the signed momentum strategy in the chinese stock...
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The signed momentum strategy in the Chinese stock market
Abstract
This paper uncovers the performance of short-term momentum in the Chinese stock market.
we find under the traditional way to construct the momentum strategy, there is no significant
momentum performance for the whole sample. We also find the momentum performance varies
with different market states: when the market continues, the momentum return is significantly
positive and when the market transits, the momentum return is significantly negative. In addition,
we find this special performance might come from the change of beta difference between winner-
decile and loser-decile during the formation period and the holding period with the market transition.
We combine the traditional momentum strategy with the market dynamic and give a signed
momentum strategy, and this improved strategy gives significant portfolio return, which can’t be
fully explained by the popular asset-pricing factors. Our finding for the relation between short-term
momentum performance and the market dynamic holds during the period of market tremendous
changing and can be a universal explanation for other markets’ momentum performance.
JEL classification: G10, G11, G12, G14
Keywords: short-term momentum, market dynamic, signed momentum
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1. Introduction
A large body of literature draws attention to the momentum anomaly in the US
stock market, since Jegadeesh and Titman (1993). 1 There is a long history for
momentum effects: Chabot, Ghysels and Jagannathan (2009) argue that the momentum
anomaly dates back to the Victorian era; Geczy and Samonov (2016) use a sample from
1801 and find the momentum profits still remain positive and statistically significant in
the pre-1927 data in the US. Similar to the US, the significant momentum profit still
exists around world.2 Besides stocks, momentum strategy is widely found in other
assets.3
However, Asian stock markets are exceptions. Fama and French (2012), Asness,
Moskowitz and Pederson (2013) show that there is no significant momentum effect in
the Japan stock market. Hameed and Kusnadi (2002) find no evidence to support the
momentum profits in the Hong Kong, Korean, Taiwan and other Asia Pacific stock
markets. Griffin, Ji and Martin (2003) and Chui, Titman and Wei (2010) extend the
scope of Asian markets and still cannot find momentum effects. Consistent with most
Asian markets, there is also no momentum effect in the Chinese stock market.
Studies try to find the reason for the insignificant momentum performance in the
Asian stock markets. Cooper, Gutierrez, and Hameed (2004) repost that the short-term
momentum return in the US stock market is conditioned by market states, and they find
the momentum return exclusively following UP markets. Motivated by this finding,
1 See Asness (1995), Jegadeesh and Titman (2001), Israel and Moskowitz (2013) and Huang et al (2018),
among others.
2 See Liu et al (1999), Nijman et al (2004), Forner and Marhuenda (2003), Mengoli (2004), and Baltzer,
Jank and Smajlbegovic (2019), among others, for the European stock markets; Rouwenhorst (1998,
1999), Chan, Hameed and Tong (2000), Grundy and Martin (2001), Lewellen (2002), Griffin, Ji and
Martin (2003), Patro and Wu (2004), Chui, Titman and Wei (2010), Fama and French (2012), Asness,
Moskowitz and Pederson (2013), and Li et al (2014) for the international stock market.
3 See Okunev and White (2003), Serban (2010), Menkhoff et al (2012) for currency; Erb and Harvey
(2006), Moskowitz, Ooi and Pedersen(2012) for exchange futures contracts; Miffre and Rallis (2007),
Bianchi, Drew and Fan (2015, 2016) for commodity futures; Gebhardt, Hvidkjaer and
Swaminathan(2005), Jostova et al (2013), Haesen, Houweling and van Zundert (2017) for government
bond.
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Asem and Tian (2010) divide the US stock market into the market continuation
subsample and the market transition subsample, and find the momentum profits are
higher when the market continues in the same state than when it transits to the different
state. After that, Hanauer (2014) presents that the relationship between momentum
performance and market dynamic is not a special case for the US stock market, and
gives some supportive evidence from the Japan, Korea, Taiwan, and Turkey stock
markets. Hanauer (2014) believes that the historically low return of traditional
momentum strategy in the Japan stock market is from the offsetting of positive
momentum returns during the market continuation periods and the negative momentum
returns during the market transition periods, and the more market transition periods in
Japan than the US stock market is the key factor for the different momentum
performances in two markets. What’s more, Lin et al (2016), Cheema and Nartea (2014,
2017b) also give the evidence of momentum states and the momentum performance
from the Taiwan stock market and the Chinese stock market.
Even though the Chinese stock market has relatively short history, it has become
the second largest stock market and the biggest emerging market. And the fact that
Chinese stock market is dominated by the individual investors especially the
uninformed retail investors could bring more significant momentum than the developed
stock market like the US stock market, considering the momentum performance reflects
the inefficiency of information diffusion. However, there is no significant evidence for
the short-term momentum in previous studies, which indicates some other disturbance
factor existing in the Chinese stock market. In this paper, we want to figure out this
disturbance factor and give an improved momentum strategy for the Chinese stock
market.
Similar to the finding in other stock markets, we find the market dynamic can be
the main disturbance factor for performance of short-term momentum in the Chinese
stock market. Using a comprehensively monthly data of all A-shares from 1997 to 2018,
we form the momentum strategy by using the cumulative returns from 12 months before
to one month before the holding month (𝑡 − 12 to 𝑡 − 2, which is the most common
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formation period used in momentum studies) and the cumulative returns from 12
months before to 7 months before the holding month (𝑡 − 12 to 𝑡 − 7, which is
motivated by the finding in Novy-Marx (2012) who find momentum is primarily driven
by firms’ performance during this period) to rank stocks, and study the performance of
short-term momentum in the holding period (𝑡) based on the difference of portfolio
return between stocks in the group 1(that means the average value of stock return in
this group is the lowest in the formation period) and stocks in the group 10 (that means
the average value of stock return in this group is the highest in the formation period).
As we have found, the performance of short-term momentum varies with different
markets states. When we divided the market into two subsamples based on the sign of
excess market return during the formation period, we find the difference of short-term
momentum performance in the subsample following the Down market (with negative
sign during the formation period) and that following the Up market (with non-negative
sign during the formation period) is significant positive from both two formation
periods (with the difference of 5.67% and the T value of 2.32 for 𝑡 − 12 to 𝑡 − 2
formation period and the difference of 4.49% and the T value of 2.36 for 𝑡 − 12 to 𝑡 −
7 formation period ). This finding is just opposite with Cooper, Gutierrez, and Hameed
(2004), and indicates the Down market may play a greater role on the performance of
short-term momentum in the Chinese stock market.
When we divide the market into four subsamples based on the sign of excess
market return during the formation period and the holding period, we find different
momentum performance in each subsample. Our subsamples include the Up & Up
subsample (constitution by the Up market in the formation period (𝑡 − 12 to 𝑡 − 2/ 𝑡 −
12 to 𝑡 − 7) and the Up market in the holding period ( 𝑡)), Up & Down subsample,
Down & Down subsample and Down & Up subsample. And we also find the different
performance in the market continuation subsample (constitution by Up & Up and Down
& Down) and the market continuation subsample (constitution by Up & Up and Down
& Down).
We take the results based on the 𝑡 − 12 to 𝑡 − 2 formation period as an example,
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and find when the market changes from Up to Down, there is significantly negative
momentum return (-8.63%, with the T value of -3.65). However, when the market sign
continues from Up to Up, the momentum performance is insignificantly positive
(0.65%, with the T value of 0.27). Results from the Up to Down subsamples dominate
the performance of momentum strategy during the Up market, so the comprehensive
result of two subsamples is significantly negative. When the market changes from
Down to Up, there is significantly negative momentum return (-15.83%, with the T
value of -6.70). And when the market sign continues from Down to Down, the
momentum performance is significantly positive (20.30%, with the T value of 8.40).
Results from these two subsamples have the similar size but in the opposite sign, so the
comprehensive result during the Down market is insignificantly positive. Results based
on the 𝑡 − 12 to 𝑡 − 7 formation period are similar (but with the smaller magnitude in
average value and T value).
In addition, we find the significant short-term momentum effect exists when the
market continues and the significant reversal effect exists when the market transits.
When we take the results based on the 𝑡 − 12 to 𝑡 − 2 formation period as an example,
result from market continuation subsample gives the significantly positive momentum
return (9.07%, with the T value of 5.25), and based on our previous result, the
significant momentum return is mainly from the Down & Down subsample. Result
from market transition subsample gives the significantly negative momentum return (-
12.06%, with the T value of -7.22), and this significant reversal effect is from both the
Up & Down and the Down & Up subsamples, but the Down & Up subsamples plays a
more important role (This finding is consistent with the study of Daniel and Moskowitz
(2016), who find the momentum effect in the US stock market suffers serious crashes
when the market rebounds from the panic states). Results from the 𝑡 − 12 to 𝑡 − 7
formation period give a similar but weaker conclusion, so in the Chinese stock market,
the traditional 𝑡 − 12 to 𝑡 − 2 formation period is a better choice to form a momentum
strategy, which is inconsistent with the result in the US stock market (see in Novy-Marx,
2012).
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We extend the study of momentum performance and the market dynamic by
studying the change of stock characteristics during different market states. The three
stock characteristic proxies used in this paper are the beta, capitalization and B/M. The
idea to relate the stock characteristics with the momentum strategy is from Kothari and
Shanken (1992) and Grundy and Martin (2001), who argue that past-return sorted
portfolio/the momentum strategy has significant time-varying exposure to systematic
factors. By longing past winner stocks and shorting past loser stocks, momentum
portfolio has positive/negative loadings on factors which have had a positive/negative
realization during the formation period. Daniel and Moskowitz (2016) furtherly give
the intuition that: when the market has fallen significantly over the momentum
formation period, a good chance exists that the firms that fall in tandem with the market
are high-beta firms, and those that performed the best are low-beta firms. Thus,
following market declines, the momentum portfolio is likely to be long low-beta stocks
and short high beta stocks. Daniel and Moskowitz (2016) find that betas for the past-
loser-decile rise above 3 and past-winner-decile fall below 0.5 after the major market
deciles, that’s, when the market rebound from panic states, the beta difference between
the past-winner group and past-loser group changes from positive in strategy formation
period into the negative (-2.5 in their paper) in the holding period. Momentum crashes
in the US stock market during the market rebound period is from the conditionally large
negative beta. Thus, in this paper, we also give the similar summary as the Daniel and
Moskowitz (2016) in more market states of the Chinese stock market to find the
explanation for the changeable momentum performance with the market states.
We give a summary of beta difference between stocks in the winner-decile and
loser-decile ranked by their return in the formation period and holding period. As we
have found, the sign of beta difference during two periods is critical for the performance
of short-term momentum in the Chinese stock market: when there is the same sign
during two periods, stocks in the winner-decile and loser-decile during formation period
have this similar performance of stocks in the winner-decile and loser-decile during
holding period, and the momentum return is likely to be positive. However, when the
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sign is opposite during two periods, stocks in the winner-decile and loser-decile during
formation period have different beta performance of stocks in the winner-decile and
loser-decile during holding period, and the momentum return is likely to be negative.
We also give the similar summary of capitalization difference and B/M (book to market)
difference, and find the signs of these two variables are unrelated to the performance of
short-momentum, so the change of beta difference is the only key factor for the special
performance of momentum in the Chinese stock market.
Based on these findings, we give an improved signed momentum strategy, which
is a combination of traditional momentum strategy and the market dynamic.
Specifically, we use the traditional way to construct the momentum strategy during the
market continuation period by ranking stocks based on their return in the formation
period and longing stocks in the winner-decile and shorting stocks in the loser decile.
But during the market transition period, we use the opposite way to construct the
momentum strategy by ranking stocks based on their return in the formation period and
longing stocks in the loser-decile and shorting stocks in the winner decile.
Our signed momentum strategy has good performance in the Chinese stock market.
When we use 𝑡 − 12 to 𝑡 − 2 as the formation period, we find an approximately
increasing trend, and the excess return between group 10 and group 1 (i.e., the strategy
profit) is significant both in the economic level and the statistics level (with the average
annual return as 10.50%, and the T value as 8.74, significant at 1% level). And we also
find the excess return from the signed momentum strategy can’t be fully explained by
these three models (with the average value of 0.90 and T value of 2.70 for the CAMP
mode, the average value of 1.04 and T value of 3.31 for Fama-French three factors
model and the average value of 0.94 and T value of 2.84 for Fama-French five factors
model, respectively), and this finding furtherly proves the efficiency of our signed
momentum strategy. Results based on the 𝑡 − 12 to 𝑡 − 7 formation period is similar
but in the smaller size, which indicates after considering the influence of market
dynamic, the 𝑡 − 12 to 𝑡 − 7 is still not a better alternation of the 𝑡 − 12 to 𝑡 − 2
formation period in the Chinese stock market.
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By giving some summary about stocks in the winner-decile and the loser-decile
during the formation period are in the same group or the counterparty group during the
holding period, we do the robustness test and confirm our finding about the momentum
performance and market dynamic. And in our further analysis about the market
dynamic and the existing conclusion about the momentum performance in other stock
markets, we find the market dynamic has a universe influence on the momentum
performance: markets with the significant momentum performance are generally with
more market continuation periods and the average absolute values of market return are
relatively smaller (therefore, the market dynamic has smaller influence on the change
of beta difference and the momentum performance is less influenced) and those with
the insignificant momentum performance are just on the opposite situation.
The possible contribution of this paper is at threefold. Firstly, we give a detailed
result about the performance of traditional momentum in the Chinese stock market and
the different performance of momentum in the different market states, compared to
those who also study about the Chinese stock market (see Kang, Liu and Ni (2002),
Pan, Tang and Xu (2013)), we give a more comprehensive result. Compared to the study
of Cheema and Nartea (2014, 2017b), we give a better way to define the Up and Down
market by using the sign of excess return of the market return to the risk-free return
during the strategy formation period, considering the fact that in all asset pricing model,
market return plays a great role by using the form of the difference between market
return and the risk-free return, that is, the market premium. Even though the value of
risk-free return is relatively low during our sample period, we believe it would be better
to define the market states after eliminating this influence. Secondly, by studying the
change of beta difference, capitalization difference and B/M difference between the
winner-decile and the loser-decile during the formation period and the holding period,
we find the important role of beta difference on the relationship between momentum
performance and the market dynamic, and that is the reason for the changed momentum
performance with market states. Finally, we give a multi-market comparison about the
market dynamic and the existing results of momentum performance, and find markets
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with significant momentum performance generally have different market dynamic to
those with the insignificance momentum performance, so our finding based on the
Chinese stock market could be universally applicable.
The remainder of this paper is organized as follows: Section 2 documents the data
and momentum strategy used in this paper. Section 3 provides the baseline results of
traditional short-term momentum in the Chinese stock market for the full sample and
during different market states. Section 4 presents our explanation for the relationship
between momentum performance and market dynamic, and gives the performance of
our improved signed momentum strategy. Section 5 performs a battery of robustness
tests and further analyses. Section 6 concludes the paper.
2. Data and Momentum Strategy
2.1. Data Sources
We get a comprehensive dataset of the Chinese A-shares over the sample period
from January 1991 to September 2018. The monthly data is retrieved from the CSMAR
Database4 . We reuuire a stock to have at least a full year’s data (12 months) to be
included in our sample. To ensure the adeuuacy and validity of data, we don’t include
the ST (special treatment) stocks, stocks with price less than 1 CNY5 at the beginning
of each month, and the financial stocks in our sample. After applying these filter rules,
our final sample contains 2825 stocks of public firms listed in the Chinese stock market.
Data used in this paper includes the monthly stock return, the risk-free return6, the
capitalization value and book to market ratio of stocks, and so on.
2.2. Momentum Strategy
In this paper, we use two universal ways to form the momentum strategy. The first
4 CSMAR Database is widely used for the Chinses studies, which is the only Chinese database used by
Wharton Research Data Services. Website of this data is http://www.gtarsc.com/.
5 The face value of stocks in the Shanghai Stock Exchange and the Shenzhen Stock Exchange.
6 Proxied by the one-year national debt coupon rate, and monthly data is converted from the yearly data
based on compound interest calculation method.
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one is based on the cumulative returns from 12 months before to one month before the
holding month (i.e., the 𝑡 − 12 to 𝑡 − 2 month returns) to rank stocks, consistent with
the literature of Jegadeesh and Titman (1993), Asness (1995), Fama and French (1996)
and the recent study from Asness, Moskowitz and Pederson (2013), Daniel and
Moskowitz (2016). The reason to give a one-month gap between the formation period
and the holding period is to avoid the short-term reversals shown by Jegadeesh (1990)
and Lehmann (1990), and the same way is also used in the recent papers. The alternative
method is based on the cumulative returns from 12 months before to 7 months before
the holding month (i.e., the 𝑡 − 12 to 𝑡 − 7 month returns) to rank stocks, which is
motivated by the finding in Novy-Marx (2012) that “Momentum is primarily driven by
firms’ performance 12 to seven months prior to portfolio formation, not by a tendency
of rising and falling stocks to keep rising and falling.”, and they find momentum
strategy based on this formation period is more profitable than the traditional way in
the US stock market and the international euuity indices, commodities, and currencies.
All data is placed into one of ten decile portfolios based on this ranking, where the
portfolio 10 includes all the winner stocks (those with the highest past return in our two
formation periods) and the portfolio 1 includes all the loser stocks. We use the euual-
weighted way to calculate the average value of holding period returns of each decile
portfolio to mitigate the bias caused by the small stock returns. All stocks in the holding
period are same to the formation periods, except the delisting.
In order to ensure the statistical validity of the results, we only retain the portfolios
with more than 30 stocks in each decile, and considering the loss of sample size caused
by using the previous 12 months data to form the momentum strategy, the final sample
period of this paper to study the short-term momentum effect in the Chinese stock
market is from July 1997 to September 2018, including 255 months.
3. Traditional Short-term Momentum
3.1. Baseline Results
In this section, we test the performance of traditional short-term momentum
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strategy in the Chinese stock market. We rank stocks by their cumulative return during
the 𝑡 − 12 to 𝑡 − 2 and 𝑡 − 12 to 𝑡 − 7 formation periods and sort them into 10
groups. The average return of stocks in the group 1 to group 10 has a monotonously
increasing trend during the formation period. If the momentum effect is significant in
the Chinese stock market, we can also see the increasing trend of the average return of
stocks in the group 1 to group 10 during the holding period (𝑡), and the difference of
average return between stocks in the group 10 and stocks in the group 1 should be
significantly positive. The baseline results of this part are given in the table 1.
[ Insert table 1 here]
As we can see from the table 1, there is no significant momentum effect in the
Chinese stock market. When we use the traditional 𝑡 − 12 to 𝑡 − 2 formation period
to form the short-term momentum strategy, the difference of portfolio return between
stocks in the group 1(that means the average value of stock return in this group is the
lowest in the formation period) and stocks in the group 10 (that means the average value
of stock return in this group is the highest in the formation period) is insignificantly
negative (-1.04%, with the T value of -0.85), which is inconsistent with the performance
of momentum effect. Result based on the 𝑡 − 12 to 𝑡 − 7 formation period gives the
similar conclusion: the difference of portfolio return between stocks in the group 1 and
stocks in the group 10 is insignificantly positive (1.00%, with the T value of 1.06), we
can’t find the evidence of short-term momentum effect in the Chinese stock market.
In addition, Cooper, Gutierrez, and Hameed (2004) find the short-term momentum
effect in the US stock market is conditioned by market states, and find momentum
returns exclusively follow the up markets. In this paper, we also give the results of
short-term momentum performance following the Up and Down market in the Chinese
stock market. Up and Down markets are defined by the sign of excess market return
(the difference between value-weighted market return and the risk-free return) during
each formation period, and if the sign of excess market return is non-negative during
the formation period then we define it as a Up market. Vice versa, if the sign of excess
market return is negative during the formation period then we define it as a Down
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market7.
However, we still can’t find the significant momentum effect in these two
subsamples. When we use the traditional 𝑡 − 12 to 𝑡 − 2 formation period to form the
short-term momentum strategy, the difference of portfolio return between stocks in the
group 1 and stocks in the group 10 following the Down market is insignificantly
positive (2.08%, with the T value of 1.19), and the result based on 𝑡 − 12 to 𝑡 − 7
formation period following the Down market is significantly positive (3.45%, with the
T value of 2.27).Performance of short-term momentum following the Down market has
the (significantly) positive return in the Chinese stock market, and the results following
the Up market is just opposite. When we use the traditional 𝑡 − 12 to 𝑡 − 2 formation
period to form the short-term momentum strategy, the difference of portfolio return
between stocks in the group 1 and stocks in the group 10 following the Up market is
significantly negative (-3.59%, with the T value of -2.13), and the result based on 𝑡 −
12 to 𝑡 − 7 formation period following the Up market is insignificantly negative (-
1.04%, with the T value of -0.88).
Another finding from the table 1 is that, the difference of short-term momentum
performance in the subsamples following the Down market and Up market is significant
positive from both two formation periods (with the difference of 5.67% and the T value
of 2.32 for 𝑡 − 12 to 𝑡 − 2 formation period and the difference of 4.49% and the T
value of 2.36 for 𝑡 − 12 to 𝑡 − 7 formation period ). This finding is just opposite with
Cooper, Gutierrez, and Hameed (2004), and indicates the Down market may play a
greater role on the performance of short-term momentum in the Chinese stock market.
To sum up, we can’t find the evidence for short-term momentum pattern in the
Chinese stock market and the performance in the subsamples following the Up and
Down market is different.
7 Our definition is similar to Cooper, Gutierrez, and Hameed (2004) and Asem and Tian (2010) who use
the past 36-month /12-month value-weighted market return to classify the up and down markets in the
US stock market, and considering we have two formation periods in this paper, we give the corresponding
classification based on each period length.
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3.2. Results during different market states
As we can also see from the table 1, the proportion of Up market and Down market
is similar in the Chinese stock market. In our whole sample of 255 months, 115/116
months are defined as the Down market and 140/130 months are defined as the Up
market based on the 𝑡 − 12 to 𝑡 − 2/ 𝑡 − 12 to 𝑡 − 7 formation period. This finding
gives the different market performance of the Chinese stock market compared to the
US stock market, taking the study of Asem and Tian (2010) as an example, who find
699 Up market and 249 Down market from January 1927 to December 2005 based on
the past 12-month value-weighted market return to classify the US stock market states.
The similar ratio of the Up market and Down market indicates there might be more
freuuent market transitions in the Chinese stock market than the US stock market
(which has the superior ratio of the Up market).
In this part, we want to study the short-term momentum effect based on the
subsamples of different market states. We have four subsamples in this part, Up & Up
gives the subsample combined by the up market in the formation period (𝑡 − 12 to 𝑡 −
2/ 𝑡 − 12 to 𝑡 − 7) and the up market in the holding period ( 𝑡); Up & Down gives the
subsample combined by the up market in the formation period and the down market in
the holding period; Down & Down gives the subsample combined by the down market
in the formation period and the down market in the holding period; Down & Up gives
the subsample combined by the down market in the formation period and the up market
in the holding period. The situation with same market states in two periods is considered
to be the market continuation (Up & Up and Down & Down) and the situation with
different market states in two periods is considered to be the market transition (Up &
Down and Down & Up). We give the results of short-term momentum during these
subsamples in the table 2.
[ Insert table 2 here]
When we take the results based on the 𝑡 − 12 to 𝑡 − 2 formation period as an
example, results from different market states subsamples are uuite different. When the
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market changes from Up to Down, there is significantly negative momentum return (-
8.63%, with the T value of -3.65). However, when the market sign continues from Up
to Up, the momentum performance is insignificantly positive (0.65%, with the T value
of 0.27). Results from the Up to Down subsamples dominate the performance of
momentum strategy during the Up market, so the comprehensive result of two
subsamples is significantly negative (given in the table 1). When the market changes
from Down to Up, there is significantly negative momentum return (-15.83%, with the
T value of -6.70). And when the market sign continues from Down to Down, the
momentum performance is significantly positive (20.30%, with the T value of 8.40).
Results from these two subsamples have the similar size but in the opposite sign, so the
comprehensive result during the Down market is insignificantly positive. Results based
on the 𝑡 − 12 to 𝑡 − 7 formation period are similar (but with the smaller magnitude in
average value and T value), so we don’t give them for brief.
Our finding of momentum performance in the Up market subsample is
inconsistent with the Cooper, Gutierrez, and Hameed (2004), who find the momentum
profits in the US stock market are in fact confined to periods following Up markets.
And our finding is contrary the behavioral models of Hong and Stein (1999) who think
the increased wealth during the Up market reduces investors’ risk aversion and leads to
higher momentum profits following Up markets. But considering the special investors
constitution of the Chinese stock market, our results are reasonable. Chinese stock
market is considered to be dominated by the retail investors (more than 50% account
belongs to investors with asset less than 0.1 million CNY), and these investors are
presumably more prone to behavioral biases. Retail investors’ trading behavior during
the Up market could be more risk-seeking8. Those investors treat the loser stocks as a
8 Taking the strange performance in 10 trading days after the 2019 Spring Festival as an example. During
this period, the Shanghai Composite Index rose 7.1%, Shenzhen Component Index rose 9.7%, and the
SME Board and the Growth Enterprise Market rose 13-14%. In all 3575 stocks of two stock markets,
only 57 fell, accounting for about 1.6%, more than 98% of the stocks were rising, and the average daily
trading amount was near to 600 billion CNY in this period. An extreme “demon stock” --Eastern
Communication rose from 3.70 CNY to 34.64 CNY, soared 9 times in 4 months, and rose 145% in 10
days; the second demon stock also rose 105% in 10 days.
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kind of lottery or a gamble during the Up market, which induces both the past winner
stocks and the loser stocks are attractive for the retail investors, and their trading
diminishes the return difference of these stocks and negating the profitability of the
momentum trading strategy9.
Even though there are successive short-sale ban lifts since 2010 in the Chinese
stock market10, the threshold of short sale is 0.5 million CNY, which is relatively high
for the individual investors (especially for the retail investors). And the trading of short
sale only accounts less than 1% of the total credit trading (margin trading and short
sale), which plays a tiny influence on retail investors’ trading. The undeveloped short
sale in the Chinese stock market limits the retail investors’ risk-seeking trading during
the Down market, and the short-term momentum effect performs well in the Down &
Down subsample.
Furtherly, we also find the significant short-term momentum effect exists when
the market continues and the significant reversal effect exists when the market transits.
When we take the results based on the 𝑡 − 12 to 𝑡 − 2 formation period as an example,
result from market continuation subsample gives the significantly positive momentum
return (9.07%, with the T value of 5.25), and based on our previous result, the
significant momentum return is mainly from the Down & Down subsample. Result
from market transition subsample gives the significantly negative momentum return (-
12.06%, with the T value of -7.22), and this significant reversal effect is from both the
Up & Down and the Down & Up subsamples, but the Down & Up subsamples plays a
more important role (This finding is consistent with the study of Daniel and Moskowitz
(2016), who find the momentum effect in the US stock market suffers serious crashes
when the market rebounds from the panic states). Results from the 𝑡 − 12 to 𝑡 − 7
formation period give a similar but weaker conclusion, so in the Chinese stock market,
the traditional 𝑡 − 12 to 𝑡 − 2 formation period is a better choice to form a momentum
9 The explanation of the short-term momentum performance in the Up & Up market states is similar to
Cheema and Nartea (2017 a).
10 See the details in Xiong, Gao and Feng (2017).
16
strategy, which is inconsistent with the result in the US stock market (see in Novy-Marx,
2012).
3.3. Results when the market changes greatly
As we have found, the short-term momentum performance relies on the market
states, so we want to furtherly study whether the extent of market continuation or
market transition has influence on this performance.
Based on the average absolute value of market excess return during each formation
period ( 𝑡 − 12 to 𝑡 − 2 / 𝑡 − 12 to 𝑡 − 7 ) and the holding period ( 𝑡 ), we get the
subsample of market with great changes. Specifically, we separate the whole sample
into two parts based on the absolute value of market excess return in each month and
the average value of absolute market excess return in the whole sample. The months
with larger absolute value of market excess return than the average level in the whole
sample during the formation period or the holding period are considered to have the big
changes. We give the results based on these largely changed subsamples in the table 3.
[ Insert table 3 here]
As we can see from the table 3, results based on the largely changed subsamples
are similar but more significant than those in the table 2. We still take the results based
on the 𝑡 − 12 to 𝑡 − 2 formation period as an example. When the market changes
from Up to Down, there is significantly negative momentum return (-24.43%, with the
T value of -7.76), which is almost tripled in size than that in the table 2. However, when
the market sign continues from Up to Up, the momentum performance is significantly
negative (-5.82%, with the T value of -1.77), and this finding proves our intuition that
the gamble behavior of retail investors is more serious in the continuous bull market.
When the market changes from Down to Up, there is significantly negative momentum
return (-25.65%, with the T value of -7.47). And when the market sign continues from
Down to Down, the momentum performance is significantly positive (26.35%, with the
T value of 6.83).
In addition, we also find the momentum performance in the market continuation
17
subsample during the largely changed periods is less significant than in the whole
sample of table 2: When we take the results based on the 𝑡 − 12 to 𝑡 − 2 formation
period as an example, results from market continuation subsample during the largely
changed periods give the significantly positive momentum return (4.47%, with the T
value of 1.72), almost half in size than that in the whole sample of table 2. Results from
market transition subsample during the largely changed periods give more significantly
negative momentum return (-24.87%, with the T value of -10.86), more than doubled
in size than that in the whole sample of table 2. Results in the subsamples of table 3
give an important finding that the momentum return in market continuation subsample
during the largely changed periods makes less contribution to the short-term momentum
in the Chinese stock market, but the reversal return in market transition subsample
during the largely changed periods has great influence on the short-term momentum
(the average reversal return is about 6 times than the momentum return), performance
in the market transition subsample during the largely changed periods maybe the main
reason for the “Chinese special short-term momentum”. Results from the 𝑡 − 12 to 𝑡 −
7 formation period give a similar but weaker conclusion, which is reasonable
considering the big changes based on the 𝑡 − 12 to 𝑡 − 2 formation period imply the
longer persistent influence from the big changes of market continuation and market
transition on investors’ behavior and the stock return.
To sum up, we give the performance of short-term momentum in the different
market states subsamples. We find the momentum return is significant during the
market continuation period, and the Down & Down subsamples dominates this result.
During the market transition period, momentum performance changes to reversal, and
the Down & Up subsamples play a more important role for this reversal performance.
The similar proportion of market continuation period and market transition period
causes the internal insignificant short-term momentum performance in the Chinese
stock market. Study in the market largely changed subsamples gives a more significant
result: The momentum effect is weaker in this market continuation period but the
reversal effect performs especially significant in the market transition period, so the
18
performance in the market transition subsample during the largely changed periods
plays an important role in the Chinese short-term momentum performance.
4. Signed Momentum
4.1. Reason for the special performance
Results in the prior subsections present that the performance of short-term
momentum in the Chinese stock market is based on the market states: momentum exists
when the market continues and reverses when the market transits, and the results are
different based on the market states during the formation periods and the holding
periods. In this section, we want to find the reason(s) for this special performance.
Our explanation for the changeable momentum performance with the market states
is consistent with the Daniel and Moskowitz (2016), who find the momentum crashes
in the US stock market when the market rebounds from the panic states, except that we
use that idea for more market states in the Chinese stock market.
In this part, we extend Daniel and Moskowitz (2016)’s intuition into all market
states, and give some summary statistics of beta difference between the winner group
and loser group based on return ranking during the formation period and the holding
period in the table 4.
[Insert table 4 here]
Our study emphasizes on all four different classifications of the market states: Up
& Down, Up & Up, Down & Down and Down & Up. Beta used in this part is calculated
by the CAPM model using the previous 36-momth data (for the month 𝑡 , beta is
calculated by using data from 𝑡 − 35 to 𝑡). Considering our summary of momentum
performance is from July 1997, we have enough data for the beta calculation and the
sample numbers of four market state classifications are same to those in the table 2.
As we can see from the table 4, the beta difference between the winner-decile and
loser-decile is heavily influenced by the sign of market return during ranking period.
Specifically, when we rank stocks based on their return in the 𝑡 − 12 to 𝑡 − 2
19
formation period, the beta difference in the holding period of Up & Down subsample
is significantly positive (0.094, with the T value of 2.83). However, the beta difference
between the winner-decile and loser-decile ranked by stock return in the holding period
is significantly negative (-0.154, with the T value of -7.26), which indicates the beta
difference based on ranking of stock return in the formation period has the opposite
sign with the profitable portfolios (the 10 − 1 ranked by stock return in the holding
period must have the positive excess return considering it is the return difference
between stocks in the winner group and the loser group). The beta difference
comparison during the Down & Up subsample gives a similar result: when stocks are
ranked by their return in the 𝑡 − 12 to 𝑡 − 2 formation period, the beta difference in
the holding period is significantly negative (-0.114, with the T value of -5.96), and the
beta difference between the winner-decile and loser-decile ranked by stock return in the
holding period is significantly positive (0.146, with the T value of 5.50). In this
subsample, the beta difference based on ranking of stock return in the formation period
has the opposite sign with the profitable portfolios. The opposite signs of beta
differences based on ranking of stock return in the formation period and the profitable
portfolios in these two market states are consistent with the fact that the short-term
momentum has negative portfolio return during these periods.
However, in the market continuation subsamples, the situation is uuite different.
The both beta differences in the holding period of Up & Up subsample are significantly
positive, whether ranked by stock returns in the 𝑡 − 12 to 𝑡 − 2 formation period or
based on the winner-decile and loser-decile in the holding period (Specifically, the beta
difference is 0.166 with the T value of 5.37 versus 0.103 with the T value of 4.12,
respectively). And the both beta differences in the holding period of Down &Down
subsample are significantly negative, whether ranked by stock returns in the 𝑡 −
12 to 𝑡 − 2 formation period or based on the winner-decile and loser-decile in the
holding period (Specifically, the beta difference is -0.126 with the T value of 6.42 versus
-0.146 with the T value of 8.31, respectively). The same sign of beta difference based
on ranking of stock return in the formation period and the profitable portfolio is
20
consistent with the positive portfolio return of short-term momentum during these
periods. The summary based on the 𝑡 − 12 to 𝑡 − 7 formation period is uuite similar,
so we don’t give it for brief.
To sum up, we find the sign of beta difference based on ranking of stock return in
the formation period and the profitable portfolio in the holding period is critical for the
performance of short-term momentum in the Chinese stock market: when there is the
same sign during two periods, the momentum return is likely to be positive, and when
the sign is opposite during two periods, the momentum return is likely to be negative.
Therefore, we make a primary conclusion that the changed beta difference is the reason
for different performance of momentum effect during different market states.
In addition, we also give the summary of the capitalization difference and B/M
(book to market ratio) difference during the different market states, and find if there is
similar trend in these two stock characteristic variables. Results are given in the table 5
and table 6.
[Insert table 5 here]
[Insert table 6 here]
As we can see from table 5, the capitalization difference based on the return
ranking in the 𝑡 − 12 to 𝑡 − 2 formation period and that based on the winner-decile
and loser-decile in the holding period have no similar correlation like the beta difference:
only two capitalization differences based on the return ranking in the 𝑡 − 12 to 𝑡 − 2
formation period are significantly positive (in the Up & Down and Down & Down
subsamples), and one capitalization difference based on the winner-decile and loser-
decile in the holding period is significantly negative (in the Down & Up subsample).
The relationship of the capitalization difference from two ranking bases is inconsistent
with the performance of short-momentum, so the capitalization difference is not the
reason for the special performance of momentum in the Chinese stock market.
The summary of B/M difference tells a similar story. Almost all B/M differences
based on the return ranking in the formation period or the winner-decile and loser-decile
21
in the holding period are (significant) negative, and this phenomenon is not changed
with different market states. The relationship of the B/M difference from two ranking
bases is inconsistent with the performance of short-momentum, so the B/M difference
is also not the reason for the special performance of momentum in the Chinese stock
market.
To sum up, we give some summary of the beta difference, capitalization difference
and B/M difference based on ranking of stock return in the formation period and from
the winner-decile and loser-decile in the holding period, and find only the change of
beta difference is correlated to the performance of short-term momentum in the Chinese
stock market. When there are same signs of beta difference from two ranking bases, the
momentum return is likely to be positive, correspondingly, when there are opposite
signs of beta difference from two ranking bases, the momentum return is likely to be
negative. The change of beta difference is the reason for different performance of
momentum effect in different market states.
4.2. Performance of Signed Momentum Strategy
Based on finding in our previous study, the momentum effect exists when the
market continues and changes to reversal effect when the market transits. Motivated by
this special performance, we want to give a signed momentum strategy, which is a
combination of traditional momentum strategy and the market dynamic.
Specifically, during the market continuation period (Up & Up and Down & Down),
we use the traditional way to construct the momentum strategy: After ranking stocks
based on their return in the formation period, we long stocks in the winner-decile and
short stocks in the loser decile. But during the market transition period (Up & Down
and Down & Up), we use the opposite way to construct the momentum strategy: After
ranking stocks based on their return in the formation period, we short stocks in the
winner-decile and long stocks in the loser decile.
We give the performance of our signed momentum strategy in the table 7.
[Insert table 7 here]
22
As we can see from the table 7, the signed momentum strategy has good
performance in the Chinese stock market. When we use 𝑡 − 12 to 𝑡 − 2 as the
formation period, we find an approximately increasing trend, and the excess return
between group 10 and group 1 (i.e., the strategy profit) is significant both in the
economic level and the statistics level (with the average annual return as 10.50%, and
the T value as 8.74, significant at 1% level).
Table 7 also reports the alphas (intercepts) and their T values from the time-series
regressions of strategy profits on the CAPM model, Fama-French three factors model
and Fama-French five factors model. According to the model specification, alpha gives
the unexplained part by the explanatory variables in each model, and a significant alpha
indicates the special information that can’t be explained by the asset-pricing models.
Alphas in the table 7 give the coincident result that excess return from the signed
momentum strategy can’t be fully explained by these three models (with the average
value of 0.90 and T value of 2.70 for the CAMP mode, the average value of 1.04 and T
value of 3.31 for Fama-French three factors model and the average value of 0.94 and T
value of 2.84 for Fama-French five factors model, respectively), and this finding
furtherly proves the efficiency of our signed momentum strategy. Results based on the
𝑡 − 12 to 𝑡 − 7 formation period is similar but in the smaller size, which indicates after
considering the influence of market dynamic, the 𝑡 − 12 to 𝑡 − 7 is still not a better
alternation of the 𝑡 − 12 to 𝑡 − 2 formation period in the Chinese stock market.
In summary, we give a signed momentum strategy in this part, which is a
combination of the traditional momentum strategy and the market dynamic. This new
strategy has the similar performance as other countries, and can earn significant
portfolio return in the Chinese stock market.11
11 In this part, we don’t give the performance of signed momentum strategy in different market states,
considering the performance of signed momentum strategy is same to the traditional momentum in the
market continuation subsample, Up & Up subsample, and Down & Down subsample and the
performance of signed momentum strategy is just opposite in sign with the traditional momentum in the
market transition subsample, Up & Down subsample and Down & Up subsample. And the similar
23
4.3. Signed momentum following Up and Down market
In this part, we give some additional evidence about the performance of signed
momentum following the Up and Down markets. The way to define the Up and Down
market is same as the section 3.1: If the sign of excess market return is non-negative
during the formation period then we define the holding month as following the Up
market. Vice versa, if the sign of excess market return is negative during the formation
period then we define the holding month as following the Down market. And the
numbers of Up market and Down market are same as the table 1. We give the results of
signed momentum strategy following Up and Down market in the table 8.
[Insert table 8 here]
As we can see from the table 8, the signed momentum strategy performs more
significant when following the Down market, whether for annualized return of the
momentum strategy (10 − 1) or for the 𝐴𝑙𝑝ℎ𝑎𝑠 from the regression of momentum
return on the market factor (𝐶𝐴𝑃𝑀), Fama-French three factors (𝐹𝐹3) and the Fama-
French five factors (𝐹𝐹5) are larger in size and significant at 1% level. While for the
signed momentum strategy following Up market, the value of signed momentum return
is smaller in size and insignificant after controlling the influence of market factor,
Fama-French three factors and the Fama-French five factors.
This finding is consistent the performance of traditional momentum strategy and
reasonable for the special investor constitution in the Chinese stock market: Retail
investors are more aggressive during the Up market, and might buy more loser-decile
stocks for speculative purpose, therefore, the abnormal return of these stocks can
influence the performance of momentum. However, limited to the practical short sale
limits in the Chinese stock market, retail investors’ gambling behavior is restricted, so
the short-term momentum performs better.
5. Robustness and Further Analyses
situations are suitable for the summary of beta difference, capitalization difference and B/M difference
in different market states.
24
5.1. Summary of same group proportion
In this subsection, we give a summary about stocks in the winner-decile and the
loser-decile during the formation period are in the same group or the counterparty group
in the holding period. Intuitively, if the short-term momentum exists, stocks in the loser-
decile/ winner-decile during the formation period are supposed to in the same group of
the holding period. Absolutely, it is an ideal story. But we still want to study the
proportion of stocks are in the same deciles during two periods, and use this as the
robustness test for the traditional grouping study. Results of this part are given in the
table 9.
[Insert table 9 here]
As we can see from the table 9, the proportion of stocks in the same deciles during
two periods is relatively small in the Chinese stock market. When we use the 𝑡 −
12 to 𝑡 − 2 as the formation period, the average value of the same decile proportion in
the whole sample is 0.119, which is consistent with the integral insignificant
performance of short-term momentum. The proportion varies with the different market
states, and just like the results from grouping study, the same decile proportion in the
Down & Down subsample is the largest in four market states, so the short-term
momentum, if existing, is mainly derived from this subsample. The same decile
proportions in other three subsamples (Up & Down, Up & Up and Down & Up) are
smaller than the whole sample, but there is no significant difference among them. The
same decile proportion in market continuation subsample is larger than the market
transition subsample, the proportion difference is 0.019 and significant at 1% statistics
level. This finding is consistent with our previous result, momentum performance is
stronger when the market continues than the time when market transits. The result get
from the 𝑡 − 12 to 𝑡 − 7 formation period is uuite similar, so we don’t give for brief.
In this subsection, we study the proportion of stocks in the same deciles during the
formation period and the holding period, and find the proportion is small in the Chinese
stock market, consisting with the integral insignificant momentum performance. And
25
the proportion is different in each market state: the proportion is higher during market
continuation period than the market transition period, and in the Down & Down
subsample, the proportion is highest. Our finding in this part is consistent with the
section 3.1 and 3.2, and can be the additional supportive evidence for the robustness
test.
5.2. Based on the top 90% stocks?
When study the performance of momentum, Asness, Moskowitz and Pederson
(2013) limit stocks in each market to a very liuuid set by ranking stocks based on the
market capitalization value at the beginning-of month, and keep the biggest stocks that
account cumulatively for 90% of the total market capitalization. By this way, they keep
only 17% largest firms in the US stock market, 13%, 20%, and 26% of firms in the UK,
Europe, and Japan stock market, respectively.
In this paper, we also do the same filtration in the Chinese stock market and find a
very different result. For the whole sample of 2825 stocks and 419363 data, after doing
the filtration, 2622 stocks and 245090 data are kept in the top 90% subsample, there is
not a special group that dominates the whole market capitalization with very small
number of stocks included.
In addition, based on our previous study in the section 3.3, stock market
capitalization is not the reason for special performance of short-term momentum in the
Chinese stock market, this top 90% filtration will not make significant change in our
results.
5.3. Prediction of market return
The classification bases of the different market states are the signs of excess market
return during the formation period and the holding period, that is, our study for the
performance of short-term momentum under different market situations is an ex post
study, considering we use the sign of market return at the holding period.
The intuition to bring our study to the practical use is to find the prediction of market
return, specifically, prediction for the (sign of) market return in the holding period. The
26
potential predictor variables we think might relate to the market return and we can get
from the stock market include: the market return on previous months, the market
turnover calculated by the ratio of total market trading volume and the total market
capitalization of all stocks, the monthly variance calculated by the sum of suuare of A-
share index’s daily return, the increase ratio of total trading volume. And we also use
some macro-economic variables as the predictors, including the increase ratio of M0
(currency in circulation) and M1 (currency in circulation and the commercial banks’
demand deposit), the inflation ratio calculated from the CPI (consumer price index), the
increasing ratio of taxation, the change of exchange rate of CNY against USD, and the
change of Chinese Leading Economic Index. The prediction period is previous 36/48
months.
By using the data of these predictors in the previous months as the explanatory
variables, we do the univariate and multivariate regressions. As we have found, even
some variables have the significant influence on the market return and the regressions
have relatively high explanatory power, the fitted values from the regression models
are lowly correlated to the real market return (the highest correlation of the fitted value
and the real market return is 0.2127; the highest correlation of the sign of fitted value
and the sign of real market return is 0.2584).
Failure to find the accuracy prediction for the (sign of) market return leaving the
ex-ante study of the short-term momentum with market dynamic is still a potential area.
5.4. Summary of market states in other stock markets
In this part, we give some summary of market states in other stock markets for
comparison, including the US stock market (using the data of S&P 500 index as
example), the UK stock market (using the data of FTSE ALL-Share index as example),
the German stock market (using the DAX index as example), the Korean stock market
(using the KOSPI index as example), the Japan stock market (using the Nikkei 225
index as an example), the Taiwan stock market (using the Taiwan Weighted index as
example) and the Chinese stock market (using value weighted-A shares index as
example). Results of summary of market states in these stock markets are given in the
27
table 1012.
[ Insert table 10 here]
According to previous studies of other countries, the US stock market, the UK
stock market and the European stock market have significant short-term momentum
performance, but in the Asian stock markets (the remaining part of our sample), there
is no significant momentum performance. The summary of market states in these
countries (city) provides some supportive evidence for this finding.
The number of market continuation subsample is relatively larger than the number
of market transition subsample in markets having significant momentum, and for
markets with insignificant momentum performance, the numbers of these two
subsamples are closer. And the conclusion still holds when market changes greatly 13,
so we can draw a primary conclusion that the proportion of market continuation in
different markets has influence on the momentum performance, and the high proportion
of market continuation is likely related to the significant momentum performance.
And we also give the summary for the average value of absolute market return
during the formation period and the holding period, based on the intuition that the
bigger average value of market change might have bigger influence on the momentum
performance. We give this result on the table 11.
[ Insert table 11 here]
Results in the table 11 also support our intuition: markets with the significant
momentum performance (the US, UK and Germany stock markets) have relative
smaller absolute market return during the formation period and the holding period than
those with the insignificant momentum performance. That is, the average value of
market change has larger influence on the momentum performance on the Korean,
12 We give the results based on the 𝑡 − 12 to 𝑡 − 2 formation period as example, and results based on
𝑡 − 12 to 𝑡 − 7 formation period are quite similar, so we don’t give for brief.
13 The period having the larger absolute value of market return during the formation period/ holding
period than the average absolute value of the whole sample is defined as with large market changes, and
if momentum performance is related to the market dynamic, these periods may play a more important
role.
28
Japan, Taiwan and Chinese stock markets, combining our finding in the table 10 that
those stock markets have relatively smaller proportion of market continuation, we can
draw our conclusion that short-term momentum is influenced by the market dynamic,
which could be a general conclusion not only for the Chinese stock market. The reason
for insignificant momentum performance in the Asian stock markets is the big changes
of market return and the less proportion of market continuation.
6. Conclusion
Based on a comprehensively monthly data of all A-shares from 1997 to 2018, we
study the performance of short-term momentum in the Chinese stock market.
Consisting with the previous studies about China, we also can’t find the evidence for
significant momentum return by using the traditional way to construct the momentum
strategy. In addition, we find the momentum performance is related to the market
dynamic, and the momentum return is significantly positive when the market continues
but changes to significantly negative when the market transits.
By studying the change of beta difference, capitalization difference and the B/M
difference between the winner-decile and the loser-decile during the formation period
and holding period, we find the change of beta difference is the key factor for the
changed momentum performance along with market dynamic. Based on these findings,
we give an improved signed momentum strategy, which is a combination of the
traditional momentum strategy and the market dynamic, and find this new momentum
strategy performs well in the Chinese stock market: from the past loser-decile to the
past winner-decile, there is an approximately increasing trend, the portfolio return is
significantly positive and can’t be fully explained by the existing asset-pricing factors.
Besides, we also find traditional momentum strategy and the improved momentum
strategy perform better following the Down market, which is caused by the retail
investors’ gambling behavior during the Up market but failure to do the opposite
aggressive trading during the Down market, limited by the short sale constraint.
By giving some summary about stocks in the winner-decile and the loser-decile
during the formation period are in the same group or the counterparty group during the
29
holding period, we do the robustness test and confirm our finding about the momentum
performance and market dynamic. And in our further analysis, we find the market
dynamic has a universe influence on the momentum performance: markets having the
significant momentum performance are generally with more market continuation
periods and the absolute value of market return is relatively smaller (therefore, the
market dynamic has smaller influence on the change of beta difference and the
momentum performance is less influenced) and those having the insignificant
momentum performance are just on the opposite situation.
Our study contributes to find that the short-term momentum performance in the
Chinese stock market is related to the market dynamic, and only when the market
continues from the formation period to the holding period, the momentum exists.
Considering the short-term momentum is a reflection of investors’ underreaction to the
public/private information, the extent of momentum performance can be considered to
be a signal of information diffusion efficiency. However, the insignificant momentum
performance makes this signal weaker, which implying the importance of keeping
market stability (therefore, increase the number of market continuation periods) for the
Chinese stock market.
30
Table 1. Baseline results of the traditional short-term momentum strategy
Results in this table present the performance of short-term of momentum strategy in the whole
sample, Up market and Down market based on 𝑡 − 12 to 𝑡 − 2 and 𝑡 − 12 to 𝑡 − 7 formation
periods. 𝐷𝑖𝑓𝑓 gives the difference between momentum performance following the Down market
and the Up market. 𝑁 in the table gives the number of each sample. 𝑀𝑒𝑎𝑛 is the equal-weighted
stock return of stocks in the group 1 and group 10, and the difference of stock return in these two
groups. 𝑆𝑡𝑑 is the standard deviation of stock return in each group, T is T value of each portfolio's
excess return, and the 𝑆𝑃 is the Sharp Ratio of each portfolio. 𝑀𝑒𝑎𝑛 and 𝑆𝑡𝑑 are the annualized
results of the monthly return, and values are given as the percentage value. Significance at the 1%,
5%, and 10% level is denoted as ***, **, and *, respectively.
𝑡 − 12 to 𝑡 − 2 𝑡 − 12 to 𝑡 − 7
𝑁 𝑀𝑒𝑎𝑛 𝑆𝑡𝑑 T 𝑆𝑃 𝑁 𝑀𝑒𝑎𝑛 𝑆𝑡𝑑 T 𝑆𝑃
Whole
sample
1
255
11.20 34.97 5.11*** 0.32
255
9.88 35.38 4.46*** 0.28
10 10.13 34.20 4.73*** 0.30 10.72 34.13 5.02*** 0.31
10 - 1 -1.04 19.42 -0.85 -0.05 1.00 15.12 1.06 0.07
Down
market
1
115
5.60 34.96 1.72* 0.16
116
7.16 33.12 2.33** 0.22
10 7.68 30.97 2.66*** 0.25 10.31 30.03 3.70*** 0.34
10 - 1 2.08 18.78 1.19 0.11 3.45 16.36 2.27** 0.21
Up
market
1
140
15.79 35.04 5.33*** 0.45
139
12.16 37.27 3.85*** 0.33
10 12.14 36.74 3.91*** 0.33 11.07 37.32 3.50*** 0.30
10 - 1 -3.59 19.97 -2.13** -0.18 -1.04 14.03 -0.88 -0.07
𝐷𝑖𝑓𝑓 5.67 19.44 2.32** 4.49 15.13 2.36**
31
Table 2. Short-term momentum in the subsamples of different market states.
Results in this table present the performance of short-term of momentum strategy in subsamples of different market states, including the Up & Down, Up & Up, Down
& Down and Down & Up subsamples. Up & Up gives the subsample combined by the up market in the formation period (𝑡 − 12 to 𝑡 − 2/ 𝑡 − 12 to 𝑡 − 7) and the up
market in the holding period ( 𝑡) and others subsamples have the similar meaning. Market continuation gives the results based on the same market states in two periods
(Up & Up and Down & Down) and the market transition gives the results based on the different market states in two periods (Up & Down and Down & Up). 𝑀𝑒𝑎𝑛
is the equal-weighted stock return of stocks in the group 1 and group 10, and the difference of stock return in these two groups. 𝑆𝑡𝑑 is the standard deviation of stock
return in each group, T is T value of each portfolio's excess return, and the 𝑆𝑃 is the Sharp Ratio of each portfolio. 𝑀𝑒𝑎𝑛 and 𝑆𝑡𝑑 are the annualized results of the
monthly return, and values are given as the percentage value. Significance at the 1%, 5%, and 10% level is denoted as ***, **, and *, respectively.
𝑡 − 12 to 𝑡 − 2 𝑡 − 12 to 𝑡 − 7
𝑁 𝑀𝑒𝑎𝑛 𝑆𝑡𝑑 T 𝑆𝑃 𝑁 𝑀𝑒𝑎𝑛 𝑆𝑡𝑑 T 𝑆𝑃
Up & Down
1
64
-68.78 24.06 -22.87*** -2.86
61
-88.31 23.87 -28.90*** -3.70
10 -77.41 26.88 -23.04*** -2.88 -93.04 24.27 -29.95*** -3.83
10 - 1 -8.63 18.90 -3.65*** -0.46 -4.73 13.04 -2.83*** -0.36
Up & Up
1
76
87.01 29.19 25.98*** 2.98
78
90.72 29.30 27.35*** 3.10
10 87.56 29.05 26.27*** 3.01 92.49 27.61 29.59*** 3.35
10 - 1 0.65 20.88 0.27 0.03 1.84 14.78 1.10 0.12
Down& Down
1
57
-81.13 22.49 -27.23*** -3.61
60
-67.23 21.47 -24.25*** -3.13
10 -60.83 23.06 -19.92*** -2.64 -50.58 22.10 -17.73*** -2.29
10 - 1 20.30 18.24 8.40*** 1.11 16.65 15.64 8.24*** 1.06
Down & Up
1
58
90.83 26.55 26.05*** 3.42
56
86.86 27.50 23.63*** 3.16
10 75.01 24.91 22.94*** 3.01 75.54 25.76 21.94*** 2.93
10 - 1 -15.83 18.00 -6.70*** -0.88 -10.69 16.26 -4.92*** -0.66
Market Continuation
1
133
14.95 35.78 4.82*** 0.42
138
22.05 34.58 7.49*** 0.64
10 23.96 34.03 8.12*** 0.70 30.29 32.57 10.92*** 0.93
10 - 1 9.07 19.92 5.25*** 0.46 8.28 15.26 6.37*** 0.54
Market Transition
1
122
7.10 34.17 2.30*** 0.21
117
-4.47 36.01 -1.34 -0.12
10 -4.95 33.99 -1.61 -0.15 -12.35 34.86 -3.83*** -0.35
10 - 1 -12.06 18.43 -7.22*** -0.65 -7.58 14.63 -5.61*** -0.52
32
Table 3. Short-term momentum when the market changes greatly
Results in this table present the performance of short-term of momentum strategy in subsamples of different market states when the market changes greatly, including
the Up & Down, Up & Up, Down & Down and Down & Up subsamples. Up & Up gives the subsample combined by the up market in the formation period (𝑡 −
12 to 𝑡 − 2/ 𝑡 − 12 to 𝑡 − 7) and the up market in the holding period ( 𝑡) and others subsamples have the similar meaning. Market continuation gives the results based
on the same market states in two periods (Up & Up and Down & Down) and the market transition gives the results based on the different market states in two periods
(Up & Down and Down & Up). 𝑀𝑒𝑎𝑛 is the equal-weighted stock return of stocks in the group 1 and group 10, and the difference of stock return in these two groups.
𝑆𝑡𝑑 is the standard deviation of stock return in each group, T is T value of each portfolio's excess return, and the 𝑆𝑃 is the Sharp Ratio of each portfolio. 𝑀𝑒𝑎𝑛 and
𝑆𝑡𝑑 are the annualized results of the monthly return, and values are given as the percentage value. Significance at the 1%, 5%, and 10% level is denoted as ***, **,
and *, respectively.
𝑡 − 12 to 𝑡 − 2 𝑡 − 12 to 𝑡 − 7
𝑁 𝑀𝑒𝑎𝑛 𝑆𝑡𝑑 T 𝑆𝑃 𝑁 𝑀𝑒𝑎𝑛 𝑆𝑡𝑑 T 𝑆𝑃
Up & Down
1
36
-95.54 27.15 -21.11*** -3.52
37
-111.82 26.79 -25.39*** -4.17
10 -119.77 28.16 -25.52*** -4.25 -122.13 26.89 -27.62*** -4.54
10 - 1 -24.23 18.72 -7.76*** -1.29 -10.31 14.25 -4.40*** -0.72
Up & Up
1
51
113.05 31.85 25.35*** 3.55
42
136.28 33.08 26.70*** 4.12
10 107.13 32.77 23.35*** 3.27 137.12 31.10 28.57*** 4.41
10 - 1 -5.82 23.54 -1.77* -0.25 0.91 17.39 0.34 0.05
Down& Down
1
24
-118.20 26.52 -21.83*** -4.46
26
-109.62 22.30 -25.07*** -4.92
10 -91.85 28.76 -15.64*** -3.19 -91.25 23.45 -19.84*** -3.89
10 - 1 26.35 18.90 6.83*** 1.39 18.37 14.70 6.37*** 1.25
Down & Up
1
30
145.42 26.18 30.42*** 5.55
32
131.34 28.11 26.43*** 4.67
10 119.77 26.95 24.35*** 4.45 111.65 27.35 23.10*** 4.08
10 - 1 -25.65 18.80 -7.47*** -1.36 -19.81 17.09 -6.56*** -1.16
Market Continuation
1
75
39.05 43.44 7.79*** 0.14
68
42.26 45.42 7.67*** 0.93
10 43.45 41.35 9.10*** 0.23 49.80 42.88 9.58*** 1.16
10 - 1 4.47 22.46 1.72* 0.46 7.58 16.48 3.79*** 0.46
Market Transition
1
66
13.99 43.83 2.59** 0.51
69
0.95 44.53 0.18 0.02
10 -10.88 44.21 -2.00** 0.36 -13.71 43.28 -2.63** -0.32
10 - 1 -24.87 18.61 -10.86*** -0.65 -14.72 15.57 -7.85*** -0.94
33
Table 4. Beta difference during the formation period and holding period
Results in this table present the average beta of stocks in the group 1 (the loser decile), the group 10
(the winner decile) and the beta difference of two deciles (10 − 1) during the formation period and
the holding period. “Ranking basis” gives the ranking period for the beta calculation and “market
state” gives the results from four subsamples: Up & Down, Down & Up, Up & Up and Down &
Down. Up & Up gives the subsample combined by the Up market in the formation period (𝑡 −
12 to 𝑡 − 2/ 𝑡 − 12 to 𝑡 − 7) and the Up market in the holding period ( 𝑡) and others subsamples
have the similar meaning. 𝑀𝑒𝑎𝑛 is the equal-weighted beta of stocks in the group 1 and group 10,
and the difference of stock return in these two groups. 𝑆𝑡𝑑 is the standard deviation of beta in each
group, and T is T value of each portfolio's excess return. Significance at the 1%, 5%, and 10% level
is denoted as ***, **, and *, respectively.
Market
state
Ranking
basis
𝑡 − 12 to 𝑡 − 2 𝑡 − 12 to 𝑡 − 7
𝑀𝑒𝑎𝑛 𝑆𝑡𝑑 T 𝑀𝑒𝑎𝑛 𝑆𝑡𝑑 T
Up &
Down
Formation
period
1 1.065 0.127 1.074 0.119
10 1.159 0.179 1.135 0.146
10 − 1 0.094 0.267 2.83*** 0.061 0.207 2.29**
Holding
period
1 1.143 0.130 1.150 0.127
10 0.989 0.095 0.983 0.092
10 − 1 -0.154 0.170 -7.26*** -0.167 0.159 -8.18***
Up &
Up
Formation
period
1 1.036 0.144 1.030 0.136
10 1.201 0.156 1.194 0.134
10 − 1 0.166 0.269 5.37*** 0.165 0.234 6.23***
Holding
period
1 1.050 0.112 1.037 0.117
10 1.153 0.164 1.148 0.151
10 − 1 0.103 0.218 4.12*** 0.110 0.206 4.73***
Down&
Down
Formation
period
1 1.134 0.092 1.129 0.105
10 1.007 0.107 0.997 0.113
10 − 1 -0.126 0.149 -6.42*** -0.133 0.162 -6.33***
Holding
period
1 1.138 0.084 1.131 0.091
10 0.992 0.099 0.998 0.101
10 − 1 -0.146 0.133 -8.31*** -0.133 0.145 -7.11***
Down
&Up
Formation
period
1 1.146 0.082 1.159 0.104
10 1.033 0.122 1.023 0.115
10 − 1 -0.114 0.145 -5.96*** -0.136 0.160 -6.34***
Holding
period
1 1.003 0.129 1.019 0.127
10 1.150 0.119 1.157 0.140
10 − 1 0.146 0.203 5.50*** 0.138 0.220 4.68***
34
Table 5. Capitalization difference during the formation period and holding period
Results in this table present the average capitalization of stocks in the group 1 (the loser decile), the
group 10 (the winner decile) and the capitalization difference of two deciles (10 − 1) during the
formation period and the holding period. “Ranking basis” gives the ranking period for the
capitalization calculation and “market state” gives the results from four subsamples: Up & Down,
Down & Up, Up & Up and Down & Down. Up & Up gives the subsample combined by the Up
market in the formation period (𝑡 − 12 to 𝑡 − 2/ 𝑡 − 12 to 𝑡 − 7) and the Up market in the holding
period ( 𝑡 ) and others subsamples have the similar meaning. 𝑀𝑒𝑎𝑛 is the equal-weighted
capitalization of stocks in the group 1 and group 10, and the difference of stock return in these two
groups. 𝑆𝑡𝑑 is the standard deviation of capitalization in each group, and T is T value of each
portfolio's excess return. Significance at the 1%, 5%, and 10% level is denoted as ***, **, and *,
respectively.
Market
state
Ranking
basis
𝑡 − 12 to 𝑡 − 2 𝑡 − 12 to 𝑡 − 7
𝑀𝑒𝑎𝑛 𝑆𝑡𝑑 T 𝑀𝑒𝑎𝑛 𝑆𝑡𝑑 T
Up &
Down
Formation
period
1 8.389 7.407 6.853 5.295
10 12.725 11.858 12.043 10.384
10 - 1 4.336 13.572 2.56*** 5.190 10.360 3.91***
Holding
period
1 8.533 7.172 7.550 6.860
10 9.041 7.864 9.376 8.023
10 - 1 0.508 9.126 0.45 1.826 8.837 1.61
Up &
Up
Formation
period
1 9.481 9.244 9.008 9.592
10 11.849 9.556 10.031 7.229
10 - 1 2.368 13.000 1.59 1.024 11.763 0.77
Holding
period
1 10.459 9.818 10.312 9.366
10 9.239 8.674 8.274 7.469
10 - 1 -1.220 12.384 -0.86 -2.037 10.904 -1.65
Down&
Down
Formation
period
1 5.388 6.784 5.958 5.977
10 7.587 4.653 6.877 3.342
10 - 1 2.199 6.981 2.38** 0.920 5.672 1.26
Holding
period
1 5.132 5.067 6.300 6.046
10 6.365 4.637 6.157 4.396
10 - 1 1.233 6.074 1.53 -0.143 6.543 -0.17
Down
&Up
Formation
period
1 7.386 8.173 7.958 8.044
10 8.349 6.153 7.560 6.167
10 - 1 0.963 9.705 0.76 -0.399 9.165 -0.33
Holding
period
1 8.383 7.434 8.514 8.160
10 6.136 5.236 7.369 7.628
10 - 1 -2.247 7.855 -2.18** -1.146 10.333 -0.83
35
Table 6. B/M difference during the formation period and holding period
Results in this table present the average B/M of stocks in the group 1 (the loser decile), the group
10 (the winner decile) and the B/M difference of two deciles (10 − 1) during the formation period
and the holding period. “Ranking basis” gives the ranking period for the B/M calculation and
“market state” gives the results from four subsamples: Up & Down, Down & Up, Up & Up and
Down & Down. Up & Up gives the subsample combined by the Up market in the formation period
( 𝑡 − 12 to 𝑡 − 2 / 𝑡 − 12 to 𝑡 − 7 ) and the Up market in the holding period ( 𝑡 ) and others
subsamples have the similar meaning. 𝑀𝑒𝑎𝑛 is the equal-weighted B/M of stocks in the group 1
and group 10, and the difference of stock return in these two groups. 𝑆𝑡𝑑 is the standard deviation
of B/M in each group, and T is T value of each portfolio's excess return. Significance at the 1%, 5%,
and 10% level is denoted as ***, **, and *, respectively.
Market
state
Ranking
basis
𝑡 − 12 to 𝑡 − 2 𝑡 − 12 to 𝑡 − 7
𝑀𝑒𝑎𝑛 𝑆𝑡𝑑 T 𝑀𝑒𝑎𝑛 𝑆𝑡𝑑 T
Up &
Down
Formation
period
1 0.917 0.459 0.806 0.348
10 0.504 0.203 0.623 0.283
10 - 1 -0.412 0.484 -6.82*** -0.175 0.394 -3.47***
Holding
period
1 0.704 0.322 0.682 0.284
10 0.618 0.196 0.664 0.238
10 - 1 -0.085 0.342 -2.00** -0.027 0.281 -0.76
Up &
Up
Formation
period
1 0.995 0.492 0.871 0.356
10 0.540 0.224 0.645 0.251
10 - 1 -0.455 0.498 -7.96*** -0.225 0.342 -5.82***
Holding
period
1 0.762 0.334 0.792 0.311
10 0.747 0.347 0.728 0.318
10 - 1 -0.015 0.416 -0.32 -0.055 0.364 -1.35
Down&
Down
Formation
period
1 1.254 0.580 1.137 0.506
10 0.648 0.237 0.690 0.292
10 - 1 -0.587 0.539 -8.23*** -0.436 0.478 -7.07***
Holding
period
1 0.914 0.410 0.936 0.425
10 0.922 0.388 0.871 0.394
10 - 1 -0.020 0.399 -0.38 -0.079 0.444 -1.38
Down
&Up
Formation
period
1 1.303 0.555 1.207 0.515
10 0.644 0.225 0.679 0.288
10 - 1 -0.659 0.532 -9.44*** -0.528 0.465 -8.51***
Holding
period
1 0.906 0.402 0.868 0.436
10 0.917 0.361 0.948 0.382
10 - 1 0.026 0.387 0.51 0.080 0.440 1.35
36
Table 7. Signed momentum in the Chinese stock market
Results in this table present the performance of momentum strategy after considering the influence
of market dynamic (i.e., the signed momentum strategy), including the portfolio return from the
group 1 (the loser decile) to group 10 (the winner decile), the difference of stock return between
group 10 and group 1, and the 𝐴𝑙𝑝ℎ𝑎𝑠 from the regression of signed momentum return on the
market factor (𝐶𝐴𝑃𝑀), Fama-French three factors (𝐹𝐹3) and the Fama-French five factors (𝐹𝐹5).
𝑀𝑒𝑎𝑛 and 𝑆𝑡𝑑 are the equal-weighted stock return of each portfolio and the standard deviation of
stock return in each group, T is T value of each portfolio's excess return, and the 𝑆𝑃 is the Sharp
Ratio of each portfolio. 𝑀𝑒𝑎𝑛 and 𝑆𝑡𝑑 are the annualized results of the monthly return (except
for three 𝐴𝑙𝑝ℎ𝑎𝑠), and values are given as the percentage value. Significance at the 1%, 5%, and
10% level is denoted as ***, **, and *, respectively.
𝑡 − 12 to 𝑡 − 2 𝑡 − 12 to 𝑡 − 7
𝑀𝑒𝑎𝑛 𝑆𝑡𝑑 T 𝑆𝑃 𝑀𝑒𝑎𝑛 𝑆𝑡𝑑 T 𝑆𝑃
1 5.45 34.72 2.51*** 0.16 6.73 34.70 3.10*** 0.19
2 7.69 33.58 3.66*** 0.23 9.50 33.39 4.54*** 0.28
3 11.97 34.14 5.60*** 0.35 13.04 33.77 6.17*** 0.39
4 12.91 33.45 6.16*** 0.39 11.41 33.11 5.50*** 0.34
5 13.57 33.27 6.51*** 0.41 14.23 32.81 6.93*** 0.43
6 14.34 33.19 6.90*** 0.43 13.08 32.98 6.33*** 0.40
7 14.54 33.39 6.95*** 0.44 13.99 33.19 6.73*** 0.42
8 13.63 33.70 6.46*** 0.40 13.43 33.02 6.50*** 0.41
9 14.91 33.78 7.05*** 0.44 15.76 34.00 7.40*** 0.46
10 15.95 34.37 7.41*** 0.46 13.77 34.80 6.32*** 0.40
10 − 1 10.50 19.19 8.74*** 0.55 7.04 17.00 5.97*** 0.37
𝐴𝑙𝑝ℎ𝑎(𝐶𝐴𝑃𝑀) 0.90 -- 2.70*** -- 0.58 -- 2.35** --
𝐴𝑙𝑝ℎ𝑎(𝐹𝐹3) 1.04 -- 3.31*** -- 0.64 -- 2.35** --
𝐴𝑙𝑝ℎ𝑎(𝐹𝐹5) 0.94 -- 2.84*** -- 0.49 -- 1.78* --
37
Table 8. Signed momentum following Up and Down market
Results in this table present following the Up market and the Down market, the performance of
momentum strategy after considering the influence of market dynamic (i.e., the signed momentum
strategy), including the difference of stock return between the group 10 (the winner decile) and
group 1 (the loser decile), and the 𝐴𝑙𝑝ℎ𝑎𝑠 from the regression of signed momentum return on the
market factor (𝐶𝐴𝑃𝑀), Fama-French three factors (𝐹𝐹3) and the Fama-French five factors (𝐹𝐹5).
𝑀𝑒𝑎𝑛 and 𝑆𝑡𝑑 are the equal-weighted stock return of each portfolio and the standard deviation of
stock return in each group, T is T value of each portfolio's excess return, and the 𝑆𝑃 is the Sharp
Ratio of each portfolio. 𝑀𝑒𝑎𝑛 and 𝑆𝑡𝑑 are the annualized results of the monthly return (only for
10 − 1), and values are given as the percentage value. Significance at the 1%, 5%, and 10% level
is denoted as ***, **, and *, respectively.
𝑡 − 12 to 𝑡 − 2 𝑡 − 12 to 𝑡 − 7
𝑀𝑒𝑎𝑛 𝑆𝑡𝑑 T 𝑆𝑃 𝑀𝑒𝑎𝑛 𝑆𝑡𝑑 T 𝑆𝑃
Follow
Up
Market
10 − 1 4.30 19.96 2.55** 0.22 2.87 13.86 2.46** 0.21
𝐴𝑙𝑝ℎ𝑎(𝐶𝐴𝑃𝑀) 0.39 -- 0.76 -- 0.26 -- 0.76 --
𝐴𝑙𝑝ℎ𝑎(𝐹𝐹3) 0.70 -- 1.41 -- 0.44 -- 1.12 --
𝐴𝑙𝑝ℎ𝑎(𝐹𝐹5) 0.82 -- 1.44 -- 0.54 -- 1.38 --
Follow
Down
Market
10 − 1 18.04 1.97 10.76*** 1.00 14.25 15.93 9.55*** 0.89
𝐴𝑙𝑝ℎ𝑎(𝐶𝐴𝑃𝑀) 1.51 -- 3.41*** -- 1.18 -- 2.98*** --
𝐴𝑙𝑝ℎ𝑎(𝐹𝐹3) 1.48 -- 3.17*** -- 1.08 -- 2.52** --
𝐴𝑙𝑝ℎ𝑎(𝐹𝐹5) 1.45 -- 3.00*** -- 1.03 -- 2.39** --
Table 9. Ratio of stocks in the same group during the formation period and holding period
Results in this table present the ratio of stocks in the same group during the formation period and
holding period. Summary includes the result from the whole sample, the Up & Up subsample, the
of Down & Down subsample, the of Up & Down subsample, the of Down & Up subsample, the
market continuation subsample, the market transition subsample, and the difference (𝐷𝑖𝑓𝑓) of result
from the market continuation subsample and the market transition subsample. 𝑁 gives the number
of months in each subsample, 𝑀𝑒𝑎𝑛, 𝑀𝑒𝑑𝑖𝑎𝑛 and Std are the average value, median value and
standard deviation of the ratio of stocks in the same group during the formation period and holding
period in each subsample. Values in the parentheses are the T values of the difference of the ratio of
stocks in the same group during the formation period and holding period between the market
continuation subsample and the market transition subsample. Significance at the 1%, 5%, and 10%
level is denoted as ***, **, and *, respectively.
𝑡 − 12 to 𝑡 − 2 𝑡 − 12 to 𝑡 − 7
𝑁 𝑀𝑒𝑎𝑛 𝑀𝑒𝑑𝑖𝑎𝑛 Std 𝑁 𝑀𝑒𝑎𝑛 𝑀𝑒𝑑𝑖𝑎𝑛 Std
Whole sample 255 0.119 0.107 0.057 255 0.116 0.108 0.047
Up & Down 64 0.109 0.103 0.046 61 0.110 0.102 0.041
Up & Up 76 0.110 0.099 0.049 78 0.112 0.104 0.044
Down & Down 57 0.151 0.157 0.067 60 0.136 0.123 0.054
Down & Up 58 0.108 0.099 0.055 56 0.104 0.099 0.043
Market continuation 133 0.128 0.117 0.061 138 0.123 0.111 0.050
Market transition 122 0.109 0.101 0.050 117 0.107 0.101 0.042
𝐷𝑖𝑓𝑓 -- 0.019
(2.72***)
-- 0.056 -- 0.015
(2.61***)
-- 0.046
38
Table 10. Summary of market states in other countries (based on 𝒕 − 𝟏𝟐 to 𝒕 − 𝟐)
Results in this table present the summary of market states from other countries, including the US
stock market, the UK stock market, the German stock market, the Korean stock market, the Japan
stock market, the Taiwan stock market and the Chinese market for comparison. Summary in this
table is given by using the 𝑡 − 12 to 𝑡 − 2 formation period as an example. Summary includes the
number of total trading months, the months of market continuation, the months of market transition,
the months of Up & Up subsample, the months of Down & Down subsample, the months of Up &
Down subsample and the months of Down & Up subsample in the whole sample and the period
when the market changes greatly.
Market Total
number
Market
continuation
Market
transition
Up &
Up
Down &
Down
Up &
Down
Down
& Up
Whole sample
US 1078 597 481 445 152 191 290
UK 407 231 176 175 56 61 115
Germany 335 194 141 139 55 55 86
Korean 346 184 162 107 77 70 92
Japan 368 195 173 109 86 87 86
Taiwan 610 327 283 226 101 108 175
China 255 133 122 76 57 58 64
Market changes greatly
US 654 348 306 253 95 123 183
UK 247 131 116 101 30 40 76
Germany 210 122 88 89 33 36 52
Korean 200 108 92 56 52 38 54
Japan 247 128 119 63 65 65 54
Taiwan 314 168 146 122 46 54 92
China 141 75 66 51 24 30 36
Table 11. Average absolute value of market return
Results in this table present the average absolute value of market return from other countries,
including the US stock market, the UK stock market, the German stock market, the Korean stock
market, the Japan stock market, the Taiwan stock market and the Chinese market for comparison.
Results include the average absolute value of market return in the holding period (𝑡 ) and two
formation periods (𝑡 − 12 to 𝑡 − 2 and 𝑡 − 12 to 𝑡 − 7).
Market 𝑡 𝑡 − 12 to 𝑡 − 2 𝑡 − 12 to 𝑡 − 7
US 0.038 0.014 0.018
UK 0.033 0.011 0.014
German 0.044 0.017 0.021
Korean 0.055 0.018 0.024
Japan 0.046 0.016 0.021
Taiwan 0.063 0.022 0.029
China 0.060 0.023 0.030
39
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