) 00007 (000) 00007 (000) 00007 (000)a1 00088 (000) -00119 (000) 00011 (000) -00036 (000)

Anomaly confirmed confirmed confirmed confirmed1959-1968 a0 00006 (000) 00006 (000) 00006 (000) 00006 (000)

a1 00128 (000) -00153 (000) 00027 (000) -00046 (000)Anomaly confirmed confirmed confirmed confirmed

1969-1978 a0 00005 (000) 00005 (000) 00005 (000) 00005 (000)a1 00185 (000) -00192 (000) 00053 (000) -00073 (000)

Anomaly confirmed confirmed confirmed confirmed1979-1988 a0 00008 (000) 00008 (000) 00008 (000) 00008 (000)

a1 00131 (000) -00172 (000) 00059 (000) -00048 (000)Anomaly confirmed confirmed confirmed confirmed

1989-1998 a0 00002 (027) 00002 (028) 00002 (028) 00002 (027)a1 00014 (007) 00010 (024) 00017 (004) -00011 (019)

Anomaly not confirmed not confirmed confirmed not confirmed1999-2008 a0 00001 (059) 00001 (062) 00001 (059) 00001 (060)

a1 00037 (000) 00026 (002) -00038 (000) -00014 (019)Anomaly confirmed not confirmed not confirmed not confirmed

2009-2018 a0 00001 (049) 00001 (049) 00001 (049) 00001 (049)a1 00038 (000) 00007 (040) 00012 (018) -00027 (000)

Anomaly confirmed not confirmed not confirmed confirmed

G6 Modified CAR approach

Table G6 Modified CAR approach

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 Multiple R 099 099 093 098F-test 5753605 (000) 100470(000) 6280421 283281a0 -00091 (000) -00349 (000) 00056 (001) 00015 (073)a1 00083 (000) -00110 (000) 00010 (000) -00031 (000)

Anomaly confirmed confirmed confirmed confirmed1959-1968 Multiple R 099 099 099 099

F-test 3923274 (000) 3005562 (000) 443198 (000) 372583 (000)a0 00096 (000) 00073 (016) -00082 (000) -00095 (004)a1 00116 (001) -00149 (000) 00025 (000) -00047 (000)

Anomaly confirmed confirmed confirmed confirmed1969-1978 Multiple R 099 099 098 099

F-test 4302608 (000) 2723953 (000) 179969 (000) 639745a0 00246 (000) -00002 (000) 00217 (000) -00514 (000)a1 00176 (000) -00182 (000) 00049 (000) -00062 (000)

Anomaly confirmed confirmed confirmed confirmed1979-1988 Multiple R 099 099 099 099

F-test 5872335 (000) 1182609 (000) 1083558 (000) 910089 (000)a0 00136 (000) -01081 (000) -00285 (000) -00101 (000)a1 00131 (000) -00167 (000) 00062 (000) -00048 (000)

Anomaly confirmed confirmed confirmed confirmed1989-1998 Multiple R 09 056 069 016

F-test 46947 (000) 4885 (000) 10131 (000) 263 (011)a0 00102 (002) -00261 (000) -0016 (001) -00237 (000)a1 00015 (000) 00010 (000) 0001 (000) 00002 (011)

Anomaly confirmed confirmed confirmed not confirmed1999-2008 Multiple R 093 087 073 037

F-test 71863 (000) 32530 (000) 13273 (000) 1669 (000)a0 00185 (004) 00311 (000) -00130 (039) -00546 (000)a1 00037 (000) 00032 (000) -00026 (000) -00007 (000)

Anomaly confirmed not confirmed not confirmed confirmed2009-2018 Multiple R 089 001 096 091

F-test 40818 (000) 000 (094) 116744 (000) 53770 (000)a0 01436 (000) -01099 (000) -01036 (000) 00697 (000)a1 00030 (000) 00000 (094) 00024 (000) -00021 (000)

Anomaly confirmed not confirmed confirmed confirmed

33

H Detailed statistical results SampP 500 sub-periods

H1 Average analysis

Table H1 Average analysis

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 Mean return (gapday)

138 -171 004 -014

Mean return(non-gap day)

0 0 0 0

Anomaly confirmed confirmed confirmed confirmed1939-1948 Mean return (gap

day)001 -042 172 -195

Mean return(non-gap day)

003 003 003 003

Anomaly confirmed confirmed confirmed confirmed1949-1958 Mean return (gap

day)165 -18 02 002

Mean return(non-gap day)

006 006 006 006

Anomaly confirmed confirmed confirmed not confirmed1959-1968 Mean return (gap

day)104 -102 015 0

Mean return(non-gap day)

002 002 002 002

Anomaly confirmed confirmed confirmed not confirmed1969-1978 Mean return (gap

day)131 -13 019 -03

Mean return(non-gap day)

0 0 0 0

Anomaly confirmed confirmed confirmed confirmed1979-1988 Mean return (gap

day)058 -042 015 003

Mean return(non-gap day)

005 005 005 005

Anomaly confirmed confirmed confirmed not confirmed1989-1998 Mean return (gap

day)02 -023 -002 01

Mean return(non-gap day)

007 007 007 007

Anomaly confirmed confirmed not confirmed not confirmed1999-2008 Mean return (gap

day)083 -089 -023 -005

Mean return(non-gap day)

001 001 001 001

Anomaly confirmed confirmed not confirmed confirmed2009-2018 Mean return (gap

day)055 -052 001 -015

Mean return(non-gap day)

004 004 004 004

Anomaly confirmed confirmed not confirmed confirmed

34

H2 Parametric tests Students t-test

Table H2 T-test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 t-criterion 101 85 029 048t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

1939-1948 t-criterion 064 479 3074 225t-critical (=095) 196 196 196 196Null hypothesis not rejected rejected rejected rejected

1949-1958 t-criterion 2964 2383 193 041t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

1959-1968 t-criterion 2281 2157 21 023t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected not rejected

1969-1978 t-criterion 1318 2034 187 321t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected rejected

1979-1988 t-criterion 435 535 07 037t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

1989-1998 t-criterion 201 396 132 052t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

1999-2008 t-criterion 362 433 117 022t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

2009-2018 t-criterion 375 382 027 132t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

H3 Parametric tests ANOVA

Table H3 ANOVA

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 F 6281 8032 005 051p-value 0 0 082 047

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

1939-1948 F 056 2603 34854 51034p-value 045 0 0 0

F critical 384 384 384 384Null hypothesis not rejected rejected rejected rejected

1949-1958 F 100174 128997 897 062p-value 0 0 0 043

F critical 384 384 384 384Null hypothesis rejected rejected rejected not rejected

1959-1968 F 36831 32858 617 01p-value 0 0 001 074

F critical 384 384 384 384Null hypothesis rejected rejected rejected not rejected

1969-1978 F 26601 3063 53 152p-value 0 0 002 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1979-1988 F 23 245 076 009p-value 0 0 039 077

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

1989-1998 F 399 1156 118 015p-value 004 0 027 069

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

1999-2008 F 4253 5622 365 024p-value 0 0 006 062

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

2009-2018 F 3064 3656 01 43p-value 0 0 075 004

F critical 384 384 384 384Null hypothesis rejected rejected not rejected rejected

35

H4 Non-parametric tests Kruskal -Wallis test

Table H4 Kruskal-Wallis test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 Adjusted H 9982 5913 332 14df 1 1 1 1

P value 0 0 007 024Null hypothesis rejected rejected not rejected not rejected

1939-1948 Adjusted H 494 1999 23387 24927df 1 1 1 1

P value 003 0 0 0Null hypothesis rejected rejected rejected rejected

1949-1958 Adjusted H 28728 28175 348 15df 1 1 1 1

P value 0 0 006 022Null hypothesis rejected rejected not rejected not rejected

1959-1968 Adjusted H 25729 21437 701 063df 1 1 1 1

P value 0 0 001 043Null hypothesis rejected rejected rejected not rejected

1969-1978 Adjusted H 14407 20078 27 1706df 1 1 1 1

P value 0 0 01 0Null hypothesis rejected rejected not rejected rejected

1979-1988 Adjusted H 1788 2836 027 034df 1 1 1 1

P value 0 0 06 056Null hypothesis rejected rejected not rejected not rejected

1989-1998 Adjusted H 251 1431 111 044df 1 1 1 1

P value 011 0 029 051Null hypothesis not rejected rejected not rejected not rejected

1999-2008 Adjusted H 1812 1788 042 002df 1 1 1 1

P value 0 0 052 089Null hypothesis rejected rejected not rejected not rejected

2009-2018 Adjusted H 1314 1783 074 37df 1 1 1 1

P value 0 0 039 005Null hypothesis rejected rejected not rejected not rejected

36

H5 Regression analysis with dummy variables

Table H5 Regression analysis with dummy variables

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 a0 00000 (097) 00000 (004) 00000 (097) 00000 (097)a1 00138 (000) -00172 (000) 00004 (082) -00014 (047)

Anomaly confirmed confirmed not confirmed not confirmed1939-1948 a0 00003 (015) 00003 (015) 00003 (015) 00003 (015)

a1 00007 (045) -00045 (000) 00170 (000) -00199 (000)Anomaly not confirmed confirmed confirmed confirmed

1949-1958 a0 00006 (000) 00006 (000) 00006 (000) 00006 (000)a1 00160 (000) -00188 (000) 00016 (000) -00004 (043)

Anomaly confirmed confirmed confirmed not confirmed1959-1968 a0 00002 (007) 00002 (004) 00002 (008) 00002 (008)

a1 00103 (000) -00105 (000) 00014 (001) -00002 (074)Anomaly confirmed confirmed confirmed not confirmed

1969-1978 a0 00000 (078) 00000 (078) 00000 (078) 00000 (078)a1 00132 (000) -00132 (000) 00019 (002) -00030 (000)

Anomaly confirmed confirmed confirmed confirmed1979-1988 a0 00006 (001) 00006 (001) 00006 (001) 00006 (000)

a1 00053 (000) -00048 (000) 00009 (040) -00003 (075)Anomaly confirmed confirmed not confirmed not confirmed

1989-1998 a0 00007 (000) 00007 (000) 00007 (000) 00007 (000)a1 00016 (005) -00030 (000) -00009 (026) 00003 (072)

Anomaly confirmed confirmed not confirmed not confirmed1999-2008 a0 00001 (075) 00001 (075) 00001 (075) 00001 (076)

a1 00083 (000) -00091 (000) -00024 (005) -00006 (062)Anomaly confirmed confirmed not confirmed not confirmed

2009-2018 a0 00004 (003) 00004 (000) 00004 (003) 00004 (003)a1 00051 (000) -00059 (000) -00003 (075) -00019 (003)

Anomaly confirmed confirmed not confirmed confirmed

37

H6 Modified CAR approach

Table H6 Modified CAR approach

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 Multiple R 096 095 046 046F-test 175935 (000) 96500 (000) 3534 (000) 2880 (000)a0 -01070 (000) 01958 (000) 00405 (000) 00535 (000)a1 00121 (000) -00160 (000) 00006 (000) -00014 (000)

Anomaly confirmed confirmed confirmed confirmed1939-1948 Multiple R 08 099 099 099

F-test 18777 (000) 755727 (000) 3572830 (000) 2696099 (000)a0 00019 (073) -00346 (000) -00373 (000) 00912 (000)a1 00012 (000) -00044 (000) 00168 (000) -00197 (000)

Anomaly confirmed confirmed confirmed confirmed1949-1958 Multiple R 099 099 094 015

F-test 1021705 (000) 7171257 (000) 75858 (000) 242 (012)a0 -00176 (000) -00191 (000) 00095 (000) -00498 (000)a1 00154 (000) -00181 (000) 00013 (000) -00002 (012)

Anomaly confirmed confirmed confirmed not confirmed1959-1968 Multiple R 099 099 094 078

F-test 1463311 (000) 6002659 (000) 82273 (000) 14352 (000)a0 -00112 (000) 00004 (085) 00151 (000) 00389 (000)a1 00098 (000) -00102 (000) 00011 (000) -00009 (000)

Anomaly confirmed confirmed confirmed confirmed1969-1978 Multiple R 098 099 093 099

F-test 241655 (000) 1451901 (000) 57333 (000) 368160 (000)a0 -00433 (000) 00276 (000) 00099 (002) -00144 (000)a1 00132 (000) -00134 (000) 00020 (000) -00030 (000)

Anomaly confirmed confirmed confirmed confirmed1979-1988 Multiple R 092 078 023 008

F-test 53757 (000) 18707 (000) 487 (003) 085 (036)a0 00813 (000) -02508 (000) 00204 (000) -00235 (000)a1 00036 (000) -00031 (000) -00003 (003) -00001 (036)

Anomaly confirmed confirmed not confirmed not confirmed1989-1998 Multiple R 079 099 074 044

F-test 19705(000) 761967 (000) 14133 (000) 2369 (000)a0 00268 (000) 00023 (021) -00381 (000) 00087 (000)a1 00013 (000) -00028 (000) -00008 (000) 00002 (000)

Anomaly confirmed confirmed not confirmed not confirmed1999-2008 Multiple R 091 093 071 065

F-test 47218 (000) 76564 (000) 9843 (000) 7768 (000)a0 -01493 (000) 01351 (000) 00397 (000) 00007 (093)a1 00081 (000) -00083 (000) -00026 (000) -00011 (000)

Anomaly confirmed confirmed not confirmed confirmed2009-2018 Multiple R 086 087 083 074

F-test 29971 (000) 32484 (000) 23228 (000) 12764 (000)a0 01711 (000) -02250 (000) 00407 (000) -00472 (000)a1 00038 (000) -00044 (000) -00010 (000) -00012 (000)

Anomaly confirmed confirmed not confirmed confirmed

38

C Detailed statistical results DJI overall data

C1 Average analysis

Table C1 Average analysis

Parameter Gap day Gap day(Positive gaps)

Gap day(Negative gaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Mean return (gap day) 003 006 0 005 -003Mean return (non-gap day) 004 004 004 004 004Anomaly not confirmed not confirmed confirmed not confirmed confirmed

C2 Parametric tests Students t-test

Table C2 T-test

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

t-criterion 016 042 053 015 104t-critical (=095) 196 196 196 196 196Null hypothesis not rejected not rejected not rejected not rejected not rejected

C3 Parametric tests ANOVA

Table C3 ANOVA

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

F 0036 018 053 003 14p-value 085 067 047 086 024F critical 384 384 384 384 384Null hypothesis not rejected not rejected not rejected not rejected not rejected

C4 Non-parametric tests Kruskal-Wallis test

Table C4 Kruskal -Wallis test

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Adjusted H 082 012 126 0 455df 1 1 1 1 1P value 037 073 026 095 003Critical value 384 384 384 384 384Null hypothesis not rejected not rejected not rejected not rejected rejected

23

C5 Regression analysis with dummy variables

Table C5 Regression analysis with dummy variables

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

a0 00004 (000) 00004 (000) 00004 (000) 00004 (000) 00004 (000)a1 -00001 (-019) 00002 (067) -00004 (047) 00001 (086) -00007 (024)Anomaly not confirmed not confirmed not confirmed not confirmed not confirmed

C6 Modified CAR approach

Table C6 Modified CAR approach

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Multiple R 049 05 025 0 092F-test 23347 (000) 12913 (000) 2207 (000) 000 (098) 1822 (000)a0 -00041 (060) 00128 (006) -00267 (000) 00354 (000) 00319 (000)a1 -00003 (000) -00003 (000) -00002 (000) 00000 (098) -00008 (000)Anomaly confirmed confirmed confirmed not confirmed confirmed

24

D Detailed statistical results SampP 500 overall data

D1 Average analysis

Table D1 Average analysis

Parameter Gap day Gap day(Positive gaps)

Gap day(Negative gaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Mean return (gap day) 006 115 -129 017 -011Mean return (non-gap day) 002 002 002 002 002Anomaly confirmed confirmed confirmed confirmed confirmed

D2 Parametric tests Students t-test

Table D2 T-test

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

t-criterion 092 4546 3579 485 271t-critical (=095) 196 196 196 196 196Null hypothesis not rejected rejected rejected rejected rejected

D3 Parametric tests ANOVA

Table D3 ANOVA

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

F 155 116211 126952 1866 136p-value 022 0 0 0 0F critical 384 384 384 384 384Null hypothesis not rejected rejected rejected not rejected not rejected

D4 Non-parametric tests Kruskal-Wallis test

Table D4 Kruskal-Wallis test

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Adjusted H 1352 70516 47237 3946 004df 1 1 1 1 1P value 0 0 0 0 084Critical value 384 384 384 384 384Null hypothesis rejected rejected rejected rejected not rejected

25

D5 Regression analysis with dummy variables

Table D5 Regression analysis with dummy variables

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

a0 00002 (000) 00002 (000) 00002 (000) 00002 (000) 00002 (000)a1 00003 (021) 00113 (000) -00132 (000) 00014 (000) -00014 (000)Anomaly not confirmed confirmed confirmed confirmed confirmed

D6 Modified CAR approach

Table D6 Modified CAR approach

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Multiple R 051 099 099 099 096F-test 69486 (000) 325351 (000) 1457582 (000) 6345973 (000) 1213344 (000)a0 -01003(000) 04081 (000) -05444 (000) -01088 (000) 00272 (000)a1 00002 (000) 00106 (000) -00127 (000) 00016 (000) -00016 (000)Anomaly confirmed confirmed confirmed confirmed confirmed

26

E Detailed statistical results NASDAQ overall data

E1 Average analysis

Table E1 Average analysis

Parameter Gap day Gap day(Positive gaps)

Gap day(Negative gaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Mean return (gap day) -009 084 -090 022 -037Mean return (non-gap day) 003 003 003 003 003Anomaly confirmed confirmed confirmed confirmed confirmed

E2 Parametric tests Students t-test

Table E2 T-test

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

t-criterion 230 1257 1341 306 664t-critical (=095) 196 196 196 196 196Null hypothesis rejected rejected rejected rejected rejected

E3 Parametric tests ANOVA

Table E3 ANOVA

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

F 2289 62720 88402 3330 17356p-value 0 0 0 0 0F critical 384 384 384 384 384Null hypothesis rejected rejected rejected rejected rejected

E4 Non-parametric tests Kruskal-Wallis test

Table E4 Kruskal-Wallis test

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Adjusted H 1892 36022 45248 4695 10437df 1 1 1 1 1P value 0 0 0 0 0Critical value 384 384 384 384 384Null hypothesis rejected rejected rejected rejected rejected

27

E5 Regression analysis with dummy variables

Table E5 Regression analysis with dummy variables

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

a0 00003 (000) 00003 (000) 00003 (000) 00003 (000) 00003 (000)a1 -00012 (000) 00081 (000) -00093 (000) 00018 (000) -00040 (000)Anomaly confirmed confirmed confirmed confirmed confirmed

E6 Modified CAR approach

Table E6 Modified CAR approach

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Multiple R 069 092 092 072 097F-test 133255 (000) 361102 (000) 442376 (000) 72903 (000) 1082812 (000)a0 -10646 (000) 11373 (000) -12888 (000) 03928 (000) -02297 (000)a1 -00011 (000) 00073 (000) -00097 (000) 00017 (000) -00039 (000)Anomaly confirmed confirmed confirmed confirmed confirmed

28

F Detailed statistical results DJI sub-periods

F1 Average analysis

Table F1 Average analysis

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 Mean return (gapday)

-001 023 015 -004

Mean return(non-gap day)

007 007 007 007

Anomaly confirmed confirmed confirmed confirmed1999-2008 Mean return (gap

day)090 -045 013 -004

Mean return(non-gap day)

-004 -004 -004 -004

Anomaly confirmed confirmed confirmed confirmed2009-2018 Mean return (gap

day)024 -024 0 -004

Mean return(non-gap day)

004 004 004 004

Anomaly confirmed confirmed not confirmed confirmed

F2 Parametric tests Students t-test

Table F2 T-test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 t-criterion 083 165 087 139t-critical (=095) 196 196 196 196Null hypothesis not rejected not rejected not rejected not rejected

1999-2008 t-criterion 347 351 054 047t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected rejected

2009-2018 t-criterion 265 207 051 058t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

F3 Parametric tests ANOVA

Table F3 ANOVA

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 F 085 409 093 179p-value 035 004 033 018

F critical 384 384 384 384Null hypothesis not rejected rejected not rejected not rejected

1999-2008 F 5405 3196 065 072p-value 0 0 042 039

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

2009-2018 F 554 697 024 058p-value 001 0 062 044

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

29

F4 Non-parametric tests Kruskal-Wallis test

Table F4 Kruskal-Wallis test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 Adjusted H 113 211 113 332df 1 1 1 1

P value 029 015 029 007Null hypothesis not rejected not rejected not rejected not rejected

1999-2008 Adjusted H 1484 1414 003 139df 1 1 1 1

P value 0 0 086 024Null hypothesis rejected rejected not rejected not rejected

2009-2018 Adjusted H 506 68 051 171df 1 1 1 1

P value 002 001 047 019Null hypothesis rejected rejected not rejected not rejected

F5 Regression analysis with dummy variables

Table F5 Regression analysis with dummy variables

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 a0 000068 (000) 00007 (000) 00007 (000) 00007 (000)a1 -000078 (035) 00016 (004) 00008 (033) -00011 (018)

Anomaly not confirmed confirmed not confirmed not confirmed1999-2008 a0 00004 (008) 00004 (008) 00004 (006) 00004 (008)

a1 00087 (000) -00049 (000) 00009 (042) -00008 (039)Anomaly confirmed confirmed not confirmed not confirmed

2009-2018 a0 00004 (006) 00004 (006) 00004 (006) 00004 (006)a1 00021 (001) -00028 (001) -00004 (062) -00008 (047)

Anomaly confirmed confirmed not confirmed not confirmed

F6 Modified CAR approach

Table F6 Modified CAR approach

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 Multiple R 083 088 082 086F-test 22779 (000) 40583 (000) 20401 (000) 3269454 (000)a0 00042 (023) 00017 (073) 00014 (058) -00266 (000)a1 -00009 (000) 00015 (000) 00006 (000) -00009 (000)

Anomaly confirmed confirmed confirmed confirmed1999-2008 Multiple R 095 093 076 019

F-test 62658 (000) 84712 (000) 10056 (000) 492 (003)a0 -00972 (000) 00365 (000) -00198 (000) -00115 (021)a1 00086 (000) -00042 (000) 00014 (000) 00002 (003)

Anomaly confirmed confirmed confirmed not confirmed2009-2018 Multiple R 096 082 08 05

F-test 150452 (000) 16731 (000) 22287 (000) 2620 (000)a0 00548 (000) -00618 (000) 00031 (020) -00112 (000)a1 00013 (000) -00014 (000) -00005 (000) -00004 (000)

Anomaly confirmed confirmed not confirmed confirmed

30

G Detailed statistical results NASDAQ sub-periods

G1 Average analysis

Table G1 Average analysis

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 Mean return (gapday)

094 -111 0189 -029

Mean return(non-gap day)

007 007 007 007

Anomaly confirmed confirmed confirmed confirmed1959-1968 Mean return (gap

day)133 -147 033 -039

Mean return(non-gap day)

006 006 006 006

Anomaly confirmed confirmed confirmed confirmed1969-1978 Mean return (gap

day)19 -186 057 -068

Mean return(non-gap day)

005 005 005 005

Anomaly confirmed confirmed confirmed confirmed1979-1988 Mean return (gap

day)138 -162 066 -04

Mean return(non-gap day)

008 008 008 008

Anomaly confirmed confirmed confirmed confirmed1989-1998 Mean return (gap

day)016 012 018 -009

Mean return(non-gap day)

002 002 002 002

Anomaly confirmed not confirmed confirmed confirmed1999-2008 Mean return (gap

day)38E-3 027 -036 -013

Mean return(non-gap day)

-01 -01 -01 -01

Anomaly confirmed not confirmed not confirmed not confirmed2009-2018 Mean return (gap

day)039 009 013 -025

Mean return(non-gap day)

001 001 001 001

Anomaly confirmed not confirmed confirmed confirmed

G2 Parametric tests Students t-test

Table G2 T-test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 t-criterion 3194 3076 201 559t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected rejected

1959-1968 t-criterion 1399 2246 443 382t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected rejected

1969-1978 t-criterion 261 4358 417 786t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected rejected

1979-1988 t-criterion 1847 1445 709 395t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected rejected

1989-1998 t-criterion 13 066 126 093t-critical (=095) 196 196 196 196Null hypothesis not rejected not rejected not rejected not rejected

1999-2008 t-criterion 192 106 111 009t-critical (=095) 196 196 196 196Null hypothesis not rejected not rejected not rejected not rejected

2009-2018 t-criterion 27 05 089 188t-critical (=095) 196 196 196 196Null hypothesis rejected not rejected not rejected not rejected

31

G3 Parametric tests ANOVA

Table G3 ANOVA

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 F 88153 190609 1272 14521p-value 0 0 0 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1959-1968 F 93974 149771 4715 10418p-value 0 0 0 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1969-1978 F 84546 145429 6295 18241p-value 0 0 0 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1979-1988 F 66952 110482 13138 8626p-value 0 0 0 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1989-1998 F 323 138 43 168p-value 007 024 003 019

F critical 384 384 384 384Null hypothesis not rejected not rejected rejected not rejected

1999-2008 F 106 512 327 003p-value 001 002 007 085

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

2009-2018 F 169 069 175 93p-value 0 04 018 0

F critical 384 384 384 384Null hypothesis rejected not rejected not rejected rejected

G4 Non-parametric tests Kruskal-Wallis test

Table G4 Kruskal-Wallis test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 Adjusted H 26254 32592 1464 3962df 1 1 1 1

P value 0 0 0 0Null hypothesis rejected rejected rejected rejected

1959-1968 Adjusted H 28235 27989 2736 332df 1 1 1 1

P value 0 0 0 0Null hypothesis rejected rejected rejected rejected

1969-1978 Adjusted H 22202 33777 3311 7591df 1 1 1 1

P value 0 0 0 0Null hypothesis rejected rejected rejected rejected

1979-1988 Adjusted H 23282 25292 4812 3964df 1 1 1 1

P value 0 0 0 0Null hypothesis rejected rejected rejected rejected

1989-1998 Adjusted H 381 017 175 132df 1 1 1 1

P value 005 068 019 025Null hypothesis not rejected not rejected not rejected not rejected

1999-2008 Adjusted H 855 023 044 004df 1 1 1 1

P value 0 063 051 084Null hypothesis rejected not rejected not rejected not rejected

2009-2018 Adjusted H 1063 009 257 709df 1 1 1 1

P value 0 077 011 001Null hypothesis rejected not rejected not rejected rejected

32

G5 Regression analysis with dummy variables

Table G5 Regression analysis with dummy variables

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 a0 00007 (000) 00007 (000) 00007 (000) 00007 (000)a1 00088 (000) -00119 (000) 00011 (000) -00036 (000)

Anomaly confirmed confirmed confirmed confirmed1959-1968 a0 00006 (000) 00006 (000) 00006 (000) 00006 (000)

a1 00128 (000) -00153 (000) 00027 (000) -00046 (000)Anomaly confirmed confirmed confirmed confirmed

1969-1978 a0 00005 (000) 00005 (000) 00005 (000) 00005 (000)a1 00185 (000) -00192 (000) 00053 (000) -00073 (000)

Anomaly confirmed confirmed confirmed confirmed1979-1988 a0 00008 (000) 00008 (000) 00008 (000) 00008 (000)

a1 00131 (000) -00172 (000) 00059 (000) -00048 (000)Anomaly confirmed confirmed confirmed confirmed

1989-1998 a0 00002 (027) 00002 (028) 00002 (028) 00002 (027)a1 00014 (007) 00010 (024) 00017 (004) -00011 (019)

Anomaly not confirmed not confirmed confirmed not confirmed1999-2008 a0 00001 (059) 00001 (062) 00001 (059) 00001 (060)

a1 00037 (000) 00026 (002) -00038 (000) -00014 (019)Anomaly confirmed not confirmed not confirmed not confirmed

2009-2018 a0 00001 (049) 00001 (049) 00001 (049) 00001 (049)a1 00038 (000) 00007 (040) 00012 (018) -00027 (000)

Anomaly confirmed not confirmed not confirmed confirmed

G6 Modified CAR approach

Table G6 Modified CAR approach

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 Multiple R 099 099 093 098F-test 5753605 (000) 100470(000) 6280421 283281a0 -00091 (000) -00349 (000) 00056 (001) 00015 (073)a1 00083 (000) -00110 (000) 00010 (000) -00031 (000)

Anomaly confirmed confirmed confirmed confirmed1959-1968 Multiple R 099 099 099 099

F-test 3923274 (000) 3005562 (000) 443198 (000) 372583 (000)a0 00096 (000) 00073 (016) -00082 (000) -00095 (004)a1 00116 (001) -00149 (000) 00025 (000) -00047 (000)

Anomaly confirmed confirmed confirmed confirmed1969-1978 Multiple R 099 099 098 099

F-test 4302608 (000) 2723953 (000) 179969 (000) 639745a0 00246 (000) -00002 (000) 00217 (000) -00514 (000)a1 00176 (000) -00182 (000) 00049 (000) -00062 (000)

Anomaly confirmed confirmed confirmed confirmed1979-1988 Multiple R 099 099 099 099

F-test 5872335 (000) 1182609 (000) 1083558 (000) 910089 (000)a0 00136 (000) -01081 (000) -00285 (000) -00101 (000)a1 00131 (000) -00167 (000) 00062 (000) -00048 (000)

Anomaly confirmed confirmed confirmed confirmed1989-1998 Multiple R 09 056 069 016

F-test 46947 (000) 4885 (000) 10131 (000) 263 (011)a0 00102 (002) -00261 (000) -0016 (001) -00237 (000)a1 00015 (000) 00010 (000) 0001 (000) 00002 (011)

Anomaly confirmed confirmed confirmed not confirmed1999-2008 Multiple R 093 087 073 037

F-test 71863 (000) 32530 (000) 13273 (000) 1669 (000)a0 00185 (004) 00311 (000) -00130 (039) -00546 (000)a1 00037 (000) 00032 (000) -00026 (000) -00007 (000)

Anomaly confirmed not confirmed not confirmed confirmed2009-2018 Multiple R 089 001 096 091

F-test 40818 (000) 000 (094) 116744 (000) 53770 (000)a0 01436 (000) -01099 (000) -01036 (000) 00697 (000)a1 00030 (000) 00000 (094) 00024 (000) -00021 (000)

Anomaly confirmed not confirmed confirmed confirmed

33

H Detailed statistical results SampP 500 sub-periods

H1 Average analysis

Table H1 Average analysis

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 Mean return (gapday)

138 -171 004 -014

Mean return(non-gap day)

0 0 0 0

Anomaly confirmed confirmed confirmed confirmed1939-1948 Mean return (gap

day)001 -042 172 -195

Mean return(non-gap day)

003 003 003 003

Anomaly confirmed confirmed confirmed confirmed1949-1958 Mean return (gap

day)165 -18 02 002

Mean return(non-gap day)

006 006 006 006

Anomaly confirmed confirmed confirmed not confirmed1959-1968 Mean return (gap

day)104 -102 015 0

Mean return(non-gap day)

002 002 002 002

Anomaly confirmed confirmed confirmed not confirmed1969-1978 Mean return (gap

day)131 -13 019 -03

Mean return(non-gap day)

0 0 0 0

Anomaly confirmed confirmed confirmed confirmed1979-1988 Mean return (gap

day)058 -042 015 003

Mean return(non-gap day)

005 005 005 005

Anomaly confirmed confirmed confirmed not confirmed1989-1998 Mean return (gap

day)02 -023 -002 01

Mean return(non-gap day)

007 007 007 007

Anomaly confirmed confirmed not confirmed not confirmed1999-2008 Mean return (gap

day)083 -089 -023 -005

Mean return(non-gap day)

001 001 001 001

Anomaly confirmed confirmed not confirmed confirmed2009-2018 Mean return (gap

day)055 -052 001 -015

Mean return(non-gap day)

004 004 004 004

Anomaly confirmed confirmed not confirmed confirmed

34

H2 Parametric tests Students t-test

Table H2 T-test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 t-criterion 101 85 029 048t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

1939-1948 t-criterion 064 479 3074 225t-critical (=095) 196 196 196 196Null hypothesis not rejected rejected rejected rejected

1949-1958 t-criterion 2964 2383 193 041t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

1959-1968 t-criterion 2281 2157 21 023t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected not rejected

1969-1978 t-criterion 1318 2034 187 321t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected rejected

1979-1988 t-criterion 435 535 07 037t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

1989-1998 t-criterion 201 396 132 052t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

1999-2008 t-criterion 362 433 117 022t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

2009-2018 t-criterion 375 382 027 132t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

H3 Parametric tests ANOVA

Table H3 ANOVA

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 F 6281 8032 005 051p-value 0 0 082 047

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

1939-1948 F 056 2603 34854 51034p-value 045 0 0 0

F critical 384 384 384 384Null hypothesis not rejected rejected rejected rejected

1949-1958 F 100174 128997 897 062p-value 0 0 0 043

F critical 384 384 384 384Null hypothesis rejected rejected rejected not rejected

1959-1968 F 36831 32858 617 01p-value 0 0 001 074

F critical 384 384 384 384Null hypothesis rejected rejected rejected not rejected

1969-1978 F 26601 3063 53 152p-value 0 0 002 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1979-1988 F 23 245 076 009p-value 0 0 039 077

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

1989-1998 F 399 1156 118 015p-value 004 0 027 069

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

1999-2008 F 4253 5622 365 024p-value 0 0 006 062

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

2009-2018 F 3064 3656 01 43p-value 0 0 075 004

F critical 384 384 384 384Null hypothesis rejected rejected not rejected rejected

35

H4 Non-parametric tests Kruskal -Wallis test

Table H4 Kruskal-Wallis test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 Adjusted H 9982 5913 332 14df 1 1 1 1

P value 0 0 007 024Null hypothesis rejected rejected not rejected not rejected

1939-1948 Adjusted H 494 1999 23387 24927df 1 1 1 1

P value 003 0 0 0Null hypothesis rejected rejected rejected rejected

1949-1958 Adjusted H 28728 28175 348 15df 1 1 1 1

P value 0 0 006 022Null hypothesis rejected rejected not rejected not rejected

1959-1968 Adjusted H 25729 21437 701 063df 1 1 1 1

P value 0 0 001 043Null hypothesis rejected rejected rejected not rejected

1969-1978 Adjusted H 14407 20078 27 1706df 1 1 1 1

P value 0 0 01 0Null hypothesis rejected rejected not rejected rejected

1979-1988 Adjusted H 1788 2836 027 034df 1 1 1 1

P value 0 0 06 056Null hypothesis rejected rejected not rejected not rejected

1989-1998 Adjusted H 251 1431 111 044df 1 1 1 1

P value 011 0 029 051Null hypothesis not rejected rejected not rejected not rejected

1999-2008 Adjusted H 1812 1788 042 002df 1 1 1 1

P value 0 0 052 089Null hypothesis rejected rejected not rejected not rejected

2009-2018 Adjusted H 1314 1783 074 37df 1 1 1 1

P value 0 0 039 005Null hypothesis rejected rejected not rejected not rejected

36

H5 Regression analysis with dummy variables

Table H5 Regression analysis with dummy variables

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 a0 00000 (097) 00000 (004) 00000 (097) 00000 (097)a1 00138 (000) -00172 (000) 00004 (082) -00014 (047)

Anomaly confirmed confirmed not confirmed not confirmed1939-1948 a0 00003 (015) 00003 (015) 00003 (015) 00003 (015)

a1 00007 (045) -00045 (000) 00170 (000) -00199 (000)Anomaly not confirmed confirmed confirmed confirmed

1949-1958 a0 00006 (000) 00006 (000) 00006 (000) 00006 (000)a1 00160 (000) -00188 (000) 00016 (000) -00004 (043)

Anomaly confirmed confirmed confirmed not confirmed1959-1968 a0 00002 (007) 00002 (004) 00002 (008) 00002 (008)

a1 00103 (000) -00105 (000) 00014 (001) -00002 (074)Anomaly confirmed confirmed confirmed not confirmed

1969-1978 a0 00000 (078) 00000 (078) 00000 (078) 00000 (078)a1 00132 (000) -00132 (000) 00019 (002) -00030 (000)

Anomaly confirmed confirmed confirmed confirmed1979-1988 a0 00006 (001) 00006 (001) 00006 (001) 00006 (000)

a1 00053 (000) -00048 (000) 00009 (040) -00003 (075)Anomaly confirmed confirmed not confirmed not confirmed

1989-1998 a0 00007 (000) 00007 (000) 00007 (000) 00007 (000)a1 00016 (005) -00030 (000) -00009 (026) 00003 (072)

Anomaly confirmed confirmed not confirmed not confirmed1999-2008 a0 00001 (075) 00001 (075) 00001 (075) 00001 (076)

a1 00083 (000) -00091 (000) -00024 (005) -00006 (062)Anomaly confirmed confirmed not confirmed not confirmed

2009-2018 a0 00004 (003) 00004 (000) 00004 (003) 00004 (003)a1 00051 (000) -00059 (000) -00003 (075) -00019 (003)

Anomaly confirmed confirmed not confirmed confirmed

37

H6 Modified CAR approach

Table H6 Modified CAR approach

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 Multiple R 096 095 046 046F-test 175935 (000) 96500 (000) 3534 (000) 2880 (000)a0 -01070 (000) 01958 (000) 00405 (000) 00535 (000)a1 00121 (000) -00160 (000) 00006 (000) -00014 (000)

Anomaly confirmed confirmed confirmed confirmed1939-1948 Multiple R 08 099 099 099

F-test 18777 (000) 755727 (000) 3572830 (000) 2696099 (000)a0 00019 (073) -00346 (000) -00373 (000) 00912 (000)a1 00012 (000) -00044 (000) 00168 (000) -00197 (000)

Anomaly confirmed confirmed confirmed confirmed1949-1958 Multiple R 099 099 094 015

F-test 1021705 (000) 7171257 (000) 75858 (000) 242 (012)a0 -00176 (000) -00191 (000) 00095 (000) -00498 (000)a1 00154 (000) -00181 (000) 00013 (000) -00002 (012)

Anomaly confirmed confirmed confirmed not confirmed1959-1968 Multiple R 099 099 094 078

F-test 1463311 (000) 6002659 (000) 82273 (000) 14352 (000)a0 -00112 (000) 00004 (085) 00151 (000) 00389 (000)a1 00098 (000) -00102 (000) 00011 (000) -00009 (000)

Anomaly confirmed confirmed confirmed confirmed1969-1978 Multiple R 098 099 093 099

F-test 241655 (000) 1451901 (000) 57333 (000) 368160 (000)a0 -00433 (000) 00276 (000) 00099 (002) -00144 (000)a1 00132 (000) -00134 (000) 00020 (000) -00030 (000)

Anomaly confirmed confirmed confirmed confirmed1979-1988 Multiple R 092 078 023 008

F-test 53757 (000) 18707 (000) 487 (003) 085 (036)a0 00813 (000) -02508 (000) 00204 (000) -00235 (000)a1 00036 (000) -00031 (000) -00003 (003) -00001 (036)

Anomaly confirmed confirmed not confirmed not confirmed1989-1998 Multiple R 079 099 074 044

F-test 19705(000) 761967 (000) 14133 (000) 2369 (000)a0 00268 (000) 00023 (021) -00381 (000) 00087 (000)a1 00013 (000) -00028 (000) -00008 (000) 00002 (000)

Anomaly confirmed confirmed not confirmed not confirmed1999-2008 Multiple R 091 093 071 065

F-test 47218 (000) 76564 (000) 9843 (000) 7768 (000)a0 -01493 (000) 01351 (000) 00397 (000) 00007 (093)a1 00081 (000) -00083 (000) -00026 (000) -00011 (000)

Anomaly confirmed confirmed not confirmed confirmed2009-2018 Multiple R 086 087 083 074

F-test 29971 (000) 32484 (000) 23228 (000) 12764 (000)a0 01711 (000) -02250 (000) 00407 (000) -00472 (000)a1 00038 (000) -00044 (000) -00010 (000) -00012 (000)

Anomaly confirmed confirmed not confirmed confirmed

38

C5 Regression analysis with dummy variables

Table C5 Regression analysis with dummy variables

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

a0 00004 (000) 00004 (000) 00004 (000) 00004 (000) 00004 (000)a1 -00001 (-019) 00002 (067) -00004 (047) 00001 (086) -00007 (024)Anomaly not confirmed not confirmed not confirmed not confirmed not confirmed

C6 Modified CAR approach

Table C6 Modified CAR approach

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Multiple R 049 05 025 0 092F-test 23347 (000) 12913 (000) 2207 (000) 000 (098) 1822 (000)a0 -00041 (060) 00128 (006) -00267 (000) 00354 (000) 00319 (000)a1 -00003 (000) -00003 (000) -00002 (000) 00000 (098) -00008 (000)Anomaly confirmed confirmed confirmed not confirmed confirmed

24

D Detailed statistical results SampP 500 overall data

D1 Average analysis

Table D1 Average analysis

Parameter Gap day Gap day(Positive gaps)

Gap day(Negative gaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Mean return (gap day) 006 115 -129 017 -011Mean return (non-gap day) 002 002 002 002 002Anomaly confirmed confirmed confirmed confirmed confirmed

D2 Parametric tests Students t-test

Table D2 T-test

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

t-criterion 092 4546 3579 485 271t-critical (=095) 196 196 196 196 196Null hypothesis not rejected rejected rejected rejected rejected

D3 Parametric tests ANOVA

Table D3 ANOVA

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

F 155 116211 126952 1866 136p-value 022 0 0 0 0F critical 384 384 384 384 384Null hypothesis not rejected rejected rejected not rejected not rejected

D4 Non-parametric tests Kruskal-Wallis test

Table D4 Kruskal-Wallis test

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Adjusted H 1352 70516 47237 3946 004df 1 1 1 1 1P value 0 0 0 0 084Critical value 384 384 384 384 384Null hypothesis rejected rejected rejected rejected not rejected

25

D5 Regression analysis with dummy variables

Table D5 Regression analysis with dummy variables

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

a0 00002 (000) 00002 (000) 00002 (000) 00002 (000) 00002 (000)a1 00003 (021) 00113 (000) -00132 (000) 00014 (000) -00014 (000)Anomaly not confirmed confirmed confirmed confirmed confirmed

D6 Modified CAR approach

Table D6 Modified CAR approach

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Multiple R 051 099 099 099 096F-test 69486 (000) 325351 (000) 1457582 (000) 6345973 (000) 1213344 (000)a0 -01003(000) 04081 (000) -05444 (000) -01088 (000) 00272 (000)a1 00002 (000) 00106 (000) -00127 (000) 00016 (000) -00016 (000)Anomaly confirmed confirmed confirmed confirmed confirmed

26

E Detailed statistical results NASDAQ overall data

E1 Average analysis

Table E1 Average analysis

Parameter Gap day Gap day(Positive gaps)

Gap day(Negative gaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Mean return (gap day) -009 084 -090 022 -037Mean return (non-gap day) 003 003 003 003 003Anomaly confirmed confirmed confirmed confirmed confirmed

E2 Parametric tests Students t-test

Table E2 T-test

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

t-criterion 230 1257 1341 306 664t-critical (=095) 196 196 196 196 196Null hypothesis rejected rejected rejected rejected rejected

E3 Parametric tests ANOVA

Table E3 ANOVA

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

F 2289 62720 88402 3330 17356p-value 0 0 0 0 0F critical 384 384 384 384 384Null hypothesis rejected rejected rejected rejected rejected

E4 Non-parametric tests Kruskal-Wallis test

Table E4 Kruskal-Wallis test

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Adjusted H 1892 36022 45248 4695 10437df 1 1 1 1 1P value 0 0 0 0 0Critical value 384 384 384 384 384Null hypothesis rejected rejected rejected rejected rejected

27

E5 Regression analysis with dummy variables

Table E5 Regression analysis with dummy variables

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

a0 00003 (000) 00003 (000) 00003 (000) 00003 (000) 00003 (000)a1 -00012 (000) 00081 (000) -00093 (000) 00018 (000) -00040 (000)Anomaly confirmed confirmed confirmed confirmed confirmed

E6 Modified CAR approach

Table E6 Modified CAR approach

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Multiple R 069 092 092 072 097F-test 133255 (000) 361102 (000) 442376 (000) 72903 (000) 1082812 (000)a0 -10646 (000) 11373 (000) -12888 (000) 03928 (000) -02297 (000)a1 -00011 (000) 00073 (000) -00097 (000) 00017 (000) -00039 (000)Anomaly confirmed confirmed confirmed confirmed confirmed

28

F Detailed statistical results DJI sub-periods

F1 Average analysis

Table F1 Average analysis

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 Mean return (gapday)

-001 023 015 -004

Mean return(non-gap day)

007 007 007 007

Anomaly confirmed confirmed confirmed confirmed1999-2008 Mean return (gap

day)090 -045 013 -004

Mean return(non-gap day)

-004 -004 -004 -004

Anomaly confirmed confirmed confirmed confirmed2009-2018 Mean return (gap

day)024 -024 0 -004

Mean return(non-gap day)

004 004 004 004

Anomaly confirmed confirmed not confirmed confirmed

F2 Parametric tests Students t-test

Table F2 T-test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 t-criterion 083 165 087 139t-critical (=095) 196 196 196 196Null hypothesis not rejected not rejected not rejected not rejected

1999-2008 t-criterion 347 351 054 047t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected rejected

2009-2018 t-criterion 265 207 051 058t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

F3 Parametric tests ANOVA

Table F3 ANOVA

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 F 085 409 093 179p-value 035 004 033 018

F critical 384 384 384 384Null hypothesis not rejected rejected not rejected not rejected

1999-2008 F 5405 3196 065 072p-value 0 0 042 039

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

2009-2018 F 554 697 024 058p-value 001 0 062 044

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

29

F4 Non-parametric tests Kruskal-Wallis test

Table F4 Kruskal-Wallis test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 Adjusted H 113 211 113 332df 1 1 1 1

P value 029 015 029 007Null hypothesis not rejected not rejected not rejected not rejected

1999-2008 Adjusted H 1484 1414 003 139df 1 1 1 1

P value 0 0 086 024Null hypothesis rejected rejected not rejected not rejected

2009-2018 Adjusted H 506 68 051 171df 1 1 1 1

P value 002 001 047 019Null hypothesis rejected rejected not rejected not rejected

F5 Regression analysis with dummy variables

Table F5 Regression analysis with dummy variables

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 a0 000068 (000) 00007 (000) 00007 (000) 00007 (000)a1 -000078 (035) 00016 (004) 00008 (033) -00011 (018)

Anomaly not confirmed confirmed not confirmed not confirmed1999-2008 a0 00004 (008) 00004 (008) 00004 (006) 00004 (008)

a1 00087 (000) -00049 (000) 00009 (042) -00008 (039)Anomaly confirmed confirmed not confirmed not confirmed

2009-2018 a0 00004 (006) 00004 (006) 00004 (006) 00004 (006)a1 00021 (001) -00028 (001) -00004 (062) -00008 (047)

Anomaly confirmed confirmed not confirmed not confirmed

F6 Modified CAR approach

Table F6 Modified CAR approach

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 Multiple R 083 088 082 086F-test 22779 (000) 40583 (000) 20401 (000) 3269454 (000)a0 00042 (023) 00017 (073) 00014 (058) -00266 (000)a1 -00009 (000) 00015 (000) 00006 (000) -00009 (000)

Anomaly confirmed confirmed confirmed confirmed1999-2008 Multiple R 095 093 076 019

F-test 62658 (000) 84712 (000) 10056 (000) 492 (003)a0 -00972 (000) 00365 (000) -00198 (000) -00115 (021)a1 00086 (000) -00042 (000) 00014 (000) 00002 (003)

Anomaly confirmed confirmed confirmed not confirmed2009-2018 Multiple R 096 082 08 05

F-test 150452 (000) 16731 (000) 22287 (000) 2620 (000)a0 00548 (000) -00618 (000) 00031 (020) -00112 (000)a1 00013 (000) -00014 (000) -00005 (000) -00004 (000)

Anomaly confirmed confirmed not confirmed confirmed

30

G Detailed statistical results NASDAQ sub-periods

G1 Average analysis

Table G1 Average analysis

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 Mean return (gapday)

094 -111 0189 -029

Mean return(non-gap day)

007 007 007 007

Anomaly confirmed confirmed confirmed confirmed1959-1968 Mean return (gap

day)133 -147 033 -039

Mean return(non-gap day)

006 006 006 006

Anomaly confirmed confirmed confirmed confirmed1969-1978 Mean return (gap

day)19 -186 057 -068

Mean return(non-gap day)

005 005 005 005

Anomaly confirmed confirmed confirmed confirmed1979-1988 Mean return (gap

day)138 -162 066 -04

Mean return(non-gap day)

008 008 008 008

Anomaly confirmed confirmed confirmed confirmed1989-1998 Mean return (gap

day)016 012 018 -009

Mean return(non-gap day)

002 002 002 002

Anomaly confirmed not confirmed confirmed confirmed1999-2008 Mean return (gap

day)38E-3 027 -036 -013

Mean return(non-gap day)

-01 -01 -01 -01

Anomaly confirmed not confirmed not confirmed not confirmed2009-2018 Mean return (gap

day)039 009 013 -025

Mean return(non-gap day)

001 001 001 001

Anomaly confirmed not confirmed confirmed confirmed

G2 Parametric tests Students t-test

Table G2 T-test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 t-criterion 3194 3076 201 559t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected rejected

1959-1968 t-criterion 1399 2246 443 382t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected rejected

1969-1978 t-criterion 261 4358 417 786t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected rejected

1979-1988 t-criterion 1847 1445 709 395t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected rejected

1989-1998 t-criterion 13 066 126 093t-critical (=095) 196 196 196 196Null hypothesis not rejected not rejected not rejected not rejected

1999-2008 t-criterion 192 106 111 009t-critical (=095) 196 196 196 196Null hypothesis not rejected not rejected not rejected not rejected

2009-2018 t-criterion 27 05 089 188t-critical (=095) 196 196 196 196Null hypothesis rejected not rejected not rejected not rejected

31

G3 Parametric tests ANOVA

Table G3 ANOVA

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 F 88153 190609 1272 14521p-value 0 0 0 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1959-1968 F 93974 149771 4715 10418p-value 0 0 0 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1969-1978 F 84546 145429 6295 18241p-value 0 0 0 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1979-1988 F 66952 110482 13138 8626p-value 0 0 0 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1989-1998 F 323 138 43 168p-value 007 024 003 019

F critical 384 384 384 384Null hypothesis not rejected not rejected rejected not rejected

1999-2008 F 106 512 327 003p-value 001 002 007 085

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

2009-2018 F 169 069 175 93p-value 0 04 018 0

F critical 384 384 384 384Null hypothesis rejected not rejected not rejected rejected

G4 Non-parametric tests Kruskal-Wallis test

Table G4 Kruskal-Wallis test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 Adjusted H 26254 32592 1464 3962df 1 1 1 1

P value 0 0 0 0Null hypothesis rejected rejected rejected rejected

1959-1968 Adjusted H 28235 27989 2736 332df 1 1 1 1

P value 0 0 0 0Null hypothesis rejected rejected rejected rejected

1969-1978 Adjusted H 22202 33777 3311 7591df 1 1 1 1

P value 0 0 0 0Null hypothesis rejected rejected rejected rejected

1979-1988 Adjusted H 23282 25292 4812 3964df 1 1 1 1

P value 0 0 0 0Null hypothesis rejected rejected rejected rejected

1989-1998 Adjusted H 381 017 175 132df 1 1 1 1

P value 005 068 019 025Null hypothesis not rejected not rejected not rejected not rejected

1999-2008 Adjusted H 855 023 044 004df 1 1 1 1

P value 0 063 051 084Null hypothesis rejected not rejected not rejected not rejected

2009-2018 Adjusted H 1063 009 257 709df 1 1 1 1

P value 0 077 011 001Null hypothesis rejected not rejected not rejected rejected

32

G5 Regression analysis with dummy variables

Table G5 Regression analysis with dummy variables

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 a0 00007 (000) 00007 (000) 00007 (000) 00007 (000)a1 00088 (000) -00119 (000) 00011 (000) -00036 (000)

Anomaly confirmed confirmed confirmed confirmed1959-1968 a0 00006 (000) 00006 (000) 00006 (000) 00006 (000)

a1 00128 (000) -00153 (000) 00027 (000) -00046 (000)Anomaly confirmed confirmed confirmed confirmed

1969-1978 a0 00005 (000) 00005 (000) 00005 (000) 00005 (000)a1 00185 (000) -00192 (000) 00053 (000) -00073 (000)

Anomaly confirmed confirmed confirmed confirmed1979-1988 a0 00008 (000) 00008 (000) 00008 (000) 00008 (000)

a1 00131 (000) -00172 (000) 00059 (000) -00048 (000)Anomaly confirmed confirmed confirmed confirmed

1989-1998 a0 00002 (027) 00002 (028) 00002 (028) 00002 (027)a1 00014 (007) 00010 (024) 00017 (004) -00011 (019)

Anomaly not confirmed not confirmed confirmed not confirmed1999-2008 a0 00001 (059) 00001 (062) 00001 (059) 00001 (060)

a1 00037 (000) 00026 (002) -00038 (000) -00014 (019)Anomaly confirmed not confirmed not confirmed not confirmed

2009-2018 a0 00001 (049) 00001 (049) 00001 (049) 00001 (049)a1 00038 (000) 00007 (040) 00012 (018) -00027 (000)

Anomaly confirmed not confirmed not confirmed confirmed

G6 Modified CAR approach

Table G6 Modified CAR approach

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 Multiple R 099 099 093 098F-test 5753605 (000) 100470(000) 6280421 283281a0 -00091 (000) -00349 (000) 00056 (001) 00015 (073)a1 00083 (000) -00110 (000) 00010 (000) -00031 (000)

Anomaly confirmed confirmed confirmed confirmed1959-1968 Multiple R 099 099 099 099

F-test 3923274 (000) 3005562 (000) 443198 (000) 372583 (000)a0 00096 (000) 00073 (016) -00082 (000) -00095 (004)a1 00116 (001) -00149 (000) 00025 (000) -00047 (000)

Anomaly confirmed confirmed confirmed confirmed1969-1978 Multiple R 099 099 098 099

F-test 4302608 (000) 2723953 (000) 179969 (000) 639745a0 00246 (000) -00002 (000) 00217 (000) -00514 (000)a1 00176 (000) -00182 (000) 00049 (000) -00062 (000)

Anomaly confirmed confirmed confirmed confirmed1979-1988 Multiple R 099 099 099 099

F-test 5872335 (000) 1182609 (000) 1083558 (000) 910089 (000)a0 00136 (000) -01081 (000) -00285 (000) -00101 (000)a1 00131 (000) -00167 (000) 00062 (000) -00048 (000)

Anomaly confirmed confirmed confirmed confirmed1989-1998 Multiple R 09 056 069 016

F-test 46947 (000) 4885 (000) 10131 (000) 263 (011)a0 00102 (002) -00261 (000) -0016 (001) -00237 (000)a1 00015 (000) 00010 (000) 0001 (000) 00002 (011)

Anomaly confirmed confirmed confirmed not confirmed1999-2008 Multiple R 093 087 073 037

F-test 71863 (000) 32530 (000) 13273 (000) 1669 (000)a0 00185 (004) 00311 (000) -00130 (039) -00546 (000)a1 00037 (000) 00032 (000) -00026 (000) -00007 (000)

Anomaly confirmed not confirmed not confirmed confirmed2009-2018 Multiple R 089 001 096 091

F-test 40818 (000) 000 (094) 116744 (000) 53770 (000)a0 01436 (000) -01099 (000) -01036 (000) 00697 (000)a1 00030 (000) 00000 (094) 00024 (000) -00021 (000)

Anomaly confirmed not confirmed confirmed confirmed

33

H Detailed statistical results SampP 500 sub-periods

H1 Average analysis

Table H1 Average analysis

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 Mean return (gapday)

138 -171 004 -014

Mean return(non-gap day)

0 0 0 0

Anomaly confirmed confirmed confirmed confirmed1939-1948 Mean return (gap

day)001 -042 172 -195

Mean return(non-gap day)

003 003 003 003

Anomaly confirmed confirmed confirmed confirmed1949-1958 Mean return (gap

day)165 -18 02 002

Mean return(non-gap day)

006 006 006 006

Anomaly confirmed confirmed confirmed not confirmed1959-1968 Mean return (gap

day)104 -102 015 0

Mean return(non-gap day)

002 002 002 002

Anomaly confirmed confirmed confirmed not confirmed1969-1978 Mean return (gap

day)131 -13 019 -03

Mean return(non-gap day)

0 0 0 0

Anomaly confirmed confirmed confirmed confirmed1979-1988 Mean return (gap

day)058 -042 015 003

Mean return(non-gap day)

005 005 005 005

Anomaly confirmed confirmed confirmed not confirmed1989-1998 Mean return (gap

day)02 -023 -002 01

Mean return(non-gap day)

007 007 007 007

Anomaly confirmed confirmed not confirmed not confirmed1999-2008 Mean return (gap

day)083 -089 -023 -005

Mean return(non-gap day)

001 001 001 001

Anomaly confirmed confirmed not confirmed confirmed2009-2018 Mean return (gap

day)055 -052 001 -015

Mean return(non-gap day)

004 004 004 004

Anomaly confirmed confirmed not confirmed confirmed

34

H2 Parametric tests Students t-test

Table H2 T-test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 t-criterion 101 85 029 048t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

1939-1948 t-criterion 064 479 3074 225t-critical (=095) 196 196 196 196Null hypothesis not rejected rejected rejected rejected

1949-1958 t-criterion 2964 2383 193 041t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

1959-1968 t-criterion 2281 2157 21 023t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected not rejected

1969-1978 t-criterion 1318 2034 187 321t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected rejected

1979-1988 t-criterion 435 535 07 037t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

1989-1998 t-criterion 201 396 132 052t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

1999-2008 t-criterion 362 433 117 022t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

2009-2018 t-criterion 375 382 027 132t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

H3 Parametric tests ANOVA

Table H3 ANOVA

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 F 6281 8032 005 051p-value 0 0 082 047

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

1939-1948 F 056 2603 34854 51034p-value 045 0 0 0

F critical 384 384 384 384Null hypothesis not rejected rejected rejected rejected

1949-1958 F 100174 128997 897 062p-value 0 0 0 043

F critical 384 384 384 384Null hypothesis rejected rejected rejected not rejected

1959-1968 F 36831 32858 617 01p-value 0 0 001 074

F critical 384 384 384 384Null hypothesis rejected rejected rejected not rejected

1969-1978 F 26601 3063 53 152p-value 0 0 002 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1979-1988 F 23 245 076 009p-value 0 0 039 077

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

1989-1998 F 399 1156 118 015p-value 004 0 027 069

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

1999-2008 F 4253 5622 365 024p-value 0 0 006 062

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

2009-2018 F 3064 3656 01 43p-value 0 0 075 004

F critical 384 384 384 384Null hypothesis rejected rejected not rejected rejected

35

H4 Non-parametric tests Kruskal -Wallis test

Table H4 Kruskal-Wallis test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 Adjusted H 9982 5913 332 14df 1 1 1 1

P value 0 0 007 024Null hypothesis rejected rejected not rejected not rejected

1939-1948 Adjusted H 494 1999 23387 24927df 1 1 1 1

P value 003 0 0 0Null hypothesis rejected rejected rejected rejected

1949-1958 Adjusted H 28728 28175 348 15df 1 1 1 1

P value 0 0 006 022Null hypothesis rejected rejected not rejected not rejected

1959-1968 Adjusted H 25729 21437 701 063df 1 1 1 1

P value 0 0 001 043Null hypothesis rejected rejected rejected not rejected

1969-1978 Adjusted H 14407 20078 27 1706df 1 1 1 1

P value 0 0 01 0Null hypothesis rejected rejected not rejected rejected

1979-1988 Adjusted H 1788 2836 027 034df 1 1 1 1

P value 0 0 06 056Null hypothesis rejected rejected not rejected not rejected

1989-1998 Adjusted H 251 1431 111 044df 1 1 1 1

P value 011 0 029 051Null hypothesis not rejected rejected not rejected not rejected

1999-2008 Adjusted H 1812 1788 042 002df 1 1 1 1

P value 0 0 052 089Null hypothesis rejected rejected not rejected not rejected

2009-2018 Adjusted H 1314 1783 074 37df 1 1 1 1

P value 0 0 039 005Null hypothesis rejected rejected not rejected not rejected

36

H5 Regression analysis with dummy variables

Table H5 Regression analysis with dummy variables

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 a0 00000 (097) 00000 (004) 00000 (097) 00000 (097)a1 00138 (000) -00172 (000) 00004 (082) -00014 (047)

Anomaly confirmed confirmed not confirmed not confirmed1939-1948 a0 00003 (015) 00003 (015) 00003 (015) 00003 (015)

a1 00007 (045) -00045 (000) 00170 (000) -00199 (000)Anomaly not confirmed confirmed confirmed confirmed

1949-1958 a0 00006 (000) 00006 (000) 00006 (000) 00006 (000)a1 00160 (000) -00188 (000) 00016 (000) -00004 (043)

Anomaly confirmed confirmed confirmed not confirmed1959-1968 a0 00002 (007) 00002 (004) 00002 (008) 00002 (008)

a1 00103 (000) -00105 (000) 00014 (001) -00002 (074)Anomaly confirmed confirmed confirmed not confirmed

1969-1978 a0 00000 (078) 00000 (078) 00000 (078) 00000 (078)a1 00132 (000) -00132 (000) 00019 (002) -00030 (000)

Anomaly confirmed confirmed confirmed confirmed1979-1988 a0 00006 (001) 00006 (001) 00006 (001) 00006 (000)

a1 00053 (000) -00048 (000) 00009 (040) -00003 (075)Anomaly confirmed confirmed not confirmed not confirmed

1989-1998 a0 00007 (000) 00007 (000) 00007 (000) 00007 (000)a1 00016 (005) -00030 (000) -00009 (026) 00003 (072)

Anomaly confirmed confirmed not confirmed not confirmed1999-2008 a0 00001 (075) 00001 (075) 00001 (075) 00001 (076)

a1 00083 (000) -00091 (000) -00024 (005) -00006 (062)Anomaly confirmed confirmed not confirmed not confirmed

2009-2018 a0 00004 (003) 00004 (000) 00004 (003) 00004 (003)a1 00051 (000) -00059 (000) -00003 (075) -00019 (003)

Anomaly confirmed confirmed not confirmed confirmed

37

H6 Modified CAR approach

Table H6 Modified CAR approach

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 Multiple R 096 095 046 046F-test 175935 (000) 96500 (000) 3534 (000) 2880 (000)a0 -01070 (000) 01958 (000) 00405 (000) 00535 (000)a1 00121 (000) -00160 (000) 00006 (000) -00014 (000)

Anomaly confirmed confirmed confirmed confirmed1939-1948 Multiple R 08 099 099 099

F-test 18777 (000) 755727 (000) 3572830 (000) 2696099 (000)a0 00019 (073) -00346 (000) -00373 (000) 00912 (000)a1 00012 (000) -00044 (000) 00168 (000) -00197 (000)

Anomaly confirmed confirmed confirmed confirmed1949-1958 Multiple R 099 099 094 015

F-test 1021705 (000) 7171257 (000) 75858 (000) 242 (012)a0 -00176 (000) -00191 (000) 00095 (000) -00498 (000)a1 00154 (000) -00181 (000) 00013 (000) -00002 (012)

Anomaly confirmed confirmed confirmed not confirmed1959-1968 Multiple R 099 099 094 078

F-test 1463311 (000) 6002659 (000) 82273 (000) 14352 (000)a0 -00112 (000) 00004 (085) 00151 (000) 00389 (000)a1 00098 (000) -00102 (000) 00011 (000) -00009 (000)

Anomaly confirmed confirmed confirmed confirmed1969-1978 Multiple R 098 099 093 099

F-test 241655 (000) 1451901 (000) 57333 (000) 368160 (000)a0 -00433 (000) 00276 (000) 00099 (002) -00144 (000)a1 00132 (000) -00134 (000) 00020 (000) -00030 (000)

Anomaly confirmed confirmed confirmed confirmed1979-1988 Multiple R 092 078 023 008

F-test 53757 (000) 18707 (000) 487 (003) 085 (036)a0 00813 (000) -02508 (000) 00204 (000) -00235 (000)a1 00036 (000) -00031 (000) -00003 (003) -00001 (036)

Anomaly confirmed confirmed not confirmed not confirmed1989-1998 Multiple R 079 099 074 044

F-test 19705(000) 761967 (000) 14133 (000) 2369 (000)a0 00268 (000) 00023 (021) -00381 (000) 00087 (000)a1 00013 (000) -00028 (000) -00008 (000) 00002 (000)

Anomaly confirmed confirmed not confirmed not confirmed1999-2008 Multiple R 091 093 071 065

F-test 47218 (000) 76564 (000) 9843 (000) 7768 (000)a0 -01493 (000) 01351 (000) 00397 (000) 00007 (093)a1 00081 (000) -00083 (000) -00026 (000) -00011 (000)

Anomaly confirmed confirmed not confirmed confirmed2009-2018 Multiple R 086 087 083 074

F-test 29971 (000) 32484 (000) 23228 (000) 12764 (000)a0 01711 (000) -02250 (000) 00407 (000) -00472 (000)a1 00038 (000) -00044 (000) -00010 (000) -00012 (000)

Anomaly confirmed confirmed not confirmed confirmed

38

D Detailed statistical results SampP 500 overall data

D1 Average analysis

Table D1 Average analysis

Parameter Gap day Gap day(Positive gaps)

Gap day(Negative gaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Mean return (gap day) 006 115 -129 017 -011Mean return (non-gap day) 002 002 002 002 002Anomaly confirmed confirmed confirmed confirmed confirmed

D2 Parametric tests Students t-test

Table D2 T-test

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

t-criterion 092 4546 3579 485 271t-critical (=095) 196 196 196 196 196Null hypothesis not rejected rejected rejected rejected rejected

D3 Parametric tests ANOVA

Table D3 ANOVA

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

F 155 116211 126952 1866 136p-value 022 0 0 0 0F critical 384 384 384 384 384Null hypothesis not rejected rejected rejected not rejected not rejected

D4 Non-parametric tests Kruskal-Wallis test

Table D4 Kruskal-Wallis test

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Adjusted H 1352 70516 47237 3946 004df 1 1 1 1 1P value 0 0 0 0 084Critical value 384 384 384 384 384Null hypothesis rejected rejected rejected rejected not rejected

25

D5 Regression analysis with dummy variables

Table D5 Regression analysis with dummy variables

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

a0 00002 (000) 00002 (000) 00002 (000) 00002 (000) 00002 (000)a1 00003 (021) 00113 (000) -00132 (000) 00014 (000) -00014 (000)Anomaly not confirmed confirmed confirmed confirmed confirmed

D6 Modified CAR approach

Table D6 Modified CAR approach

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Multiple R 051 099 099 099 096F-test 69486 (000) 325351 (000) 1457582 (000) 6345973 (000) 1213344 (000)a0 -01003(000) 04081 (000) -05444 (000) -01088 (000) 00272 (000)a1 00002 (000) 00106 (000) -00127 (000) 00016 (000) -00016 (000)Anomaly confirmed confirmed confirmed confirmed confirmed

26

E Detailed statistical results NASDAQ overall data

E1 Average analysis

Table E1 Average analysis

Parameter Gap day Gap day(Positive gaps)

Gap day(Negative gaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Mean return (gap day) -009 084 -090 022 -037Mean return (non-gap day) 003 003 003 003 003Anomaly confirmed confirmed confirmed confirmed confirmed

E2 Parametric tests Students t-test

Table E2 T-test

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

t-criterion 230 1257 1341 306 664t-critical (=095) 196 196 196 196 196Null hypothesis rejected rejected rejected rejected rejected

E3 Parametric tests ANOVA

Table E3 ANOVA

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

F 2289 62720 88402 3330 17356p-value 0 0 0 0 0F critical 384 384 384 384 384Null hypothesis rejected rejected rejected rejected rejected

E4 Non-parametric tests Kruskal-Wallis test

Table E4 Kruskal-Wallis test

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Adjusted H 1892 36022 45248 4695 10437df 1 1 1 1 1P value 0 0 0 0 0Critical value 384 384 384 384 384Null hypothesis rejected rejected rejected rejected rejected

27

E5 Regression analysis with dummy variables

Table E5 Regression analysis with dummy variables

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

a0 00003 (000) 00003 (000) 00003 (000) 00003 (000) 00003 (000)a1 -00012 (000) 00081 (000) -00093 (000) 00018 (000) -00040 (000)Anomaly confirmed confirmed confirmed confirmed confirmed

E6 Modified CAR approach

Table E6 Modified CAR approach

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Multiple R 069 092 092 072 097F-test 133255 (000) 361102 (000) 442376 (000) 72903 (000) 1082812 (000)a0 -10646 (000) 11373 (000) -12888 (000) 03928 (000) -02297 (000)a1 -00011 (000) 00073 (000) -00097 (000) 00017 (000) -00039 (000)Anomaly confirmed confirmed confirmed confirmed confirmed

28

F Detailed statistical results DJI sub-periods

F1 Average analysis

Table F1 Average analysis

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 Mean return (gapday)

-001 023 015 -004

Mean return(non-gap day)

007 007 007 007

Anomaly confirmed confirmed confirmed confirmed1999-2008 Mean return (gap

day)090 -045 013 -004

Mean return(non-gap day)

-004 -004 -004 -004

Anomaly confirmed confirmed confirmed confirmed2009-2018 Mean return (gap

day)024 -024 0 -004

Mean return(non-gap day)

004 004 004 004

Anomaly confirmed confirmed not confirmed confirmed

F2 Parametric tests Students t-test

Table F2 T-test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 t-criterion 083 165 087 139t-critical (=095) 196 196 196 196Null hypothesis not rejected not rejected not rejected not rejected

1999-2008 t-criterion 347 351 054 047t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected rejected

2009-2018 t-criterion 265 207 051 058t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

F3 Parametric tests ANOVA

Table F3 ANOVA

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 F 085 409 093 179p-value 035 004 033 018

F critical 384 384 384 384Null hypothesis not rejected rejected not rejected not rejected

1999-2008 F 5405 3196 065 072p-value 0 0 042 039

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

2009-2018 F 554 697 024 058p-value 001 0 062 044

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

29

F4 Non-parametric tests Kruskal-Wallis test

Table F4 Kruskal-Wallis test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 Adjusted H 113 211 113 332df 1 1 1 1

P value 029 015 029 007Null hypothesis not rejected not rejected not rejected not rejected

1999-2008 Adjusted H 1484 1414 003 139df 1 1 1 1

P value 0 0 086 024Null hypothesis rejected rejected not rejected not rejected

2009-2018 Adjusted H 506 68 051 171df 1 1 1 1

P value 002 001 047 019Null hypothesis rejected rejected not rejected not rejected

F5 Regression analysis with dummy variables

Table F5 Regression analysis with dummy variables

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 a0 000068 (000) 00007 (000) 00007 (000) 00007 (000)a1 -000078 (035) 00016 (004) 00008 (033) -00011 (018)

Anomaly not confirmed confirmed not confirmed not confirmed1999-2008 a0 00004 (008) 00004 (008) 00004 (006) 00004 (008)

a1 00087 (000) -00049 (000) 00009 (042) -00008 (039)Anomaly confirmed confirmed not confirmed not confirmed

2009-2018 a0 00004 (006) 00004 (006) 00004 (006) 00004 (006)a1 00021 (001) -00028 (001) -00004 (062) -00008 (047)

Anomaly confirmed confirmed not confirmed not confirmed

F6 Modified CAR approach

Table F6 Modified CAR approach

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 Multiple R 083 088 082 086F-test 22779 (000) 40583 (000) 20401 (000) 3269454 (000)a0 00042 (023) 00017 (073) 00014 (058) -00266 (000)a1 -00009 (000) 00015 (000) 00006 (000) -00009 (000)

Anomaly confirmed confirmed confirmed confirmed1999-2008 Multiple R 095 093 076 019

F-test 62658 (000) 84712 (000) 10056 (000) 492 (003)a0 -00972 (000) 00365 (000) -00198 (000) -00115 (021)a1 00086 (000) -00042 (000) 00014 (000) 00002 (003)

Anomaly confirmed confirmed confirmed not confirmed2009-2018 Multiple R 096 082 08 05

F-test 150452 (000) 16731 (000) 22287 (000) 2620 (000)a0 00548 (000) -00618 (000) 00031 (020) -00112 (000)a1 00013 (000) -00014 (000) -00005 (000) -00004 (000)

Anomaly confirmed confirmed not confirmed confirmed

30

G Detailed statistical results NASDAQ sub-periods

G1 Average analysis

Table G1 Average analysis

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 Mean return (gapday)

094 -111 0189 -029

Mean return(non-gap day)

007 007 007 007

Anomaly confirmed confirmed confirmed confirmed1959-1968 Mean return (gap

day)133 -147 033 -039

Mean return(non-gap day)

006 006 006 006

Anomaly confirmed confirmed confirmed confirmed1969-1978 Mean return (gap

day)19 -186 057 -068

Mean return(non-gap day)

005 005 005 005

Anomaly confirmed confirmed confirmed confirmed1979-1988 Mean return (gap

day)138 -162 066 -04

Mean return(non-gap day)

008 008 008 008

Anomaly confirmed confirmed confirmed confirmed1989-1998 Mean return (gap

day)016 012 018 -009

Mean return(non-gap day)

002 002 002 002

Anomaly confirmed not confirmed confirmed confirmed1999-2008 Mean return (gap

day)38E-3 027 -036 -013

Mean return(non-gap day)

-01 -01 -01 -01

Anomaly confirmed not confirmed not confirmed not confirmed2009-2018 Mean return (gap

day)039 009 013 -025

Mean return(non-gap day)

001 001 001 001

Anomaly confirmed not confirmed confirmed confirmed

G2 Parametric tests Students t-test

Table G2 T-test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 t-criterion 3194 3076 201 559t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected rejected

1959-1968 t-criterion 1399 2246 443 382t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected rejected

1969-1978 t-criterion 261 4358 417 786t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected rejected

1979-1988 t-criterion 1847 1445 709 395t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected rejected

1989-1998 t-criterion 13 066 126 093t-critical (=095) 196 196 196 196Null hypothesis not rejected not rejected not rejected not rejected

1999-2008 t-criterion 192 106 111 009t-critical (=095) 196 196 196 196Null hypothesis not rejected not rejected not rejected not rejected

2009-2018 t-criterion 27 05 089 188t-critical (=095) 196 196 196 196Null hypothesis rejected not rejected not rejected not rejected

31

G3 Parametric tests ANOVA

Table G3 ANOVA

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 F 88153 190609 1272 14521p-value 0 0 0 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1959-1968 F 93974 149771 4715 10418p-value 0 0 0 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1969-1978 F 84546 145429 6295 18241p-value 0 0 0 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1979-1988 F 66952 110482 13138 8626p-value 0 0 0 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1989-1998 F 323 138 43 168p-value 007 024 003 019

F critical 384 384 384 384Null hypothesis not rejected not rejected rejected not rejected

1999-2008 F 106 512 327 003p-value 001 002 007 085

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

2009-2018 F 169 069 175 93p-value 0 04 018 0

F critical 384 384 384 384Null hypothesis rejected not rejected not rejected rejected

G4 Non-parametric tests Kruskal-Wallis test

Table G4 Kruskal-Wallis test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 Adjusted H 26254 32592 1464 3962df 1 1 1 1

P value 0 0 0 0Null hypothesis rejected rejected rejected rejected

1959-1968 Adjusted H 28235 27989 2736 332df 1 1 1 1

P value 0 0 0 0Null hypothesis rejected rejected rejected rejected

1969-1978 Adjusted H 22202 33777 3311 7591df 1 1 1 1

P value 0 0 0 0Null hypothesis rejected rejected rejected rejected

1979-1988 Adjusted H 23282 25292 4812 3964df 1 1 1 1

P value 0 0 0 0Null hypothesis rejected rejected rejected rejected

1989-1998 Adjusted H 381 017 175 132df 1 1 1 1

P value 005 068 019 025Null hypothesis not rejected not rejected not rejected not rejected

1999-2008 Adjusted H 855 023 044 004df 1 1 1 1

P value 0 063 051 084Null hypothesis rejected not rejected not rejected not rejected

2009-2018 Adjusted H 1063 009 257 709df 1 1 1 1

P value 0 077 011 001Null hypothesis rejected not rejected not rejected rejected

32

G5 Regression analysis with dummy variables

Table G5 Regression analysis with dummy variables

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 a0 00007 (000) 00007 (000) 00007 (000) 00007 (000)a1 00088 (000) -00119 (000) 00011 (000) -00036 (000)

Anomaly confirmed confirmed confirmed confirmed1959-1968 a0 00006 (000) 00006 (000) 00006 (000) 00006 (000)

a1 00128 (000) -00153 (000) 00027 (000) -00046 (000)Anomaly confirmed confirmed confirmed confirmed

1969-1978 a0 00005 (000) 00005 (000) 00005 (000) 00005 (000)a1 00185 (000) -00192 (000) 00053 (000) -00073 (000)

Anomaly confirmed confirmed confirmed confirmed1979-1988 a0 00008 (000) 00008 (000) 00008 (000) 00008 (000)

a1 00131 (000) -00172 (000) 00059 (000) -00048 (000)Anomaly confirmed confirmed confirmed confirmed

1989-1998 a0 00002 (027) 00002 (028) 00002 (028) 00002 (027)a1 00014 (007) 00010 (024) 00017 (004) -00011 (019)

Anomaly not confirmed not confirmed confirmed not confirmed1999-2008 a0 00001 (059) 00001 (062) 00001 (059) 00001 (060)

a1 00037 (000) 00026 (002) -00038 (000) -00014 (019)Anomaly confirmed not confirmed not confirmed not confirmed

2009-2018 a0 00001 (049) 00001 (049) 00001 (049) 00001 (049)a1 00038 (000) 00007 (040) 00012 (018) -00027 (000)

Anomaly confirmed not confirmed not confirmed confirmed

G6 Modified CAR approach

Table G6 Modified CAR approach

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 Multiple R 099 099 093 098F-test 5753605 (000) 100470(000) 6280421 283281a0 -00091 (000) -00349 (000) 00056 (001) 00015 (073)a1 00083 (000) -00110 (000) 00010 (000) -00031 (000)

Anomaly confirmed confirmed confirmed confirmed1959-1968 Multiple R 099 099 099 099

F-test 3923274 (000) 3005562 (000) 443198 (000) 372583 (000)a0 00096 (000) 00073 (016) -00082 (000) -00095 (004)a1 00116 (001) -00149 (000) 00025 (000) -00047 (000)

Anomaly confirmed confirmed confirmed confirmed1969-1978 Multiple R 099 099 098 099

F-test 4302608 (000) 2723953 (000) 179969 (000) 639745a0 00246 (000) -00002 (000) 00217 (000) -00514 (000)a1 00176 (000) -00182 (000) 00049 (000) -00062 (000)

Anomaly confirmed confirmed confirmed confirmed1979-1988 Multiple R 099 099 099 099

F-test 5872335 (000) 1182609 (000) 1083558 (000) 910089 (000)a0 00136 (000) -01081 (000) -00285 (000) -00101 (000)a1 00131 (000) -00167 (000) 00062 (000) -00048 (000)

Anomaly confirmed confirmed confirmed confirmed1989-1998 Multiple R 09 056 069 016

F-test 46947 (000) 4885 (000) 10131 (000) 263 (011)a0 00102 (002) -00261 (000) -0016 (001) -00237 (000)a1 00015 (000) 00010 (000) 0001 (000) 00002 (011)

Anomaly confirmed confirmed confirmed not confirmed1999-2008 Multiple R 093 087 073 037

F-test 71863 (000) 32530 (000) 13273 (000) 1669 (000)a0 00185 (004) 00311 (000) -00130 (039) -00546 (000)a1 00037 (000) 00032 (000) -00026 (000) -00007 (000)

Anomaly confirmed not confirmed not confirmed confirmed2009-2018 Multiple R 089 001 096 091

F-test 40818 (000) 000 (094) 116744 (000) 53770 (000)a0 01436 (000) -01099 (000) -01036 (000) 00697 (000)a1 00030 (000) 00000 (094) 00024 (000) -00021 (000)

Anomaly confirmed not confirmed confirmed confirmed

33

H Detailed statistical results SampP 500 sub-periods

H1 Average analysis

Table H1 Average analysis

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 Mean return (gapday)

138 -171 004 -014

Mean return(non-gap day)

0 0 0 0

Anomaly confirmed confirmed confirmed confirmed1939-1948 Mean return (gap

day)001 -042 172 -195

Mean return(non-gap day)

003 003 003 003

Anomaly confirmed confirmed confirmed confirmed1949-1958 Mean return (gap

day)165 -18 02 002

Mean return(non-gap day)

006 006 006 006

Anomaly confirmed confirmed confirmed not confirmed1959-1968 Mean return (gap

day)104 -102 015 0

Mean return(non-gap day)

002 002 002 002

Anomaly confirmed confirmed confirmed not confirmed1969-1978 Mean return (gap

day)131 -13 019 -03

Mean return(non-gap day)

0 0 0 0

Anomaly confirmed confirmed confirmed confirmed1979-1988 Mean return (gap

day)058 -042 015 003

Mean return(non-gap day)

005 005 005 005

Anomaly confirmed confirmed confirmed not confirmed1989-1998 Mean return (gap

day)02 -023 -002 01

Mean return(non-gap day)

007 007 007 007

Anomaly confirmed confirmed not confirmed not confirmed1999-2008 Mean return (gap

day)083 -089 -023 -005

Mean return(non-gap day)

001 001 001 001

Anomaly confirmed confirmed not confirmed confirmed2009-2018 Mean return (gap

day)055 -052 001 -015

Mean return(non-gap day)

004 004 004 004

Anomaly confirmed confirmed not confirmed confirmed

34

H2 Parametric tests Students t-test

Table H2 T-test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 t-criterion 101 85 029 048t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

1939-1948 t-criterion 064 479 3074 225t-critical (=095) 196 196 196 196Null hypothesis not rejected rejected rejected rejected

1949-1958 t-criterion 2964 2383 193 041t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

1959-1968 t-criterion 2281 2157 21 023t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected not rejected

1969-1978 t-criterion 1318 2034 187 321t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected rejected

1979-1988 t-criterion 435 535 07 037t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

1989-1998 t-criterion 201 396 132 052t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

1999-2008 t-criterion 362 433 117 022t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

2009-2018 t-criterion 375 382 027 132t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

H3 Parametric tests ANOVA

Table H3 ANOVA

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 F 6281 8032 005 051p-value 0 0 082 047

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

1939-1948 F 056 2603 34854 51034p-value 045 0 0 0

F critical 384 384 384 384Null hypothesis not rejected rejected rejected rejected

1949-1958 F 100174 128997 897 062p-value 0 0 0 043

F critical 384 384 384 384Null hypothesis rejected rejected rejected not rejected

1959-1968 F 36831 32858 617 01p-value 0 0 001 074

F critical 384 384 384 384Null hypothesis rejected rejected rejected not rejected

1969-1978 F 26601 3063 53 152p-value 0 0 002 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1979-1988 F 23 245 076 009p-value 0 0 039 077

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

1989-1998 F 399 1156 118 015p-value 004 0 027 069

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

1999-2008 F 4253 5622 365 024p-value 0 0 006 062

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

2009-2018 F 3064 3656 01 43p-value 0 0 075 004

F critical 384 384 384 384Null hypothesis rejected rejected not rejected rejected

35

H4 Non-parametric tests Kruskal -Wallis test

Table H4 Kruskal-Wallis test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 Adjusted H 9982 5913 332 14df 1 1 1 1

P value 0 0 007 024Null hypothesis rejected rejected not rejected not rejected

1939-1948 Adjusted H 494 1999 23387 24927df 1 1 1 1

P value 003 0 0 0Null hypothesis rejected rejected rejected rejected

1949-1958 Adjusted H 28728 28175 348 15df 1 1 1 1

P value 0 0 006 022Null hypothesis rejected rejected not rejected not rejected

1959-1968 Adjusted H 25729 21437 701 063df 1 1 1 1

P value 0 0 001 043Null hypothesis rejected rejected rejected not rejected

1969-1978 Adjusted H 14407 20078 27 1706df 1 1 1 1

P value 0 0 01 0Null hypothesis rejected rejected not rejected rejected

1979-1988 Adjusted H 1788 2836 027 034df 1 1 1 1

P value 0 0 06 056Null hypothesis rejected rejected not rejected not rejected

1989-1998 Adjusted H 251 1431 111 044df 1 1 1 1

P value 011 0 029 051Null hypothesis not rejected rejected not rejected not rejected

1999-2008 Adjusted H 1812 1788 042 002df 1 1 1 1

P value 0 0 052 089Null hypothesis rejected rejected not rejected not rejected

2009-2018 Adjusted H 1314 1783 074 37df 1 1 1 1

P value 0 0 039 005Null hypothesis rejected rejected not rejected not rejected

36

H5 Regression analysis with dummy variables

Table H5 Regression analysis with dummy variables

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 a0 00000 (097) 00000 (004) 00000 (097) 00000 (097)a1 00138 (000) -00172 (000) 00004 (082) -00014 (047)

Anomaly confirmed confirmed not confirmed not confirmed1939-1948 a0 00003 (015) 00003 (015) 00003 (015) 00003 (015)

a1 00007 (045) -00045 (000) 00170 (000) -00199 (000)Anomaly not confirmed confirmed confirmed confirmed

1949-1958 a0 00006 (000) 00006 (000) 00006 (000) 00006 (000)a1 00160 (000) -00188 (000) 00016 (000) -00004 (043)

Anomaly confirmed confirmed confirmed not confirmed1959-1968 a0 00002 (007) 00002 (004) 00002 (008) 00002 (008)

a1 00103 (000) -00105 (000) 00014 (001) -00002 (074)Anomaly confirmed confirmed confirmed not confirmed

1969-1978 a0 00000 (078) 00000 (078) 00000 (078) 00000 (078)a1 00132 (000) -00132 (000) 00019 (002) -00030 (000)

Anomaly confirmed confirmed confirmed confirmed1979-1988 a0 00006 (001) 00006 (001) 00006 (001) 00006 (000)

a1 00053 (000) -00048 (000) 00009 (040) -00003 (075)Anomaly confirmed confirmed not confirmed not confirmed

1989-1998 a0 00007 (000) 00007 (000) 00007 (000) 00007 (000)a1 00016 (005) -00030 (000) -00009 (026) 00003 (072)

Anomaly confirmed confirmed not confirmed not confirmed1999-2008 a0 00001 (075) 00001 (075) 00001 (075) 00001 (076)

a1 00083 (000) -00091 (000) -00024 (005) -00006 (062)Anomaly confirmed confirmed not confirmed not confirmed

2009-2018 a0 00004 (003) 00004 (000) 00004 (003) 00004 (003)a1 00051 (000) -00059 (000) -00003 (075) -00019 (003)

Anomaly confirmed confirmed not confirmed confirmed

37

H6 Modified CAR approach

Table H6 Modified CAR approach

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 Multiple R 096 095 046 046F-test 175935 (000) 96500 (000) 3534 (000) 2880 (000)a0 -01070 (000) 01958 (000) 00405 (000) 00535 (000)a1 00121 (000) -00160 (000) 00006 (000) -00014 (000)

Anomaly confirmed confirmed confirmed confirmed1939-1948 Multiple R 08 099 099 099

F-test 18777 (000) 755727 (000) 3572830 (000) 2696099 (000)a0 00019 (073) -00346 (000) -00373 (000) 00912 (000)a1 00012 (000) -00044 (000) 00168 (000) -00197 (000)

Anomaly confirmed confirmed confirmed confirmed1949-1958 Multiple R 099 099 094 015

F-test 1021705 (000) 7171257 (000) 75858 (000) 242 (012)a0 -00176 (000) -00191 (000) 00095 (000) -00498 (000)a1 00154 (000) -00181 (000) 00013 (000) -00002 (012)

Anomaly confirmed confirmed confirmed not confirmed1959-1968 Multiple R 099 099 094 078

F-test 1463311 (000) 6002659 (000) 82273 (000) 14352 (000)a0 -00112 (000) 00004 (085) 00151 (000) 00389 (000)a1 00098 (000) -00102 (000) 00011 (000) -00009 (000)

Anomaly confirmed confirmed confirmed confirmed1969-1978 Multiple R 098 099 093 099

F-test 241655 (000) 1451901 (000) 57333 (000) 368160 (000)a0 -00433 (000) 00276 (000) 00099 (002) -00144 (000)a1 00132 (000) -00134 (000) 00020 (000) -00030 (000)

Anomaly confirmed confirmed confirmed confirmed1979-1988 Multiple R 092 078 023 008

F-test 53757 (000) 18707 (000) 487 (003) 085 (036)a0 00813 (000) -02508 (000) 00204 (000) -00235 (000)a1 00036 (000) -00031 (000) -00003 (003) -00001 (036)

Anomaly confirmed confirmed not confirmed not confirmed1989-1998 Multiple R 079 099 074 044

F-test 19705(000) 761967 (000) 14133 (000) 2369 (000)a0 00268 (000) 00023 (021) -00381 (000) 00087 (000)a1 00013 (000) -00028 (000) -00008 (000) 00002 (000)

Anomaly confirmed confirmed not confirmed not confirmed1999-2008 Multiple R 091 093 071 065

F-test 47218 (000) 76564 (000) 9843 (000) 7768 (000)a0 -01493 (000) 01351 (000) 00397 (000) 00007 (093)a1 00081 (000) -00083 (000) -00026 (000) -00011 (000)

Anomaly confirmed confirmed not confirmed confirmed2009-2018 Multiple R 086 087 083 074

F-test 29971 (000) 32484 (000) 23228 (000) 12764 (000)a0 01711 (000) -02250 (000) 00407 (000) -00472 (000)a1 00038 (000) -00044 (000) -00010 (000) -00012 (000)

Anomaly confirmed confirmed not confirmed confirmed

38

D5 Regression analysis with dummy variables

Table D5 Regression analysis with dummy variables

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

a0 00002 (000) 00002 (000) 00002 (000) 00002 (000) 00002 (000)a1 00003 (021) 00113 (000) -00132 (000) 00014 (000) -00014 (000)Anomaly not confirmed confirmed confirmed confirmed confirmed

D6 Modified CAR approach

Table D6 Modified CAR approach

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Multiple R 051 099 099 099 096F-test 69486 (000) 325351 (000) 1457582 (000) 6345973 (000) 1213344 (000)a0 -01003(000) 04081 (000) -05444 (000) -01088 (000) 00272 (000)a1 00002 (000) 00106 (000) -00127 (000) 00016 (000) -00016 (000)Anomaly confirmed confirmed confirmed confirmed confirmed

26

E Detailed statistical results NASDAQ overall data

E1 Average analysis

Table E1 Average analysis

Parameter Gap day Gap day(Positive gaps)

Gap day(Negative gaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Mean return (gap day) -009 084 -090 022 -037Mean return (non-gap day) 003 003 003 003 003Anomaly confirmed confirmed confirmed confirmed confirmed

E2 Parametric tests Students t-test

Table E2 T-test

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

t-criterion 230 1257 1341 306 664t-critical (=095) 196 196 196 196 196Null hypothesis rejected rejected rejected rejected rejected

E3 Parametric tests ANOVA

Table E3 ANOVA

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

F 2289 62720 88402 3330 17356p-value 0 0 0 0 0F critical 384 384 384 384 384Null hypothesis rejected rejected rejected rejected rejected

E4 Non-parametric tests Kruskal-Wallis test

Table E4 Kruskal-Wallis test

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Adjusted H 1892 36022 45248 4695 10437df 1 1 1 1 1P value 0 0 0 0 0Critical value 384 384 384 384 384Null hypothesis rejected rejected rejected rejected rejected

27

E5 Regression analysis with dummy variables

Table E5 Regression analysis with dummy variables

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

a0 00003 (000) 00003 (000) 00003 (000) 00003 (000) 00003 (000)a1 -00012 (000) 00081 (000) -00093 (000) 00018 (000) -00040 (000)Anomaly confirmed confirmed confirmed confirmed confirmed

E6 Modified CAR approach

Table E6 Modified CAR approach

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Multiple R 069 092 092 072 097F-test 133255 (000) 361102 (000) 442376 (000) 72903 (000) 1082812 (000)a0 -10646 (000) 11373 (000) -12888 (000) 03928 (000) -02297 (000)a1 -00011 (000) 00073 (000) -00097 (000) 00017 (000) -00039 (000)Anomaly confirmed confirmed confirmed confirmed confirmed

28

F Detailed statistical results DJI sub-periods

F1 Average analysis

Table F1 Average analysis

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 Mean return (gapday)

-001 023 015 -004

Mean return(non-gap day)

007 007 007 007

Anomaly confirmed confirmed confirmed confirmed1999-2008 Mean return (gap

day)090 -045 013 -004

Mean return(non-gap day)

-004 -004 -004 -004

Anomaly confirmed confirmed confirmed confirmed2009-2018 Mean return (gap

day)024 -024 0 -004

Mean return(non-gap day)

004 004 004 004

Anomaly confirmed confirmed not confirmed confirmed

F2 Parametric tests Students t-test

Table F2 T-test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 t-criterion 083 165 087 139t-critical (=095) 196 196 196 196Null hypothesis not rejected not rejected not rejected not rejected

1999-2008 t-criterion 347 351 054 047t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected rejected

2009-2018 t-criterion 265 207 051 058t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

F3 Parametric tests ANOVA

Table F3 ANOVA

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 F 085 409 093 179p-value 035 004 033 018

F critical 384 384 384 384Null hypothesis not rejected rejected not rejected not rejected

1999-2008 F 5405 3196 065 072p-value 0 0 042 039

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

2009-2018 F 554 697 024 058p-value 001 0 062 044

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

29

F4 Non-parametric tests Kruskal-Wallis test

Table F4 Kruskal-Wallis test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 Adjusted H 113 211 113 332df 1 1 1 1

P value 029 015 029 007Null hypothesis not rejected not rejected not rejected not rejected

1999-2008 Adjusted H 1484 1414 003 139df 1 1 1 1

P value 0 0 086 024Null hypothesis rejected rejected not rejected not rejected

2009-2018 Adjusted H 506 68 051 171df 1 1 1 1

P value 002 001 047 019Null hypothesis rejected rejected not rejected not rejected

F5 Regression analysis with dummy variables

Table F5 Regression analysis with dummy variables

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 a0 000068 (000) 00007 (000) 00007 (000) 00007 (000)a1 -000078 (035) 00016 (004) 00008 (033) -00011 (018)

Anomaly not confirmed confirmed not confirmed not confirmed1999-2008 a0 00004 (008) 00004 (008) 00004 (006) 00004 (008)

a1 00087 (000) -00049 (000) 00009 (042) -00008 (039)Anomaly confirmed confirmed not confirmed not confirmed

2009-2018 a0 00004 (006) 00004 (006) 00004 (006) 00004 (006)a1 00021 (001) -00028 (001) -00004 (062) -00008 (047)

Anomaly confirmed confirmed not confirmed not confirmed

F6 Modified CAR approach

Table F6 Modified CAR approach

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 Multiple R 083 088 082 086F-test 22779 (000) 40583 (000) 20401 (000) 3269454 (000)a0 00042 (023) 00017 (073) 00014 (058) -00266 (000)a1 -00009 (000) 00015 (000) 00006 (000) -00009 (000)

Anomaly confirmed confirmed confirmed confirmed1999-2008 Multiple R 095 093 076 019

F-test 62658 (000) 84712 (000) 10056 (000) 492 (003)a0 -00972 (000) 00365 (000) -00198 (000) -00115 (021)a1 00086 (000) -00042 (000) 00014 (000) 00002 (003)

Anomaly confirmed confirmed confirmed not confirmed2009-2018 Multiple R 096 082 08 05

F-test 150452 (000) 16731 (000) 22287 (000) 2620 (000)a0 00548 (000) -00618 (000) 00031 (020) -00112 (000)a1 00013 (000) -00014 (000) -00005 (000) -00004 (000)

Anomaly confirmed confirmed not confirmed confirmed

30

G Detailed statistical results NASDAQ sub-periods

G1 Average analysis

Table G1 Average analysis

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 Mean return (gapday)

094 -111 0189 -029

Mean return(non-gap day)

007 007 007 007

Anomaly confirmed confirmed confirmed confirmed1959-1968 Mean return (gap

day)133 -147 033 -039

Mean return(non-gap day)

006 006 006 006

Anomaly confirmed confirmed confirmed confirmed1969-1978 Mean return (gap

day)19 -186 057 -068

Mean return(non-gap day)

005 005 005 005

Anomaly confirmed confirmed confirmed confirmed1979-1988 Mean return (gap

day)138 -162 066 -04

Mean return(non-gap day)

008 008 008 008

Anomaly confirmed confirmed confirmed confirmed1989-1998 Mean return (gap

day)016 012 018 -009

Mean return(non-gap day)

002 002 002 002

Anomaly confirmed not confirmed confirmed confirmed1999-2008 Mean return (gap

day)38E-3 027 -036 -013

Mean return(non-gap day)

-01 -01 -01 -01

Anomaly confirmed not confirmed not confirmed not confirmed2009-2018 Mean return (gap

day)039 009 013 -025

Mean return(non-gap day)

001 001 001 001

Anomaly confirmed not confirmed confirmed confirmed

G2 Parametric tests Students t-test

Table G2 T-test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 t-criterion 3194 3076 201 559t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected rejected

1959-1968 t-criterion 1399 2246 443 382t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected rejected

1969-1978 t-criterion 261 4358 417 786t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected rejected

1979-1988 t-criterion 1847 1445 709 395t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected rejected

1989-1998 t-criterion 13 066 126 093t-critical (=095) 196 196 196 196Null hypothesis not rejected not rejected not rejected not rejected

1999-2008 t-criterion 192 106 111 009t-critical (=095) 196 196 196 196Null hypothesis not rejected not rejected not rejected not rejected

2009-2018 t-criterion 27 05 089 188t-critical (=095) 196 196 196 196Null hypothesis rejected not rejected not rejected not rejected

31

G3 Parametric tests ANOVA

Table G3 ANOVA

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 F 88153 190609 1272 14521p-value 0 0 0 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1959-1968 F 93974 149771 4715 10418p-value 0 0 0 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1969-1978 F 84546 145429 6295 18241p-value 0 0 0 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1979-1988 F 66952 110482 13138 8626p-value 0 0 0 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1989-1998 F 323 138 43 168p-value 007 024 003 019

F critical 384 384 384 384Null hypothesis not rejected not rejected rejected not rejected

1999-2008 F 106 512 327 003p-value 001 002 007 085

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

2009-2018 F 169 069 175 93p-value 0 04 018 0

F critical 384 384 384 384Null hypothesis rejected not rejected not rejected rejected

G4 Non-parametric tests Kruskal-Wallis test

Table G4 Kruskal-Wallis test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 Adjusted H 26254 32592 1464 3962df 1 1 1 1

P value 0 0 0 0Null hypothesis rejected rejected rejected rejected

1959-1968 Adjusted H 28235 27989 2736 332df 1 1 1 1

P value 0 0 0 0Null hypothesis rejected rejected rejected rejected

1969-1978 Adjusted H 22202 33777 3311 7591df 1 1 1 1

P value 0 0 0 0Null hypothesis rejected rejected rejected rejected

1979-1988 Adjusted H 23282 25292 4812 3964df 1 1 1 1

P value 0 0 0 0Null hypothesis rejected rejected rejected rejected

1989-1998 Adjusted H 381 017 175 132df 1 1 1 1

P value 005 068 019 025Null hypothesis not rejected not rejected not rejected not rejected

1999-2008 Adjusted H 855 023 044 004df 1 1 1 1

P value 0 063 051 084Null hypothesis rejected not rejected not rejected not rejected

2009-2018 Adjusted H 1063 009 257 709df 1 1 1 1

P value 0 077 011 001Null hypothesis rejected not rejected not rejected rejected

32

G5 Regression analysis with dummy variables

Table G5 Regression analysis with dummy variables

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 a0 00007 (000) 00007 (000) 00007 (000) 00007 (000)a1 00088 (000) -00119 (000) 00011 (000) -00036 (000)

Anomaly confirmed confirmed confirmed confirmed1959-1968 a0 00006 (000) 00006 (000) 00006 (000) 00006 (000)

a1 00128 (000) -00153 (000) 00027 (000) -00046 (000)Anomaly confirmed confirmed confirmed confirmed

1969-1978 a0 00005 (000) 00005 (000) 00005 (000) 00005 (000)a1 00185 (000) -00192 (000) 00053 (000) -00073 (000)

Anomaly confirmed confirmed confirmed confirmed1979-1988 a0 00008 (000) 00008 (000) 00008 (000) 00008 (000)

a1 00131 (000) -00172 (000) 00059 (000) -00048 (000)Anomaly confirmed confirmed confirmed confirmed

1989-1998 a0 00002 (027) 00002 (028) 00002 (028) 00002 (027)a1 00014 (007) 00010 (024) 00017 (004) -00011 (019)

Anomaly not confirmed not confirmed confirmed not confirmed1999-2008 a0 00001 (059) 00001 (062) 00001 (059) 00001 (060)

a1 00037 (000) 00026 (002) -00038 (000) -00014 (019)Anomaly confirmed not confirmed not confirmed not confirmed

2009-2018 a0 00001 (049) 00001 (049) 00001 (049) 00001 (049)a1 00038 (000) 00007 (040) 00012 (018) -00027 (000)

Anomaly confirmed not confirmed not confirmed confirmed

G6 Modified CAR approach

Table G6 Modified CAR approach

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 Multiple R 099 099 093 098F-test 5753605 (000) 100470(000) 6280421 283281a0 -00091 (000) -00349 (000) 00056 (001) 00015 (073)a1 00083 (000) -00110 (000) 00010 (000) -00031 (000)

Anomaly confirmed confirmed confirmed confirmed1959-1968 Multiple R 099 099 099 099

F-test 3923274 (000) 3005562 (000) 443198 (000) 372583 (000)a0 00096 (000) 00073 (016) -00082 (000) -00095 (004)a1 00116 (001) -00149 (000) 00025 (000) -00047 (000)

Anomaly confirmed confirmed confirmed confirmed1969-1978 Multiple R 099 099 098 099

F-test 4302608 (000) 2723953 (000) 179969 (000) 639745a0 00246 (000) -00002 (000) 00217 (000) -00514 (000)a1 00176 (000) -00182 (000) 00049 (000) -00062 (000)

Anomaly confirmed confirmed confirmed confirmed1979-1988 Multiple R 099 099 099 099

F-test 5872335 (000) 1182609 (000) 1083558 (000) 910089 (000)a0 00136 (000) -01081 (000) -00285 (000) -00101 (000)a1 00131 (000) -00167 (000) 00062 (000) -00048 (000)

Anomaly confirmed confirmed confirmed confirmed1989-1998 Multiple R 09 056 069 016

F-test 46947 (000) 4885 (000) 10131 (000) 263 (011)a0 00102 (002) -00261 (000) -0016 (001) -00237 (000)a1 00015 (000) 00010 (000) 0001 (000) 00002 (011)

Anomaly confirmed confirmed confirmed not confirmed1999-2008 Multiple R 093 087 073 037

F-test 71863 (000) 32530 (000) 13273 (000) 1669 (000)a0 00185 (004) 00311 (000) -00130 (039) -00546 (000)a1 00037 (000) 00032 (000) -00026 (000) -00007 (000)

Anomaly confirmed not confirmed not confirmed confirmed2009-2018 Multiple R 089 001 096 091

F-test 40818 (000) 000 (094) 116744 (000) 53770 (000)a0 01436 (000) -01099 (000) -01036 (000) 00697 (000)a1 00030 (000) 00000 (094) 00024 (000) -00021 (000)

Anomaly confirmed not confirmed confirmed confirmed

33

H Detailed statistical results SampP 500 sub-periods

H1 Average analysis

Table H1 Average analysis

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 Mean return (gapday)

138 -171 004 -014

Mean return(non-gap day)

0 0 0 0

Anomaly confirmed confirmed confirmed confirmed1939-1948 Mean return (gap

day)001 -042 172 -195

Mean return(non-gap day)

003 003 003 003

Anomaly confirmed confirmed confirmed confirmed1949-1958 Mean return (gap

day)165 -18 02 002

Mean return(non-gap day)

006 006 006 006

Anomaly confirmed confirmed confirmed not confirmed1959-1968 Mean return (gap

day)104 -102 015 0

Mean return(non-gap day)

002 002 002 002

Anomaly confirmed confirmed confirmed not confirmed1969-1978 Mean return (gap

day)131 -13 019 -03

Mean return(non-gap day)

0 0 0 0

Anomaly confirmed confirmed confirmed confirmed1979-1988 Mean return (gap

day)058 -042 015 003

Mean return(non-gap day)

005 005 005 005

Anomaly confirmed confirmed confirmed not confirmed1989-1998 Mean return (gap

day)02 -023 -002 01

Mean return(non-gap day)

007 007 007 007

Anomaly confirmed confirmed not confirmed not confirmed1999-2008 Mean return (gap

day)083 -089 -023 -005

Mean return(non-gap day)

001 001 001 001

Anomaly confirmed confirmed not confirmed confirmed2009-2018 Mean return (gap

day)055 -052 001 -015

Mean return(non-gap day)

004 004 004 004

Anomaly confirmed confirmed not confirmed confirmed

34

H2 Parametric tests Students t-test

Table H2 T-test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 t-criterion 101 85 029 048t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

1939-1948 t-criterion 064 479 3074 225t-critical (=095) 196 196 196 196Null hypothesis not rejected rejected rejected rejected

1949-1958 t-criterion 2964 2383 193 041t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

1959-1968 t-criterion 2281 2157 21 023t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected not rejected

1969-1978 t-criterion 1318 2034 187 321t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected rejected

1979-1988 t-criterion 435 535 07 037t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

1989-1998 t-criterion 201 396 132 052t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

1999-2008 t-criterion 362 433 117 022t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

2009-2018 t-criterion 375 382 027 132t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

H3 Parametric tests ANOVA

Table H3 ANOVA

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 F 6281 8032 005 051p-value 0 0 082 047

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

1939-1948 F 056 2603 34854 51034p-value 045 0 0 0

F critical 384 384 384 384Null hypothesis not rejected rejected rejected rejected

1949-1958 F 100174 128997 897 062p-value 0 0 0 043

F critical 384 384 384 384Null hypothesis rejected rejected rejected not rejected

1959-1968 F 36831 32858 617 01p-value 0 0 001 074

F critical 384 384 384 384Null hypothesis rejected rejected rejected not rejected

1969-1978 F 26601 3063 53 152p-value 0 0 002 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1979-1988 F 23 245 076 009p-value 0 0 039 077

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

1989-1998 F 399 1156 118 015p-value 004 0 027 069

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

1999-2008 F 4253 5622 365 024p-value 0 0 006 062

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

2009-2018 F 3064 3656 01 43p-value 0 0 075 004

F critical 384 384 384 384Null hypothesis rejected rejected not rejected rejected

35

H4 Non-parametric tests Kruskal -Wallis test

Table H4 Kruskal-Wallis test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 Adjusted H 9982 5913 332 14df 1 1 1 1

P value 0 0 007 024Null hypothesis rejected rejected not rejected not rejected

1939-1948 Adjusted H 494 1999 23387 24927df 1 1 1 1

P value 003 0 0 0Null hypothesis rejected rejected rejected rejected

1949-1958 Adjusted H 28728 28175 348 15df 1 1 1 1

P value 0 0 006 022Null hypothesis rejected rejected not rejected not rejected

1959-1968 Adjusted H 25729 21437 701 063df 1 1 1 1

P value 0 0 001 043Null hypothesis rejected rejected rejected not rejected

1969-1978 Adjusted H 14407 20078 27 1706df 1 1 1 1

P value 0 0 01 0Null hypothesis rejected rejected not rejected rejected

1979-1988 Adjusted H 1788 2836 027 034df 1 1 1 1

P value 0 0 06 056Null hypothesis rejected rejected not rejected not rejected

1989-1998 Adjusted H 251 1431 111 044df 1 1 1 1

P value 011 0 029 051Null hypothesis not rejected rejected not rejected not rejected

1999-2008 Adjusted H 1812 1788 042 002df 1 1 1 1

P value 0 0 052 089Null hypothesis rejected rejected not rejected not rejected

2009-2018 Adjusted H 1314 1783 074 37df 1 1 1 1

P value 0 0 039 005Null hypothesis rejected rejected not rejected not rejected

36

H5 Regression analysis with dummy variables

Table H5 Regression analysis with dummy variables

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 a0 00000 (097) 00000 (004) 00000 (097) 00000 (097)a1 00138 (000) -00172 (000) 00004 (082) -00014 (047)

Anomaly confirmed confirmed not confirmed not confirmed1939-1948 a0 00003 (015) 00003 (015) 00003 (015) 00003 (015)

a1 00007 (045) -00045 (000) 00170 (000) -00199 (000)Anomaly not confirmed confirmed confirmed confirmed

1949-1958 a0 00006 (000) 00006 (000) 00006 (000) 00006 (000)a1 00160 (000) -00188 (000) 00016 (000) -00004 (043)

Anomaly confirmed confirmed confirmed not confirmed1959-1968 a0 00002 (007) 00002 (004) 00002 (008) 00002 (008)

a1 00103 (000) -00105 (000) 00014 (001) -00002 (074)Anomaly confirmed confirmed confirmed not confirmed

1969-1978 a0 00000 (078) 00000 (078) 00000 (078) 00000 (078)a1 00132 (000) -00132 (000) 00019 (002) -00030 (000)

Anomaly confirmed confirmed confirmed confirmed1979-1988 a0 00006 (001) 00006 (001) 00006 (001) 00006 (000)

a1 00053 (000) -00048 (000) 00009 (040) -00003 (075)Anomaly confirmed confirmed not confirmed not confirmed

1989-1998 a0 00007 (000) 00007 (000) 00007 (000) 00007 (000)a1 00016 (005) -00030 (000) -00009 (026) 00003 (072)

Anomaly confirmed confirmed not confirmed not confirmed1999-2008 a0 00001 (075) 00001 (075) 00001 (075) 00001 (076)

a1 00083 (000) -00091 (000) -00024 (005) -00006 (062)Anomaly confirmed confirmed not confirmed not confirmed

2009-2018 a0 00004 (003) 00004 (000) 00004 (003) 00004 (003)a1 00051 (000) -00059 (000) -00003 (075) -00019 (003)

Anomaly confirmed confirmed not confirmed confirmed

37

H6 Modified CAR approach

Table H6 Modified CAR approach

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 Multiple R 096 095 046 046F-test 175935 (000) 96500 (000) 3534 (000) 2880 (000)a0 -01070 (000) 01958 (000) 00405 (000) 00535 (000)a1 00121 (000) -00160 (000) 00006 (000) -00014 (000)

Anomaly confirmed confirmed confirmed confirmed1939-1948 Multiple R 08 099 099 099

F-test 18777 (000) 755727 (000) 3572830 (000) 2696099 (000)a0 00019 (073) -00346 (000) -00373 (000) 00912 (000)a1 00012 (000) -00044 (000) 00168 (000) -00197 (000)

Anomaly confirmed confirmed confirmed confirmed1949-1958 Multiple R 099 099 094 015

F-test 1021705 (000) 7171257 (000) 75858 (000) 242 (012)a0 -00176 (000) -00191 (000) 00095 (000) -00498 (000)a1 00154 (000) -00181 (000) 00013 (000) -00002 (012)

Anomaly confirmed confirmed confirmed not confirmed1959-1968 Multiple R 099 099 094 078

F-test 1463311 (000) 6002659 (000) 82273 (000) 14352 (000)a0 -00112 (000) 00004 (085) 00151 (000) 00389 (000)a1 00098 (000) -00102 (000) 00011 (000) -00009 (000)

Anomaly confirmed confirmed confirmed confirmed1969-1978 Multiple R 098 099 093 099

F-test 241655 (000) 1451901 (000) 57333 (000) 368160 (000)a0 -00433 (000) 00276 (000) 00099 (002) -00144 (000)a1 00132 (000) -00134 (000) 00020 (000) -00030 (000)

Anomaly confirmed confirmed confirmed confirmed1979-1988 Multiple R 092 078 023 008

F-test 53757 (000) 18707 (000) 487 (003) 085 (036)a0 00813 (000) -02508 (000) 00204 (000) -00235 (000)a1 00036 (000) -00031 (000) -00003 (003) -00001 (036)

Anomaly confirmed confirmed not confirmed not confirmed1989-1998 Multiple R 079 099 074 044

F-test 19705(000) 761967 (000) 14133 (000) 2369 (000)a0 00268 (000) 00023 (021) -00381 (000) 00087 (000)a1 00013 (000) -00028 (000) -00008 (000) 00002 (000)

Anomaly confirmed confirmed not confirmed not confirmed1999-2008 Multiple R 091 093 071 065

F-test 47218 (000) 76564 (000) 9843 (000) 7768 (000)a0 -01493 (000) 01351 (000) 00397 (000) 00007 (093)a1 00081 (000) -00083 (000) -00026 (000) -00011 (000)

Anomaly confirmed confirmed not confirmed confirmed2009-2018 Multiple R 086 087 083 074

F-test 29971 (000) 32484 (000) 23228 (000) 12764 (000)a0 01711 (000) -02250 (000) 00407 (000) -00472 (000)a1 00038 (000) -00044 (000) -00010 (000) -00012 (000)

Anomaly confirmed confirmed not confirmed confirmed

38

E Detailed statistical results NASDAQ overall data

E1 Average analysis

Table E1 Average analysis

Parameter Gap day Gap day(Positive gaps)

Gap day(Negative gaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Mean return (gap day) -009 084 -090 022 -037Mean return (non-gap day) 003 003 003 003 003Anomaly confirmed confirmed confirmed confirmed confirmed

E2 Parametric tests Students t-test

Table E2 T-test

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

t-criterion 230 1257 1341 306 664t-critical (=095) 196 196 196 196 196Null hypothesis rejected rejected rejected rejected rejected

E3 Parametric tests ANOVA

Table E3 ANOVA

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

F 2289 62720 88402 3330 17356p-value 0 0 0 0 0F critical 384 384 384 384 384Null hypothesis rejected rejected rejected rejected rejected

E4 Non-parametric tests Kruskal-Wallis test

Table E4 Kruskal-Wallis test

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Adjusted H 1892 36022 45248 4695 10437df 1 1 1 1 1P value 0 0 0 0 0Critical value 384 384 384 384 384Null hypothesis rejected rejected rejected rejected rejected

27

E5 Regression analysis with dummy variables

Table E5 Regression analysis with dummy variables

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

a0 00003 (000) 00003 (000) 00003 (000) 00003 (000) 00003 (000)a1 -00012 (000) 00081 (000) -00093 (000) 00018 (000) -00040 (000)Anomaly confirmed confirmed confirmed confirmed confirmed

E6 Modified CAR approach

Table E6 Modified CAR approach

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Multiple R 069 092 092 072 097F-test 133255 (000) 361102 (000) 442376 (000) 72903 (000) 1082812 (000)a0 -10646 (000) 11373 (000) -12888 (000) 03928 (000) -02297 (000)a1 -00011 (000) 00073 (000) -00097 (000) 00017 (000) -00039 (000)Anomaly confirmed confirmed confirmed confirmed confirmed

28

F Detailed statistical results DJI sub-periods

F1 Average analysis

Table F1 Average analysis

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 Mean return (gapday)

-001 023 015 -004

Mean return(non-gap day)

007 007 007 007

Anomaly confirmed confirmed confirmed confirmed1999-2008 Mean return (gap

day)090 -045 013 -004

Mean return(non-gap day)

-004 -004 -004 -004

Anomaly confirmed confirmed confirmed confirmed2009-2018 Mean return (gap

day)024 -024 0 -004

Mean return(non-gap day)

004 004 004 004

Anomaly confirmed confirmed not confirmed confirmed

F2 Parametric tests Students t-test

Table F2 T-test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 t-criterion 083 165 087 139t-critical (=095) 196 196 196 196Null hypothesis not rejected not rejected not rejected not rejected

1999-2008 t-criterion 347 351 054 047t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected rejected

2009-2018 t-criterion 265 207 051 058t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

F3 Parametric tests ANOVA

Table F3 ANOVA

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 F 085 409 093 179p-value 035 004 033 018

F critical 384 384 384 384Null hypothesis not rejected rejected not rejected not rejected

1999-2008 F 5405 3196 065 072p-value 0 0 042 039

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

2009-2018 F 554 697 024 058p-value 001 0 062 044

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

29

F4 Non-parametric tests Kruskal-Wallis test

Table F4 Kruskal-Wallis test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 Adjusted H 113 211 113 332df 1 1 1 1

P value 029 015 029 007Null hypothesis not rejected not rejected not rejected not rejected

1999-2008 Adjusted H 1484 1414 003 139df 1 1 1 1

P value 0 0 086 024Null hypothesis rejected rejected not rejected not rejected

2009-2018 Adjusted H 506 68 051 171df 1 1 1 1

P value 002 001 047 019Null hypothesis rejected rejected not rejected not rejected

F5 Regression analysis with dummy variables

Table F5 Regression analysis with dummy variables

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 a0 000068 (000) 00007 (000) 00007 (000) 00007 (000)a1 -000078 (035) 00016 (004) 00008 (033) -00011 (018)

Anomaly not confirmed confirmed not confirmed not confirmed1999-2008 a0 00004 (008) 00004 (008) 00004 (006) 00004 (008)

a1 00087 (000) -00049 (000) 00009 (042) -00008 (039)Anomaly confirmed confirmed not confirmed not confirmed

2009-2018 a0 00004 (006) 00004 (006) 00004 (006) 00004 (006)a1 00021 (001) -00028 (001) -00004 (062) -00008 (047)

Anomaly confirmed confirmed not confirmed not confirmed

F6 Modified CAR approach

Table F6 Modified CAR approach

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 Multiple R 083 088 082 086F-test 22779 (000) 40583 (000) 20401 (000) 3269454 (000)a0 00042 (023) 00017 (073) 00014 (058) -00266 (000)a1 -00009 (000) 00015 (000) 00006 (000) -00009 (000)

Anomaly confirmed confirmed confirmed confirmed1999-2008 Multiple R 095 093 076 019

F-test 62658 (000) 84712 (000) 10056 (000) 492 (003)a0 -00972 (000) 00365 (000) -00198 (000) -00115 (021)a1 00086 (000) -00042 (000) 00014 (000) 00002 (003)

Anomaly confirmed confirmed confirmed not confirmed2009-2018 Multiple R 096 082 08 05

F-test 150452 (000) 16731 (000) 22287 (000) 2620 (000)a0 00548 (000) -00618 (000) 00031 (020) -00112 (000)a1 00013 (000) -00014 (000) -00005 (000) -00004 (000)

Anomaly confirmed confirmed not confirmed confirmed

30

G Detailed statistical results NASDAQ sub-periods

G1 Average analysis

Table G1 Average analysis

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 Mean return (gapday)

094 -111 0189 -029

Mean return(non-gap day)

007 007 007 007

Anomaly confirmed confirmed confirmed confirmed1959-1968 Mean return (gap

day)133 -147 033 -039

Mean return(non-gap day)

006 006 006 006

Anomaly confirmed confirmed confirmed confirmed1969-1978 Mean return (gap

day)19 -186 057 -068

Mean return(non-gap day)

005 005 005 005

Anomaly confirmed confirmed confirmed confirmed1979-1988 Mean return (gap

day)138 -162 066 -04

Mean return(non-gap day)

008 008 008 008

Anomaly confirmed confirmed confirmed confirmed1989-1998 Mean return (gap

day)016 012 018 -009

Mean return(non-gap day)

002 002 002 002

Anomaly confirmed not confirmed confirmed confirmed1999-2008 Mean return (gap

day)38E-3 027 -036 -013

Mean return(non-gap day)

-01 -01 -01 -01

Anomaly confirmed not confirmed not confirmed not confirmed2009-2018 Mean return (gap

day)039 009 013 -025

Mean return(non-gap day)

001 001 001 001

Anomaly confirmed not confirmed confirmed confirmed

G2 Parametric tests Students t-test

Table G2 T-test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 t-criterion 3194 3076 201 559t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected rejected

1959-1968 t-criterion 1399 2246 443 382t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected rejected

1969-1978 t-criterion 261 4358 417 786t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected rejected

1979-1988 t-criterion 1847 1445 709 395t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected rejected

1989-1998 t-criterion 13 066 126 093t-critical (=095) 196 196 196 196Null hypothesis not rejected not rejected not rejected not rejected

1999-2008 t-criterion 192 106 111 009t-critical (=095) 196 196 196 196Null hypothesis not rejected not rejected not rejected not rejected

2009-2018 t-criterion 27 05 089 188t-critical (=095) 196 196 196 196Null hypothesis rejected not rejected not rejected not rejected

31

G3 Parametric tests ANOVA

Table G3 ANOVA

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 F 88153 190609 1272 14521p-value 0 0 0 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1959-1968 F 93974 149771 4715 10418p-value 0 0 0 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1969-1978 F 84546 145429 6295 18241p-value 0 0 0 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1979-1988 F 66952 110482 13138 8626p-value 0 0 0 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1989-1998 F 323 138 43 168p-value 007 024 003 019

F critical 384 384 384 384Null hypothesis not rejected not rejected rejected not rejected

1999-2008 F 106 512 327 003p-value 001 002 007 085

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

2009-2018 F 169 069 175 93p-value 0 04 018 0

F critical 384 384 384 384Null hypothesis rejected not rejected not rejected rejected

G4 Non-parametric tests Kruskal-Wallis test

Table G4 Kruskal-Wallis test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 Adjusted H 26254 32592 1464 3962df 1 1 1 1

P value 0 0 0 0Null hypothesis rejected rejected rejected rejected

1959-1968 Adjusted H 28235 27989 2736 332df 1 1 1 1

P value 0 0 0 0Null hypothesis rejected rejected rejected rejected

1969-1978 Adjusted H 22202 33777 3311 7591df 1 1 1 1

P value 0 0 0 0Null hypothesis rejected rejected rejected rejected

1979-1988 Adjusted H 23282 25292 4812 3964df 1 1 1 1

P value 0 0 0 0Null hypothesis rejected rejected rejected rejected

1989-1998 Adjusted H 381 017 175 132df 1 1 1 1

P value 005 068 019 025Null hypothesis not rejected not rejected not rejected not rejected

1999-2008 Adjusted H 855 023 044 004df 1 1 1 1

P value 0 063 051 084Null hypothesis rejected not rejected not rejected not rejected

2009-2018 Adjusted H 1063 009 257 709df 1 1 1 1

P value 0 077 011 001Null hypothesis rejected not rejected not rejected rejected

32

G5 Regression analysis with dummy variables

Table G5 Regression analysis with dummy variables

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 a0 00007 (000) 00007 (000) 00007 (000) 00007 (000)a1 00088 (000) -00119 (000) 00011 (000) -00036 (000)

Anomaly confirmed confirmed confirmed confirmed1959-1968 a0 00006 (000) 00006 (000) 00006 (000) 00006 (000)

a1 00128 (000) -00153 (000) 00027 (000) -00046 (000)Anomaly confirmed confirmed confirmed confirmed

1969-1978 a0 00005 (000) 00005 (000) 00005 (000) 00005 (000)a1 00185 (000) -00192 (000) 00053 (000) -00073 (000)

Anomaly confirmed confirmed confirmed confirmed1979-1988 a0 00008 (000) 00008 (000) 00008 (000) 00008 (000)

a1 00131 (000) -00172 (000) 00059 (000) -00048 (000)Anomaly confirmed confirmed confirmed confirmed

1989-1998 a0 00002 (027) 00002 (028) 00002 (028) 00002 (027)a1 00014 (007) 00010 (024) 00017 (004) -00011 (019)

Anomaly not confirmed not confirmed confirmed not confirmed1999-2008 a0 00001 (059) 00001 (062) 00001 (059) 00001 (060)

a1 00037 (000) 00026 (002) -00038 (000) -00014 (019)Anomaly confirmed not confirmed not confirmed not confirmed

2009-2018 a0 00001 (049) 00001 (049) 00001 (049) 00001 (049)a1 00038 (000) 00007 (040) 00012 (018) -00027 (000)

Anomaly confirmed not confirmed not confirmed confirmed

G6 Modified CAR approach

Table G6 Modified CAR approach

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 Multiple R 099 099 093 098F-test 5753605 (000) 100470(000) 6280421 283281a0 -00091 (000) -00349 (000) 00056 (001) 00015 (073)a1 00083 (000) -00110 (000) 00010 (000) -00031 (000)

Anomaly confirmed confirmed confirmed confirmed1959-1968 Multiple R 099 099 099 099

F-test 3923274 (000) 3005562 (000) 443198 (000) 372583 (000)a0 00096 (000) 00073 (016) -00082 (000) -00095 (004)a1 00116 (001) -00149 (000) 00025 (000) -00047 (000)

Anomaly confirmed confirmed confirmed confirmed1969-1978 Multiple R 099 099 098 099

F-test 4302608 (000) 2723953 (000) 179969 (000) 639745a0 00246 (000) -00002 (000) 00217 (000) -00514 (000)a1 00176 (000) -00182 (000) 00049 (000) -00062 (000)

Anomaly confirmed confirmed confirmed confirmed1979-1988 Multiple R 099 099 099 099

F-test 5872335 (000) 1182609 (000) 1083558 (000) 910089 (000)a0 00136 (000) -01081 (000) -00285 (000) -00101 (000)a1 00131 (000) -00167 (000) 00062 (000) -00048 (000)

Anomaly confirmed confirmed confirmed confirmed1989-1998 Multiple R 09 056 069 016

F-test 46947 (000) 4885 (000) 10131 (000) 263 (011)a0 00102 (002) -00261 (000) -0016 (001) -00237 (000)a1 00015 (000) 00010 (000) 0001 (000) 00002 (011)

Anomaly confirmed confirmed confirmed not confirmed1999-2008 Multiple R 093 087 073 037

F-test 71863 (000) 32530 (000) 13273 (000) 1669 (000)a0 00185 (004) 00311 (000) -00130 (039) -00546 (000)a1 00037 (000) 00032 (000) -00026 (000) -00007 (000)

Anomaly confirmed not confirmed not confirmed confirmed2009-2018 Multiple R 089 001 096 091

F-test 40818 (000) 000 (094) 116744 (000) 53770 (000)a0 01436 (000) -01099 (000) -01036 (000) 00697 (000)a1 00030 (000) 00000 (094) 00024 (000) -00021 (000)

Anomaly confirmed not confirmed confirmed confirmed

33

H Detailed statistical results SampP 500 sub-periods

H1 Average analysis

Table H1 Average analysis

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 Mean return (gapday)

138 -171 004 -014

Mean return(non-gap day)

0 0 0 0

Anomaly confirmed confirmed confirmed confirmed1939-1948 Mean return (gap

day)001 -042 172 -195

Mean return(non-gap day)

003 003 003 003

Anomaly confirmed confirmed confirmed confirmed1949-1958 Mean return (gap

day)165 -18 02 002

Mean return(non-gap day)

006 006 006 006

Anomaly confirmed confirmed confirmed not confirmed1959-1968 Mean return (gap

day)104 -102 015 0

Mean return(non-gap day)

002 002 002 002

Anomaly confirmed confirmed confirmed not confirmed1969-1978 Mean return (gap

day)131 -13 019 -03

Mean return(non-gap day)

0 0 0 0

Anomaly confirmed confirmed confirmed confirmed1979-1988 Mean return (gap

day)058 -042 015 003

Mean return(non-gap day)

005 005 005 005

Anomaly confirmed confirmed confirmed not confirmed1989-1998 Mean return (gap

day)02 -023 -002 01

Mean return(non-gap day)

007 007 007 007

Anomaly confirmed confirmed not confirmed not confirmed1999-2008 Mean return (gap

day)083 -089 -023 -005

Mean return(non-gap day)

001 001 001 001

Anomaly confirmed confirmed not confirmed confirmed2009-2018 Mean return (gap

day)055 -052 001 -015

Mean return(non-gap day)

004 004 004 004

Anomaly confirmed confirmed not confirmed confirmed

34

H2 Parametric tests Students t-test

Table H2 T-test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 t-criterion 101 85 029 048t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

1939-1948 t-criterion 064 479 3074 225t-critical (=095) 196 196 196 196Null hypothesis not rejected rejected rejected rejected

1949-1958 t-criterion 2964 2383 193 041t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

1959-1968 t-criterion 2281 2157 21 023t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected not rejected

1969-1978 t-criterion 1318 2034 187 321t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected rejected

1979-1988 t-criterion 435 535 07 037t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

1989-1998 t-criterion 201 396 132 052t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

1999-2008 t-criterion 362 433 117 022t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

2009-2018 t-criterion 375 382 027 132t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

H3 Parametric tests ANOVA

Table H3 ANOVA

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 F 6281 8032 005 051p-value 0 0 082 047

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

1939-1948 F 056 2603 34854 51034p-value 045 0 0 0

F critical 384 384 384 384Null hypothesis not rejected rejected rejected rejected

1949-1958 F 100174 128997 897 062p-value 0 0 0 043

F critical 384 384 384 384Null hypothesis rejected rejected rejected not rejected

1959-1968 F 36831 32858 617 01p-value 0 0 001 074

F critical 384 384 384 384Null hypothesis rejected rejected rejected not rejected

1969-1978 F 26601 3063 53 152p-value 0 0 002 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1979-1988 F 23 245 076 009p-value 0 0 039 077

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

1989-1998 F 399 1156 118 015p-value 004 0 027 069

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

1999-2008 F 4253 5622 365 024p-value 0 0 006 062

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

2009-2018 F 3064 3656 01 43p-value 0 0 075 004

F critical 384 384 384 384Null hypothesis rejected rejected not rejected rejected

35

H4 Non-parametric tests Kruskal -Wallis test

Table H4 Kruskal-Wallis test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 Adjusted H 9982 5913 332 14df 1 1 1 1

P value 0 0 007 024Null hypothesis rejected rejected not rejected not rejected

1939-1948 Adjusted H 494 1999 23387 24927df 1 1 1 1

P value 003 0 0 0Null hypothesis rejected rejected rejected rejected

1949-1958 Adjusted H 28728 28175 348 15df 1 1 1 1

P value 0 0 006 022Null hypothesis rejected rejected not rejected not rejected

1959-1968 Adjusted H 25729 21437 701 063df 1 1 1 1

P value 0 0 001 043Null hypothesis rejected rejected rejected not rejected

1969-1978 Adjusted H 14407 20078 27 1706df 1 1 1 1

P value 0 0 01 0Null hypothesis rejected rejected not rejected rejected

1979-1988 Adjusted H 1788 2836 027 034df 1 1 1 1

P value 0 0 06 056Null hypothesis rejected rejected not rejected not rejected

1989-1998 Adjusted H 251 1431 111 044df 1 1 1 1

P value 011 0 029 051Null hypothesis not rejected rejected not rejected not rejected

1999-2008 Adjusted H 1812 1788 042 002df 1 1 1 1

P value 0 0 052 089Null hypothesis rejected rejected not rejected not rejected

2009-2018 Adjusted H 1314 1783 074 37df 1 1 1 1

P value 0 0 039 005Null hypothesis rejected rejected not rejected not rejected

36

H5 Regression analysis with dummy variables

Table H5 Regression analysis with dummy variables

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 a0 00000 (097) 00000 (004) 00000 (097) 00000 (097)a1 00138 (000) -00172 (000) 00004 (082) -00014 (047)

Anomaly confirmed confirmed not confirmed not confirmed1939-1948 a0 00003 (015) 00003 (015) 00003 (015) 00003 (015)

a1 00007 (045) -00045 (000) 00170 (000) -00199 (000)Anomaly not confirmed confirmed confirmed confirmed

1949-1958 a0 00006 (000) 00006 (000) 00006 (000) 00006 (000)a1 00160 (000) -00188 (000) 00016 (000) -00004 (043)

Anomaly confirmed confirmed confirmed not confirmed1959-1968 a0 00002 (007) 00002 (004) 00002 (008) 00002 (008)

a1 00103 (000) -00105 (000) 00014 (001) -00002 (074)Anomaly confirmed confirmed confirmed not confirmed

1969-1978 a0 00000 (078) 00000 (078) 00000 (078) 00000 (078)a1 00132 (000) -00132 (000) 00019 (002) -00030 (000)

Anomaly confirmed confirmed confirmed confirmed1979-1988 a0 00006 (001) 00006 (001) 00006 (001) 00006 (000)

a1 00053 (000) -00048 (000) 00009 (040) -00003 (075)Anomaly confirmed confirmed not confirmed not confirmed

1989-1998 a0 00007 (000) 00007 (000) 00007 (000) 00007 (000)a1 00016 (005) -00030 (000) -00009 (026) 00003 (072)

Anomaly confirmed confirmed not confirmed not confirmed1999-2008 a0 00001 (075) 00001 (075) 00001 (075) 00001 (076)

a1 00083 (000) -00091 (000) -00024 (005) -00006 (062)Anomaly confirmed confirmed not confirmed not confirmed

2009-2018 a0 00004 (003) 00004 (000) 00004 (003) 00004 (003)a1 00051 (000) -00059 (000) -00003 (075) -00019 (003)

Anomaly confirmed confirmed not confirmed confirmed

37

H6 Modified CAR approach

Table H6 Modified CAR approach

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 Multiple R 096 095 046 046F-test 175935 (000) 96500 (000) 3534 (000) 2880 (000)a0 -01070 (000) 01958 (000) 00405 (000) 00535 (000)a1 00121 (000) -00160 (000) 00006 (000) -00014 (000)

Anomaly confirmed confirmed confirmed confirmed1939-1948 Multiple R 08 099 099 099

F-test 18777 (000) 755727 (000) 3572830 (000) 2696099 (000)a0 00019 (073) -00346 (000) -00373 (000) 00912 (000)a1 00012 (000) -00044 (000) 00168 (000) -00197 (000)

Anomaly confirmed confirmed confirmed confirmed1949-1958 Multiple R 099 099 094 015

F-test 1021705 (000) 7171257 (000) 75858 (000) 242 (012)a0 -00176 (000) -00191 (000) 00095 (000) -00498 (000)a1 00154 (000) -00181 (000) 00013 (000) -00002 (012)

Anomaly confirmed confirmed confirmed not confirmed1959-1968 Multiple R 099 099 094 078

F-test 1463311 (000) 6002659 (000) 82273 (000) 14352 (000)a0 -00112 (000) 00004 (085) 00151 (000) 00389 (000)a1 00098 (000) -00102 (000) 00011 (000) -00009 (000)

Anomaly confirmed confirmed confirmed confirmed1969-1978 Multiple R 098 099 093 099

F-test 241655 (000) 1451901 (000) 57333 (000) 368160 (000)a0 -00433 (000) 00276 (000) 00099 (002) -00144 (000)a1 00132 (000) -00134 (000) 00020 (000) -00030 (000)

Anomaly confirmed confirmed confirmed confirmed1979-1988 Multiple R 092 078 023 008

F-test 53757 (000) 18707 (000) 487 (003) 085 (036)a0 00813 (000) -02508 (000) 00204 (000) -00235 (000)a1 00036 (000) -00031 (000) -00003 (003) -00001 (036)

Anomaly confirmed confirmed not confirmed not confirmed1989-1998 Multiple R 079 099 074 044

F-test 19705(000) 761967 (000) 14133 (000) 2369 (000)a0 00268 (000) 00023 (021) -00381 (000) 00087 (000)a1 00013 (000) -00028 (000) -00008 (000) 00002 (000)

Anomaly confirmed confirmed not confirmed not confirmed1999-2008 Multiple R 091 093 071 065

F-test 47218 (000) 76564 (000) 9843 (000) 7768 (000)a0 -01493 (000) 01351 (000) 00397 (000) 00007 (093)a1 00081 (000) -00083 (000) -00026 (000) -00011 (000)

Anomaly confirmed confirmed not confirmed confirmed2009-2018 Multiple R 086 087 083 074

F-test 29971 (000) 32484 (000) 23228 (000) 12764 (000)a0 01711 (000) -02250 (000) 00407 (000) -00472 (000)a1 00038 (000) -00044 (000) -00010 (000) -00012 (000)

Anomaly confirmed confirmed not confirmed confirmed

38

E5 Regression analysis with dummy variables

Table E5 Regression analysis with dummy variables

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

a0 00003 (000) 00003 (000) 00003 (000) 00003 (000) 00003 (000)a1 -00012 (000) 00081 (000) -00093 (000) 00018 (000) -00040 (000)Anomaly confirmed confirmed confirmed confirmed confirmed

E6 Modified CAR approach

Table E6 Modified CAR approach

Parameter Gap day Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

Multiple R 069 092 092 072 097F-test 133255 (000) 361102 (000) 442376 (000) 72903 (000) 1082812 (000)a0 -10646 (000) 11373 (000) -12888 (000) 03928 (000) -02297 (000)a1 -00011 (000) 00073 (000) -00097 (000) 00017 (000) -00039 (000)Anomaly confirmed confirmed confirmed confirmed confirmed

28

F Detailed statistical results DJI sub-periods

F1 Average analysis

Table F1 Average analysis

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 Mean return (gapday)

-001 023 015 -004

Mean return(non-gap day)

007 007 007 007

Anomaly confirmed confirmed confirmed confirmed1999-2008 Mean return (gap

day)090 -045 013 -004

Mean return(non-gap day)

-004 -004 -004 -004

Anomaly confirmed confirmed confirmed confirmed2009-2018 Mean return (gap

day)024 -024 0 -004

Mean return(non-gap day)

004 004 004 004

Anomaly confirmed confirmed not confirmed confirmed

F2 Parametric tests Students t-test

Table F2 T-test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 t-criterion 083 165 087 139t-critical (=095) 196 196 196 196Null hypothesis not rejected not rejected not rejected not rejected

1999-2008 t-criterion 347 351 054 047t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected rejected

2009-2018 t-criterion 265 207 051 058t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

F3 Parametric tests ANOVA

Table F3 ANOVA

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 F 085 409 093 179p-value 035 004 033 018

F critical 384 384 384 384Null hypothesis not rejected rejected not rejected not rejected

1999-2008 F 5405 3196 065 072p-value 0 0 042 039

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

2009-2018 F 554 697 024 058p-value 001 0 062 044

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

29

F4 Non-parametric tests Kruskal-Wallis test

Table F4 Kruskal-Wallis test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 Adjusted H 113 211 113 332df 1 1 1 1

P value 029 015 029 007Null hypothesis not rejected not rejected not rejected not rejected

1999-2008 Adjusted H 1484 1414 003 139df 1 1 1 1

P value 0 0 086 024Null hypothesis rejected rejected not rejected not rejected

2009-2018 Adjusted H 506 68 051 171df 1 1 1 1

P value 002 001 047 019Null hypothesis rejected rejected not rejected not rejected

F5 Regression analysis with dummy variables

Table F5 Regression analysis with dummy variables

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 a0 000068 (000) 00007 (000) 00007 (000) 00007 (000)a1 -000078 (035) 00016 (004) 00008 (033) -00011 (018)

Anomaly not confirmed confirmed not confirmed not confirmed1999-2008 a0 00004 (008) 00004 (008) 00004 (006) 00004 (008)

a1 00087 (000) -00049 (000) 00009 (042) -00008 (039)Anomaly confirmed confirmed not confirmed not confirmed

2009-2018 a0 00004 (006) 00004 (006) 00004 (006) 00004 (006)a1 00021 (001) -00028 (001) -00004 (062) -00008 (047)

Anomaly confirmed confirmed not confirmed not confirmed

F6 Modified CAR approach

Table F6 Modified CAR approach

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 Multiple R 083 088 082 086F-test 22779 (000) 40583 (000) 20401 (000) 3269454 (000)a0 00042 (023) 00017 (073) 00014 (058) -00266 (000)a1 -00009 (000) 00015 (000) 00006 (000) -00009 (000)

Anomaly confirmed confirmed confirmed confirmed1999-2008 Multiple R 095 093 076 019

F-test 62658 (000) 84712 (000) 10056 (000) 492 (003)a0 -00972 (000) 00365 (000) -00198 (000) -00115 (021)a1 00086 (000) -00042 (000) 00014 (000) 00002 (003)

Anomaly confirmed confirmed confirmed not confirmed2009-2018 Multiple R 096 082 08 05

F-test 150452 (000) 16731 (000) 22287 (000) 2620 (000)a0 00548 (000) -00618 (000) 00031 (020) -00112 (000)a1 00013 (000) -00014 (000) -00005 (000) -00004 (000)

Anomaly confirmed confirmed not confirmed confirmed

30

G Detailed statistical results NASDAQ sub-periods

G1 Average analysis

Table G1 Average analysis

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 Mean return (gapday)

094 -111 0189 -029

Mean return(non-gap day)

007 007 007 007

Anomaly confirmed confirmed confirmed confirmed1959-1968 Mean return (gap

day)133 -147 033 -039

Mean return(non-gap day)

006 006 006 006

Anomaly confirmed confirmed confirmed confirmed1969-1978 Mean return (gap

day)19 -186 057 -068

Mean return(non-gap day)

005 005 005 005

Anomaly confirmed confirmed confirmed confirmed1979-1988 Mean return (gap

day)138 -162 066 -04

Mean return(non-gap day)

008 008 008 008

Anomaly confirmed confirmed confirmed confirmed1989-1998 Mean return (gap

day)016 012 018 -009

Mean return(non-gap day)

002 002 002 002

Anomaly confirmed not confirmed confirmed confirmed1999-2008 Mean return (gap

day)38E-3 027 -036 -013

Mean return(non-gap day)

-01 -01 -01 -01

Anomaly confirmed not confirmed not confirmed not confirmed2009-2018 Mean return (gap

day)039 009 013 -025

Mean return(non-gap day)

001 001 001 001

Anomaly confirmed not confirmed confirmed confirmed

G2 Parametric tests Students t-test

Table G2 T-test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 t-criterion 3194 3076 201 559t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected rejected

1959-1968 t-criterion 1399 2246 443 382t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected rejected

1969-1978 t-criterion 261 4358 417 786t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected rejected

1979-1988 t-criterion 1847 1445 709 395t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected rejected

1989-1998 t-criterion 13 066 126 093t-critical (=095) 196 196 196 196Null hypothesis not rejected not rejected not rejected not rejected

1999-2008 t-criterion 192 106 111 009t-critical (=095) 196 196 196 196Null hypothesis not rejected not rejected not rejected not rejected

2009-2018 t-criterion 27 05 089 188t-critical (=095) 196 196 196 196Null hypothesis rejected not rejected not rejected not rejected

31

G3 Parametric tests ANOVA

Table G3 ANOVA

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 F 88153 190609 1272 14521p-value 0 0 0 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1959-1968 F 93974 149771 4715 10418p-value 0 0 0 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1969-1978 F 84546 145429 6295 18241p-value 0 0 0 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1979-1988 F 66952 110482 13138 8626p-value 0 0 0 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1989-1998 F 323 138 43 168p-value 007 024 003 019

F critical 384 384 384 384Null hypothesis not rejected not rejected rejected not rejected

1999-2008 F 106 512 327 003p-value 001 002 007 085

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

2009-2018 F 169 069 175 93p-value 0 04 018 0

F critical 384 384 384 384Null hypothesis rejected not rejected not rejected rejected

G4 Non-parametric tests Kruskal-Wallis test

Table G4 Kruskal-Wallis test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 Adjusted H 26254 32592 1464 3962df 1 1 1 1

P value 0 0 0 0Null hypothesis rejected rejected rejected rejected

1959-1968 Adjusted H 28235 27989 2736 332df 1 1 1 1

P value 0 0 0 0Null hypothesis rejected rejected rejected rejected

1969-1978 Adjusted H 22202 33777 3311 7591df 1 1 1 1

P value 0 0 0 0Null hypothesis rejected rejected rejected rejected

1979-1988 Adjusted H 23282 25292 4812 3964df 1 1 1 1

P value 0 0 0 0Null hypothesis rejected rejected rejected rejected

1989-1998 Adjusted H 381 017 175 132df 1 1 1 1

P value 005 068 019 025Null hypothesis not rejected not rejected not rejected not rejected

1999-2008 Adjusted H 855 023 044 004df 1 1 1 1

P value 0 063 051 084Null hypothesis rejected not rejected not rejected not rejected

2009-2018 Adjusted H 1063 009 257 709df 1 1 1 1

P value 0 077 011 001Null hypothesis rejected not rejected not rejected rejected

32

G5 Regression analysis with dummy variables

Table G5 Regression analysis with dummy variables

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 a0 00007 (000) 00007 (000) 00007 (000) 00007 (000)a1 00088 (000) -00119 (000) 00011 (000) -00036 (000)

Anomaly confirmed confirmed confirmed confirmed1959-1968 a0 00006 (000) 00006 (000) 00006 (000) 00006 (000)

a1 00128 (000) -00153 (000) 00027 (000) -00046 (000)Anomaly confirmed confirmed confirmed confirmed

1969-1978 a0 00005 (000) 00005 (000) 00005 (000) 00005 (000)a1 00185 (000) -00192 (000) 00053 (000) -00073 (000)

Anomaly confirmed confirmed confirmed confirmed1979-1988 a0 00008 (000) 00008 (000) 00008 (000) 00008 (000)

a1 00131 (000) -00172 (000) 00059 (000) -00048 (000)Anomaly confirmed confirmed confirmed confirmed

1989-1998 a0 00002 (027) 00002 (028) 00002 (028) 00002 (027)a1 00014 (007) 00010 (024) 00017 (004) -00011 (019)

Anomaly not confirmed not confirmed confirmed not confirmed1999-2008 a0 00001 (059) 00001 (062) 00001 (059) 00001 (060)

a1 00037 (000) 00026 (002) -00038 (000) -00014 (019)Anomaly confirmed not confirmed not confirmed not confirmed

2009-2018 a0 00001 (049) 00001 (049) 00001 (049) 00001 (049)a1 00038 (000) 00007 (040) 00012 (018) -00027 (000)

Anomaly confirmed not confirmed not confirmed confirmed

G6 Modified CAR approach

Table G6 Modified CAR approach

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 Multiple R 099 099 093 098F-test 5753605 (000) 100470(000) 6280421 283281a0 -00091 (000) -00349 (000) 00056 (001) 00015 (073)a1 00083 (000) -00110 (000) 00010 (000) -00031 (000)

Anomaly confirmed confirmed confirmed confirmed1959-1968 Multiple R 099 099 099 099

F-test 3923274 (000) 3005562 (000) 443198 (000) 372583 (000)a0 00096 (000) 00073 (016) -00082 (000) -00095 (004)a1 00116 (001) -00149 (000) 00025 (000) -00047 (000)

Anomaly confirmed confirmed confirmed confirmed1969-1978 Multiple R 099 099 098 099

F-test 4302608 (000) 2723953 (000) 179969 (000) 639745a0 00246 (000) -00002 (000) 00217 (000) -00514 (000)a1 00176 (000) -00182 (000) 00049 (000) -00062 (000)

Anomaly confirmed confirmed confirmed confirmed1979-1988 Multiple R 099 099 099 099

F-test 5872335 (000) 1182609 (000) 1083558 (000) 910089 (000)a0 00136 (000) -01081 (000) -00285 (000) -00101 (000)a1 00131 (000) -00167 (000) 00062 (000) -00048 (000)

Anomaly confirmed confirmed confirmed confirmed1989-1998 Multiple R 09 056 069 016

F-test 46947 (000) 4885 (000) 10131 (000) 263 (011)a0 00102 (002) -00261 (000) -0016 (001) -00237 (000)a1 00015 (000) 00010 (000) 0001 (000) 00002 (011)

Anomaly confirmed confirmed confirmed not confirmed1999-2008 Multiple R 093 087 073 037

F-test 71863 (000) 32530 (000) 13273 (000) 1669 (000)a0 00185 (004) 00311 (000) -00130 (039) -00546 (000)a1 00037 (000) 00032 (000) -00026 (000) -00007 (000)

Anomaly confirmed not confirmed not confirmed confirmed2009-2018 Multiple R 089 001 096 091

F-test 40818 (000) 000 (094) 116744 (000) 53770 (000)a0 01436 (000) -01099 (000) -01036 (000) 00697 (000)a1 00030 (000) 00000 (094) 00024 (000) -00021 (000)

Anomaly confirmed not confirmed confirmed confirmed

33

H Detailed statistical results SampP 500 sub-periods

H1 Average analysis

Table H1 Average analysis

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 Mean return (gapday)

138 -171 004 -014

Mean return(non-gap day)

0 0 0 0

Anomaly confirmed confirmed confirmed confirmed1939-1948 Mean return (gap

day)001 -042 172 -195

Mean return(non-gap day)

003 003 003 003

Anomaly confirmed confirmed confirmed confirmed1949-1958 Mean return (gap

day)165 -18 02 002

Mean return(non-gap day)

006 006 006 006

Anomaly confirmed confirmed confirmed not confirmed1959-1968 Mean return (gap

day)104 -102 015 0

Mean return(non-gap day)

002 002 002 002

Anomaly confirmed confirmed confirmed not confirmed1969-1978 Mean return (gap

day)131 -13 019 -03

Mean return(non-gap day)

0 0 0 0

Anomaly confirmed confirmed confirmed confirmed1979-1988 Mean return (gap

day)058 -042 015 003

Mean return(non-gap day)

005 005 005 005

Anomaly confirmed confirmed confirmed not confirmed1989-1998 Mean return (gap

day)02 -023 -002 01

Mean return(non-gap day)

007 007 007 007

Anomaly confirmed confirmed not confirmed not confirmed1999-2008 Mean return (gap

day)083 -089 -023 -005

Mean return(non-gap day)

001 001 001 001

Anomaly confirmed confirmed not confirmed confirmed2009-2018 Mean return (gap

day)055 -052 001 -015

Mean return(non-gap day)

004 004 004 004

Anomaly confirmed confirmed not confirmed confirmed

34

H2 Parametric tests Students t-test

Table H2 T-test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 t-criterion 101 85 029 048t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

1939-1948 t-criterion 064 479 3074 225t-critical (=095) 196 196 196 196Null hypothesis not rejected rejected rejected rejected

1949-1958 t-criterion 2964 2383 193 041t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

1959-1968 t-criterion 2281 2157 21 023t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected not rejected

1969-1978 t-criterion 1318 2034 187 321t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected rejected

1979-1988 t-criterion 435 535 07 037t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

1989-1998 t-criterion 201 396 132 052t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

1999-2008 t-criterion 362 433 117 022t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

2009-2018 t-criterion 375 382 027 132t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

H3 Parametric tests ANOVA

Table H3 ANOVA

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 F 6281 8032 005 051p-value 0 0 082 047

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

1939-1948 F 056 2603 34854 51034p-value 045 0 0 0

F critical 384 384 384 384Null hypothesis not rejected rejected rejected rejected

1949-1958 F 100174 128997 897 062p-value 0 0 0 043

F critical 384 384 384 384Null hypothesis rejected rejected rejected not rejected

1959-1968 F 36831 32858 617 01p-value 0 0 001 074

F critical 384 384 384 384Null hypothesis rejected rejected rejected not rejected

1969-1978 F 26601 3063 53 152p-value 0 0 002 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1979-1988 F 23 245 076 009p-value 0 0 039 077

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

1989-1998 F 399 1156 118 015p-value 004 0 027 069

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

1999-2008 F 4253 5622 365 024p-value 0 0 006 062

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

2009-2018 F 3064 3656 01 43p-value 0 0 075 004

F critical 384 384 384 384Null hypothesis rejected rejected not rejected rejected

35

H4 Non-parametric tests Kruskal -Wallis test

Table H4 Kruskal-Wallis test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 Adjusted H 9982 5913 332 14df 1 1 1 1

P value 0 0 007 024Null hypothesis rejected rejected not rejected not rejected

1939-1948 Adjusted H 494 1999 23387 24927df 1 1 1 1

P value 003 0 0 0Null hypothesis rejected rejected rejected rejected

1949-1958 Adjusted H 28728 28175 348 15df 1 1 1 1

P value 0 0 006 022Null hypothesis rejected rejected not rejected not rejected

1959-1968 Adjusted H 25729 21437 701 063df 1 1 1 1

P value 0 0 001 043Null hypothesis rejected rejected rejected not rejected

1969-1978 Adjusted H 14407 20078 27 1706df 1 1 1 1

P value 0 0 01 0Null hypothesis rejected rejected not rejected rejected

1979-1988 Adjusted H 1788 2836 027 034df 1 1 1 1

P value 0 0 06 056Null hypothesis rejected rejected not rejected not rejected

1989-1998 Adjusted H 251 1431 111 044df 1 1 1 1

P value 011 0 029 051Null hypothesis not rejected rejected not rejected not rejected

1999-2008 Adjusted H 1812 1788 042 002df 1 1 1 1

P value 0 0 052 089Null hypothesis rejected rejected not rejected not rejected

2009-2018 Adjusted H 1314 1783 074 37df 1 1 1 1

P value 0 0 039 005Null hypothesis rejected rejected not rejected not rejected

36

H5 Regression analysis with dummy variables

Table H5 Regression analysis with dummy variables

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 a0 00000 (097) 00000 (004) 00000 (097) 00000 (097)a1 00138 (000) -00172 (000) 00004 (082) -00014 (047)

Anomaly confirmed confirmed not confirmed not confirmed1939-1948 a0 00003 (015) 00003 (015) 00003 (015) 00003 (015)

a1 00007 (045) -00045 (000) 00170 (000) -00199 (000)Anomaly not confirmed confirmed confirmed confirmed

1949-1958 a0 00006 (000) 00006 (000) 00006 (000) 00006 (000)a1 00160 (000) -00188 (000) 00016 (000) -00004 (043)

Anomaly confirmed confirmed confirmed not confirmed1959-1968 a0 00002 (007) 00002 (004) 00002 (008) 00002 (008)

a1 00103 (000) -00105 (000) 00014 (001) -00002 (074)Anomaly confirmed confirmed confirmed not confirmed

1969-1978 a0 00000 (078) 00000 (078) 00000 (078) 00000 (078)a1 00132 (000) -00132 (000) 00019 (002) -00030 (000)

Anomaly confirmed confirmed confirmed confirmed1979-1988 a0 00006 (001) 00006 (001) 00006 (001) 00006 (000)

a1 00053 (000) -00048 (000) 00009 (040) -00003 (075)Anomaly confirmed confirmed not confirmed not confirmed

1989-1998 a0 00007 (000) 00007 (000) 00007 (000) 00007 (000)a1 00016 (005) -00030 (000) -00009 (026) 00003 (072)

Anomaly confirmed confirmed not confirmed not confirmed1999-2008 a0 00001 (075) 00001 (075) 00001 (075) 00001 (076)

a1 00083 (000) -00091 (000) -00024 (005) -00006 (062)Anomaly confirmed confirmed not confirmed not confirmed

2009-2018 a0 00004 (003) 00004 (000) 00004 (003) 00004 (003)a1 00051 (000) -00059 (000) -00003 (075) -00019 (003)

Anomaly confirmed confirmed not confirmed confirmed

37

H6 Modified CAR approach

Table H6 Modified CAR approach

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 Multiple R 096 095 046 046F-test 175935 (000) 96500 (000) 3534 (000) 2880 (000)a0 -01070 (000) 01958 (000) 00405 (000) 00535 (000)a1 00121 (000) -00160 (000) 00006 (000) -00014 (000)

Anomaly confirmed confirmed confirmed confirmed1939-1948 Multiple R 08 099 099 099

F-test 18777 (000) 755727 (000) 3572830 (000) 2696099 (000)a0 00019 (073) -00346 (000) -00373 (000) 00912 (000)a1 00012 (000) -00044 (000) 00168 (000) -00197 (000)

Anomaly confirmed confirmed confirmed confirmed1949-1958 Multiple R 099 099 094 015

F-test 1021705 (000) 7171257 (000) 75858 (000) 242 (012)a0 -00176 (000) -00191 (000) 00095 (000) -00498 (000)a1 00154 (000) -00181 (000) 00013 (000) -00002 (012)

Anomaly confirmed confirmed confirmed not confirmed1959-1968 Multiple R 099 099 094 078

F-test 1463311 (000) 6002659 (000) 82273 (000) 14352 (000)a0 -00112 (000) 00004 (085) 00151 (000) 00389 (000)a1 00098 (000) -00102 (000) 00011 (000) -00009 (000)

Anomaly confirmed confirmed confirmed confirmed1969-1978 Multiple R 098 099 093 099

F-test 241655 (000) 1451901 (000) 57333 (000) 368160 (000)a0 -00433 (000) 00276 (000) 00099 (002) -00144 (000)a1 00132 (000) -00134 (000) 00020 (000) -00030 (000)

Anomaly confirmed confirmed confirmed confirmed1979-1988 Multiple R 092 078 023 008

F-test 53757 (000) 18707 (000) 487 (003) 085 (036)a0 00813 (000) -02508 (000) 00204 (000) -00235 (000)a1 00036 (000) -00031 (000) -00003 (003) -00001 (036)

Anomaly confirmed confirmed not confirmed not confirmed1989-1998 Multiple R 079 099 074 044

F-test 19705(000) 761967 (000) 14133 (000) 2369 (000)a0 00268 (000) 00023 (021) -00381 (000) 00087 (000)a1 00013 (000) -00028 (000) -00008 (000) 00002 (000)

Anomaly confirmed confirmed not confirmed not confirmed1999-2008 Multiple R 091 093 071 065

F-test 47218 (000) 76564 (000) 9843 (000) 7768 (000)a0 -01493 (000) 01351 (000) 00397 (000) 00007 (093)a1 00081 (000) -00083 (000) -00026 (000) -00011 (000)

Anomaly confirmed confirmed not confirmed confirmed2009-2018 Multiple R 086 087 083 074

F-test 29971 (000) 32484 (000) 23228 (000) 12764 (000)a0 01711 (000) -02250 (000) 00407 (000) -00472 (000)a1 00038 (000) -00044 (000) -00010 (000) -00012 (000)

Anomaly confirmed confirmed not confirmed confirmed

38

F Detailed statistical results DJI sub-periods

F1 Average analysis

Table F1 Average analysis

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 Mean return (gapday)

-001 023 015 -004

Mean return(non-gap day)

007 007 007 007

Anomaly confirmed confirmed confirmed confirmed1999-2008 Mean return (gap

day)090 -045 013 -004

Mean return(non-gap day)

-004 -004 -004 -004

Anomaly confirmed confirmed confirmed confirmed2009-2018 Mean return (gap

day)024 -024 0 -004

Mean return(non-gap day)

004 004 004 004

Anomaly confirmed confirmed not confirmed confirmed

F2 Parametric tests Students t-test

Table F2 T-test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 t-criterion 083 165 087 139t-critical (=095) 196 196 196 196Null hypothesis not rejected not rejected not rejected not rejected

1999-2008 t-criterion 347 351 054 047t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected rejected

2009-2018 t-criterion 265 207 051 058t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

F3 Parametric tests ANOVA

Table F3 ANOVA

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 F 085 409 093 179p-value 035 004 033 018

F critical 384 384 384 384Null hypothesis not rejected rejected not rejected not rejected

1999-2008 F 5405 3196 065 072p-value 0 0 042 039

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

2009-2018 F 554 697 024 058p-value 001 0 062 044

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

29

F4 Non-parametric tests Kruskal-Wallis test

Table F4 Kruskal-Wallis test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 Adjusted H 113 211 113 332df 1 1 1 1

P value 029 015 029 007Null hypothesis not rejected not rejected not rejected not rejected

1999-2008 Adjusted H 1484 1414 003 139df 1 1 1 1

P value 0 0 086 024Null hypothesis rejected rejected not rejected not rejected

2009-2018 Adjusted H 506 68 051 171df 1 1 1 1

P value 002 001 047 019Null hypothesis rejected rejected not rejected not rejected

F5 Regression analysis with dummy variables

Table F5 Regression analysis with dummy variables

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 a0 000068 (000) 00007 (000) 00007 (000) 00007 (000)a1 -000078 (035) 00016 (004) 00008 (033) -00011 (018)

Anomaly not confirmed confirmed not confirmed not confirmed1999-2008 a0 00004 (008) 00004 (008) 00004 (006) 00004 (008)

a1 00087 (000) -00049 (000) 00009 (042) -00008 (039)Anomaly confirmed confirmed not confirmed not confirmed

2009-2018 a0 00004 (006) 00004 (006) 00004 (006) 00004 (006)a1 00021 (001) -00028 (001) -00004 (062) -00008 (047)

Anomaly confirmed confirmed not confirmed not confirmed

F6 Modified CAR approach

Table F6 Modified CAR approach

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 Multiple R 083 088 082 086F-test 22779 (000) 40583 (000) 20401 (000) 3269454 (000)a0 00042 (023) 00017 (073) 00014 (058) -00266 (000)a1 -00009 (000) 00015 (000) 00006 (000) -00009 (000)

Anomaly confirmed confirmed confirmed confirmed1999-2008 Multiple R 095 093 076 019

F-test 62658 (000) 84712 (000) 10056 (000) 492 (003)a0 -00972 (000) 00365 (000) -00198 (000) -00115 (021)a1 00086 (000) -00042 (000) 00014 (000) 00002 (003)

Anomaly confirmed confirmed confirmed not confirmed2009-2018 Multiple R 096 082 08 05

F-test 150452 (000) 16731 (000) 22287 (000) 2620 (000)a0 00548 (000) -00618 (000) 00031 (020) -00112 (000)a1 00013 (000) -00014 (000) -00005 (000) -00004 (000)

Anomaly confirmed confirmed not confirmed confirmed

30

G Detailed statistical results NASDAQ sub-periods

G1 Average analysis

Table G1 Average analysis

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 Mean return (gapday)

094 -111 0189 -029

Mean return(non-gap day)

007 007 007 007

Anomaly confirmed confirmed confirmed confirmed1959-1968 Mean return (gap

day)133 -147 033 -039

Mean return(non-gap day)

006 006 006 006

Anomaly confirmed confirmed confirmed confirmed1969-1978 Mean return (gap

day)19 -186 057 -068

Mean return(non-gap day)

005 005 005 005

Anomaly confirmed confirmed confirmed confirmed1979-1988 Mean return (gap

day)138 -162 066 -04

Mean return(non-gap day)

008 008 008 008

Anomaly confirmed confirmed confirmed confirmed1989-1998 Mean return (gap

day)016 012 018 -009

Mean return(non-gap day)

002 002 002 002

Anomaly confirmed not confirmed confirmed confirmed1999-2008 Mean return (gap

day)38E-3 027 -036 -013

Mean return(non-gap day)

-01 -01 -01 -01

Anomaly confirmed not confirmed not confirmed not confirmed2009-2018 Mean return (gap

day)039 009 013 -025

Mean return(non-gap day)

001 001 001 001

Anomaly confirmed not confirmed confirmed confirmed

G2 Parametric tests Students t-test

Table G2 T-test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 t-criterion 3194 3076 201 559t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected rejected

1959-1968 t-criterion 1399 2246 443 382t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected rejected

1969-1978 t-criterion 261 4358 417 786t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected rejected

1979-1988 t-criterion 1847 1445 709 395t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected rejected

1989-1998 t-criterion 13 066 126 093t-critical (=095) 196 196 196 196Null hypothesis not rejected not rejected not rejected not rejected

1999-2008 t-criterion 192 106 111 009t-critical (=095) 196 196 196 196Null hypothesis not rejected not rejected not rejected not rejected

2009-2018 t-criterion 27 05 089 188t-critical (=095) 196 196 196 196Null hypothesis rejected not rejected not rejected not rejected

31

G3 Parametric tests ANOVA

Table G3 ANOVA

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 F 88153 190609 1272 14521p-value 0 0 0 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1959-1968 F 93974 149771 4715 10418p-value 0 0 0 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1969-1978 F 84546 145429 6295 18241p-value 0 0 0 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1979-1988 F 66952 110482 13138 8626p-value 0 0 0 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1989-1998 F 323 138 43 168p-value 007 024 003 019

F critical 384 384 384 384Null hypothesis not rejected not rejected rejected not rejected

1999-2008 F 106 512 327 003p-value 001 002 007 085

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

2009-2018 F 169 069 175 93p-value 0 04 018 0

F critical 384 384 384 384Null hypothesis rejected not rejected not rejected rejected

G4 Non-parametric tests Kruskal-Wallis test

Table G4 Kruskal-Wallis test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 Adjusted H 26254 32592 1464 3962df 1 1 1 1

P value 0 0 0 0Null hypothesis rejected rejected rejected rejected

1959-1968 Adjusted H 28235 27989 2736 332df 1 1 1 1

P value 0 0 0 0Null hypothesis rejected rejected rejected rejected

1969-1978 Adjusted H 22202 33777 3311 7591df 1 1 1 1

P value 0 0 0 0Null hypothesis rejected rejected rejected rejected

1979-1988 Adjusted H 23282 25292 4812 3964df 1 1 1 1

P value 0 0 0 0Null hypothesis rejected rejected rejected rejected

1989-1998 Adjusted H 381 017 175 132df 1 1 1 1

P value 005 068 019 025Null hypothesis not rejected not rejected not rejected not rejected

1999-2008 Adjusted H 855 023 044 004df 1 1 1 1

P value 0 063 051 084Null hypothesis rejected not rejected not rejected not rejected

2009-2018 Adjusted H 1063 009 257 709df 1 1 1 1

P value 0 077 011 001Null hypothesis rejected not rejected not rejected rejected

32

G5 Regression analysis with dummy variables

Table G5 Regression analysis with dummy variables

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 a0 00007 (000) 00007 (000) 00007 (000) 00007 (000)a1 00088 (000) -00119 (000) 00011 (000) -00036 (000)

Anomaly confirmed confirmed confirmed confirmed1959-1968 a0 00006 (000) 00006 (000) 00006 (000) 00006 (000)

a1 00128 (000) -00153 (000) 00027 (000) -00046 (000)Anomaly confirmed confirmed confirmed confirmed

1969-1978 a0 00005 (000) 00005 (000) 00005 (000) 00005 (000)a1 00185 (000) -00192 (000) 00053 (000) -00073 (000)

Anomaly confirmed confirmed confirmed confirmed1979-1988 a0 00008 (000) 00008 (000) 00008 (000) 00008 (000)

a1 00131 (000) -00172 (000) 00059 (000) -00048 (000)Anomaly confirmed confirmed confirmed confirmed

1989-1998 a0 00002 (027) 00002 (028) 00002 (028) 00002 (027)a1 00014 (007) 00010 (024) 00017 (004) -00011 (019)

Anomaly not confirmed not confirmed confirmed not confirmed1999-2008 a0 00001 (059) 00001 (062) 00001 (059) 00001 (060)

a1 00037 (000) 00026 (002) -00038 (000) -00014 (019)Anomaly confirmed not confirmed not confirmed not confirmed

2009-2018 a0 00001 (049) 00001 (049) 00001 (049) 00001 (049)a1 00038 (000) 00007 (040) 00012 (018) -00027 (000)

Anomaly confirmed not confirmed not confirmed confirmed

G6 Modified CAR approach

Table G6 Modified CAR approach

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 Multiple R 099 099 093 098F-test 5753605 (000) 100470(000) 6280421 283281a0 -00091 (000) -00349 (000) 00056 (001) 00015 (073)a1 00083 (000) -00110 (000) 00010 (000) -00031 (000)

Anomaly confirmed confirmed confirmed confirmed1959-1968 Multiple R 099 099 099 099

F-test 3923274 (000) 3005562 (000) 443198 (000) 372583 (000)a0 00096 (000) 00073 (016) -00082 (000) -00095 (004)a1 00116 (001) -00149 (000) 00025 (000) -00047 (000)

Anomaly confirmed confirmed confirmed confirmed1969-1978 Multiple R 099 099 098 099

F-test 4302608 (000) 2723953 (000) 179969 (000) 639745a0 00246 (000) -00002 (000) 00217 (000) -00514 (000)a1 00176 (000) -00182 (000) 00049 (000) -00062 (000)

Anomaly confirmed confirmed confirmed confirmed1979-1988 Multiple R 099 099 099 099

F-test 5872335 (000) 1182609 (000) 1083558 (000) 910089 (000)a0 00136 (000) -01081 (000) -00285 (000) -00101 (000)a1 00131 (000) -00167 (000) 00062 (000) -00048 (000)

Anomaly confirmed confirmed confirmed confirmed1989-1998 Multiple R 09 056 069 016

F-test 46947 (000) 4885 (000) 10131 (000) 263 (011)a0 00102 (002) -00261 (000) -0016 (001) -00237 (000)a1 00015 (000) 00010 (000) 0001 (000) 00002 (011)

Anomaly confirmed confirmed confirmed not confirmed1999-2008 Multiple R 093 087 073 037

F-test 71863 (000) 32530 (000) 13273 (000) 1669 (000)a0 00185 (004) 00311 (000) -00130 (039) -00546 (000)a1 00037 (000) 00032 (000) -00026 (000) -00007 (000)

Anomaly confirmed not confirmed not confirmed confirmed2009-2018 Multiple R 089 001 096 091

F-test 40818 (000) 000 (094) 116744 (000) 53770 (000)a0 01436 (000) -01099 (000) -01036 (000) 00697 (000)a1 00030 (000) 00000 (094) 00024 (000) -00021 (000)

Anomaly confirmed not confirmed confirmed confirmed

33

H Detailed statistical results SampP 500 sub-periods

H1 Average analysis

Table H1 Average analysis

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 Mean return (gapday)

138 -171 004 -014

Mean return(non-gap day)

0 0 0 0

Anomaly confirmed confirmed confirmed confirmed1939-1948 Mean return (gap

day)001 -042 172 -195

Mean return(non-gap day)

003 003 003 003

Anomaly confirmed confirmed confirmed confirmed1949-1958 Mean return (gap

day)165 -18 02 002

Mean return(non-gap day)

006 006 006 006

Anomaly confirmed confirmed confirmed not confirmed1959-1968 Mean return (gap

day)104 -102 015 0

Mean return(non-gap day)

002 002 002 002

Anomaly confirmed confirmed confirmed not confirmed1969-1978 Mean return (gap

day)131 -13 019 -03

Mean return(non-gap day)

0 0 0 0

Anomaly confirmed confirmed confirmed confirmed1979-1988 Mean return (gap

day)058 -042 015 003

Mean return(non-gap day)

005 005 005 005

Anomaly confirmed confirmed confirmed not confirmed1989-1998 Mean return (gap

day)02 -023 -002 01

Mean return(non-gap day)

007 007 007 007

Anomaly confirmed confirmed not confirmed not confirmed1999-2008 Mean return (gap

day)083 -089 -023 -005

Mean return(non-gap day)

001 001 001 001

Anomaly confirmed confirmed not confirmed confirmed2009-2018 Mean return (gap

day)055 -052 001 -015

Mean return(non-gap day)

004 004 004 004

Anomaly confirmed confirmed not confirmed confirmed

34

H2 Parametric tests Students t-test

Table H2 T-test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 t-criterion 101 85 029 048t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

1939-1948 t-criterion 064 479 3074 225t-critical (=095) 196 196 196 196Null hypothesis not rejected rejected rejected rejected

1949-1958 t-criterion 2964 2383 193 041t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

1959-1968 t-criterion 2281 2157 21 023t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected not rejected

1969-1978 t-criterion 1318 2034 187 321t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected rejected

1979-1988 t-criterion 435 535 07 037t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

1989-1998 t-criterion 201 396 132 052t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

1999-2008 t-criterion 362 433 117 022t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

2009-2018 t-criterion 375 382 027 132t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

H3 Parametric tests ANOVA

Table H3 ANOVA

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 F 6281 8032 005 051p-value 0 0 082 047

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

1939-1948 F 056 2603 34854 51034p-value 045 0 0 0

F critical 384 384 384 384Null hypothesis not rejected rejected rejected rejected

1949-1958 F 100174 128997 897 062p-value 0 0 0 043

F critical 384 384 384 384Null hypothesis rejected rejected rejected not rejected

1959-1968 F 36831 32858 617 01p-value 0 0 001 074

F critical 384 384 384 384Null hypothesis rejected rejected rejected not rejected

1969-1978 F 26601 3063 53 152p-value 0 0 002 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1979-1988 F 23 245 076 009p-value 0 0 039 077

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

1989-1998 F 399 1156 118 015p-value 004 0 027 069

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

1999-2008 F 4253 5622 365 024p-value 0 0 006 062

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

2009-2018 F 3064 3656 01 43p-value 0 0 075 004

F critical 384 384 384 384Null hypothesis rejected rejected not rejected rejected

35

H4 Non-parametric tests Kruskal -Wallis test

Table H4 Kruskal-Wallis test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 Adjusted H 9982 5913 332 14df 1 1 1 1

P value 0 0 007 024Null hypothesis rejected rejected not rejected not rejected

1939-1948 Adjusted H 494 1999 23387 24927df 1 1 1 1

P value 003 0 0 0Null hypothesis rejected rejected rejected rejected

1949-1958 Adjusted H 28728 28175 348 15df 1 1 1 1

P value 0 0 006 022Null hypothesis rejected rejected not rejected not rejected

1959-1968 Adjusted H 25729 21437 701 063df 1 1 1 1

P value 0 0 001 043Null hypothesis rejected rejected rejected not rejected

1969-1978 Adjusted H 14407 20078 27 1706df 1 1 1 1

P value 0 0 01 0Null hypothesis rejected rejected not rejected rejected

1979-1988 Adjusted H 1788 2836 027 034df 1 1 1 1

P value 0 0 06 056Null hypothesis rejected rejected not rejected not rejected

1989-1998 Adjusted H 251 1431 111 044df 1 1 1 1

P value 011 0 029 051Null hypothesis not rejected rejected not rejected not rejected

1999-2008 Adjusted H 1812 1788 042 002df 1 1 1 1

P value 0 0 052 089Null hypothesis rejected rejected not rejected not rejected

2009-2018 Adjusted H 1314 1783 074 37df 1 1 1 1

P value 0 0 039 005Null hypothesis rejected rejected not rejected not rejected

36

H5 Regression analysis with dummy variables

Table H5 Regression analysis with dummy variables

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 a0 00000 (097) 00000 (004) 00000 (097) 00000 (097)a1 00138 (000) -00172 (000) 00004 (082) -00014 (047)

Anomaly confirmed confirmed not confirmed not confirmed1939-1948 a0 00003 (015) 00003 (015) 00003 (015) 00003 (015)

a1 00007 (045) -00045 (000) 00170 (000) -00199 (000)Anomaly not confirmed confirmed confirmed confirmed

1949-1958 a0 00006 (000) 00006 (000) 00006 (000) 00006 (000)a1 00160 (000) -00188 (000) 00016 (000) -00004 (043)

Anomaly confirmed confirmed confirmed not confirmed1959-1968 a0 00002 (007) 00002 (004) 00002 (008) 00002 (008)

a1 00103 (000) -00105 (000) 00014 (001) -00002 (074)Anomaly confirmed confirmed confirmed not confirmed

1969-1978 a0 00000 (078) 00000 (078) 00000 (078) 00000 (078)a1 00132 (000) -00132 (000) 00019 (002) -00030 (000)

Anomaly confirmed confirmed confirmed confirmed1979-1988 a0 00006 (001) 00006 (001) 00006 (001) 00006 (000)

a1 00053 (000) -00048 (000) 00009 (040) -00003 (075)Anomaly confirmed confirmed not confirmed not confirmed

1989-1998 a0 00007 (000) 00007 (000) 00007 (000) 00007 (000)a1 00016 (005) -00030 (000) -00009 (026) 00003 (072)

Anomaly confirmed confirmed not confirmed not confirmed1999-2008 a0 00001 (075) 00001 (075) 00001 (075) 00001 (076)

a1 00083 (000) -00091 (000) -00024 (005) -00006 (062)Anomaly confirmed confirmed not confirmed not confirmed

2009-2018 a0 00004 (003) 00004 (000) 00004 (003) 00004 (003)a1 00051 (000) -00059 (000) -00003 (075) -00019 (003)

Anomaly confirmed confirmed not confirmed confirmed

37

H6 Modified CAR approach

Table H6 Modified CAR approach

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 Multiple R 096 095 046 046F-test 175935 (000) 96500 (000) 3534 (000) 2880 (000)a0 -01070 (000) 01958 (000) 00405 (000) 00535 (000)a1 00121 (000) -00160 (000) 00006 (000) -00014 (000)

Anomaly confirmed confirmed confirmed confirmed1939-1948 Multiple R 08 099 099 099

F-test 18777 (000) 755727 (000) 3572830 (000) 2696099 (000)a0 00019 (073) -00346 (000) -00373 (000) 00912 (000)a1 00012 (000) -00044 (000) 00168 (000) -00197 (000)

Anomaly confirmed confirmed confirmed confirmed1949-1958 Multiple R 099 099 094 015

F-test 1021705 (000) 7171257 (000) 75858 (000) 242 (012)a0 -00176 (000) -00191 (000) 00095 (000) -00498 (000)a1 00154 (000) -00181 (000) 00013 (000) -00002 (012)

Anomaly confirmed confirmed confirmed not confirmed1959-1968 Multiple R 099 099 094 078

F-test 1463311 (000) 6002659 (000) 82273 (000) 14352 (000)a0 -00112 (000) 00004 (085) 00151 (000) 00389 (000)a1 00098 (000) -00102 (000) 00011 (000) -00009 (000)

Anomaly confirmed confirmed confirmed confirmed1969-1978 Multiple R 098 099 093 099

F-test 241655 (000) 1451901 (000) 57333 (000) 368160 (000)a0 -00433 (000) 00276 (000) 00099 (002) -00144 (000)a1 00132 (000) -00134 (000) 00020 (000) -00030 (000)

Anomaly confirmed confirmed confirmed confirmed1979-1988 Multiple R 092 078 023 008

F-test 53757 (000) 18707 (000) 487 (003) 085 (036)a0 00813 (000) -02508 (000) 00204 (000) -00235 (000)a1 00036 (000) -00031 (000) -00003 (003) -00001 (036)

Anomaly confirmed confirmed not confirmed not confirmed1989-1998 Multiple R 079 099 074 044

F-test 19705(000) 761967 (000) 14133 (000) 2369 (000)a0 00268 (000) 00023 (021) -00381 (000) 00087 (000)a1 00013 (000) -00028 (000) -00008 (000) 00002 (000)

Anomaly confirmed confirmed not confirmed not confirmed1999-2008 Multiple R 091 093 071 065

F-test 47218 (000) 76564 (000) 9843 (000) 7768 (000)a0 -01493 (000) 01351 (000) 00397 (000) 00007 (093)a1 00081 (000) -00083 (000) -00026 (000) -00011 (000)

Anomaly confirmed confirmed not confirmed confirmed2009-2018 Multiple R 086 087 083 074

F-test 29971 (000) 32484 (000) 23228 (000) 12764 (000)a0 01711 (000) -02250 (000) 00407 (000) -00472 (000)a1 00038 (000) -00044 (000) -00010 (000) -00012 (000)

Anomaly confirmed confirmed not confirmed confirmed

38

F4 Non-parametric tests Kruskal-Wallis test

Table F4 Kruskal-Wallis test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 Adjusted H 113 211 113 332df 1 1 1 1

P value 029 015 029 007Null hypothesis not rejected not rejected not rejected not rejected

1999-2008 Adjusted H 1484 1414 003 139df 1 1 1 1

P value 0 0 086 024Null hypothesis rejected rejected not rejected not rejected

2009-2018 Adjusted H 506 68 051 171df 1 1 1 1

P value 002 001 047 019Null hypothesis rejected rejected not rejected not rejected

F5 Regression analysis with dummy variables

Table F5 Regression analysis with dummy variables

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 a0 000068 (000) 00007 (000) 00007 (000) 00007 (000)a1 -000078 (035) 00016 (004) 00008 (033) -00011 (018)

Anomaly not confirmed confirmed not confirmed not confirmed1999-2008 a0 00004 (008) 00004 (008) 00004 (006) 00004 (008)

a1 00087 (000) -00049 (000) 00009 (042) -00008 (039)Anomaly confirmed confirmed not confirmed not confirmed

2009-2018 a0 00004 (006) 00004 (006) 00004 (006) 00004 (006)a1 00021 (001) -00028 (001) -00004 (062) -00008 (047)

Anomaly confirmed confirmed not confirmed not confirmed

F6 Modified CAR approach

Table F6 Modified CAR approach

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1989-1998 Multiple R 083 088 082 086F-test 22779 (000) 40583 (000) 20401 (000) 3269454 (000)a0 00042 (023) 00017 (073) 00014 (058) -00266 (000)a1 -00009 (000) 00015 (000) 00006 (000) -00009 (000)

Anomaly confirmed confirmed confirmed confirmed1999-2008 Multiple R 095 093 076 019

F-test 62658 (000) 84712 (000) 10056 (000) 492 (003)a0 -00972 (000) 00365 (000) -00198 (000) -00115 (021)a1 00086 (000) -00042 (000) 00014 (000) 00002 (003)

Anomaly confirmed confirmed confirmed not confirmed2009-2018 Multiple R 096 082 08 05

F-test 150452 (000) 16731 (000) 22287 (000) 2620 (000)a0 00548 (000) -00618 (000) 00031 (020) -00112 (000)a1 00013 (000) -00014 (000) -00005 (000) -00004 (000)

Anomaly confirmed confirmed not confirmed confirmed

30

G Detailed statistical results NASDAQ sub-periods

G1 Average analysis

Table G1 Average analysis

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 Mean return (gapday)

094 -111 0189 -029

Mean return(non-gap day)

007 007 007 007

Anomaly confirmed confirmed confirmed confirmed1959-1968 Mean return (gap

day)133 -147 033 -039

Mean return(non-gap day)

006 006 006 006

Anomaly confirmed confirmed confirmed confirmed1969-1978 Mean return (gap

day)19 -186 057 -068

Mean return(non-gap day)

005 005 005 005

Anomaly confirmed confirmed confirmed confirmed1979-1988 Mean return (gap

day)138 -162 066 -04

Mean return(non-gap day)

008 008 008 008

Anomaly confirmed confirmed confirmed confirmed1989-1998 Mean return (gap

day)016 012 018 -009

Mean return(non-gap day)

002 002 002 002

Anomaly confirmed not confirmed confirmed confirmed1999-2008 Mean return (gap

day)38E-3 027 -036 -013

Mean return(non-gap day)

-01 -01 -01 -01

Anomaly confirmed not confirmed not confirmed not confirmed2009-2018 Mean return (gap

day)039 009 013 -025

Mean return(non-gap day)

001 001 001 001

Anomaly confirmed not confirmed confirmed confirmed

G2 Parametric tests Students t-test

Table G2 T-test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 t-criterion 3194 3076 201 559t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected rejected

1959-1968 t-criterion 1399 2246 443 382t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected rejected

1969-1978 t-criterion 261 4358 417 786t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected rejected

1979-1988 t-criterion 1847 1445 709 395t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected rejected

1989-1998 t-criterion 13 066 126 093t-critical (=095) 196 196 196 196Null hypothesis not rejected not rejected not rejected not rejected

1999-2008 t-criterion 192 106 111 009t-critical (=095) 196 196 196 196Null hypothesis not rejected not rejected not rejected not rejected

2009-2018 t-criterion 27 05 089 188t-critical (=095) 196 196 196 196Null hypothesis rejected not rejected not rejected not rejected

31

G3 Parametric tests ANOVA

Table G3 ANOVA

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 F 88153 190609 1272 14521p-value 0 0 0 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1959-1968 F 93974 149771 4715 10418p-value 0 0 0 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1969-1978 F 84546 145429 6295 18241p-value 0 0 0 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1979-1988 F 66952 110482 13138 8626p-value 0 0 0 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1989-1998 F 323 138 43 168p-value 007 024 003 019

F critical 384 384 384 384Null hypothesis not rejected not rejected rejected not rejected

1999-2008 F 106 512 327 003p-value 001 002 007 085

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

2009-2018 F 169 069 175 93p-value 0 04 018 0

F critical 384 384 384 384Null hypothesis rejected not rejected not rejected rejected

G4 Non-parametric tests Kruskal-Wallis test

Table G4 Kruskal-Wallis test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 Adjusted H 26254 32592 1464 3962df 1 1 1 1

P value 0 0 0 0Null hypothesis rejected rejected rejected rejected

1959-1968 Adjusted H 28235 27989 2736 332df 1 1 1 1

P value 0 0 0 0Null hypothesis rejected rejected rejected rejected

1969-1978 Adjusted H 22202 33777 3311 7591df 1 1 1 1

P value 0 0 0 0Null hypothesis rejected rejected rejected rejected

1979-1988 Adjusted H 23282 25292 4812 3964df 1 1 1 1

P value 0 0 0 0Null hypothesis rejected rejected rejected rejected

1989-1998 Adjusted H 381 017 175 132df 1 1 1 1

P value 005 068 019 025Null hypothesis not rejected not rejected not rejected not rejected

1999-2008 Adjusted H 855 023 044 004df 1 1 1 1

P value 0 063 051 084Null hypothesis rejected not rejected not rejected not rejected

2009-2018 Adjusted H 1063 009 257 709df 1 1 1 1

P value 0 077 011 001Null hypothesis rejected not rejected not rejected rejected

32

G5 Regression analysis with dummy variables

Table G5 Regression analysis with dummy variables

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 a0 00007 (000) 00007 (000) 00007 (000) 00007 (000)a1 00088 (000) -00119 (000) 00011 (000) -00036 (000)

Anomaly confirmed confirmed confirmed confirmed1959-1968 a0 00006 (000) 00006 (000) 00006 (000) 00006 (000)

a1 00128 (000) -00153 (000) 00027 (000) -00046 (000)Anomaly confirmed confirmed confirmed confirmed

1969-1978 a0 00005 (000) 00005 (000) 00005 (000) 00005 (000)a1 00185 (000) -00192 (000) 00053 (000) -00073 (000)

Anomaly confirmed confirmed confirmed confirmed1979-1988 a0 00008 (000) 00008 (000) 00008 (000) 00008 (000)

a1 00131 (000) -00172 (000) 00059 (000) -00048 (000)Anomaly confirmed confirmed confirmed confirmed

1989-1998 a0 00002 (027) 00002 (028) 00002 (028) 00002 (027)a1 00014 (007) 00010 (024) 00017 (004) -00011 (019)

Anomaly not confirmed not confirmed confirmed not confirmed1999-2008 a0 00001 (059) 00001 (062) 00001 (059) 00001 (060)

a1 00037 (000) 00026 (002) -00038 (000) -00014 (019)Anomaly confirmed not confirmed not confirmed not confirmed

2009-2018 a0 00001 (049) 00001 (049) 00001 (049) 00001 (049)a1 00038 (000) 00007 (040) 00012 (018) -00027 (000)

Anomaly confirmed not confirmed not confirmed confirmed

G6 Modified CAR approach

Table G6 Modified CAR approach

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 Multiple R 099 099 093 098F-test 5753605 (000) 100470(000) 6280421 283281a0 -00091 (000) -00349 (000) 00056 (001) 00015 (073)a1 00083 (000) -00110 (000) 00010 (000) -00031 (000)

Anomaly confirmed confirmed confirmed confirmed1959-1968 Multiple R 099 099 099 099

F-test 3923274 (000) 3005562 (000) 443198 (000) 372583 (000)a0 00096 (000) 00073 (016) -00082 (000) -00095 (004)a1 00116 (001) -00149 (000) 00025 (000) -00047 (000)

Anomaly confirmed confirmed confirmed confirmed1969-1978 Multiple R 099 099 098 099

F-test 4302608 (000) 2723953 (000) 179969 (000) 639745a0 00246 (000) -00002 (000) 00217 (000) -00514 (000)a1 00176 (000) -00182 (000) 00049 (000) -00062 (000)

Anomaly confirmed confirmed confirmed confirmed1979-1988 Multiple R 099 099 099 099

F-test 5872335 (000) 1182609 (000) 1083558 (000) 910089 (000)a0 00136 (000) -01081 (000) -00285 (000) -00101 (000)a1 00131 (000) -00167 (000) 00062 (000) -00048 (000)

Anomaly confirmed confirmed confirmed confirmed1989-1998 Multiple R 09 056 069 016

F-test 46947 (000) 4885 (000) 10131 (000) 263 (011)a0 00102 (002) -00261 (000) -0016 (001) -00237 (000)a1 00015 (000) 00010 (000) 0001 (000) 00002 (011)

Anomaly confirmed confirmed confirmed not confirmed1999-2008 Multiple R 093 087 073 037

F-test 71863 (000) 32530 (000) 13273 (000) 1669 (000)a0 00185 (004) 00311 (000) -00130 (039) -00546 (000)a1 00037 (000) 00032 (000) -00026 (000) -00007 (000)

Anomaly confirmed not confirmed not confirmed confirmed2009-2018 Multiple R 089 001 096 091

F-test 40818 (000) 000 (094) 116744 (000) 53770 (000)a0 01436 (000) -01099 (000) -01036 (000) 00697 (000)a1 00030 (000) 00000 (094) 00024 (000) -00021 (000)

Anomaly confirmed not confirmed confirmed confirmed

33

H Detailed statistical results SampP 500 sub-periods

H1 Average analysis

Table H1 Average analysis

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 Mean return (gapday)

138 -171 004 -014

Mean return(non-gap day)

0 0 0 0

Anomaly confirmed confirmed confirmed confirmed1939-1948 Mean return (gap

day)001 -042 172 -195

Mean return(non-gap day)

003 003 003 003

Anomaly confirmed confirmed confirmed confirmed1949-1958 Mean return (gap

day)165 -18 02 002

Mean return(non-gap day)

006 006 006 006

Anomaly confirmed confirmed confirmed not confirmed1959-1968 Mean return (gap

day)104 -102 015 0

Mean return(non-gap day)

002 002 002 002

Anomaly confirmed confirmed confirmed not confirmed1969-1978 Mean return (gap

day)131 -13 019 -03

Mean return(non-gap day)

0 0 0 0

Anomaly confirmed confirmed confirmed confirmed1979-1988 Mean return (gap

day)058 -042 015 003

Mean return(non-gap day)

005 005 005 005

Anomaly confirmed confirmed confirmed not confirmed1989-1998 Mean return (gap

day)02 -023 -002 01

Mean return(non-gap day)

007 007 007 007

Anomaly confirmed confirmed not confirmed not confirmed1999-2008 Mean return (gap

day)083 -089 -023 -005

Mean return(non-gap day)

001 001 001 001

Anomaly confirmed confirmed not confirmed confirmed2009-2018 Mean return (gap

day)055 -052 001 -015

Mean return(non-gap day)

004 004 004 004

Anomaly confirmed confirmed not confirmed confirmed

34

H2 Parametric tests Students t-test

Table H2 T-test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 t-criterion 101 85 029 048t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

1939-1948 t-criterion 064 479 3074 225t-critical (=095) 196 196 196 196Null hypothesis not rejected rejected rejected rejected

1949-1958 t-criterion 2964 2383 193 041t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

1959-1968 t-criterion 2281 2157 21 023t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected not rejected

1969-1978 t-criterion 1318 2034 187 321t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected rejected

1979-1988 t-criterion 435 535 07 037t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

1989-1998 t-criterion 201 396 132 052t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

1999-2008 t-criterion 362 433 117 022t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

2009-2018 t-criterion 375 382 027 132t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

H3 Parametric tests ANOVA

Table H3 ANOVA

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 F 6281 8032 005 051p-value 0 0 082 047

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

1939-1948 F 056 2603 34854 51034p-value 045 0 0 0

F critical 384 384 384 384Null hypothesis not rejected rejected rejected rejected

1949-1958 F 100174 128997 897 062p-value 0 0 0 043

F critical 384 384 384 384Null hypothesis rejected rejected rejected not rejected

1959-1968 F 36831 32858 617 01p-value 0 0 001 074

F critical 384 384 384 384Null hypothesis rejected rejected rejected not rejected

1969-1978 F 26601 3063 53 152p-value 0 0 002 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1979-1988 F 23 245 076 009p-value 0 0 039 077

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

1989-1998 F 399 1156 118 015p-value 004 0 027 069

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

1999-2008 F 4253 5622 365 024p-value 0 0 006 062

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

2009-2018 F 3064 3656 01 43p-value 0 0 075 004

F critical 384 384 384 384Null hypothesis rejected rejected not rejected rejected

35

H4 Non-parametric tests Kruskal -Wallis test

Table H4 Kruskal-Wallis test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 Adjusted H 9982 5913 332 14df 1 1 1 1

P value 0 0 007 024Null hypothesis rejected rejected not rejected not rejected

1939-1948 Adjusted H 494 1999 23387 24927df 1 1 1 1

P value 003 0 0 0Null hypothesis rejected rejected rejected rejected

1949-1958 Adjusted H 28728 28175 348 15df 1 1 1 1

P value 0 0 006 022Null hypothesis rejected rejected not rejected not rejected

1959-1968 Adjusted H 25729 21437 701 063df 1 1 1 1

P value 0 0 001 043Null hypothesis rejected rejected rejected not rejected

1969-1978 Adjusted H 14407 20078 27 1706df 1 1 1 1

P value 0 0 01 0Null hypothesis rejected rejected not rejected rejected

1979-1988 Adjusted H 1788 2836 027 034df 1 1 1 1

P value 0 0 06 056Null hypothesis rejected rejected not rejected not rejected

1989-1998 Adjusted H 251 1431 111 044df 1 1 1 1

P value 011 0 029 051Null hypothesis not rejected rejected not rejected not rejected

1999-2008 Adjusted H 1812 1788 042 002df 1 1 1 1

P value 0 0 052 089Null hypothesis rejected rejected not rejected not rejected

2009-2018 Adjusted H 1314 1783 074 37df 1 1 1 1

P value 0 0 039 005Null hypothesis rejected rejected not rejected not rejected

36

H5 Regression analysis with dummy variables

Table H5 Regression analysis with dummy variables

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 a0 00000 (097) 00000 (004) 00000 (097) 00000 (097)a1 00138 (000) -00172 (000) 00004 (082) -00014 (047)

Anomaly confirmed confirmed not confirmed not confirmed1939-1948 a0 00003 (015) 00003 (015) 00003 (015) 00003 (015)

a1 00007 (045) -00045 (000) 00170 (000) -00199 (000)Anomaly not confirmed confirmed confirmed confirmed

1949-1958 a0 00006 (000) 00006 (000) 00006 (000) 00006 (000)a1 00160 (000) -00188 (000) 00016 (000) -00004 (043)

Anomaly confirmed confirmed confirmed not confirmed1959-1968 a0 00002 (007) 00002 (004) 00002 (008) 00002 (008)

a1 00103 (000) -00105 (000) 00014 (001) -00002 (074)Anomaly confirmed confirmed confirmed not confirmed

1969-1978 a0 00000 (078) 00000 (078) 00000 (078) 00000 (078)a1 00132 (000) -00132 (000) 00019 (002) -00030 (000)

Anomaly confirmed confirmed confirmed confirmed1979-1988 a0 00006 (001) 00006 (001) 00006 (001) 00006 (000)

a1 00053 (000) -00048 (000) 00009 (040) -00003 (075)Anomaly confirmed confirmed not confirmed not confirmed

1989-1998 a0 00007 (000) 00007 (000) 00007 (000) 00007 (000)a1 00016 (005) -00030 (000) -00009 (026) 00003 (072)

Anomaly confirmed confirmed not confirmed not confirmed1999-2008 a0 00001 (075) 00001 (075) 00001 (075) 00001 (076)

a1 00083 (000) -00091 (000) -00024 (005) -00006 (062)Anomaly confirmed confirmed not confirmed not confirmed

2009-2018 a0 00004 (003) 00004 (000) 00004 (003) 00004 (003)a1 00051 (000) -00059 (000) -00003 (075) -00019 (003)

Anomaly confirmed confirmed not confirmed confirmed

37

H6 Modified CAR approach

Table H6 Modified CAR approach

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 Multiple R 096 095 046 046F-test 175935 (000) 96500 (000) 3534 (000) 2880 (000)a0 -01070 (000) 01958 (000) 00405 (000) 00535 (000)a1 00121 (000) -00160 (000) 00006 (000) -00014 (000)

Anomaly confirmed confirmed confirmed confirmed1939-1948 Multiple R 08 099 099 099

F-test 18777 (000) 755727 (000) 3572830 (000) 2696099 (000)a0 00019 (073) -00346 (000) -00373 (000) 00912 (000)a1 00012 (000) -00044 (000) 00168 (000) -00197 (000)

Anomaly confirmed confirmed confirmed confirmed1949-1958 Multiple R 099 099 094 015

F-test 1021705 (000) 7171257 (000) 75858 (000) 242 (012)a0 -00176 (000) -00191 (000) 00095 (000) -00498 (000)a1 00154 (000) -00181 (000) 00013 (000) -00002 (012)

Anomaly confirmed confirmed confirmed not confirmed1959-1968 Multiple R 099 099 094 078

F-test 1463311 (000) 6002659 (000) 82273 (000) 14352 (000)a0 -00112 (000) 00004 (085) 00151 (000) 00389 (000)a1 00098 (000) -00102 (000) 00011 (000) -00009 (000)

Anomaly confirmed confirmed confirmed confirmed1969-1978 Multiple R 098 099 093 099

F-test 241655 (000) 1451901 (000) 57333 (000) 368160 (000)a0 -00433 (000) 00276 (000) 00099 (002) -00144 (000)a1 00132 (000) -00134 (000) 00020 (000) -00030 (000)

Anomaly confirmed confirmed confirmed confirmed1979-1988 Multiple R 092 078 023 008

F-test 53757 (000) 18707 (000) 487 (003) 085 (036)a0 00813 (000) -02508 (000) 00204 (000) -00235 (000)a1 00036 (000) -00031 (000) -00003 (003) -00001 (036)

Anomaly confirmed confirmed not confirmed not confirmed1989-1998 Multiple R 079 099 074 044

F-test 19705(000) 761967 (000) 14133 (000) 2369 (000)a0 00268 (000) 00023 (021) -00381 (000) 00087 (000)a1 00013 (000) -00028 (000) -00008 (000) 00002 (000)

Anomaly confirmed confirmed not confirmed not confirmed1999-2008 Multiple R 091 093 071 065

F-test 47218 (000) 76564 (000) 9843 (000) 7768 (000)a0 -01493 (000) 01351 (000) 00397 (000) 00007 (093)a1 00081 (000) -00083 (000) -00026 (000) -00011 (000)

Anomaly confirmed confirmed not confirmed confirmed2009-2018 Multiple R 086 087 083 074

F-test 29971 (000) 32484 (000) 23228 (000) 12764 (000)a0 01711 (000) -02250 (000) 00407 (000) -00472 (000)a1 00038 (000) -00044 (000) -00010 (000) -00012 (000)

Anomaly confirmed confirmed not confirmed confirmed

38

G Detailed statistical results NASDAQ sub-periods

G1 Average analysis

Table G1 Average analysis

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 Mean return (gapday)

094 -111 0189 -029

Mean return(non-gap day)

007 007 007 007

Anomaly confirmed confirmed confirmed confirmed1959-1968 Mean return (gap

day)133 -147 033 -039

Mean return(non-gap day)

006 006 006 006

Anomaly confirmed confirmed confirmed confirmed1969-1978 Mean return (gap

day)19 -186 057 -068

Mean return(non-gap day)

005 005 005 005

Anomaly confirmed confirmed confirmed confirmed1979-1988 Mean return (gap

day)138 -162 066 -04

Mean return(non-gap day)

008 008 008 008

Anomaly confirmed confirmed confirmed confirmed1989-1998 Mean return (gap

day)016 012 018 -009

Mean return(non-gap day)

002 002 002 002

Anomaly confirmed not confirmed confirmed confirmed1999-2008 Mean return (gap

day)38E-3 027 -036 -013

Mean return(non-gap day)

-01 -01 -01 -01

Anomaly confirmed not confirmed not confirmed not confirmed2009-2018 Mean return (gap

day)039 009 013 -025

Mean return(non-gap day)

001 001 001 001

Anomaly confirmed not confirmed confirmed confirmed

G2 Parametric tests Students t-test

Table G2 T-test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 t-criterion 3194 3076 201 559t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected rejected

1959-1968 t-criterion 1399 2246 443 382t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected rejected

1969-1978 t-criterion 261 4358 417 786t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected rejected

1979-1988 t-criterion 1847 1445 709 395t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected rejected

1989-1998 t-criterion 13 066 126 093t-critical (=095) 196 196 196 196Null hypothesis not rejected not rejected not rejected not rejected

1999-2008 t-criterion 192 106 111 009t-critical (=095) 196 196 196 196Null hypothesis not rejected not rejected not rejected not rejected

2009-2018 t-criterion 27 05 089 188t-critical (=095) 196 196 196 196Null hypothesis rejected not rejected not rejected not rejected

31

G3 Parametric tests ANOVA

Table G3 ANOVA

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 F 88153 190609 1272 14521p-value 0 0 0 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1959-1968 F 93974 149771 4715 10418p-value 0 0 0 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1969-1978 F 84546 145429 6295 18241p-value 0 0 0 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1979-1988 F 66952 110482 13138 8626p-value 0 0 0 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1989-1998 F 323 138 43 168p-value 007 024 003 019

F critical 384 384 384 384Null hypothesis not rejected not rejected rejected not rejected

1999-2008 F 106 512 327 003p-value 001 002 007 085

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

2009-2018 F 169 069 175 93p-value 0 04 018 0

F critical 384 384 384 384Null hypothesis rejected not rejected not rejected rejected

G4 Non-parametric tests Kruskal-Wallis test

Table G4 Kruskal-Wallis test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 Adjusted H 26254 32592 1464 3962df 1 1 1 1

P value 0 0 0 0Null hypothesis rejected rejected rejected rejected

1959-1968 Adjusted H 28235 27989 2736 332df 1 1 1 1

P value 0 0 0 0Null hypothesis rejected rejected rejected rejected

1969-1978 Adjusted H 22202 33777 3311 7591df 1 1 1 1

P value 0 0 0 0Null hypothesis rejected rejected rejected rejected

1979-1988 Adjusted H 23282 25292 4812 3964df 1 1 1 1

P value 0 0 0 0Null hypothesis rejected rejected rejected rejected

1989-1998 Adjusted H 381 017 175 132df 1 1 1 1

P value 005 068 019 025Null hypothesis not rejected not rejected not rejected not rejected

1999-2008 Adjusted H 855 023 044 004df 1 1 1 1

P value 0 063 051 084Null hypothesis rejected not rejected not rejected not rejected

2009-2018 Adjusted H 1063 009 257 709df 1 1 1 1

P value 0 077 011 001Null hypothesis rejected not rejected not rejected rejected

32

G5 Regression analysis with dummy variables

Table G5 Regression analysis with dummy variables

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 a0 00007 (000) 00007 (000) 00007 (000) 00007 (000)a1 00088 (000) -00119 (000) 00011 (000) -00036 (000)

Anomaly confirmed confirmed confirmed confirmed1959-1968 a0 00006 (000) 00006 (000) 00006 (000) 00006 (000)

a1 00128 (000) -00153 (000) 00027 (000) -00046 (000)Anomaly confirmed confirmed confirmed confirmed

1969-1978 a0 00005 (000) 00005 (000) 00005 (000) 00005 (000)a1 00185 (000) -00192 (000) 00053 (000) -00073 (000)

Anomaly confirmed confirmed confirmed confirmed1979-1988 a0 00008 (000) 00008 (000) 00008 (000) 00008 (000)

a1 00131 (000) -00172 (000) 00059 (000) -00048 (000)Anomaly confirmed confirmed confirmed confirmed

1989-1998 a0 00002 (027) 00002 (028) 00002 (028) 00002 (027)a1 00014 (007) 00010 (024) 00017 (004) -00011 (019)

Anomaly not confirmed not confirmed confirmed not confirmed1999-2008 a0 00001 (059) 00001 (062) 00001 (059) 00001 (060)

a1 00037 (000) 00026 (002) -00038 (000) -00014 (019)Anomaly confirmed not confirmed not confirmed not confirmed

2009-2018 a0 00001 (049) 00001 (049) 00001 (049) 00001 (049)a1 00038 (000) 00007 (040) 00012 (018) -00027 (000)

Anomaly confirmed not confirmed not confirmed confirmed

G6 Modified CAR approach

Table G6 Modified CAR approach

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 Multiple R 099 099 093 098F-test 5753605 (000) 100470(000) 6280421 283281a0 -00091 (000) -00349 (000) 00056 (001) 00015 (073)a1 00083 (000) -00110 (000) 00010 (000) -00031 (000)

Anomaly confirmed confirmed confirmed confirmed1959-1968 Multiple R 099 099 099 099

F-test 3923274 (000) 3005562 (000) 443198 (000) 372583 (000)a0 00096 (000) 00073 (016) -00082 (000) -00095 (004)a1 00116 (001) -00149 (000) 00025 (000) -00047 (000)

Anomaly confirmed confirmed confirmed confirmed1969-1978 Multiple R 099 099 098 099

F-test 4302608 (000) 2723953 (000) 179969 (000) 639745a0 00246 (000) -00002 (000) 00217 (000) -00514 (000)a1 00176 (000) -00182 (000) 00049 (000) -00062 (000)

Anomaly confirmed confirmed confirmed confirmed1979-1988 Multiple R 099 099 099 099

F-test 5872335 (000) 1182609 (000) 1083558 (000) 910089 (000)a0 00136 (000) -01081 (000) -00285 (000) -00101 (000)a1 00131 (000) -00167 (000) 00062 (000) -00048 (000)

Anomaly confirmed confirmed confirmed confirmed1989-1998 Multiple R 09 056 069 016

F-test 46947 (000) 4885 (000) 10131 (000) 263 (011)a0 00102 (002) -00261 (000) -0016 (001) -00237 (000)a1 00015 (000) 00010 (000) 0001 (000) 00002 (011)

Anomaly confirmed confirmed confirmed not confirmed1999-2008 Multiple R 093 087 073 037

F-test 71863 (000) 32530 (000) 13273 (000) 1669 (000)a0 00185 (004) 00311 (000) -00130 (039) -00546 (000)a1 00037 (000) 00032 (000) -00026 (000) -00007 (000)

Anomaly confirmed not confirmed not confirmed confirmed2009-2018 Multiple R 089 001 096 091

F-test 40818 (000) 000 (094) 116744 (000) 53770 (000)a0 01436 (000) -01099 (000) -01036 (000) 00697 (000)a1 00030 (000) 00000 (094) 00024 (000) -00021 (000)

Anomaly confirmed not confirmed confirmed confirmed

33

H Detailed statistical results SampP 500 sub-periods

H1 Average analysis

Table H1 Average analysis

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 Mean return (gapday)

138 -171 004 -014

Mean return(non-gap day)

0 0 0 0

Anomaly confirmed confirmed confirmed confirmed1939-1948 Mean return (gap

day)001 -042 172 -195

Mean return(non-gap day)

003 003 003 003

Anomaly confirmed confirmed confirmed confirmed1949-1958 Mean return (gap

day)165 -18 02 002

Mean return(non-gap day)

006 006 006 006

Anomaly confirmed confirmed confirmed not confirmed1959-1968 Mean return (gap

day)104 -102 015 0

Mean return(non-gap day)

002 002 002 002

Anomaly confirmed confirmed confirmed not confirmed1969-1978 Mean return (gap

day)131 -13 019 -03

Mean return(non-gap day)

0 0 0 0

Anomaly confirmed confirmed confirmed confirmed1979-1988 Mean return (gap

day)058 -042 015 003

Mean return(non-gap day)

005 005 005 005

Anomaly confirmed confirmed confirmed not confirmed1989-1998 Mean return (gap

day)02 -023 -002 01

Mean return(non-gap day)

007 007 007 007

Anomaly confirmed confirmed not confirmed not confirmed1999-2008 Mean return (gap

day)083 -089 -023 -005

Mean return(non-gap day)

001 001 001 001

Anomaly confirmed confirmed not confirmed confirmed2009-2018 Mean return (gap

day)055 -052 001 -015

Mean return(non-gap day)

004 004 004 004

Anomaly confirmed confirmed not confirmed confirmed

34

H2 Parametric tests Students t-test

Table H2 T-test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 t-criterion 101 85 029 048t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

1939-1948 t-criterion 064 479 3074 225t-critical (=095) 196 196 196 196Null hypothesis not rejected rejected rejected rejected

1949-1958 t-criterion 2964 2383 193 041t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

1959-1968 t-criterion 2281 2157 21 023t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected not rejected

1969-1978 t-criterion 1318 2034 187 321t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected rejected

1979-1988 t-criterion 435 535 07 037t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

1989-1998 t-criterion 201 396 132 052t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

1999-2008 t-criterion 362 433 117 022t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

2009-2018 t-criterion 375 382 027 132t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

H3 Parametric tests ANOVA

Table H3 ANOVA

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 F 6281 8032 005 051p-value 0 0 082 047

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

1939-1948 F 056 2603 34854 51034p-value 045 0 0 0

F critical 384 384 384 384Null hypothesis not rejected rejected rejected rejected

1949-1958 F 100174 128997 897 062p-value 0 0 0 043

F critical 384 384 384 384Null hypothesis rejected rejected rejected not rejected

1959-1968 F 36831 32858 617 01p-value 0 0 001 074

F critical 384 384 384 384Null hypothesis rejected rejected rejected not rejected

1969-1978 F 26601 3063 53 152p-value 0 0 002 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1979-1988 F 23 245 076 009p-value 0 0 039 077

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

1989-1998 F 399 1156 118 015p-value 004 0 027 069

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

1999-2008 F 4253 5622 365 024p-value 0 0 006 062

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

2009-2018 F 3064 3656 01 43p-value 0 0 075 004

F critical 384 384 384 384Null hypothesis rejected rejected not rejected rejected

35

H4 Non-parametric tests Kruskal -Wallis test

Table H4 Kruskal-Wallis test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 Adjusted H 9982 5913 332 14df 1 1 1 1

P value 0 0 007 024Null hypothesis rejected rejected not rejected not rejected

1939-1948 Adjusted H 494 1999 23387 24927df 1 1 1 1

P value 003 0 0 0Null hypothesis rejected rejected rejected rejected

1949-1958 Adjusted H 28728 28175 348 15df 1 1 1 1

P value 0 0 006 022Null hypothesis rejected rejected not rejected not rejected

1959-1968 Adjusted H 25729 21437 701 063df 1 1 1 1

P value 0 0 001 043Null hypothesis rejected rejected rejected not rejected

1969-1978 Adjusted H 14407 20078 27 1706df 1 1 1 1

P value 0 0 01 0Null hypothesis rejected rejected not rejected rejected

1979-1988 Adjusted H 1788 2836 027 034df 1 1 1 1

P value 0 0 06 056Null hypothesis rejected rejected not rejected not rejected

1989-1998 Adjusted H 251 1431 111 044df 1 1 1 1

P value 011 0 029 051Null hypothesis not rejected rejected not rejected not rejected

1999-2008 Adjusted H 1812 1788 042 002df 1 1 1 1

P value 0 0 052 089Null hypothesis rejected rejected not rejected not rejected

2009-2018 Adjusted H 1314 1783 074 37df 1 1 1 1

P value 0 0 039 005Null hypothesis rejected rejected not rejected not rejected

36

H5 Regression analysis with dummy variables

Table H5 Regression analysis with dummy variables

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 a0 00000 (097) 00000 (004) 00000 (097) 00000 (097)a1 00138 (000) -00172 (000) 00004 (082) -00014 (047)

Anomaly confirmed confirmed not confirmed not confirmed1939-1948 a0 00003 (015) 00003 (015) 00003 (015) 00003 (015)

a1 00007 (045) -00045 (000) 00170 (000) -00199 (000)Anomaly not confirmed confirmed confirmed confirmed

1949-1958 a0 00006 (000) 00006 (000) 00006 (000) 00006 (000)a1 00160 (000) -00188 (000) 00016 (000) -00004 (043)

Anomaly confirmed confirmed confirmed not confirmed1959-1968 a0 00002 (007) 00002 (004) 00002 (008) 00002 (008)

a1 00103 (000) -00105 (000) 00014 (001) -00002 (074)Anomaly confirmed confirmed confirmed not confirmed

1969-1978 a0 00000 (078) 00000 (078) 00000 (078) 00000 (078)a1 00132 (000) -00132 (000) 00019 (002) -00030 (000)

Anomaly confirmed confirmed confirmed confirmed1979-1988 a0 00006 (001) 00006 (001) 00006 (001) 00006 (000)

a1 00053 (000) -00048 (000) 00009 (040) -00003 (075)Anomaly confirmed confirmed not confirmed not confirmed

1989-1998 a0 00007 (000) 00007 (000) 00007 (000) 00007 (000)a1 00016 (005) -00030 (000) -00009 (026) 00003 (072)

Anomaly confirmed confirmed not confirmed not confirmed1999-2008 a0 00001 (075) 00001 (075) 00001 (075) 00001 (076)

a1 00083 (000) -00091 (000) -00024 (005) -00006 (062)Anomaly confirmed confirmed not confirmed not confirmed

2009-2018 a0 00004 (003) 00004 (000) 00004 (003) 00004 (003)a1 00051 (000) -00059 (000) -00003 (075) -00019 (003)

Anomaly confirmed confirmed not confirmed confirmed

37

H6 Modified CAR approach

Table H6 Modified CAR approach

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 Multiple R 096 095 046 046F-test 175935 (000) 96500 (000) 3534 (000) 2880 (000)a0 -01070 (000) 01958 (000) 00405 (000) 00535 (000)a1 00121 (000) -00160 (000) 00006 (000) -00014 (000)

Anomaly confirmed confirmed confirmed confirmed1939-1948 Multiple R 08 099 099 099

F-test 18777 (000) 755727 (000) 3572830 (000) 2696099 (000)a0 00019 (073) -00346 (000) -00373 (000) 00912 (000)a1 00012 (000) -00044 (000) 00168 (000) -00197 (000)

Anomaly confirmed confirmed confirmed confirmed1949-1958 Multiple R 099 099 094 015

F-test 1021705 (000) 7171257 (000) 75858 (000) 242 (012)a0 -00176 (000) -00191 (000) 00095 (000) -00498 (000)a1 00154 (000) -00181 (000) 00013 (000) -00002 (012)

Anomaly confirmed confirmed confirmed not confirmed1959-1968 Multiple R 099 099 094 078

F-test 1463311 (000) 6002659 (000) 82273 (000) 14352 (000)a0 -00112 (000) 00004 (085) 00151 (000) 00389 (000)a1 00098 (000) -00102 (000) 00011 (000) -00009 (000)

Anomaly confirmed confirmed confirmed confirmed1969-1978 Multiple R 098 099 093 099

F-test 241655 (000) 1451901 (000) 57333 (000) 368160 (000)a0 -00433 (000) 00276 (000) 00099 (002) -00144 (000)a1 00132 (000) -00134 (000) 00020 (000) -00030 (000)

Anomaly confirmed confirmed confirmed confirmed1979-1988 Multiple R 092 078 023 008

F-test 53757 (000) 18707 (000) 487 (003) 085 (036)a0 00813 (000) -02508 (000) 00204 (000) -00235 (000)a1 00036 (000) -00031 (000) -00003 (003) -00001 (036)

Anomaly confirmed confirmed not confirmed not confirmed1989-1998 Multiple R 079 099 074 044

F-test 19705(000) 761967 (000) 14133 (000) 2369 (000)a0 00268 (000) 00023 (021) -00381 (000) 00087 (000)a1 00013 (000) -00028 (000) -00008 (000) 00002 (000)

Anomaly confirmed confirmed not confirmed not confirmed1999-2008 Multiple R 091 093 071 065

F-test 47218 (000) 76564 (000) 9843 (000) 7768 (000)a0 -01493 (000) 01351 (000) 00397 (000) 00007 (093)a1 00081 (000) -00083 (000) -00026 (000) -00011 (000)

Anomaly confirmed confirmed not confirmed confirmed2009-2018 Multiple R 086 087 083 074

F-test 29971 (000) 32484 (000) 23228 (000) 12764 (000)a0 01711 (000) -02250 (000) 00407 (000) -00472 (000)a1 00038 (000) -00044 (000) -00010 (000) -00012 (000)

Anomaly confirmed confirmed not confirmed confirmed

38

G3 Parametric tests ANOVA

Table G3 ANOVA

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 F 88153 190609 1272 14521p-value 0 0 0 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1959-1968 F 93974 149771 4715 10418p-value 0 0 0 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1969-1978 F 84546 145429 6295 18241p-value 0 0 0 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1979-1988 F 66952 110482 13138 8626p-value 0 0 0 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1989-1998 F 323 138 43 168p-value 007 024 003 019

F critical 384 384 384 384Null hypothesis not rejected not rejected rejected not rejected

1999-2008 F 106 512 327 003p-value 001 002 007 085

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

2009-2018 F 169 069 175 93p-value 0 04 018 0

F critical 384 384 384 384Null hypothesis rejected not rejected not rejected rejected

G4 Non-parametric tests Kruskal-Wallis test

Table G4 Kruskal-Wallis test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 Adjusted H 26254 32592 1464 3962df 1 1 1 1

P value 0 0 0 0Null hypothesis rejected rejected rejected rejected

1959-1968 Adjusted H 28235 27989 2736 332df 1 1 1 1

P value 0 0 0 0Null hypothesis rejected rejected rejected rejected

1969-1978 Adjusted H 22202 33777 3311 7591df 1 1 1 1

P value 0 0 0 0Null hypothesis rejected rejected rejected rejected

1979-1988 Adjusted H 23282 25292 4812 3964df 1 1 1 1

P value 0 0 0 0Null hypothesis rejected rejected rejected rejected

1989-1998 Adjusted H 381 017 175 132df 1 1 1 1

P value 005 068 019 025Null hypothesis not rejected not rejected not rejected not rejected

1999-2008 Adjusted H 855 023 044 004df 1 1 1 1

P value 0 063 051 084Null hypothesis rejected not rejected not rejected not rejected

2009-2018 Adjusted H 1063 009 257 709df 1 1 1 1

P value 0 077 011 001Null hypothesis rejected not rejected not rejected rejected

32

G5 Regression analysis with dummy variables

Table G5 Regression analysis with dummy variables

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 a0 00007 (000) 00007 (000) 00007 (000) 00007 (000)a1 00088 (000) -00119 (000) 00011 (000) -00036 (000)

Anomaly confirmed confirmed confirmed confirmed1959-1968 a0 00006 (000) 00006 (000) 00006 (000) 00006 (000)

a1 00128 (000) -00153 (000) 00027 (000) -00046 (000)Anomaly confirmed confirmed confirmed confirmed

1969-1978 a0 00005 (000) 00005 (000) 00005 (000) 00005 (000)a1 00185 (000) -00192 (000) 00053 (000) -00073 (000)

Anomaly confirmed confirmed confirmed confirmed1979-1988 a0 00008 (000) 00008 (000) 00008 (000) 00008 (000)

a1 00131 (000) -00172 (000) 00059 (000) -00048 (000)Anomaly confirmed confirmed confirmed confirmed

1989-1998 a0 00002 (027) 00002 (028) 00002 (028) 00002 (027)a1 00014 (007) 00010 (024) 00017 (004) -00011 (019)

Anomaly not confirmed not confirmed confirmed not confirmed1999-2008 a0 00001 (059) 00001 (062) 00001 (059) 00001 (060)

a1 00037 (000) 00026 (002) -00038 (000) -00014 (019)Anomaly confirmed not confirmed not confirmed not confirmed

2009-2018 a0 00001 (049) 00001 (049) 00001 (049) 00001 (049)a1 00038 (000) 00007 (040) 00012 (018) -00027 (000)

Anomaly confirmed not confirmed not confirmed confirmed

G6 Modified CAR approach

Table G6 Modified CAR approach

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 Multiple R 099 099 093 098F-test 5753605 (000) 100470(000) 6280421 283281a0 -00091 (000) -00349 (000) 00056 (001) 00015 (073)a1 00083 (000) -00110 (000) 00010 (000) -00031 (000)

Anomaly confirmed confirmed confirmed confirmed1959-1968 Multiple R 099 099 099 099

F-test 3923274 (000) 3005562 (000) 443198 (000) 372583 (000)a0 00096 (000) 00073 (016) -00082 (000) -00095 (004)a1 00116 (001) -00149 (000) 00025 (000) -00047 (000)

Anomaly confirmed confirmed confirmed confirmed1969-1978 Multiple R 099 099 098 099

F-test 4302608 (000) 2723953 (000) 179969 (000) 639745a0 00246 (000) -00002 (000) 00217 (000) -00514 (000)a1 00176 (000) -00182 (000) 00049 (000) -00062 (000)

Anomaly confirmed confirmed confirmed confirmed1979-1988 Multiple R 099 099 099 099

F-test 5872335 (000) 1182609 (000) 1083558 (000) 910089 (000)a0 00136 (000) -01081 (000) -00285 (000) -00101 (000)a1 00131 (000) -00167 (000) 00062 (000) -00048 (000)

Anomaly confirmed confirmed confirmed confirmed1989-1998 Multiple R 09 056 069 016

F-test 46947 (000) 4885 (000) 10131 (000) 263 (011)a0 00102 (002) -00261 (000) -0016 (001) -00237 (000)a1 00015 (000) 00010 (000) 0001 (000) 00002 (011)

Anomaly confirmed confirmed confirmed not confirmed1999-2008 Multiple R 093 087 073 037

F-test 71863 (000) 32530 (000) 13273 (000) 1669 (000)a0 00185 (004) 00311 (000) -00130 (039) -00546 (000)a1 00037 (000) 00032 (000) -00026 (000) -00007 (000)

Anomaly confirmed not confirmed not confirmed confirmed2009-2018 Multiple R 089 001 096 091

F-test 40818 (000) 000 (094) 116744 (000) 53770 (000)a0 01436 (000) -01099 (000) -01036 (000) 00697 (000)a1 00030 (000) 00000 (094) 00024 (000) -00021 (000)

Anomaly confirmed not confirmed confirmed confirmed

33

H Detailed statistical results SampP 500 sub-periods

H1 Average analysis

Table H1 Average analysis

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 Mean return (gapday)

138 -171 004 -014

Mean return(non-gap day)

0 0 0 0

Anomaly confirmed confirmed confirmed confirmed1939-1948 Mean return (gap

day)001 -042 172 -195

Mean return(non-gap day)

003 003 003 003

Anomaly confirmed confirmed confirmed confirmed1949-1958 Mean return (gap

day)165 -18 02 002

Mean return(non-gap day)

006 006 006 006

Anomaly confirmed confirmed confirmed not confirmed1959-1968 Mean return (gap

day)104 -102 015 0

Mean return(non-gap day)

002 002 002 002

Anomaly confirmed confirmed confirmed not confirmed1969-1978 Mean return (gap

day)131 -13 019 -03

Mean return(non-gap day)

0 0 0 0

Anomaly confirmed confirmed confirmed confirmed1979-1988 Mean return (gap

day)058 -042 015 003

Mean return(non-gap day)

005 005 005 005

Anomaly confirmed confirmed confirmed not confirmed1989-1998 Mean return (gap

day)02 -023 -002 01

Mean return(non-gap day)

007 007 007 007

Anomaly confirmed confirmed not confirmed not confirmed1999-2008 Mean return (gap

day)083 -089 -023 -005

Mean return(non-gap day)

001 001 001 001

Anomaly confirmed confirmed not confirmed confirmed2009-2018 Mean return (gap

day)055 -052 001 -015

Mean return(non-gap day)

004 004 004 004

Anomaly confirmed confirmed not confirmed confirmed

34

H2 Parametric tests Students t-test

Table H2 T-test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 t-criterion 101 85 029 048t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

1939-1948 t-criterion 064 479 3074 225t-critical (=095) 196 196 196 196Null hypothesis not rejected rejected rejected rejected

1949-1958 t-criterion 2964 2383 193 041t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

1959-1968 t-criterion 2281 2157 21 023t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected not rejected

1969-1978 t-criterion 1318 2034 187 321t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected rejected

1979-1988 t-criterion 435 535 07 037t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

1989-1998 t-criterion 201 396 132 052t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

1999-2008 t-criterion 362 433 117 022t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

2009-2018 t-criterion 375 382 027 132t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

H3 Parametric tests ANOVA

Table H3 ANOVA

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 F 6281 8032 005 051p-value 0 0 082 047

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

1939-1948 F 056 2603 34854 51034p-value 045 0 0 0

F critical 384 384 384 384Null hypothesis not rejected rejected rejected rejected

1949-1958 F 100174 128997 897 062p-value 0 0 0 043

F critical 384 384 384 384Null hypothesis rejected rejected rejected not rejected

1959-1968 F 36831 32858 617 01p-value 0 0 001 074

F critical 384 384 384 384Null hypothesis rejected rejected rejected not rejected

1969-1978 F 26601 3063 53 152p-value 0 0 002 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1979-1988 F 23 245 076 009p-value 0 0 039 077

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

1989-1998 F 399 1156 118 015p-value 004 0 027 069

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

1999-2008 F 4253 5622 365 024p-value 0 0 006 062

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

2009-2018 F 3064 3656 01 43p-value 0 0 075 004

F critical 384 384 384 384Null hypothesis rejected rejected not rejected rejected

35

H4 Non-parametric tests Kruskal -Wallis test

Table H4 Kruskal-Wallis test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 Adjusted H 9982 5913 332 14df 1 1 1 1

P value 0 0 007 024Null hypothesis rejected rejected not rejected not rejected

1939-1948 Adjusted H 494 1999 23387 24927df 1 1 1 1

P value 003 0 0 0Null hypothesis rejected rejected rejected rejected

1949-1958 Adjusted H 28728 28175 348 15df 1 1 1 1

P value 0 0 006 022Null hypothesis rejected rejected not rejected not rejected

1959-1968 Adjusted H 25729 21437 701 063df 1 1 1 1

P value 0 0 001 043Null hypothesis rejected rejected rejected not rejected

1969-1978 Adjusted H 14407 20078 27 1706df 1 1 1 1

P value 0 0 01 0Null hypothesis rejected rejected not rejected rejected

1979-1988 Adjusted H 1788 2836 027 034df 1 1 1 1

P value 0 0 06 056Null hypothesis rejected rejected not rejected not rejected

1989-1998 Adjusted H 251 1431 111 044df 1 1 1 1

P value 011 0 029 051Null hypothesis not rejected rejected not rejected not rejected

1999-2008 Adjusted H 1812 1788 042 002df 1 1 1 1

P value 0 0 052 089Null hypothesis rejected rejected not rejected not rejected

2009-2018 Adjusted H 1314 1783 074 37df 1 1 1 1

P value 0 0 039 005Null hypothesis rejected rejected not rejected not rejected

36

H5 Regression analysis with dummy variables

Table H5 Regression analysis with dummy variables

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 a0 00000 (097) 00000 (004) 00000 (097) 00000 (097)a1 00138 (000) -00172 (000) 00004 (082) -00014 (047)

Anomaly confirmed confirmed not confirmed not confirmed1939-1948 a0 00003 (015) 00003 (015) 00003 (015) 00003 (015)

a1 00007 (045) -00045 (000) 00170 (000) -00199 (000)Anomaly not confirmed confirmed confirmed confirmed

1949-1958 a0 00006 (000) 00006 (000) 00006 (000) 00006 (000)a1 00160 (000) -00188 (000) 00016 (000) -00004 (043)

Anomaly confirmed confirmed confirmed not confirmed1959-1968 a0 00002 (007) 00002 (004) 00002 (008) 00002 (008)

a1 00103 (000) -00105 (000) 00014 (001) -00002 (074)Anomaly confirmed confirmed confirmed not confirmed

1969-1978 a0 00000 (078) 00000 (078) 00000 (078) 00000 (078)a1 00132 (000) -00132 (000) 00019 (002) -00030 (000)

Anomaly confirmed confirmed confirmed confirmed1979-1988 a0 00006 (001) 00006 (001) 00006 (001) 00006 (000)

a1 00053 (000) -00048 (000) 00009 (040) -00003 (075)Anomaly confirmed confirmed not confirmed not confirmed

1989-1998 a0 00007 (000) 00007 (000) 00007 (000) 00007 (000)a1 00016 (005) -00030 (000) -00009 (026) 00003 (072)

Anomaly confirmed confirmed not confirmed not confirmed1999-2008 a0 00001 (075) 00001 (075) 00001 (075) 00001 (076)

a1 00083 (000) -00091 (000) -00024 (005) -00006 (062)Anomaly confirmed confirmed not confirmed not confirmed

2009-2018 a0 00004 (003) 00004 (000) 00004 (003) 00004 (003)a1 00051 (000) -00059 (000) -00003 (075) -00019 (003)

Anomaly confirmed confirmed not confirmed confirmed

37

H6 Modified CAR approach

Table H6 Modified CAR approach

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 Multiple R 096 095 046 046F-test 175935 (000) 96500 (000) 3534 (000) 2880 (000)a0 -01070 (000) 01958 (000) 00405 (000) 00535 (000)a1 00121 (000) -00160 (000) 00006 (000) -00014 (000)

Anomaly confirmed confirmed confirmed confirmed1939-1948 Multiple R 08 099 099 099

F-test 18777 (000) 755727 (000) 3572830 (000) 2696099 (000)a0 00019 (073) -00346 (000) -00373 (000) 00912 (000)a1 00012 (000) -00044 (000) 00168 (000) -00197 (000)

Anomaly confirmed confirmed confirmed confirmed1949-1958 Multiple R 099 099 094 015

F-test 1021705 (000) 7171257 (000) 75858 (000) 242 (012)a0 -00176 (000) -00191 (000) 00095 (000) -00498 (000)a1 00154 (000) -00181 (000) 00013 (000) -00002 (012)

Anomaly confirmed confirmed confirmed not confirmed1959-1968 Multiple R 099 099 094 078

F-test 1463311 (000) 6002659 (000) 82273 (000) 14352 (000)a0 -00112 (000) 00004 (085) 00151 (000) 00389 (000)a1 00098 (000) -00102 (000) 00011 (000) -00009 (000)

Anomaly confirmed confirmed confirmed confirmed1969-1978 Multiple R 098 099 093 099

F-test 241655 (000) 1451901 (000) 57333 (000) 368160 (000)a0 -00433 (000) 00276 (000) 00099 (002) -00144 (000)a1 00132 (000) -00134 (000) 00020 (000) -00030 (000)

Anomaly confirmed confirmed confirmed confirmed1979-1988 Multiple R 092 078 023 008

F-test 53757 (000) 18707 (000) 487 (003) 085 (036)a0 00813 (000) -02508 (000) 00204 (000) -00235 (000)a1 00036 (000) -00031 (000) -00003 (003) -00001 (036)

Anomaly confirmed confirmed not confirmed not confirmed1989-1998 Multiple R 079 099 074 044

F-test 19705(000) 761967 (000) 14133 (000) 2369 (000)a0 00268 (000) 00023 (021) -00381 (000) 00087 (000)a1 00013 (000) -00028 (000) -00008 (000) 00002 (000)

Anomaly confirmed confirmed not confirmed not confirmed1999-2008 Multiple R 091 093 071 065

F-test 47218 (000) 76564 (000) 9843 (000) 7768 (000)a0 -01493 (000) 01351 (000) 00397 (000) 00007 (093)a1 00081 (000) -00083 (000) -00026 (000) -00011 (000)

Anomaly confirmed confirmed not confirmed confirmed2009-2018 Multiple R 086 087 083 074

F-test 29971 (000) 32484 (000) 23228 (000) 12764 (000)a0 01711 (000) -02250 (000) 00407 (000) -00472 (000)a1 00038 (000) -00044 (000) -00010 (000) -00012 (000)

Anomaly confirmed confirmed not confirmed confirmed

38

G5 Regression analysis with dummy variables

Table G5 Regression analysis with dummy variables

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 a0 00007 (000) 00007 (000) 00007 (000) 00007 (000)a1 00088 (000) -00119 (000) 00011 (000) -00036 (000)

Anomaly confirmed confirmed confirmed confirmed1959-1968 a0 00006 (000) 00006 (000) 00006 (000) 00006 (000)

a1 00128 (000) -00153 (000) 00027 (000) -00046 (000)Anomaly confirmed confirmed confirmed confirmed

1969-1978 a0 00005 (000) 00005 (000) 00005 (000) 00005 (000)a1 00185 (000) -00192 (000) 00053 (000) -00073 (000)

Anomaly confirmed confirmed confirmed confirmed1979-1988 a0 00008 (000) 00008 (000) 00008 (000) 00008 (000)

a1 00131 (000) -00172 (000) 00059 (000) -00048 (000)Anomaly confirmed confirmed confirmed confirmed

1989-1998 a0 00002 (027) 00002 (028) 00002 (028) 00002 (027)a1 00014 (007) 00010 (024) 00017 (004) -00011 (019)

Anomaly not confirmed not confirmed confirmed not confirmed1999-2008 a0 00001 (059) 00001 (062) 00001 (059) 00001 (060)

a1 00037 (000) 00026 (002) -00038 (000) -00014 (019)Anomaly confirmed not confirmed not confirmed not confirmed

2009-2018 a0 00001 (049) 00001 (049) 00001 (049) 00001 (049)a1 00038 (000) 00007 (040) 00012 (018) -00027 (000)

Anomaly confirmed not confirmed not confirmed confirmed

G6 Modified CAR approach

Table G6 Modified CAR approach

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1949-1958 Multiple R 099 099 093 098F-test 5753605 (000) 100470(000) 6280421 283281a0 -00091 (000) -00349 (000) 00056 (001) 00015 (073)a1 00083 (000) -00110 (000) 00010 (000) -00031 (000)

Anomaly confirmed confirmed confirmed confirmed1959-1968 Multiple R 099 099 099 099

F-test 3923274 (000) 3005562 (000) 443198 (000) 372583 (000)a0 00096 (000) 00073 (016) -00082 (000) -00095 (004)a1 00116 (001) -00149 (000) 00025 (000) -00047 (000)

Anomaly confirmed confirmed confirmed confirmed1969-1978 Multiple R 099 099 098 099

F-test 4302608 (000) 2723953 (000) 179969 (000) 639745a0 00246 (000) -00002 (000) 00217 (000) -00514 (000)a1 00176 (000) -00182 (000) 00049 (000) -00062 (000)

Anomaly confirmed confirmed confirmed confirmed1979-1988 Multiple R 099 099 099 099

F-test 5872335 (000) 1182609 (000) 1083558 (000) 910089 (000)a0 00136 (000) -01081 (000) -00285 (000) -00101 (000)a1 00131 (000) -00167 (000) 00062 (000) -00048 (000)

Anomaly confirmed confirmed confirmed confirmed1989-1998 Multiple R 09 056 069 016

F-test 46947 (000) 4885 (000) 10131 (000) 263 (011)a0 00102 (002) -00261 (000) -0016 (001) -00237 (000)a1 00015 (000) 00010 (000) 0001 (000) 00002 (011)

Anomaly confirmed confirmed confirmed not confirmed1999-2008 Multiple R 093 087 073 037

F-test 71863 (000) 32530 (000) 13273 (000) 1669 (000)a0 00185 (004) 00311 (000) -00130 (039) -00546 (000)a1 00037 (000) 00032 (000) -00026 (000) -00007 (000)

Anomaly confirmed not confirmed not confirmed confirmed2009-2018 Multiple R 089 001 096 091

F-test 40818 (000) 000 (094) 116744 (000) 53770 (000)a0 01436 (000) -01099 (000) -01036 (000) 00697 (000)a1 00030 (000) 00000 (094) 00024 (000) -00021 (000)

Anomaly confirmed not confirmed confirmed confirmed

33

H Detailed statistical results SampP 500 sub-periods

H1 Average analysis

Table H1 Average analysis

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 Mean return (gapday)

138 -171 004 -014

Mean return(non-gap day)

0 0 0 0

Anomaly confirmed confirmed confirmed confirmed1939-1948 Mean return (gap

day)001 -042 172 -195

Mean return(non-gap day)

003 003 003 003

Anomaly confirmed confirmed confirmed confirmed1949-1958 Mean return (gap

day)165 -18 02 002

Mean return(non-gap day)

006 006 006 006

Anomaly confirmed confirmed confirmed not confirmed1959-1968 Mean return (gap

day)104 -102 015 0

Mean return(non-gap day)

002 002 002 002

Anomaly confirmed confirmed confirmed not confirmed1969-1978 Mean return (gap

day)131 -13 019 -03

Mean return(non-gap day)

0 0 0 0

Anomaly confirmed confirmed confirmed confirmed1979-1988 Mean return (gap

day)058 -042 015 003

Mean return(non-gap day)

005 005 005 005

Anomaly confirmed confirmed confirmed not confirmed1989-1998 Mean return (gap

day)02 -023 -002 01

Mean return(non-gap day)

007 007 007 007

Anomaly confirmed confirmed not confirmed not confirmed1999-2008 Mean return (gap

day)083 -089 -023 -005

Mean return(non-gap day)

001 001 001 001

Anomaly confirmed confirmed not confirmed confirmed2009-2018 Mean return (gap

day)055 -052 001 -015

Mean return(non-gap day)

004 004 004 004

Anomaly confirmed confirmed not confirmed confirmed

34

H2 Parametric tests Students t-test

Table H2 T-test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 t-criterion 101 85 029 048t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

1939-1948 t-criterion 064 479 3074 225t-critical (=095) 196 196 196 196Null hypothesis not rejected rejected rejected rejected

1949-1958 t-criterion 2964 2383 193 041t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

1959-1968 t-criterion 2281 2157 21 023t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected not rejected

1969-1978 t-criterion 1318 2034 187 321t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected rejected

1979-1988 t-criterion 435 535 07 037t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

1989-1998 t-criterion 201 396 132 052t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

1999-2008 t-criterion 362 433 117 022t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

2009-2018 t-criterion 375 382 027 132t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

H3 Parametric tests ANOVA

Table H3 ANOVA

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 F 6281 8032 005 051p-value 0 0 082 047

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

1939-1948 F 056 2603 34854 51034p-value 045 0 0 0

F critical 384 384 384 384Null hypothesis not rejected rejected rejected rejected

1949-1958 F 100174 128997 897 062p-value 0 0 0 043

F critical 384 384 384 384Null hypothesis rejected rejected rejected not rejected

1959-1968 F 36831 32858 617 01p-value 0 0 001 074

F critical 384 384 384 384Null hypothesis rejected rejected rejected not rejected

1969-1978 F 26601 3063 53 152p-value 0 0 002 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1979-1988 F 23 245 076 009p-value 0 0 039 077

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

1989-1998 F 399 1156 118 015p-value 004 0 027 069

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

1999-2008 F 4253 5622 365 024p-value 0 0 006 062

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

2009-2018 F 3064 3656 01 43p-value 0 0 075 004

F critical 384 384 384 384Null hypothesis rejected rejected not rejected rejected

35

H4 Non-parametric tests Kruskal -Wallis test

Table H4 Kruskal-Wallis test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 Adjusted H 9982 5913 332 14df 1 1 1 1

P value 0 0 007 024Null hypothesis rejected rejected not rejected not rejected

1939-1948 Adjusted H 494 1999 23387 24927df 1 1 1 1

P value 003 0 0 0Null hypothesis rejected rejected rejected rejected

1949-1958 Adjusted H 28728 28175 348 15df 1 1 1 1

P value 0 0 006 022Null hypothesis rejected rejected not rejected not rejected

1959-1968 Adjusted H 25729 21437 701 063df 1 1 1 1

P value 0 0 001 043Null hypothesis rejected rejected rejected not rejected

1969-1978 Adjusted H 14407 20078 27 1706df 1 1 1 1

P value 0 0 01 0Null hypothesis rejected rejected not rejected rejected

1979-1988 Adjusted H 1788 2836 027 034df 1 1 1 1

P value 0 0 06 056Null hypothesis rejected rejected not rejected not rejected

1989-1998 Adjusted H 251 1431 111 044df 1 1 1 1

P value 011 0 029 051Null hypothesis not rejected rejected not rejected not rejected

1999-2008 Adjusted H 1812 1788 042 002df 1 1 1 1

P value 0 0 052 089Null hypothesis rejected rejected not rejected not rejected

2009-2018 Adjusted H 1314 1783 074 37df 1 1 1 1

P value 0 0 039 005Null hypothesis rejected rejected not rejected not rejected

36

H5 Regression analysis with dummy variables

Table H5 Regression analysis with dummy variables

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 a0 00000 (097) 00000 (004) 00000 (097) 00000 (097)a1 00138 (000) -00172 (000) 00004 (082) -00014 (047)

Anomaly confirmed confirmed not confirmed not confirmed1939-1948 a0 00003 (015) 00003 (015) 00003 (015) 00003 (015)

a1 00007 (045) -00045 (000) 00170 (000) -00199 (000)Anomaly not confirmed confirmed confirmed confirmed

1949-1958 a0 00006 (000) 00006 (000) 00006 (000) 00006 (000)a1 00160 (000) -00188 (000) 00016 (000) -00004 (043)

Anomaly confirmed confirmed confirmed not confirmed1959-1968 a0 00002 (007) 00002 (004) 00002 (008) 00002 (008)

a1 00103 (000) -00105 (000) 00014 (001) -00002 (074)Anomaly confirmed confirmed confirmed not confirmed

1969-1978 a0 00000 (078) 00000 (078) 00000 (078) 00000 (078)a1 00132 (000) -00132 (000) 00019 (002) -00030 (000)

Anomaly confirmed confirmed confirmed confirmed1979-1988 a0 00006 (001) 00006 (001) 00006 (001) 00006 (000)

a1 00053 (000) -00048 (000) 00009 (040) -00003 (075)Anomaly confirmed confirmed not confirmed not confirmed

1989-1998 a0 00007 (000) 00007 (000) 00007 (000) 00007 (000)a1 00016 (005) -00030 (000) -00009 (026) 00003 (072)

Anomaly confirmed confirmed not confirmed not confirmed1999-2008 a0 00001 (075) 00001 (075) 00001 (075) 00001 (076)

a1 00083 (000) -00091 (000) -00024 (005) -00006 (062)Anomaly confirmed confirmed not confirmed not confirmed

2009-2018 a0 00004 (003) 00004 (000) 00004 (003) 00004 (003)a1 00051 (000) -00059 (000) -00003 (075) -00019 (003)

Anomaly confirmed confirmed not confirmed confirmed

37

H6 Modified CAR approach

Table H6 Modified CAR approach

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 Multiple R 096 095 046 046F-test 175935 (000) 96500 (000) 3534 (000) 2880 (000)a0 -01070 (000) 01958 (000) 00405 (000) 00535 (000)a1 00121 (000) -00160 (000) 00006 (000) -00014 (000)

Anomaly confirmed confirmed confirmed confirmed1939-1948 Multiple R 08 099 099 099

F-test 18777 (000) 755727 (000) 3572830 (000) 2696099 (000)a0 00019 (073) -00346 (000) -00373 (000) 00912 (000)a1 00012 (000) -00044 (000) 00168 (000) -00197 (000)

Anomaly confirmed confirmed confirmed confirmed1949-1958 Multiple R 099 099 094 015

F-test 1021705 (000) 7171257 (000) 75858 (000) 242 (012)a0 -00176 (000) -00191 (000) 00095 (000) -00498 (000)a1 00154 (000) -00181 (000) 00013 (000) -00002 (012)

Anomaly confirmed confirmed confirmed not confirmed1959-1968 Multiple R 099 099 094 078

F-test 1463311 (000) 6002659 (000) 82273 (000) 14352 (000)a0 -00112 (000) 00004 (085) 00151 (000) 00389 (000)a1 00098 (000) -00102 (000) 00011 (000) -00009 (000)

Anomaly confirmed confirmed confirmed confirmed1969-1978 Multiple R 098 099 093 099

F-test 241655 (000) 1451901 (000) 57333 (000) 368160 (000)a0 -00433 (000) 00276 (000) 00099 (002) -00144 (000)a1 00132 (000) -00134 (000) 00020 (000) -00030 (000)

Anomaly confirmed confirmed confirmed confirmed1979-1988 Multiple R 092 078 023 008

F-test 53757 (000) 18707 (000) 487 (003) 085 (036)a0 00813 (000) -02508 (000) 00204 (000) -00235 (000)a1 00036 (000) -00031 (000) -00003 (003) -00001 (036)

Anomaly confirmed confirmed not confirmed not confirmed1989-1998 Multiple R 079 099 074 044

F-test 19705(000) 761967 (000) 14133 (000) 2369 (000)a0 00268 (000) 00023 (021) -00381 (000) 00087 (000)a1 00013 (000) -00028 (000) -00008 (000) 00002 (000)

Anomaly confirmed confirmed not confirmed not confirmed1999-2008 Multiple R 091 093 071 065

F-test 47218 (000) 76564 (000) 9843 (000) 7768 (000)a0 -01493 (000) 01351 (000) 00397 (000) 00007 (093)a1 00081 (000) -00083 (000) -00026 (000) -00011 (000)

Anomaly confirmed confirmed not confirmed confirmed2009-2018 Multiple R 086 087 083 074

F-test 29971 (000) 32484 (000) 23228 (000) 12764 (000)a0 01711 (000) -02250 (000) 00407 (000) -00472 (000)a1 00038 (000) -00044 (000) -00010 (000) -00012 (000)

Anomaly confirmed confirmed not confirmed confirmed

38

H Detailed statistical results SampP 500 sub-periods

H1 Average analysis

Table H1 Average analysis

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 Mean return (gapday)

138 -171 004 -014

Mean return(non-gap day)

0 0 0 0

Anomaly confirmed confirmed confirmed confirmed1939-1948 Mean return (gap

day)001 -042 172 -195

Mean return(non-gap day)

003 003 003 003

Anomaly confirmed confirmed confirmed confirmed1949-1958 Mean return (gap

day)165 -18 02 002

Mean return(non-gap day)

006 006 006 006

Anomaly confirmed confirmed confirmed not confirmed1959-1968 Mean return (gap

day)104 -102 015 0

Mean return(non-gap day)

002 002 002 002

Anomaly confirmed confirmed confirmed not confirmed1969-1978 Mean return (gap

day)131 -13 019 -03

Mean return(non-gap day)

0 0 0 0

Anomaly confirmed confirmed confirmed confirmed1979-1988 Mean return (gap

day)058 -042 015 003

Mean return(non-gap day)

005 005 005 005

Anomaly confirmed confirmed confirmed not confirmed1989-1998 Mean return (gap

day)02 -023 -002 01

Mean return(non-gap day)

007 007 007 007

Anomaly confirmed confirmed not confirmed not confirmed1999-2008 Mean return (gap

day)083 -089 -023 -005

Mean return(non-gap day)

001 001 001 001

Anomaly confirmed confirmed not confirmed confirmed2009-2018 Mean return (gap

day)055 -052 001 -015

Mean return(non-gap day)

004 004 004 004

Anomaly confirmed confirmed not confirmed confirmed

34

H2 Parametric tests Students t-test

Table H2 T-test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 t-criterion 101 85 029 048t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

1939-1948 t-criterion 064 479 3074 225t-critical (=095) 196 196 196 196Null hypothesis not rejected rejected rejected rejected

1949-1958 t-criterion 2964 2383 193 041t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

1959-1968 t-criterion 2281 2157 21 023t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected not rejected

1969-1978 t-criterion 1318 2034 187 321t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected rejected

1979-1988 t-criterion 435 535 07 037t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

1989-1998 t-criterion 201 396 132 052t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

1999-2008 t-criterion 362 433 117 022t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

2009-2018 t-criterion 375 382 027 132t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

H3 Parametric tests ANOVA

Table H3 ANOVA

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 F 6281 8032 005 051p-value 0 0 082 047

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

1939-1948 F 056 2603 34854 51034p-value 045 0 0 0

F critical 384 384 384 384Null hypothesis not rejected rejected rejected rejected

1949-1958 F 100174 128997 897 062p-value 0 0 0 043

F critical 384 384 384 384Null hypothesis rejected rejected rejected not rejected

1959-1968 F 36831 32858 617 01p-value 0 0 001 074

F critical 384 384 384 384Null hypothesis rejected rejected rejected not rejected

1969-1978 F 26601 3063 53 152p-value 0 0 002 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1979-1988 F 23 245 076 009p-value 0 0 039 077

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

1989-1998 F 399 1156 118 015p-value 004 0 027 069

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

1999-2008 F 4253 5622 365 024p-value 0 0 006 062

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

2009-2018 F 3064 3656 01 43p-value 0 0 075 004

F critical 384 384 384 384Null hypothesis rejected rejected not rejected rejected

35

H4 Non-parametric tests Kruskal -Wallis test

Table H4 Kruskal-Wallis test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 Adjusted H 9982 5913 332 14df 1 1 1 1

P value 0 0 007 024Null hypothesis rejected rejected not rejected not rejected

1939-1948 Adjusted H 494 1999 23387 24927df 1 1 1 1

P value 003 0 0 0Null hypothesis rejected rejected rejected rejected

1949-1958 Adjusted H 28728 28175 348 15df 1 1 1 1

P value 0 0 006 022Null hypothesis rejected rejected not rejected not rejected

1959-1968 Adjusted H 25729 21437 701 063df 1 1 1 1

P value 0 0 001 043Null hypothesis rejected rejected rejected not rejected

1969-1978 Adjusted H 14407 20078 27 1706df 1 1 1 1

P value 0 0 01 0Null hypothesis rejected rejected not rejected rejected

1979-1988 Adjusted H 1788 2836 027 034df 1 1 1 1

P value 0 0 06 056Null hypothesis rejected rejected not rejected not rejected

1989-1998 Adjusted H 251 1431 111 044df 1 1 1 1

P value 011 0 029 051Null hypothesis not rejected rejected not rejected not rejected

1999-2008 Adjusted H 1812 1788 042 002df 1 1 1 1

P value 0 0 052 089Null hypothesis rejected rejected not rejected not rejected

2009-2018 Adjusted H 1314 1783 074 37df 1 1 1 1

P value 0 0 039 005Null hypothesis rejected rejected not rejected not rejected

36

H5 Regression analysis with dummy variables

Table H5 Regression analysis with dummy variables

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 a0 00000 (097) 00000 (004) 00000 (097) 00000 (097)a1 00138 (000) -00172 (000) 00004 (082) -00014 (047)

Anomaly confirmed confirmed not confirmed not confirmed1939-1948 a0 00003 (015) 00003 (015) 00003 (015) 00003 (015)

a1 00007 (045) -00045 (000) 00170 (000) -00199 (000)Anomaly not confirmed confirmed confirmed confirmed

1949-1958 a0 00006 (000) 00006 (000) 00006 (000) 00006 (000)a1 00160 (000) -00188 (000) 00016 (000) -00004 (043)

Anomaly confirmed confirmed confirmed not confirmed1959-1968 a0 00002 (007) 00002 (004) 00002 (008) 00002 (008)

a1 00103 (000) -00105 (000) 00014 (001) -00002 (074)Anomaly confirmed confirmed confirmed not confirmed

1969-1978 a0 00000 (078) 00000 (078) 00000 (078) 00000 (078)a1 00132 (000) -00132 (000) 00019 (002) -00030 (000)

Anomaly confirmed confirmed confirmed confirmed1979-1988 a0 00006 (001) 00006 (001) 00006 (001) 00006 (000)

a1 00053 (000) -00048 (000) 00009 (040) -00003 (075)Anomaly confirmed confirmed not confirmed not confirmed

1989-1998 a0 00007 (000) 00007 (000) 00007 (000) 00007 (000)a1 00016 (005) -00030 (000) -00009 (026) 00003 (072)

Anomaly confirmed confirmed not confirmed not confirmed1999-2008 a0 00001 (075) 00001 (075) 00001 (075) 00001 (076)

a1 00083 (000) -00091 (000) -00024 (005) -00006 (062)Anomaly confirmed confirmed not confirmed not confirmed

2009-2018 a0 00004 (003) 00004 (000) 00004 (003) 00004 (003)a1 00051 (000) -00059 (000) -00003 (075) -00019 (003)

Anomaly confirmed confirmed not confirmed confirmed

37

H6 Modified CAR approach

Table H6 Modified CAR approach

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 Multiple R 096 095 046 046F-test 175935 (000) 96500 (000) 3534 (000) 2880 (000)a0 -01070 (000) 01958 (000) 00405 (000) 00535 (000)a1 00121 (000) -00160 (000) 00006 (000) -00014 (000)

Anomaly confirmed confirmed confirmed confirmed1939-1948 Multiple R 08 099 099 099

F-test 18777 (000) 755727 (000) 3572830 (000) 2696099 (000)a0 00019 (073) -00346 (000) -00373 (000) 00912 (000)a1 00012 (000) -00044 (000) 00168 (000) -00197 (000)

Anomaly confirmed confirmed confirmed confirmed1949-1958 Multiple R 099 099 094 015

F-test 1021705 (000) 7171257 (000) 75858 (000) 242 (012)a0 -00176 (000) -00191 (000) 00095 (000) -00498 (000)a1 00154 (000) -00181 (000) 00013 (000) -00002 (012)

Anomaly confirmed confirmed confirmed not confirmed1959-1968 Multiple R 099 099 094 078

F-test 1463311 (000) 6002659 (000) 82273 (000) 14352 (000)a0 -00112 (000) 00004 (085) 00151 (000) 00389 (000)a1 00098 (000) -00102 (000) 00011 (000) -00009 (000)

Anomaly confirmed confirmed confirmed confirmed1969-1978 Multiple R 098 099 093 099

F-test 241655 (000) 1451901 (000) 57333 (000) 368160 (000)a0 -00433 (000) 00276 (000) 00099 (002) -00144 (000)a1 00132 (000) -00134 (000) 00020 (000) -00030 (000)

Anomaly confirmed confirmed confirmed confirmed1979-1988 Multiple R 092 078 023 008

F-test 53757 (000) 18707 (000) 487 (003) 085 (036)a0 00813 (000) -02508 (000) 00204 (000) -00235 (000)a1 00036 (000) -00031 (000) -00003 (003) -00001 (036)

Anomaly confirmed confirmed not confirmed not confirmed1989-1998 Multiple R 079 099 074 044

F-test 19705(000) 761967 (000) 14133 (000) 2369 (000)a0 00268 (000) 00023 (021) -00381 (000) 00087 (000)a1 00013 (000) -00028 (000) -00008 (000) 00002 (000)

Anomaly confirmed confirmed not confirmed not confirmed1999-2008 Multiple R 091 093 071 065

F-test 47218 (000) 76564 (000) 9843 (000) 7768 (000)a0 -01493 (000) 01351 (000) 00397 (000) 00007 (093)a1 00081 (000) -00083 (000) -00026 (000) -00011 (000)

Anomaly confirmed confirmed not confirmed confirmed2009-2018 Multiple R 086 087 083 074

F-test 29971 (000) 32484 (000) 23228 (000) 12764 (000)a0 01711 (000) -02250 (000) 00407 (000) -00472 (000)a1 00038 (000) -00044 (000) -00010 (000) -00012 (000)

Anomaly confirmed confirmed not confirmed confirmed

38

H2 Parametric tests Students t-test

Table H2 T-test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 t-criterion 101 85 029 048t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

1939-1948 t-criterion 064 479 3074 225t-critical (=095) 196 196 196 196Null hypothesis not rejected rejected rejected rejected

1949-1958 t-criterion 2964 2383 193 041t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

1959-1968 t-criterion 2281 2157 21 023t-critical (=095) 196 196 196 196Null hypothesis rejected rejected rejected not rejected

1969-1978 t-criterion 1318 2034 187 321t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected rejected

1979-1988 t-criterion 435 535 07 037t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

1989-1998 t-criterion 201 396 132 052t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

1999-2008 t-criterion 362 433 117 022t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

2009-2018 t-criterion 375 382 027 132t-critical (=095) 196 196 196 196Null hypothesis rejected rejected not rejected not rejected

H3 Parametric tests ANOVA

Table H3 ANOVA

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 F 6281 8032 005 051p-value 0 0 082 047

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

1939-1948 F 056 2603 34854 51034p-value 045 0 0 0

F critical 384 384 384 384Null hypothesis not rejected rejected rejected rejected

1949-1958 F 100174 128997 897 062p-value 0 0 0 043

F critical 384 384 384 384Null hypothesis rejected rejected rejected not rejected

1959-1968 F 36831 32858 617 01p-value 0 0 001 074

F critical 384 384 384 384Null hypothesis rejected rejected rejected not rejected

1969-1978 F 26601 3063 53 152p-value 0 0 002 0

F critical 384 384 384 384Null hypothesis rejected rejected rejected rejected

1979-1988 F 23 245 076 009p-value 0 0 039 077

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

1989-1998 F 399 1156 118 015p-value 004 0 027 069

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

1999-2008 F 4253 5622 365 024p-value 0 0 006 062

F critical 384 384 384 384Null hypothesis rejected rejected not rejected not rejected

2009-2018 F 3064 3656 01 43p-value 0 0 075 004

F critical 384 384 384 384Null hypothesis rejected rejected not rejected rejected

35

H4 Non-parametric tests Kruskal -Wallis test

Table H4 Kruskal-Wallis test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 Adjusted H 9982 5913 332 14df 1 1 1 1

P value 0 0 007 024Null hypothesis rejected rejected not rejected not rejected

1939-1948 Adjusted H 494 1999 23387 24927df 1 1 1 1

P value 003 0 0 0Null hypothesis rejected rejected rejected rejected

1949-1958 Adjusted H 28728 28175 348 15df 1 1 1 1

P value 0 0 006 022Null hypothesis rejected rejected not rejected not rejected

1959-1968 Adjusted H 25729 21437 701 063df 1 1 1 1

P value 0 0 001 043Null hypothesis rejected rejected rejected not rejected

1969-1978 Adjusted H 14407 20078 27 1706df 1 1 1 1

P value 0 0 01 0Null hypothesis rejected rejected not rejected rejected

1979-1988 Adjusted H 1788 2836 027 034df 1 1 1 1

P value 0 0 06 056Null hypothesis rejected rejected not rejected not rejected

1989-1998 Adjusted H 251 1431 111 044df 1 1 1 1

P value 011 0 029 051Null hypothesis not rejected rejected not rejected not rejected

1999-2008 Adjusted H 1812 1788 042 002df 1 1 1 1

P value 0 0 052 089Null hypothesis rejected rejected not rejected not rejected

2009-2018 Adjusted H 1314 1783 074 37df 1 1 1 1

P value 0 0 039 005Null hypothesis rejected rejected not rejected not rejected

36

H5 Regression analysis with dummy variables

Table H5 Regression analysis with dummy variables

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 a0 00000 (097) 00000 (004) 00000 (097) 00000 (097)a1 00138 (000) -00172 (000) 00004 (082) -00014 (047)

Anomaly confirmed confirmed not confirmed not confirmed1939-1948 a0 00003 (015) 00003 (015) 00003 (015) 00003 (015)

a1 00007 (045) -00045 (000) 00170 (000) -00199 (000)Anomaly not confirmed confirmed confirmed confirmed

1949-1958 a0 00006 (000) 00006 (000) 00006 (000) 00006 (000)a1 00160 (000) -00188 (000) 00016 (000) -00004 (043)

Anomaly confirmed confirmed confirmed not confirmed1959-1968 a0 00002 (007) 00002 (004) 00002 (008) 00002 (008)

a1 00103 (000) -00105 (000) 00014 (001) -00002 (074)Anomaly confirmed confirmed confirmed not confirmed

1969-1978 a0 00000 (078) 00000 (078) 00000 (078) 00000 (078)a1 00132 (000) -00132 (000) 00019 (002) -00030 (000)

Anomaly confirmed confirmed confirmed confirmed1979-1988 a0 00006 (001) 00006 (001) 00006 (001) 00006 (000)

a1 00053 (000) -00048 (000) 00009 (040) -00003 (075)Anomaly confirmed confirmed not confirmed not confirmed

1989-1998 a0 00007 (000) 00007 (000) 00007 (000) 00007 (000)a1 00016 (005) -00030 (000) -00009 (026) 00003 (072)

Anomaly confirmed confirmed not confirmed not confirmed1999-2008 a0 00001 (075) 00001 (075) 00001 (075) 00001 (076)

a1 00083 (000) -00091 (000) -00024 (005) -00006 (062)Anomaly confirmed confirmed not confirmed not confirmed

2009-2018 a0 00004 (003) 00004 (000) 00004 (003) 00004 (003)a1 00051 (000) -00059 (000) -00003 (075) -00019 (003)

Anomaly confirmed confirmed not confirmed confirmed

37

H6 Modified CAR approach

Table H6 Modified CAR approach

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 Multiple R 096 095 046 046F-test 175935 (000) 96500 (000) 3534 (000) 2880 (000)a0 -01070 (000) 01958 (000) 00405 (000) 00535 (000)a1 00121 (000) -00160 (000) 00006 (000) -00014 (000)

Anomaly confirmed confirmed confirmed confirmed1939-1948 Multiple R 08 099 099 099

F-test 18777 (000) 755727 (000) 3572830 (000) 2696099 (000)a0 00019 (073) -00346 (000) -00373 (000) 00912 (000)a1 00012 (000) -00044 (000) 00168 (000) -00197 (000)

Anomaly confirmed confirmed confirmed confirmed1949-1958 Multiple R 099 099 094 015

F-test 1021705 (000) 7171257 (000) 75858 (000) 242 (012)a0 -00176 (000) -00191 (000) 00095 (000) -00498 (000)a1 00154 (000) -00181 (000) 00013 (000) -00002 (012)

Anomaly confirmed confirmed confirmed not confirmed1959-1968 Multiple R 099 099 094 078

F-test 1463311 (000) 6002659 (000) 82273 (000) 14352 (000)a0 -00112 (000) 00004 (085) 00151 (000) 00389 (000)a1 00098 (000) -00102 (000) 00011 (000) -00009 (000)

Anomaly confirmed confirmed confirmed confirmed1969-1978 Multiple R 098 099 093 099

F-test 241655 (000) 1451901 (000) 57333 (000) 368160 (000)a0 -00433 (000) 00276 (000) 00099 (002) -00144 (000)a1 00132 (000) -00134 (000) 00020 (000) -00030 (000)

Anomaly confirmed confirmed confirmed confirmed1979-1988 Multiple R 092 078 023 008

F-test 53757 (000) 18707 (000) 487 (003) 085 (036)a0 00813 (000) -02508 (000) 00204 (000) -00235 (000)a1 00036 (000) -00031 (000) -00003 (003) -00001 (036)

Anomaly confirmed confirmed not confirmed not confirmed1989-1998 Multiple R 079 099 074 044

F-test 19705(000) 761967 (000) 14133 (000) 2369 (000)a0 00268 (000) 00023 (021) -00381 (000) 00087 (000)a1 00013 (000) -00028 (000) -00008 (000) 00002 (000)

Anomaly confirmed confirmed not confirmed not confirmed1999-2008 Multiple R 091 093 071 065

F-test 47218 (000) 76564 (000) 9843 (000) 7768 (000)a0 -01493 (000) 01351 (000) 00397 (000) 00007 (093)a1 00081 (000) -00083 (000) -00026 (000) -00011 (000)

Anomaly confirmed confirmed not confirmed confirmed2009-2018 Multiple R 086 087 083 074

F-test 29971 (000) 32484 (000) 23228 (000) 12764 (000)a0 01711 (000) -02250 (000) 00407 (000) -00472 (000)a1 00038 (000) -00044 (000) -00010 (000) -00012 (000)

Anomaly confirmed confirmed not confirmed confirmed

38

H4 Non-parametric tests Kruskal -Wallis test

Table H4 Kruskal-Wallis test

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 Adjusted H 9982 5913 332 14df 1 1 1 1

P value 0 0 007 024Null hypothesis rejected rejected not rejected not rejected

1939-1948 Adjusted H 494 1999 23387 24927df 1 1 1 1

P value 003 0 0 0Null hypothesis rejected rejected rejected rejected

1949-1958 Adjusted H 28728 28175 348 15df 1 1 1 1

P value 0 0 006 022Null hypothesis rejected rejected not rejected not rejected

1959-1968 Adjusted H 25729 21437 701 063df 1 1 1 1

P value 0 0 001 043Null hypothesis rejected rejected rejected not rejected

1969-1978 Adjusted H 14407 20078 27 1706df 1 1 1 1

P value 0 0 01 0Null hypothesis rejected rejected not rejected rejected

1979-1988 Adjusted H 1788 2836 027 034df 1 1 1 1

P value 0 0 06 056Null hypothesis rejected rejected not rejected not rejected

1989-1998 Adjusted H 251 1431 111 044df 1 1 1 1

P value 011 0 029 051Null hypothesis not rejected rejected not rejected not rejected

1999-2008 Adjusted H 1812 1788 042 002df 1 1 1 1

P value 0 0 052 089Null hypothesis rejected rejected not rejected not rejected

2009-2018 Adjusted H 1314 1783 074 37df 1 1 1 1

P value 0 0 039 005Null hypothesis rejected rejected not rejected not rejected

36

H5 Regression analysis with dummy variables

Table H5 Regression analysis with dummy variables

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 a0 00000 (097) 00000 (004) 00000 (097) 00000 (097)a1 00138 (000) -00172 (000) 00004 (082) -00014 (047)

Anomaly confirmed confirmed not confirmed not confirmed1939-1948 a0 00003 (015) 00003 (015) 00003 (015) 00003 (015)

a1 00007 (045) -00045 (000) 00170 (000) -00199 (000)Anomaly not confirmed confirmed confirmed confirmed

1949-1958 a0 00006 (000) 00006 (000) 00006 (000) 00006 (000)a1 00160 (000) -00188 (000) 00016 (000) -00004 (043)

Anomaly confirmed confirmed confirmed not confirmed1959-1968 a0 00002 (007) 00002 (004) 00002 (008) 00002 (008)

a1 00103 (000) -00105 (000) 00014 (001) -00002 (074)Anomaly confirmed confirmed confirmed not confirmed

1969-1978 a0 00000 (078) 00000 (078) 00000 (078) 00000 (078)a1 00132 (000) -00132 (000) 00019 (002) -00030 (000)

Anomaly confirmed confirmed confirmed confirmed1979-1988 a0 00006 (001) 00006 (001) 00006 (001) 00006 (000)

a1 00053 (000) -00048 (000) 00009 (040) -00003 (075)Anomaly confirmed confirmed not confirmed not confirmed

1989-1998 a0 00007 (000) 00007 (000) 00007 (000) 00007 (000)a1 00016 (005) -00030 (000) -00009 (026) 00003 (072)

Anomaly confirmed confirmed not confirmed not confirmed1999-2008 a0 00001 (075) 00001 (075) 00001 (075) 00001 (076)

a1 00083 (000) -00091 (000) -00024 (005) -00006 (062)Anomaly confirmed confirmed not confirmed not confirmed

2009-2018 a0 00004 (003) 00004 (000) 00004 (003) 00004 (003)a1 00051 (000) -00059 (000) -00003 (075) -00019 (003)

Anomaly confirmed confirmed not confirmed confirmed

37

H6 Modified CAR approach

Table H6 Modified CAR approach

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 Multiple R 096 095 046 046F-test 175935 (000) 96500 (000) 3534 (000) 2880 (000)a0 -01070 (000) 01958 (000) 00405 (000) 00535 (000)a1 00121 (000) -00160 (000) 00006 (000) -00014 (000)

Anomaly confirmed confirmed confirmed confirmed1939-1948 Multiple R 08 099 099 099

F-test 18777 (000) 755727 (000) 3572830 (000) 2696099 (000)a0 00019 (073) -00346 (000) -00373 (000) 00912 (000)a1 00012 (000) -00044 (000) 00168 (000) -00197 (000)

Anomaly confirmed confirmed confirmed confirmed1949-1958 Multiple R 099 099 094 015

F-test 1021705 (000) 7171257 (000) 75858 (000) 242 (012)a0 -00176 (000) -00191 (000) 00095 (000) -00498 (000)a1 00154 (000) -00181 (000) 00013 (000) -00002 (012)

Anomaly confirmed confirmed confirmed not confirmed1959-1968 Multiple R 099 099 094 078

F-test 1463311 (000) 6002659 (000) 82273 (000) 14352 (000)a0 -00112 (000) 00004 (085) 00151 (000) 00389 (000)a1 00098 (000) -00102 (000) 00011 (000) -00009 (000)

Anomaly confirmed confirmed confirmed confirmed1969-1978 Multiple R 098 099 093 099

F-test 241655 (000) 1451901 (000) 57333 (000) 368160 (000)a0 -00433 (000) 00276 (000) 00099 (002) -00144 (000)a1 00132 (000) -00134 (000) 00020 (000) -00030 (000)

Anomaly confirmed confirmed confirmed confirmed1979-1988 Multiple R 092 078 023 008

F-test 53757 (000) 18707 (000) 487 (003) 085 (036)a0 00813 (000) -02508 (000) 00204 (000) -00235 (000)a1 00036 (000) -00031 (000) -00003 (003) -00001 (036)

Anomaly confirmed confirmed not confirmed not confirmed1989-1998 Multiple R 079 099 074 044

F-test 19705(000) 761967 (000) 14133 (000) 2369 (000)a0 00268 (000) 00023 (021) -00381 (000) 00087 (000)a1 00013 (000) -00028 (000) -00008 (000) 00002 (000)

Anomaly confirmed confirmed not confirmed not confirmed1999-2008 Multiple R 091 093 071 065

F-test 47218 (000) 76564 (000) 9843 (000) 7768 (000)a0 -01493 (000) 01351 (000) 00397 (000) 00007 (093)a1 00081 (000) -00083 (000) -00026 (000) -00011 (000)

Anomaly confirmed confirmed not confirmed confirmed2009-2018 Multiple R 086 087 083 074

F-test 29971 (000) 32484 (000) 23228 (000) 12764 (000)a0 01711 (000) -02250 (000) 00407 (000) -00472 (000)a1 00038 (000) -00044 (000) -00010 (000) -00012 (000)

Anomaly confirmed confirmed not confirmed confirmed

38

H5 Regression analysis with dummy variables

Table H5 Regression analysis with dummy variables

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 a0 00000 (097) 00000 (004) 00000 (097) 00000 (097)a1 00138 (000) -00172 (000) 00004 (082) -00014 (047)

Anomaly confirmed confirmed not confirmed not confirmed1939-1948 a0 00003 (015) 00003 (015) 00003 (015) 00003 (015)

a1 00007 (045) -00045 (000) 00170 (000) -00199 (000)Anomaly not confirmed confirmed confirmed confirmed

1949-1958 a0 00006 (000) 00006 (000) 00006 (000) 00006 (000)a1 00160 (000) -00188 (000) 00016 (000) -00004 (043)

Anomaly confirmed confirmed confirmed not confirmed1959-1968 a0 00002 (007) 00002 (004) 00002 (008) 00002 (008)

a1 00103 (000) -00105 (000) 00014 (001) -00002 (074)Anomaly confirmed confirmed confirmed not confirmed

1969-1978 a0 00000 (078) 00000 (078) 00000 (078) 00000 (078)a1 00132 (000) -00132 (000) 00019 (002) -00030 (000)

Anomaly confirmed confirmed confirmed confirmed1979-1988 a0 00006 (001) 00006 (001) 00006 (001) 00006 (000)

a1 00053 (000) -00048 (000) 00009 (040) -00003 (075)Anomaly confirmed confirmed not confirmed not confirmed

1989-1998 a0 00007 (000) 00007 (000) 00007 (000) 00007 (000)a1 00016 (005) -00030 (000) -00009 (026) 00003 (072)

Anomaly confirmed confirmed not confirmed not confirmed1999-2008 a0 00001 (075) 00001 (075) 00001 (075) 00001 (076)

a1 00083 (000) -00091 (000) -00024 (005) -00006 (062)Anomaly confirmed confirmed not confirmed not confirmed

2009-2018 a0 00004 (003) 00004 (000) 00004 (003) 00004 (003)a1 00051 (000) -00059 (000) -00003 (075) -00019 (003)

Anomaly confirmed confirmed not confirmed confirmed

37

H6 Modified CAR approach

Table H6 Modified CAR approach

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 Multiple R 096 095 046 046F-test 175935 (000) 96500 (000) 3534 (000) 2880 (000)a0 -01070 (000) 01958 (000) 00405 (000) 00535 (000)a1 00121 (000) -00160 (000) 00006 (000) -00014 (000)

Anomaly confirmed confirmed confirmed confirmed1939-1948 Multiple R 08 099 099 099

F-test 18777 (000) 755727 (000) 3572830 (000) 2696099 (000)a0 00019 (073) -00346 (000) -00373 (000) 00912 (000)a1 00012 (000) -00044 (000) 00168 (000) -00197 (000)

Anomaly confirmed confirmed confirmed confirmed1949-1958 Multiple R 099 099 094 015

F-test 1021705 (000) 7171257 (000) 75858 (000) 242 (012)a0 -00176 (000) -00191 (000) 00095 (000) -00498 (000)a1 00154 (000) -00181 (000) 00013 (000) -00002 (012)

Anomaly confirmed confirmed confirmed not confirmed1959-1968 Multiple R 099 099 094 078

F-test 1463311 (000) 6002659 (000) 82273 (000) 14352 (000)a0 -00112 (000) 00004 (085) 00151 (000) 00389 (000)a1 00098 (000) -00102 (000) 00011 (000) -00009 (000)

Anomaly confirmed confirmed confirmed confirmed1969-1978 Multiple R 098 099 093 099

F-test 241655 (000) 1451901 (000) 57333 (000) 368160 (000)a0 -00433 (000) 00276 (000) 00099 (002) -00144 (000)a1 00132 (000) -00134 (000) 00020 (000) -00030 (000)

Anomaly confirmed confirmed confirmed confirmed1979-1988 Multiple R 092 078 023 008

F-test 53757 (000) 18707 (000) 487 (003) 085 (036)a0 00813 (000) -02508 (000) 00204 (000) -00235 (000)a1 00036 (000) -00031 (000) -00003 (003) -00001 (036)

Anomaly confirmed confirmed not confirmed not confirmed1989-1998 Multiple R 079 099 074 044

F-test 19705(000) 761967 (000) 14133 (000) 2369 (000)a0 00268 (000) 00023 (021) -00381 (000) 00087 (000)a1 00013 (000) -00028 (000) -00008 (000) 00002 (000)

Anomaly confirmed confirmed not confirmed not confirmed1999-2008 Multiple R 091 093 071 065

F-test 47218 (000) 76564 (000) 9843 (000) 7768 (000)a0 -01493 (000) 01351 (000) 00397 (000) 00007 (093)a1 00081 (000) -00083 (000) -00026 (000) -00011 (000)

Anomaly confirmed confirmed not confirmed confirmed2009-2018 Multiple R 086 087 083 074

F-test 29971 (000) 32484 (000) 23228 (000) 12764 (000)a0 01711 (000) -02250 (000) 00407 (000) -00472 (000)a1 00038 (000) -00044 (000) -00010 (000) -00012 (000)

Anomaly confirmed confirmed not confirmed confirmed

38

H6 Modified CAR approach

Table H6 Modified CAR approach

Period Parameter Gap day (Positivegaps)

Gap day (Negativegaps)

Day after gap(Positive gaps)

Day after gap(Negative gaps)

1929-1938 Multiple R 096 095 046 046F-test 175935 (000) 96500 (000) 3534 (000) 2880 (000)a0 -01070 (000) 01958 (000) 00405 (000) 00535 (000)a1 00121 (000) -00160 (000) 00006 (000) -00014 (000)

Anomaly confirmed confirmed confirmed confirmed1939-1948 Multiple R 08 099 099 099

F-test 18777 (000) 755727 (000) 3572830 (000) 2696099 (000)a0 00019 (073) -00346 (000) -00373 (000) 00912 (000)a1 00012 (000) -00044 (000) 00168 (000) -00197 (000)

Anomaly confirmed confirmed confirmed confirmed1949-1958 Multiple R 099 099 094 015

F-test 1021705 (000) 7171257 (000) 75858 (000) 242 (012)a0 -00176 (000) -00191 (000) 00095 (000) -00498 (000)a1 00154 (000) -00181 (000) 00013 (000) -00002 (012)

Anomaly confirmed confirmed confirmed not confirmed1959-1968 Multiple R 099 099 094 078

F-test 1463311 (000) 6002659 (000) 82273 (000) 14352 (000)a0 -00112 (000) 00004 (085) 00151 (000) 00389 (000)a1 00098 (000) -00102 (000) 00011 (000) -00009 (000)

Anomaly confirmed confirmed confirmed confirmed1969-1978 Multiple R 098 099 093 099

F-test 241655 (000) 1451901 (000) 57333 (000) 368160 (000)a0 -00433 (000) 00276 (000) 00099 (002) -00144 (000)a1 00132 (000) -00134 (000) 00020 (000) -00030 (000)

Anomaly confirmed confirmed confirmed confirmed1979-1988 Multiple R 092 078 023 008

F-test 53757 (000) 18707 (000) 487 (003) 085 (036)a0 00813 (000) -02508 (000) 00204 (000) -00235 (000)a1 00036 (000) -00031 (000) -00003 (003) -00001 (036)

Anomaly confirmed confirmed not confirmed not confirmed1989-1998 Multiple R 079 099 074 044

F-test 19705(000) 761967 (000) 14133 (000) 2369 (000)a0 00268 (000) 00023 (021) -00381 (000) 00087 (000)a1 00013 (000) -00028 (000) -00008 (000) 00002 (000)

Anomaly confirmed confirmed not confirmed not confirmed1999-2008 Multiple R 091 093 071 065

F-test 47218 (000) 76564 (000) 9843 (000) 7768 (000)a0 -01493 (000) 01351 (000) 00397 (000) 00007 (093)a1 00081 (000) -00083 (000) -00026 (000) -00011 (000)

Anomaly confirmed confirmed not confirmed confirmed2009-2018 Multiple R 086 087 083 074

F-test 29971 (000) 32484 (000) 23228 (000) 12764 (000)a0 01711 (000) -02250 (000) 00407 (000) -00472 (000)a1 00038 (000) -00044 (000) -00010 (000) -00012 (000)

Anomaly confirmed confirmed not confirmed confirmed

38