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Trading Volume, Volatility and Leverage:

A Dynamic Analysis of the Indian Stock Market

Naliniprava Tripathy* Aditya Prakash Goreand Mayank Arora

ABSTRACT

This study investigates the relationship between leverage effect and daily stock returns,

volume and volatility for the 30 stocks included in the Bombay Stock Exchange SENSEX

index in India during the period January 2005 to June 2009, by using GARCH, ARCH,

EGARCH and TARCH models. The analysis shows that there exist substantial ARCH

effects in the residuals and the volatility shocks are quite persistent in the market. Thestudy found that the recent news and the old news both have an impact on the volatility of

the stock. This study also finds evidence of leverage and asymmetric effect on stock

market. The study concludes that bad news generate more impact on change in trading

volumes and volatility of the market. It is also observed that asymmetric GARCH models

provide better fit than the symmetric GARCH model. So it is evident from the study that

systematic variations in trading volume are assumed to be caused only by the arrival of

new information.

Key words: Trading volume, BSE SENSEX, Stock price, GARCH, ARCH, EGARCH, TARCH

INTRODUCTION

Trading volume and volatility indicate potential importance as indicators of the current stock market activity on theone hand and a potential source of information for the future behavior of stock market on the other hand. Numerouspapers have documented the fact that high stock market volume is associated with volatile returns. An increase in

stock market volatility brings a large stock price change of advances or declines. It has also been noted that volumetends to be higher when stock prices are increasing than when prices are falling. Pricing of securities depends onvolatility of each asset. Therefore, price changes indicate the average reaction of investors to news. The arrival ofnew information makes investors to adapt their expectations and this is the main cause for price and return changes.However, since investors are heterogeneous when interpreting new information, stock returns may stay unchangedeven though new information is brought to the market. On the other hand, stock returns may only change if there ispositive trading volume.

According to the efficient market hypothesis, past price or volume changes in a competitively traded stock market

do not help predict future prices. However, recent studies have questioned the efficient market hypothesis and havesupported the notion that stock market excess returns can be predicted by publicly available information (Fama &

French, 1995; Pesaran & Timmennan, 1995; Ferson & Harvey, 1993).Various studies reported that there aresignificant relationships between volume and stock price movement and volatility, due to the fact that tradingvolume is a source of risk because of the flow of information. For example, Saatccioglu and Starks (1998) foundthat volume led stock prices changes in four out of the six emerging markets. Blume, et al, (1989) stated that a

* Associate Professor (Finance), Indian Institute of Management Shillong, Mayurbhanj Complex, Nongthammai, Shillong, Meghalaya, India,

PIN 793 014, Phone: +91-364-2308037, Fax: +91-364-2230041, Email: [email protected], [email protected]

Final year PGP Participant, Indian Institute of Management Shillong, India, Phone: +91 94367 00531, +91 99690 07150,Email: [email protected], [email protected] (Conference presenter)

Final year PGP Participant, Indian Institute of Management Shillong, India, Phone: +91 94367 00528,

Email: [email protected], [email protected] (Conference presenter)


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portion of the losses on S & P stocks in October, 1987 were related to the magnitude of the trading volume. Chan etal. (2000) found that trading volume for foreign stocks is strongly associated with NYSE opening price volatility.Sfvenblad, 2000 found that Swedish index returns exhibit high autocorrelation when trading volume is low.Swanminathan (2000) finds that past trading volume can be used to predict future stock price momentum. However,

Jones, et al, (1994) found that the positive volatility-volume relation documented by numerous researchers reflectedpositive relationship between volatility and the number of transactions. Mei, et al. (2005) found that trading caused

by investors speculative motives could explain a significant fraction of the price difference between the dual-classshares. Griffin, et al. (2007) investigated the dynamic relation between market-wide trading activity and returns in46 markets and reported strong positive relationship between turnover and past returns. In addition, other studiesreported that stock trading volume represents the highest positive correlation to the emerging stock price changes;thus represent the most predicted variables in increasing price volatility in both emerging and developing stockmarkets (Sabri, 2004, Sabri, 2008b). The analysis of the relationship between stock prices, returns on stock index

and volumes traded has been conducted from various perspectives. More recently, the use of conditional volatility toinvestigate the relationship between stock returns and trading volume became very popular. Although conditional

volatility have always been used, realized volatility, which is also called historical volatility is the sum of squaredintraday returns over a certain interval such as a day, has recently attracted the attention of financial economists andeconometricians as an accurate measure of the true volatility.In the last three decades, a large number of countries had initiated reform process to open up their economies.Emerging markets have received huge inflows of capital in the recent past and became viable alternative for

investors seeking international diversification. Among the emerging markets, India has received its more than fairshare of foreign investment inflows since its reform process began. One reason could be that India was not affected

by the Asian crisis and has maintained its high economic growth during that period (Gupta and Basu 2005). TodayIndia is one of the fastest growing emerging economies in the world. The reform process in India officially startedin 1991. As a result, demand for investment funds is growing significantly and capital market growth is expected to play an increasingly important role in the process. The capital market reforms in India present a case where a judicious combination of competition, deregulation and regulation has led to sustained reforms and increasedefficiency (Datar and Basu 2004). At this transitional stage, it is necessary to assess the level of efficiency of the

Indian stock market in order to establish its longer term role in world economy. The analysis of stock market is animportant segment through which countries exposure to the outer world could be readily felt. This research is

motivated to focuses the predictability of stock returns and the role of trading volume and volatility in the dynamicsof the price discovery process in India. Since both volume and volatility both serve as measures of information flow(e.g. Andersen, 1996), examining the links between stock returns, volume and volatility provides us further

understanding of how new information is impounded in stock prices. In this context, deeper understanding of therole of trading volume and volatility in the dynamics of stock prices may help investors to identify future patterns ofthe stock market which can be exploited in their investment decisions.

This paper adds to the growing literature on the stock market by a further examination of the return-volume

relationship and we raise three research questions. First, the presented study reinvestigates the effects on volatilityof the Indian stock market issue using GARCH model to see to what extent the change could be attributed to thetrading volume. Secondly, we examine whether the stock markets reaction to the arrival of news changed whentrading commenced. During the last few years leverage effect has became quite noticeable, particularly in stockmarkets. Changes in stock prices tend to be negatively related to changes in volatility (Black, 1976; Christie, 1982).This has been attributed to the leverage effect where stock price declines increase the financial leverage andconsequently, the degree of risk (volatility). To capture this, many researchers have developed different asymmetric

GARCH models [exponential GARCH (EGARCH) by Nelson (1991) and TGARCH by Zakoian (1994)]. Since the

vanilla GARCH model specifies a symmetric volatility response to market news, it cannot capture the leverage orasymmetric response. GARCH model fails to respond differently to positive and negative shocks. No prior studymade so far to find asymmetric effect of stock return, trading volume in stock market volatility in India. So, thirdlywe use EGARCH and TGARCH model to determine asymmetric effect of stock return in stock market volatility inIndia to obtain new insights. Therefore, the presented work improves the earlier studies and offers a value addition

to the existing literature and proves to be useful to the investors as well as regulators. The paper is organized asfollows: In section 2 we review the existing literature on the volume-volatility-return dynamics. In section 3

describe the methods used in our empirical investigation. In section 4 we show our findings Section 5 we make ourconcluding remarks.

LITERATURE REVIEW

The stock return-volume relation in both developed and emerging financial markets has been subject to extensiveresearch. This section presents a brief review of the literature relating to developed financial markets, emerging stock


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markets and the Indian stock market, respectively. Smirlock and Starks (1985) find that the return-volume relation isasymmetric and later, Smirlock and Starks (1988) find a strong positive lagged relationship between volume andabsolute price changes using individual stock data. Hiemstra and Jones (1994) use non-linear Granger causality tests toexamine the non-linear causal relation between volume and return and find there is a positive bi-directional relation

between them. Bhagat and Bhatia (1996) also employ daily data to test the causal relationship between volume andreturn, finding return causes volume rather but not vice versa. Basci et al (1996) use weekly data on 29 individual

stocks in Turkey and find the price level and volume are co integrated. Saatcioglu and Starks (1998) use monthly datafrom six Latin American stock markets to test the relation between price changes and volume, finding a positive price-volume relation and a causal relationship from volume to stock price changes but not vice versa. Silvapulle and Choi(1999) use daily Korean Composite Stock Index data to study the linear and non-linear Granger causality between stockprice and trading volume, finding that there is a significant bi-directional linear and non-linear causality between thetwo series. Lee and Swaminathan (2000) used monthly returns and daily trading volume of all the firms listed on NYSE

and American Exchange (AMEX) and find that momentum and trading volume appear to predict subsequent returns inthe US equity market. Bekaert and Wu (2000) not only support this finding, but also suggest that negative shocks

generate a greater response in volatility than positive shocks of an equal magnitude, evidence of the speed ofinformation transmission in markets. Thus, the findings of past studies are strong indications of information content ofvolatility on the markets, which could be used by investors to earn abnormal profit.

Ratner and Leal (2001) examine the Latin American and Asian financial markets and find a positive contemporaneous

relation between return and volume in these countries except India. At the same time they observed that there exists a bi-directional causal relation between return and volume. In summary, the return and volume are strongly related

contemporaneously but there is little evidence that either can be used to predict the other. Medeiros and Doornik (2006)investigated the empirical relationship between stock returns, return volatility and trading volume using data from theBrazilian stock market. The study found out there is a contemporaneous and dynamic relationship between returnvolatility and trading volume and return volatility contains information about upcoming trading volumes. Atmeh andDobbs (2006) investigated the performance of moving average trading rules in the Jordanian stock market and foundthat technical trading rules can help to predict market movements. Zolontoy and Melenberg (2007) studied the dynamic

relationship between trading volume, volatility, and stock returns at the international stock markets and found noevidence of the trading volume affecting the serial correlation of stock market returns, as predicted by Campbell et al.

(1993) and Wang (1994). Second, the stock market volatility has a negative and statistically significant impact on theserial correlation of the stock market returns, consistent with the positive feedback trading model of Sentana andWadhwani (1992). Third, the lagged trading volume is positively related to the stock market volatility, supporting the

information flow theory. Fourth, they found the trading volume to have both an economically and statisticallysignificant impact on the price discovery process and the co-movement between the international stock markets.Overall, these findings suggested the importance of the trading volume as an information variable. Rashid Sabri (2008)explained the impact of trading volume on stock market volatility in the Arab Economy. The study found that there isan increasing in both trading volume and stock price volatility and volume-stock price movements are significantly

integrated for all selected markets in the study. Diebold and Yilmaz (2008) found out a clear link betweenmacroeconomic fundamentals and stock market volatilities, with volatile fundamentals translating into volatile stockmarkets. Kiymaz & Girard (2009) found that the persistency of conditional volatility is high and very close to unityimplying that current information can be used to predict future volatility. By including trading volume in the analysisthe study finds that even though the persistence of the conditional volatility is present, it is lower with the introductionof volume.

TIME SERIES DATA & METHODOLOGY

The required time series data is based on daily closing price of BSE SENSEX, actively traded 30 scripts andTrading volume have been collected from Bombay Stock Exchange for a period of five years from January 2005 toJune 2009. Returns are proxied by the log difference change in the price index. The stock return is calculated as thecontinuously-compounded return using the closing price:

Where ln (Pt) denotes the natural logarithm of the closing price at time t. We use daily turnover by volume as the raw

trading volume series (Volt).


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The Augmented Dickey-Fuller test simply includes AR (p) terms of the Xt, term in the three alternative models.

Where, is the difference operator, t is time trend, e t is error term and 0, , i are the parameters to be estimated.

The difference between the three regressions again concerns the presence of the deterministic elements a0and a2t. If

=0, the series contains a unit root.

Conditional volatility and trading volume

Volatility of the stock markets is measured by using Standard Deviation or GARCH model. GARCH model hasbeen a preferred measure of volatility by many researchers. The GARCH model provides for Heteroscedasticity inthe observed returns. It is a time series modelling technique that uses past variance and the past variance forecasts toforecast future variances. The ordinary regression model proved to be inefficient because of the untenability of oneof its key assumptions that the errors have the same variance throughout sample. It is called Homoscedasticity. If

the error variance is not constant, the data is said to be Heteroscedasticity. It is observed that the model that takesinto account the changing variance can make more efficient use of the data.

Financial time series usually exhibits a characteristic called volatility clustering which means that large changestend to follow large changes and small changes tend to follow small changes. GARCH model accounts for certaincharacteristics like thick tails and volatility clustering that are commonly associated with financial time series.Graphical analysis and computation of some basic statistics like Kurtosis and Skewness can help to provide relevant

empirical evidence of the presence of volatility clustering tendencies. The thick tail phenomena in the data areknown as excess kurtosis. Time series data that exhibit a thick tail distribution is often referred to as Leptokurtic.Generally, the presence of Leptokurtic tendencies on the time series returns suggests the presence of volatilityclustering; hence the modelling of such phenomena is recommended through the adjustment of Auto RegressiveConditional Heteroscedasticity. The Generalized Autoregressive Conditional Heteroscedasticity (GARCH) model isa variation of the Auto Regressive Conditional Heteroscedasticity (ARCH) model developed by Engle in 1982.Bollerslev originally proposed the GARCH model in 1986. A distinguishing feature of this model was that the error

variance might be correlated over time because of the phenomenon of volatility clustering. Following Antonion &Holmes (1995) and others, the return series is modelled as a univariate GARCH process. Today, the most widely

used model to estimate the conditional (hence time-varying) variance of stock and stock-index returns is theGeneralized Autoregressive Conditional Heteroscedasticity (GARCH) model. In analyzing the behaviour of

volatility due to derivative products, it is necessary to eliminate the influences of other factors. The GARCH (1, 1)is estimated for measuring volatility. The GARCH (1, 1) framework has been found to have the best specification inboth the works.

Since the information flow into the market is widely unobservable, we use trading volume as a proxy. Systematic

variations in trading volume are assumed to be caused only by the arrival of new information. Trading volumetypically exhibit the assumed time dependence. We specify the stochastic process of stock returns as a simpleGARCH (1,1) process with an autoregressive term in the mean equation and trading volume as an additionalpredetermined regressor in the conditional variance equation.

The GARCH (1, 1) Model

Any GARCH model consists of two distinct specifications. The first is the conditional mean equation. The simple

GARCH models used in practice take the simple possible conditional equation:


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Where R t is the daily return on equity and Rt-1 is the lagged return, is a fixed parameter vector and t is the

residual error term for the day t,t is treated as a collective measure of news at times t. A positive t suggests the

arrival of good news, while a negative t suggests the arrival of bad news. The second equation in a GARCH model

is the conditional variance equation. The conditional variance equation is a function of three terms:

Where 0 is mean. News about volatility from the previous period, measured as the lag of the squared residual

from the mean equation2

1t (the ARCH term). Last periods forecast variance is ht-1 (the GARCH term). GARCH

(1, 1) refers to the presence of a first-order GARCH term (the first term in parentheses) and first-order ARCH term

(the second term in parentheses). An ordinary ARCH model is a special case of a GARCH specification in which

there are no lagged forecast variances in the conditional variance equation.

Asymmetry and Leverage Effects

Though ARCH and GARCH models are responds to good and bad news and quite useful in forecasting andmodelling volatility, they lack in capturing leverage effect and information asymmetry. The rational and

underlying logic of asymmetric or leverage effect is that the distribution of stock return is highly asymmetric. Badnews is followed by larger increase in price volatility than good news (positive returns) of the same size. It is knownthat the magnitude of the response of asset prices to shocks dependents on whether the shock is negative or positive.

To demonstrate this point Engle and Ng (1990) mapped the relationship between the conditional variance of assetreturns to exogenous shocks which resulted in what they termed a news impact curve. They found evidence ofasymmetry is stock returns. In an attempt to explain the asymmetry of volatility in speculative prices, Black (1976)

posited that when stock price falls the value of the associated companys equity declines. As a result, the debt-equityratios of firms tend to rises, thereby signalling that the company has become riskier. Increased risk is considered anindicator for higher volatility. Used in this context, it is widely accepted that the statistically interpretation ofBlacks leverage effect implies that negative surprises increases predictable volatility in asset markets more thanpositive surprises. Another explanation of asymmetry is called the volatility feedback hypothesis (Campbell andHentschel, 1992). This was developed to explain stock price volatility. A negative shock to volatility increases thefuture risk premia. This would cause the stock price to fall if the future dividends are expected to remain the same.

Schwert (1989) also agreed with this explanation. Schwert (1989) and Black (1976) had shown that the returns arenegatively correlated with volatility. This implied that the returns were more volatile in response to bad newscompared to the good news.Some scholars argue that the asymmetry effect may stem from the feedback from

volatility to stock price as changes in volatility trigger change in risk premiums.

Nelson (1991) proposed an exponential GARCH model or EGARCH model which is the earliest extension of theGARCH model that incorporates asymmetric effects in returns from speculative prices based on a logarithmicexpression of the conditional variability of variable under analysis. Later on the Threshold ARCH (TARCH) modelwas introduced by Zakoian (1994).The TARCH model developed by Glosten et al. (1993) is considered to be mostsuitable in estimating the impact of positive and negative shocks on volatility. To answer the third research questionregarding leverage effect and changes in the asymmetric pattern of the impact of positive and negative return shocks

on conditional volatility we estimated the volatility equation by using EGARCH,TARCH and CARCH model.

The EGARCH Model

Glosten et al. (1994) illustrated how to allow the effects of good and bad news to have different effects on volatilityin their TARCH model. In the volatility equation positive and negative shocks can have different effects on

subsequent volatility. The first asymmetric GARCH model that precipitated considerable academic interest was the


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EGARCH or exponential GARCH model proposed by Nelson (1991). The conditional variance equation in theEGARCH (1, 1) model is

Where, ht is an asymmetric function of past t, , , , are constant parameters.

Note that the left hand side is the lag of the conditional variance. This implies that the leverage effect is exponential,rather than quadratic and that forecasts of the conditional variance are guaranteed to be nonnegative. In this model

specification, is the GARCH term that measures the impact of last periods forecast variance. A positive indicates volatility clustering implying that positive stock price changes are associated with further positive changesand vice versa. is the ARCH term that measures the effect of news about volatility from the previous period on

current period volatility. measures the leverage/asymmetric effect. Ideally is expected to be negative implyingthat bad news has a bigger impact on volatility than good news of the same magnitude. The sum of the ARCH-GARCH coefficients indicates the extent to which a volatility shock is persistent over time. A persistent volatility

shock raises the asset price volatility.

The TARCH Model

The TARCH model is another volatility model that allows asymmetric effects. TARCH or Threshold ARCH was

introduced independently by Zakeian (1990) and Glosten et al. (1993).The conditional variance is

Where dt = 1 if 0

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