An Empirical Analysis of Return, Volatility, Volume Relationship in An

An Empirical Analysis of Return, Volatility, Volume Relationship in an

Emerging Stock Market: Evidence of Chinese Stock market

MASTER’S THESIS 16th of October, 2009

Ming Zhang

S1751158

MSc in Business Administration, Finance

University of Groningen, The Netherlands

Supervised by Dr. T.T.T. Pham

Ming Zhang Master’s Thesis

Abstract

Using the data of two representative stock indices in Shanghai and Shenzhen Stock Exchange for the period 2000-2008, this paper reports an empirical analysis of the relationship between return, volatility and volume in relation to Chinese stock market. In particular, the period as a whole has been divided into concussive, bullish and bearish market and examined separately.

Major findings in this paper are listed as follows: (1) there exists a contemporaneous positive relationship between stock return and volume change in both direct and indirect way and it is evident that contemporaneous change in trading volume has relatively stronger effect on stock return in bearish market than in bullish market. Additionally, the day-of-the-week effects are inconsistent under three different state of the market; (2) Granger linear causality test suggests a uni-directional relationship from stock return to volume change in all three sub-periods, in consistence with many other studies in developed countries. As expected, it is also observed that return tends to have relatively stronger predictive power on volume change in bullish and concussive markets; (3) there exists a strong positive correlation between return volatility and volume change in all three markets. It also represents a substantial reduction in the persistence of volatility in bull and bear market. In contrast, the volatility persistence remains unchanged in concussive market.

Keywords: stock return, volatility, volume, persistence of volatility, Chinese stock market

JEL Classification: G14, G15

Ming Zhang Master’s Thesis

Table of Content

1 Introduction ...... 4

2 Literature Review ...... 6

2.1 Theory Framework ...... 6

2.2 Empirical Literature ...... 8

2.2.1 Contemporaneous relationship between return and volume ...... 8

2.2.2 Causal relationship between return and volume ...... 10

2.2.3 Relationship between volatility and volume ...... 12

3 Data and Methodology ...... 14

3.1 Methodology ...... 14

3.1.1 Simple Regression Model ...... 14

3.1.2 Vector Autoregressive (VAR) Model ...... 15

3.1.3 AR-GARCH-in-Mean Model ...... 16

3.2 Data and Summary Statistic ...... 18

4 Empirical Results and Analysis ...... 21

4.1 Contemporaneous relationship between return and volume ...... 21

4.2 Causal relationship between return and volume ...... 26

4.3 Relationship between volatility and volume ...... 27

5 Summary and Conclusion ...... 28

Ming Zhang Master’s Thesis

1 Introduction

Stock price and trading volume are two main indicators for examining and analyzing stock market performance. The study of the association among return, volatility and trading volume on financial asset mostly attributes to the needs for asset pricing and risk management. The test for the relationship between stock price and volume of each particular financial asset has always been given considerable attention, both contemporaneous and dynamic, particularly in relation to the equity market. A common finding emerged from numerous studies is a positive contemporaneous relation between stock return and trading volume. In a dynamic context, the causal relation has been examined in attempt to find out whether one has the power to predict the other and there reaches no consensus. It is worth mentioning that an old Wall Street adage

“it takes volume to make price move” implies that volume causes price move. It is important to distinguish contemporaneous and dynamic casual relationship between return and volume.

Additionally, return volatility-volume relation also plays an important role in the analysis of the stock market. An important feature of stock return series is “Volatility Clustering”, for which ARCH, GARCH and GARCH-M model has been developed and successfully used to model financial time-series data. On the basis of Mixture of Distribution Hypothesis (MDH)

Model, trading volume has been included as an explanatory variable in the variance equation suggested by Lamoureax and Lastrapes (1990), which shows a positive relationship between volatility and trading volume.

The main topic of this paper is to investigate the relationship between return, volatility and volume on one of the most fast-growing emerging markets, Chinese stock market. It is known that most of the researches have been done on the stock market in developed countries, while not much has been carried out on emerging market and China is no exception. Hence, it is interesting to find out whether the relationship between these variables exhibits similar characteristics as in developed markets. In addition, it is possible that different conclusions are reached among the emerging stock markets that is may be due to the pace of development

Ming Zhang Master’s Thesis and distinctive country regulations or policies. As such, it is necessary to address a few points related to the Chinese stock market below:

The two official Stock Exchange, Shanghai Stock Exchange and Shenzhen Stock Exchange, were both established in early 1990s. Chinese stock market expands so rapidly that surpassed

Tokyo Stock Exchange, and now ranks the first in Asia and the second in the world in terms of size: capitalization. The most common types of shares traded on exchange are A-shares and

B-shares. A-shares and B-shares are denominated in local currency RMB and US dollars respectively and only foreign individuals and institutional investors are allowed to trade

B-shares. For almost two decades passed, the growth of Chinese stock market is attributed to a series of significant structural and regulatory changes. On 16th December 1996, both

Shanghai and Shenzhen stock exchange finally implemented a 10 percent price limit for unification, both price increase and decrease for A-shares and B-shares. On 29th April 2005, the reform on split-share structure has been officially launched that is a remarkable progress for the Chinese stock market, which improved the entire system as well as the quality and managerial supervision of listed companies. Short selling is not permitted as before and the derivative market is still underdeveloped. China’s entry into World Trade Organization (WTO) enforced and accelerated the enhancement of financial system and regime in an international manner. Taken the above facts into account, the empirical results regarding the relationship between return, volatility and volume on U.S. and many other developing countries cannot be taken for granted.

This paper has three primary objectives: (1) apply simple OLS regression and AR-GARCH-M model to test whether there is a positive contemporaneous relationship between stock return and volume; (2) apply linear Granger causality test to examine whether there is a bidirectional or unidirectional dynamic causal relationship between return and volume. In other words, that is whether the knowledge of lagged trading volume can be used to predict current stock price or vice versa; (3) test for a positive volatility-volume relation and the degree of volatility persistence by introducing volume into the conditional variance equation in AR-GARCH-M

Ming Zhang Master’s Thesis specification. The significance and new about the study is the entire sample period is divided into three sub-periods: concussive market, bull market and bear market. In concussive market, it is observed no apparent upward or downward price trend for a specified period of time, and the price fluctuation stays within a relatively small range due to inactive trading behavior. It is interesting to differentiate and show the similarities among three sub-periods. It is commonly accepted that volume is relatively heavy in bull market and light in bear market. As such, a stronger return-volume relationship in bull market is expected in this paper. Additionally, the indirect contemporaneous relationship between return and volume change has been addressed.

There is lack of empirical findings in this field, particularly relating to the emerging stock market. Besides, five dummy variables are included in the return equation while re-examining the direct contemporaneous relation, allowing the return to vary with the day of the week.

The remainder of the paper is structured as follows: theoretical framework and empirical literatures are discussed in Section2. Section 3 presents data set and methodology, while the empirical findings are analyzed in Section 4. Finally, Section 5 provides some concluding remarks of the study.

2 Literature Review

2.1 Theory Framework

The attempt to study the price-volume relationship for the first time by Osborn (1959) can be traced back to late 1950s and he found that the variance of change in logarithm of stock price depend on the trading volume and concluded that log return series follows a Brownian motion process. It implies that there exists a positive relationship between price volatility and trading volume. Since then, a larger amount of researches with various perspectives have been carried out in different market and a series of theoretical models have been developed that can be divided into three main categories according to Marilyn and Robert (1999): (1) Information

Theory: information flows are joint determinants for the change of trading volume and stock

Ming Zhang Master’s Thesis price; (2) Trading Theory: this model provides an explanation for return-volume association on the basis of participant’s trading behavior. Daily volume change and stock return show the characteristic of “volatility clustering” because investors are inclined to trade in a more active market; (3) Dispersion Beliefs: it suggest a positive relationship between dispersion of beliefs and both volume and price volatility.

Among three theories mentioned above, Information Theory is the one that has been widely accepted in western world in particular. The study on microstructure of the stock market also specifies that the changes of stock price stem from the flow of the information into the market and the process where new information has passed onto the stock price. So far, Information

Theory Model has been mostly developed, including Sequential Information Arrival (SIA)

Model, Mixture of Distribution Hypothesis (MDH) Model, and Noise Trader Model.

The theoretical models mentioned above provide various explanations for the existence of the relationship between return, volatility and volume, which are illustrated in detail as follows:

(1) In the sequential-information-arrival (SIA) model of Copeland (1976) and Jennings, starks and Fellingham (1981), new information that flows into the market is not disseminated to all participants simultaneously, however, only one of them is allowed to receive it at a time and respond on it accordingly. As such, final market equilibrium will be established only after several transitional equilibriums when all participants have been informed sequentially. Hence, they suggest that both lagged trading volume and lagged stock return could have predictive power to current stock return and current trading volume respectively due to the sequential information flow. It implies that there is a positive causal return-volume relationship in either direction; (2) Mixture of Distribution Hypothesis (MDH) Models were initially developed by

Clark (1973), Epps and Epps (1976) and they argued that there exists a contemporaneous return-volume relation and price volatility and trading volume are positively correlated for the fact that they are jointly determined by a common underlying variable. This variable could be explained as the speed of information flow into the market. Furthermore, Epps and Epps

(1976) concluded a positive causal relation from trading volume to stock return, while Clark

Ming Zhang Master’s Thesis

(1973) provided a different explanation that there is no significant casual relationship running from trading volume to stock return. The difference lies in the fact that trading volume in the mixture model of Clark (1973) is used as a proxy for the speed of information flow that affects contemporaneous stock return and trading volume simultaneously, however, Epps and

Epps (1976) employed trading volume as a proxy to measure the degree of disagreement among traders as they revise their respective reservation price when the new information becomes available in the market; (3) Delong, Shleifer, Summers and Waldmann (1990) used a framework in noisy rational expectation equilibrium that represents a positive bi-directional casual relation between stock return and trading volume by assuming that stock price movement is caused by noise traders on pursuit of trading volume strategy; (4) Blume, Easley and O’Hara(1994) examined the information content of trading volume in financial markets.

In their model, they suggested that trading volume provides information on the precision of informational signals that flows into the market, which can be regarded as an additional informative statistic to explain the movement of stock price. More specifically, traded volume has predictive power for price variability and valuable information can be obtained by observing the data on past stock price movement and trading volume. Among the above four information theory models, it turns out that MDH Model is the most predominant one based on extensive empirical studies.

2.2 Empirical Literature

2.2.1 Contemporaneous relationship between return and volume

In conventional economic theory, it exhibits a contemporaneous positive relationship between price change and trading volume as shifts occur on supply side, while such relation reverse as demand curve shifts. However, early empirical attempt by Godfrey, Granger and Morgenstern

(1963) found no price-volume relation by employing cross-spectral analysis on the data set of

SEC composite index price and total trading volume on New York Stock Exchange (NYSE).

After that, Ying (1966) applied a series of statistical tests to daily series of standard & Poor

500 index returns and aggregate trading volume of New York Stock Exchange (NYSE) for a

Ming Zhang Master’s Thesis

6-year period from January 1957 to December 1962. The significant finding of Ying (1966) explained that a lager increase in volume is usually accompanied by either a larger rise or fall in price and the price tends to rise or fall over the next four trading days if the trading volume has increased or decreased consecutively for five trading days. Although Ying’s data and empirical methods have been criticized, he was the pioneer to document a strong positive price-volume relation. Since then, numerous studies have been carried out to investigate the contemporaneous relationship between price change and trading volume by Crouch (1970),

Cornell (1981), Tauchen and Pitts (1983), and Smirlock and Starks (1985). Karpoff (1987) indicated the significance of the study on price-volume relation and summarized two common findings: (1) there is a positive relationship between trading volume and absolute price change in equity and future market; (2) there is a positive relationship between trading volume and price change per se in equity market. Subsequently, Jain and Joh (1988) discovered contemporaneous relation between trading volume and return by applying the hourly data of common stocks on NYSE and such relation tends to be relatively strong in bull market than in bear market. Chen, Firth and Rui (2001), using transaction data of nine developed national markets from 1973 to 2000, found a positive correlation between trading volume and absolute price change in all nine stock markets. In addition, a positive contemporaneous relationship between trading volume and price change per se has only been found in Japan, Switzerland, the Netherlands, Hong Kong and France, the result for the U.S. market was contradicted with the previous studies. Lee and Rui (2001) found a positive contemporaneous relationship between stock return and traded volume on the exchange of U.S., U.K. and Japan by applying

Generalized Method of Moments (GMM) framework.

With regards to Chinese stock market, Chen and Song (2000) analyzed data of 20 randomly selected stocks form Shanghai and Shenzhen Stock Exchange and also reported a positive linear relationship between the trading volume and absolute price change. Similar results were achieved by Zhang (2003), using data of daily index return and trading volume change in

Shanghai Stock Exchange. To sum up, the common finding is that contemporaneous trading volume has a positive effect on stock return in most countries, as well as in China.

Ming Zhang Master’s Thesis

In the field of behavior finance, it turns out that people do not always behave and respond in a rational and logical way, which is in violation of conventional economic and financial theory.

The phenomenon caused by these irrational behaviors is so-called anomaly. French (1980),

Gibbon and Hess (1981), Keim and Stambaugh (1984), Jain and Joh (1988) attempted to examine day-of-the-week effect for stock returns. The common finding is returns on Monday are low and negative, while high on Friday. Given consideration on day-of-the-week effect,

Zhao (1994) analyzed the data of Shanghai Stock Exchange (SSE) Composite Index and 12 individual stocks in Shanghai Stock Exchange. He found that Monday reports the lowest with negative return, and return on Thursday is positive and higher than the other days of the week.

Gu and Wan (2004) discovered Tuesday and Friday of the week effect in Shanghai Stock

Exchange by applying Value at Risk model. Apparently, empirical results on day-of-the-week effect in Chinese stock market are inconsistent.

2.2.2 Causal relationship between return and volume

Gallant, Rossi and Tauchen (1992) argued that most of the prior studies have mainly focused on the contemporaneous relationship between price change and trading volume. Despite that, only few have been carried out to examine the casual relationship between these two variables, although some models have implications for the dynamic relation. Causality test can provide useful information for investors on whether further movement of stock price can be forecasted by trading volume or not. The empirical findings for U.S. and some emerging stock markets are discussed separately as follows:

In case of U.S. stock market, Rogalski(1978), Smirlock and Starks (1988) and Jain and Joh

(1998) analyzed for a linear Granger causality between stock prices and trading volume and found that only stock return Granger-causes trading volume, not vice versa. Hiemstra and

Jones (1994) employed linear and nonlinear Granger causality test to investigate the dynamic relationship between return and volume. They reported evidence of uni-directional causal relationship running from Dow Jones returns to percentage change of trading volume in New

York Stock Exchange (NYSE), but strong bi-directional nonlinear causality between returns

Ming Zhang Master’s Thesis and volume. Chordia and Swaminathan (2000) tested the interaction between trading volume and predictability of short-run stock returns. They documented that returns of portfolios containing stocks with high trading volume lead returns of portfolios with low trading volume stocks. They also concluded that “trading volume plays a significant role in the dissemination of market wide information”. Chen, Firth and Rui (2001) investigated the causality between return and volume of stock indices. Their data set comprises the series of daily market index price and trading volume for nine of the largest stock exchanges and the evidence that return

Granger causes volume can only be found for some countries, and vice versa. Despite their finding on contemporaneous relationship between stock return and trading volume mentioned earlier, Lee and Rui (2002) also detected causality. They found evidence of causality from return to volume in U.S. and Japanese market, but no causal relation running from volume to return on each of three stock markets. They also found that financial variables in U.S. market have strong predictive power for the ones in U.K. and Japanese market.

In case of emerging markets, Zhang and Yan (1998) found uni-directional causal relation from stock return to trading volume on Shanghai Stock Exchange. In contrast, Silvapulle and Choi

(1999) found evidence of bi-directional causality between stock returns and volume series in

Korean stock market and Zhang (2002) found a bi-directional causality in Shanghai Stock

Exchange. Using data for two Chinese A-share markets and 10 individual stocks in the energy sector, Fan, Groenwold and Wu (2003) examined the relationship between trading volume and stock returns. The sample period covers from 1st January 1997 to 31st December 2002.

Based on Causality test, they reported that returns cause volume and volume has strong predictable power on absolute return but only a weak effect on future returns. Rashid (2007) examined the dynamic relationship between daily stock index returns and percentage change in trading volume by applying liner and nonlinear causality tests. Their data set consists of

1266 daily observations on Karachi Stock Exchange (KSE) for a period of five years. Using standard Granger causality test, they reported uni-directional causality from stock return to trading volume for the entire period as well for two sub-periods.

Ming Zhang Master’s Thesis

Taken together, the evidence found in U.S. and some developed countries supports that stock returns Granger-cause trading volume, and not vice versa. And it appears inconsistent with sequential-information-arrival (SIA) model and Mixture of Distribution Hypothesis (MDH)

Model that developed in early times. Nevertheless, there reaches no clear-cut consensus in emerging markets and China is no exception.

2.2.3 Relationship between volatility and volume

Prior researches also provide evidence on the relationship between return volatility and traded volume. The volatility of financial assets refers to the degree of deviation from the expected return within a specific time horizon and it is usually measured as the standard deviation of the expected return. In earlier studies, Epps and Epps (1976) investigated the relation between variance of the price change and volume for individual stocks and found positive correlation on the basis of the Mixture of Distribution Hypothesis (MDH) theory. Similar conclusion was provided for testing the same relation by Morgan (1976). Lamoureax and Lastrapes (1990) argued that for individual stocks, the GARCH effect of the returns can be explained by the rate of new information flow into the market. Upon that, they employed asymmetric GARCH model after accounting for the trading volume in the variance equation as a proxy for the arrival of new information and the inclusion of trading volume tends to reduce the persistence of conditional volatility significantly. They also concluded that there is a positive relationship between volatility and trading volume.

Subsequently, Sharma, Mougoue and Kamath (1996) re-examined the same relationship for the market as a whole on a macro level. Using the data of NYSE daily return and volume for a period of four years, they found that the introduction of trading volume as an explanatory variable in the variance equation weakened but does not fully eliminated the GARCH effect in conflict with Mixture of Distribution Hypothesis (MDH) theory. Besides, it is found that trading volume has a significant positive effect on the volatility of return, in consistence with the finding of Lamoureux and Lastrapes (1990). Once again, Lee and Rui (2001) concluded a positive relationship between return volatility and trading volume in three largest stock

Ming Zhang Master’s Thesis markets: New York, London and Tokyo. Using daily data of ISE composite index in Ystanbul

Stock Exchange (ISE) for the period 2nd January 1992 to 29th May 1998, Salman(2001) employed GARCH-in-Mean model to investigate the risk-return-volume relation. It is found there is a positive relation lies in both contemporaneous change in trading volume and returns, and risk and returns. In addition, it is reported that lagged change in trading volume has a positive effect on conditional variance of returns and daily conditional variance of return is time-varying and highly persistent. Chen, Firth and Rui (2001) documented that persistence of volatility remains after incorporating the trading volume in the GARCH model in nine developed markets. Likewise, studying nine international stock exchange indices for a 5-year period, similar result was obtained by Arago and Nieto (2004).

In contrast, Brailsford (1996) has documented a significant reduction in the magnitude and significance of volatility persistence in the Australia stock market by introducing the trading volume as a proxy measure for information arrival. Despite that, it is found that there exists a significant positive volatility-volume relation. Using data of ten actively traded U.S. stocks,

Gallo and Pacini (2000) have shown similar results by using GARCH-type models. Likewise,

Gallagher and Kiely (2005) concluded that for Irish shares, the trading volume have strong explanatory power for return volatility and the persistence of volatility falls dramatically by accounting for the effect of trading volume.

Regarding the case of China, Wang and Liu (2005) used data of individual listed stocks and two market portfolios of A-shares and B-shares in Chinese stock market and have shown that trading volume have significant positive effect on the conditional variance. Furthermore, the persistence of volatility has been reduced significantly with the inclusion of trading volume in the conditional variance equation for all individual stocks and B-shares portfolio, except for

A-shares portfolio. Using the dataset of Shenzhen Stock Exchange (SZSE) Component Index,

Dai and Zhang (2005) reported evidence that the persistence of volatility remains unchanged after introducing trading volume in the conditional variance equation.

Ming Zhang Master’s Thesis

To sum up, it is commonly believed that volatility and volume are positively correlated. For the GARCH effect, it seems mostly that the introduction of trading volume as a proxy for the arrival of information flow into conditional variance equation tends to reduce the persistence of volatility significantly for individual stocks, while volatility persistence remains unchanged for the entire market.

3 Data and Methodology

3.1 Methodology

3.1.1 Simple Regression Model

As mentioned in the previous section, it is widely accepted that there is a positive relationship between contemporaneous stock return and trading volume. We first investigate whether such relation fit the data in Chinese stock market by applying simple regression model, as shown in the following equation:

t 0 bVaR ++= ε tt ()1

In this paper, daily returns are calculated as 100 times the continuously compounded return:

Rt 100×= ()()t − (PLnPLn t−1 )

where ()PLn t represents the natural logarithm of end-of-day closing index price at time t.

Owing to the reason that the aggregate trading volume of major indices have been increasing constantly for the past several years, therefore it is preferable to convert the aggregate trading volume into the difference in natural logarithm of aggregate trading volume, as shown below:

Vt 100 ()()t −×= (TVLnTVLn t−1 )

where (TVLn t ) represents the natural logarithm of daily aggregate trading volume at time t.

Ming Zhang Master’s Thesis

If the slope coefficient of the trading volume (Vt ) is positive and statistically significant at the 5% level, then we can report a positive relationship between daily return and trading volume. For robust test, the GARCH model will be employed to test whether the positive return-volume relation still exits after taking serial return autocorrelation, heteroskedasticity and day-of-the-week effect into account, which will be discussed in detail later.

3.1.2 Vector Autoregressive (VAR) Model

In this section, the study proceeds to test whether trading volume causes return, and vice versa.

Granger causality tests whether variable X causes variable Y, that is, whether X occurs before

Y after controlling for past value of Y. As such, causality test can provide useful information on whether current and further movements of one time series can be forecasted by the past of another time series. We make use of the following bivariate Vector Autoregressive Model to characterize the dynamic relation between return and volume:

m n t 1 += α −iti ∑∑ VRaR − ++ εβ titi ()2 i=1 i=1

m n t 1 += −iti ∑∑ VRbV − ++ ηδγ titi ()3 i=1 i=1

in which Rt and Vt represent (log) return and (log) volume change respectively, m and

n are autoregressive lag orders, ε t and η are error terms. The regression residuals ε t and η are assumed to be uncorrelated, mutually independent and normally distributed with zero mean and constant variance.

The benefit of VAR model is that it captures linear interdependencies between two time series.

Within the context of VAR model, the assumption that time series of return and volume are stationary must be satisfied. It is important to choose the optimal lag lengths for VAR model since the results of Granger causality test are very sensitive to lag orders. Based on the Akaike

Information Criterion (AIC, 1971), we choose lag lengths of five for both return and trading volume, including week-long information in the regression.

Ming Zhang Master’s Thesis

In equation (2), if the null hypothesis that the coefficients of V −it are jointly equal to zero is rejected by standard F-test, volume does Granger cause return. Similarly in equation (3), if

F-test rejects the null hypothesis that γ i = 0 for all lagged orders, it is argued that return

Granger causes volume. Bi-directional causality exists if both null hypotheses are rejected.

3.1.3 AR-GARCH-in-Mean Model

It has been well documented that there exists time-dependent conditional heteroscedasticity in financial time series. Mandelbrot (1963) and Fama (1965) recognized that return volatility is timing-varying and the returns of financial time series exhibit the phenomenon of “volatility clustering”. In contrast to ordinary least square (OLS) regression, the features of financial time series can be better captured by using the autoregressive conditional heteroscedasticity

(ARCH) model set forth by Engle (1982). Under the ARCH model, the “autocorrelation in volatility” is modeled by allowing the conditional variance to vary over time as a function of past squared errors. The strength of the ARCH technique lies in the fact that the conditional means and variances can be estimated jointly. An extension of ARCH model, the Generalized

ARCH (GARCH) model, was proposed independently by Bollerslev (1986) and Taylor

(1986). The GARCH application allows the conditional variance to depend on previous own lag, in which high order ARCH specification can be easily estimated. It is well-known that risk is one of the primary factors that determine return. In risk-return tradeoff theory, investors should be rewarded for higher risk premium by taking additional risk, which suggests a positive relationship. In order to incorporate this idea into the ARCH class of models, an

(G)ARCH-M specification has been developed by Engle, Lilien and Robins (1987). Within the context of GARCH-M model, the conditional variance of asset returns has been included in the conditional mean equation.

Now, GARCH-M process has been widely used in modeling financial time-series data. In this paper, AR (3)-GARCH-M (1, 1) model is chosen as the base model by taking the existence of autocorrelation in stock returns and day-of-the-week effect into account.

Ming Zhang Master’s Thesis

The AR (3)-GARCH-M (1, 1) model is structured as follows:

m 5 t = α RR −iti +∑∑ − ++ εϕβ ttiti (),0~ hNhD t (4) i=1 i=1

2 ht 0 t −1 ++= δγεα ht −1 ()5

th where R −it are the i lagged daily stock return, D −it are the dummy variables representing

the days of the week, ht is the conditional variance as a proxy for risk, and ε t is the error term that is assumed to be normally distributed. In equation (5), the conditions of γ δ > 0, and γ δ ≤+ 1 should be satisfied in order to guarantee the non-negativity and stationarity of the conditional variance.

By including the natural logarithm of volume change (Vt ) as an explanatory variable in the conditional mean equation, the contemporaneous relationship between daily stock return and volume change will be re-examined to see whether the result is in line with simple regression model. As known, the GARCH-M specification is more appropriate to model financial time series data, which is expressed as below:

m 5 t = α RR −iti +∑∑ − +++ εηϕβ tttiti (),0~ hNVhD t (6) i=1 i=1

2 ht 0 t−1 ++= δγεα ht−1 (5)

If η is positive and statistically significantly at the 5% level, there exists a contemporaneous positive relationship between stock return and trading volume. It is also interesting to see the sign and significance level of the coefficients of day-of-the-week dummy variables.

As mentioned earlier, MDH theory suggests that the trading volume has explanatory power on the volatility of stock return. As such, the AR-GARCH-M model is modified by introducing the trading volume as a proxy measure for the amount of information flow into the market in the conditional variance equation suggested by Lamoureax and Lastrapes (1990). The model

Ming Zhang Master’s Thesis is structured as follows:

m 5 t = α RR −iti +∑∑ − ++ εϕβ ttiti (),0~ hNhD t (4) i=1 i=1

2 ht 0 t−1 t−1 +++= μδγεα Vh t ()7

By observing the above two equations, it is evidently that ht connects the conditional mean and conditional variance equations, which implies that volume has an indirect effect on return. If both ϕ and μ are positive and statistically significant, we can conclude that trading volume affects stock return positively in an indirect way that strengthen the direct relationship between return and volume.

By including Vt in the conditional variance equation, we can conclude a positive correlation between volatility and volume if μ is positive and statistically significant. The sum of the parameters γ and δ measures the persistence of the variance to a shock. If trading volume represents a suitable proxy for information arrival, the persistence of volatility as measured by

(γ + δ ) should fall significantly once trading volume is included in the variance equation.

3.2 Data and Summary Statistic

The dataset comprises of daily closing prices and trading volume series for two major stock indices in China, so called Shanghai Stock Exchange (SSE) Composite Index (1990) and

Shenzhen Stock Exchange (SZSE) Component Index (1994). SSE Composite Index tracks all listed A-shares and B-shares at the Shanghai Stock Exchange. SZSE Component Index is comprised of the top 40 companies that issue A-shares on Shenzhen Stock Exchange. The reason we choose these two capitalization-weighted stock indices lies in the fact that they are the representatives of Chinese stock market with sufficient data for statistic tests. The total number of daily observations is 3868 with a sample period covering from 31st July 2000 to

31st July 2008. All data were collected from the website: www.Stockstar.com. Since 2000, the

Ming Zhang Master’s Thesis

Chinese stock market became more regulated and stabilized after the implementation of price limit in later 1996 and a series of adjustments afterwards. The total sample period is divided into three non-overlapping sub-periods and each one of the sub-periods ranges from 31st July

2000 to 29th April 2005, from 09th May 2005 to 16th October 2007 and from 17th October 2007 to 31st July 2008, respectively. The rationale for partitioning the 8-year period into three sub-periods is that the development of Chinese stock market can be characterized into three stages. (1) The period before the reform of split share structure in late April 2005 is specified as sub-period 1. It is observed no obvious upward or downward price trend for sub-period 1 that can be characterized as concussive market. (2) As shown in Graph 1, there is a big boom in index values and trading volumes afterwards in sub-period 2 of bullish market, following a relative stagnation over the past five years in sub-period 1. (3) From the last quarter of 2007, the stock market as a whole experienced continuous drop in sub-period 3 of bearish market that is affected by the economic downturn in the United States. Non-strictly speaking, three sub-periods can be characterized in terms of the state of stock market: concussive market, bull market and bear market, respectively. It is interesting to see if there yields any different results among three situations. It is commonly believed that volume is relatively heavy in bull market and light in bear market. As such, a stronger return-volume relationship in bull market is expected in this paper.

Graph 1 SZSE Component Index SSE Composite Index

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0 2001 2002 2003 2004 2005 2006 2007 2008

CLOSING PRICE

Because causality test is very sensitive to non-stationary time series, it is necessary to test for

stationarity of stock return ()Rt and volume change (Vt ). In other words, we need to test

Ming Zhang Master’s Thesis

whether Rt and Vt contain a unit root. In this paper, both Augmented Dickey-Fuller (ADF) test and Phillips-Perron (PP) test are used to test for a unit root. The null hypothesis is a series is not stationary. The significance level is taken to be 5% for all the following statistic tests.

Table 1 and Table 2 report the computed ADF and PP t-statistics and summary statistics for the entire sample period. The descriptive statistic shows that index returns has excess kurtosis and negative skewness, and (log) trading volume change is positively skewed with significant excess kurtosis. The test results reported in Table 2 indicate that the null hypothesis of unit

root is strongly rejected for both Rt and Vt in all three sub-periods. Therefore, it can be confirmed that stock return and logarithm change in trading volume are both stationary.

Table 1 Summary Statistics for the entire period The descriptive statistics of stock return and volume change for the entire period are summarized in the table. It is observed that two representative stock indices in China show similar characteristics. Statistics SSE Composite Index SZSE Component Index

Rt Vt Rt Vt Mean 0.016351 0.066528 0.034150 0.143268 S.D. 1.629267 26.99630 1.769255 36.53059 Skewness -0.140951 0.632826 -0.092596 0.292582 Kurtosis 7.536711 14.61033 6.951220 111.8515

Table 2 Computed ADF and PP t-statistics ADF and PP testes are both employed to test whether stock return and volume change series have a unit root. The null hypothesis of ADF and PP test is “a series is not stationary”. The computed ADF and PP t-statistics are reported in the table below. Concussive Bullish Bearish SSE Composite Index

ADF test Rt -15.24854 -9.872639 -6.115521

Vt -20.08915 -13.44287 -8.104405

PP test Rt -33.52166 -24.52421 -14.61808

Vt -47.93345 -30.26588 -18.41411 SZSE Component Index

ADF test Rt -14.92464 -10.21579 -6.335664

Vt -21.09521 -14.38638 -6.874680

PP test Rt -33.05156 -23.95974 -13.21459

Vt -55.13573 -32.91175 -16.30551

Ming Zhang Master’s Thesis

4 Empirical Results and Analysis

4.1 Contemporaneous relationship between return and volume

Table 3 reports that the coefficients of regressing stock return (Rt ) on volume change ()Vt in simple OLS regression are all significantly positive at the 5% level. Therefore, there exists a positive contemporaneous relationship between return and volume change in all sub-periods.

Our findings are consistent with previous empirical results in developed markets and Chinese stock market.

Table 3 Simple Regression Model The simple regression model, expressed in Equation (1), is applied to return and volume time series. The estimated coefficients of constant term and volume change, along with corresponding p-values are reported in the table below. The indicated (*) p-values are all statistically significant at the 5% level, even at the 1% level. SSE Composite Index SZSE Component Index Coefficient p-value Coefficient p-value

1. Concussive a0 -0.048925 (0.1926) -0.038499 (0.3356) b 0.011416 (0.0000)* 0.006676 (0.0000)*

2. Bullish a0 0.273295 (0.0001) 0.301986 (0.0001) b 0.018116 (0.0000)* 0.014596 (0.0000)*

3. Bearish a0 -0.390850 (0.0357) -0.382444 (0.0599) b 0.029303 (0.0013)* 0.023912 (0.0046)*

According to the descriptive statistic, it is observed that stock return exhibits the properties of non-normality, serial autocorrelation and heteroscedasticity. In violation with the assumptions of classical OLS regression, this may lead to inconsistency in the estimates of coefficient and misleading statistical inference. Therefore, AR (3)-GARCH-M (1, 1) model is extended to re-examine return-volume relation by entering trading volume into the mean equation and the results are reported in Table 4 and 5. As shown, the t-statistics of coefficient η is significant for all three sub-periods, suggesting a positive contemporaneous relationship between return and volume change. Evidently, the conclusion of positive relationship remains unchanged. In addition, day-of-the-week effects are also taken into account by adding five dummy variables into the return equation other than volume. In sub-period 1, it turns out that Monday,

Ming Zhang Master’s Thesis

Thursday and Friday dummy variables are negatively related to return and statistically significant. Only Monday dummies are positively related to return at the 5% significance level for sub-period 2. And in the relatively bearish sub-period 3, day-of-the-week effect does not exist that is probably due to investors’ negative sentiment about the market.

It is also interesting to examine the indirect linkage between stock return and trading volume, which is neglected by most of the studies. Table 4 and 5 shows that the coefficient estimates of trading volume and conditional variance in Equation (4) and (7) are both positive. In addition, the t-statistics for all coefficients ϕ and μ are jointly significant, suggesting an indirect contemporaneous positive relation. Overall, there exists a direct contemporaneous positive relation between return and volume, strengthened by a significant indirect relation.

Although positive contemporaneous relationship between stock return and volume change has been detected as expected, it is surprising that contemporaneous change in trading volume has relatively stronger effect on stock return in bearish market than in bullish market. This may be due to compulsive government intervention and short sale constraints.

Table 4 AR (3)-GARCH-M (1, 1) Model: Shanghai Stock Exchange Composite Index Firstly, the AR (3)-GARCH-M (1, 1) Model is employed. Mean equation and conditional variance equation are estimated simultaneously, expressed in Equation (4) and (5). Secondly, run the modified model by including volume change as an explanatory variable in the mean equation to re-examine the contemporaneous return-volume relation, expressed in Equation (6) and (5). Thirdly, run the modified model by the introduction of volume change as a proxy for information flow in the conditional variance equation, expressed in Equation (4) and (7). The indirect contemporaneous relationship between return and volume and volatility-volume relation are examined though this specification. F-statistics and corresponding p-values in parentheses are reported in the table. The indicated (*) p-values are specified in the main context. Additionally, the sum of the parameters γ and δ measures the persistence of the variance to a shock. It is tested that whether the persistence of volatility as measured by (+ δγ ) remain unchanged or fall significantly once trading volume is included in the conditional variance equation. Equation (4) and (5) Equation (6) and (5) Equation (4) and (7) (without V) (with V in mean equation) (with V in variance equation) 1. Concussive Market Mean Equation ht 0.124805 (0.0062) 0.183578 (0.0001) 0.113033 (0.0089)*

Ming Zhang Master’s Thesis

Rt-1 -0.002722 (0.9358) -0.006731 (0.8392) -0.021532 (0.5248)

Rt-2 -0.047314 (0.1359) -0.014359 (0.6403) -0.043550 (0.1653)

Rt-3 0.017424 (0.5759) 0.027502 (0.3514) 0.015490 (0.6112)

Vt -- -- 0.008921 (0.0000)* -- --

D1 -0.294308 (0.0010) -0.325451 (0.0003) -0.364870 (0.0000)

D2 0.017486 (0.8653) -0.086821 (0.4020) 0.025138 (0.7929)

D3 -0.159139 (0.0731) -0.255138 (0.0042) -0.167745 (0.0360)

D4 -0.356992 (0.0002) -0.473184 (0.0000) -0.362736 (0.0000)

D5 -0.259118 (0.0042) -0.353917 (0.0001) -0.261465 (0.0037) Variance Equation

α 0 0.138253 (0.0000) 0.114937 (0.0000) 0.047373 (0.0006)

2 ε t − 1 0.168735 (0.0000) 0.145059 (0.0000) 0.119397 (0.0000) 2 h t-1 0.759469 (0.0000) 0.789589 (0.0000) 0.853065 (0.0000)

Vt ------0.005629 (0.0000)* γ + δ 0.928204 ------0.972462 -- 2. Bull Market Mean Equation ht 0.020717 (0.6725) 0.041930 (0.4074) 0.292905 (0.0000)*

Rt-1 0.000650 (0.9879) -0.054731 (0.2063) 0.005749 (0.9095)

Rt-2 -0.034302 (0.4626) -0.014145 (0.7657) -0.028029 (0.5106)

Rt-3 0.037501 (0.4348) 0.038164 (0.4114) 0.066301 (0.0920)

Vt -- -- 0.017823 (0.0000)* -- --

D1 0.433144 (0.0053) 0.439585 (0.0042) -0.087416 (0.6837)

D2 0.099973 (0.5820) 0.005212 (0.9761) -0.612831 (0.0169)

D3 0.272511 (0.1053) 0.173453 (0.3244) -0.564296 (0.0068)

D4 -0.080146 (0.5975) -0.172509 (0.2740) -0.738209 (0.0013)

D5 0.154277 (0.3726) 0.084083 (0.6233) -0.479346 (0.0025) Variance Equation

α 0 0.024337 (0.0881) 0.022444 (0.0731) 1.129948 (0.0000)

2 ε t − 1 0.062775 (0.0000) 0.065394 (0.0000) 0.168397 (0.0000) 2 h t-1 0.931235 (0.0000) 0.929867 (0.0000) 0.403594 (0.0002)

Vt ------0.040365 (0.0000)* γ + δ 0.99401 ------0.571991 -- 3. Bear Market Mean Equation ht 0.151727 (0.4148) 0.555113 (0.3896) 0.090746 (0.1469)*

Rt-1 -0.106834 (0.0970) -0.056381 (0.5073) -0.164414 (0.0039)

Rt-2 -0.035420 (0.6731) -0.029969 (0.7266) -0.067190 (0.2439)

Rt-3 0.001130 (0.9880) 0.066703 (0.3945) -0.009435 (0.8774)

Vt -- -- 0.031874 (0.0025)* -- --

D1 0.324737 (0.8043) -4.068973 (0.3136) -1.725007 (0.0000)

D2 -0.013102 (0.9916) -4.472572 (0.2527) -1.153065 (0.0386)

D3 1.467130 (0.2534) -3.239699 (0.4300) -0.705737 (0.1679)

Ming Zhang Master’s Thesis

D4 0.572209 (0.6731) -4.054013 (0.3178) -1.101721 (0.0329)

D5 0.510072 (0.5971) -3.407893 (0.4018) -0.757702 (0.2234) Variance Equation

α 0 6.372770 (0.3192) 0.628411 (0.5478) 4.285274 (0.0286)

2 ε t − 1 0.076429 (0.1323) 0.029041 (0.4452) 0.042260 (0.3463) 2 h t-1 0.841144 (0.8775) 0.870799 (0.0000) 0.345597 (0.2656)

Vt ------0.108909 (0.0000)* γ + δ 0.917573 ------0.387857 --

Table 5 AR (3)-GARCH-M (1, 1) Model: Shenzhen Stock Exchange Component Index Firstly, the AR (3)-GARCH-M (1, 1) Model is employed. Mean equation and conditional variance equation are estimated simultaneously, expressed in Equation (4) and (5). Secondly, run the modified model by including volume change as an explanatory variable in the mean equation to re-examine the contemporaneous return-volume relation, expressed in Equation (6) and (5). Thirdly, run the modified model by the introduction of volume change as a proxy for information flow in the conditional variance equation, expressed in Equation (4) and (7). The indirect contemporaneous relationship between return and volume and volatility-volume relation are examined though this specification. F-statistics and corresponding p-values in parentheses are reported in the table. The indicated (*) p-values are specified in the main context. Additionally, the sum of the parameters γ and δ measures the persistence of the variance to a shock. It is tested that whether the persistence of volatility as measured by (+ δγ ) remain unchanged or fall significantly once trading volume is included in the conditional variance equation. Equation (4) and (5) Equation (6) and (5) Equation (4) and (7) (without V) (with V in mean equation) (with V in variance equation) 1. Concussive Market Mean Equation ht 0.111738 (0.0116) 0.143290 (0.0015) 0.109775 (0.0181)*

Rt-1 0.011552 (0.7412) -0.005443 (0.8732) -0.000655 (0.9848)

Rt-2 -0.039684 (0.1934) -0.012599 (0.6776) -0.034579 (0.2543)

Rt-3 0.026757 (0.3793) 0.028546 (0.3437) 0.031685 (0.3001)

Vt -- -- 0.005616 (0.0000)* -- --

D1 -0.357907 (0.0004) -0.394835 (0.0001) -0.353583 (0.0005)

D2 -0.009455 (0.9306) -0.071482 (0.5185) -0.006761 (0.9530)

D3 -0.120140 (0.2285) -0.157150 (0.1146) -0.106942 (0.3045)

D4 -0.330577 (0.0010) -0.401337 (0.0001) -0.328212 (0.0018)

D5 -0.242529 (0.0146) -0.274004 (0.0040) -0.192843 (0.0649) Variance Equation

α 0 0.117599 (0.0000) 0.112763 (0.0000) 0.062437 (0.0000)

2 ε t − 1 0.150028 (0.0000) 0.138119 (0.0000) 0.097090 (0.0000) 2 h t-1 0.797274 (0.0000) 0.806355 (0.0000) 0.870818 (0.0000)

Vt ------0.001878 (0.0015)* γ + δ 0.947302 ------0.967908 --

Ming Zhang Master’s Thesis

2. Bull Market Mean Equation ht 0.044245 (0.2832) 0.052522 (0.1954) 0.243678 (0.0000)*

Rt-1 0.049991 (0.2316) 0.015438 (0.7020) 0.033605 (0.4669)

Rt-2 -0.012519 (0.7723) 0.019729 (0.6563) 0.026898 (0.4603)

Rt-3 0.023957 (0.5982) 0.025754 (0.5594) 0.005622 (0.8550)

Vt -- -- 0.013347 (0.0000)* -- --

D1 0.396038 (0.0151) 0.419647 (0.0090) -0.098065 (0.5948)

D2 -0.040296 (0.8409) -0.073607 (0.7000) -0.734021 (0.0002)

D3 0.114809 (0.5352) 0.070326 (0.6891) -0.653092 (0.0016)

D4 -0.138711 (0.4414) -0.214256 (0.2000) -0.771481 (0.0002)

D5 0.111036 (0.5826) 0.074137 (0.6953) -0.429315 (0.0194) Variance Equation

α 0 0.050851 (0.0486) 0.055652 (0.0298) 1.930657 (0.0000)

2 ε t − 1 0.077857 (0.0000) 0.094527 (0.0000) 0.162805 (0.0000) 2 h t-1 0.910034 (0.0000) 0.893638 (0.0000) 0.299417 (0.0000)

Vt ------0.056923 (0.0000)* γ + δ 0.987891 ------0.462222 -- 3. Bear Market Mean Equation ht 0.212489 (0.1814) 0.227023 (0.1731) 0.098654 (0.1296)*

Rt-1 0.069713 (0.4536) 0.062545 (0.4994) -0.099480 (0.1445)

Rt-2 -0.049877 (0.5617) -0.055538 (0.5165) -0.040228 (0.5056)

Rt-3 0.001326 (0.9860) 0.002683 (0.9716) -0.000869 (0.9881)

Vt -- -- 0.022007 (0.0059)* -- --

D1 -2.005051 (0.1139) -2.085630 (0.1187) -1.417926 (0.0014)

D2 -2.728286 (0.0216) -2.841716 (0.0509) -1.061324 (0.1655)

D3 -1.025047 (0.4460) -1.155940 (0.4075) -0.716009 (0.2627)

D4 -2.269496 (0.0765) -2.404051 (0.0727) -1.370448 (0.0221)

D5 -1.827061 (0.1873) -1.952026 (0.1742) -0.942996 (0.1309) Variance Equation

α 0 0.655152 (0.4561) 0.081120 (0.0000) 5.895650 (0.0069)

2 ε t − 1 0.064761 (0.2480) -0.035880 (0.0000) 0.014564 (0.8162) 2 h t-1 0.853468 (0.0000) 1.029638 (0.0000) 0.184138 (0.4782)

Vt ------0.149817 (0.0000)* γ + δ 0.918229 ------0.198702 --

Ming Zhang Master’s Thesis

4.2 Causal relationship between return and volume

As mentioned earlier, it has been confirmed that stock returns and volume change series are both stationary by unit root tests. To proceed with Granger causality test, bivariate Vector

Autoregressive (VAR) model is employed to investigate whether trading volume causes stock returns, and vice versa. The results of the causal relationship are reported in Table 6, with

F-statistics and corresponding p-values. Firstly, Granger causality test fails to reject the null hypothesis that volume change does not cause stock return for all three sub-periods with an exception of SSE Composite Index in sub-period 1. And the finding of no causal relation from trading volume to stock returns is consistent with MDH model developed by Clark (1973).

Secondly, it also shows that the null hypothesis that stock return does not cause volume change is strongly rejected in all three sub-periods for both SSE Composite Index and SEZE

Component Index. In brief, it implies that there is uni-birectional relation running from stock

return to volume change. More specifically, stock return (Rt ) has strong linear predictive

power on future volume change ()Vt . It is worth mentioning that in the presence of lagged returns, current return is not influenced by lagged volume, although there is a positive relationship between contemporaneous return and volume. The finding is in consistence with the weak form of market efficiency hypothesis (MEH) that future returns cannot be predicted by publicly available information. As expected, it is also observed that stock return tends to have relatively stronger predictive power on trading volume in sub-periods 1and 2, under the state of bullish and concussive markets correspondingly. It is understandable since investors are likely to trade more actively in bullish market. Overall, the results are in agreement with most of the previous findings for U.S. as well as other developed stock markets that the knowledge of past trading volume does not improve the ability to forecast further returns, and not vice versa. As such, there is no denying that the Chinese stock market has become more efficient along with continuously rapid growth.

Ming Zhang Master’s Thesis

Table 6 Vector Autoregressive Model: Liner Granger causality test The bivariate Vector Autoregressive (VAR) models, expressed in Equation (2) and (3), are employed to test causality between return and volume. F-statistics and corresponding p-values in parentheses are reported in the table. The results for SSE Composite Index and SZSE Component Index are represented separately. The indicated (*) p-values are below the 5% significance level, the null hypotheses are rejected accordingly. SSE Composite Index SZSE Component Index

Null Hypothesis: Vt does not Granger cause Rt 1. Concussive 2.132362 ( 0.019747)* 0.980761 (0.458232) 2. Bullish 0.927171 (0.507469) 0.472025 (0.908254) 3. Bearish 0.394378 (0.947920) 0.276112 (0.985734)

Null Hypothesis: Rt does not Granger cause Vt 1. Concussive 21.21359 (0.000000)* 33.66769 (0.000000)* 2. Bullish 13.40980 (0.000000)* 14.76759 (0.000000)* 3. Bearish 3.606866 (0.000217)* 2.273952 (0.012767)*

4.3 Relationship between volatility and volume

The study proceeds to test the relationship between volatility and volume. Table 4 and Table 5 report the estimated parameters for AR (3)-GARCH-M (1, 1) model. It is observed that the coefficient μ in each conditional variance equation is significant at the 1% level, which suggests a strong positive correlation between stock return and volume change. It is evident that there exists strong GARCH effect, since γ and δ are statistically significant with an exception of bearish market in sub-period 3. This may be due to the lack of daily observations in sub-period 3. In equation (4) and (5), the GARCH-in-Mean specification shows a very high sum of γ and δ that approaches 1 for all cases. In literature, it is generally accepted that return volatility is related to trading volume lies in the fact that volume can be employed as a proxy for the rate of information arrival. After including trading volume into the conditional variance equation as shown in Equation (4) and (7), there represents a significant reduction in persistence of volatility as measured by γ + δ in both sub-periods 2 and 3. The finding is consistent with the argument that trading volume is a reasonable proxy for the arrival of information into the market for explaining the persistence of return volatility as suggested

Lamoureax and Lastrapes (1990). In contrast, the volatility persistence remains unchanged in

Ming Zhang Master’s Thesis concussive market of sub-period 1. And similar results have been obtained by Sharma,

Mougoue, Kamath (1996) and Lee and Rui (2001), Salman (2001) and Arago and Nieto (2004) for U.S. and some of the emerging stock market. The finding implies that conditional variance is highly persistent and cannot be well explained by trading volume in concussive market.

As witnessed in China, majority of stock market participants frequently engage in short-term speculative activities and short sales are constrained. In bullish and bearish market, they may overact to new available information that will be reflected in trading volume. As such, trading volume can be regarded as a good proxy for information flow. In concussive market, investors are likely to trade less actively on the arrival of new information flow, suggesting that trading volume is not a reasonable proxy for fully explaining the persistence of conditional variance.

Not surprisingly, it is found that the volatility persistence remains unchanged in concussive market of sub-period 1.

5 Summary and Conclusion

Using the data of two representative stock indices in Shanghai and Shenzhen Stock Exchange for a period of 8 years, this paper investigates the relationship between volume, return and volatility under three different state of market in relation to Chinese stock market. And it is interesting to differentiate and show the similarities in each of the sub-periods. Unlike most of the previous empirical studies, aggregate trading volume is converted to the natural logarithm of volume change to examine the volume-return-volatility relation. The statistical tests on two stock indices are run separately. Not surprisingly, the result exhibits similar results. The main findings in this paper are listed as follows:

Firstly, there is indeed a contemporaneous positive relationship between return and volume in both direct and indirect way. It is argued that the strengthening in this relation adds additional evidence to the existing empirical findings, particularly relating to the Chinese stock market.

Additionally, the day-of-the-week effects are inconsistent under different state of the market.

Ming Zhang Master’s Thesis

Secondly, Granger linear causality suggests a uni-directional relationship running from stock return to volume change in all three sub-periods, in line with many other studies. Nevertheless, the finding that lagged volume has no predictive power on current stock return is contradicted with the theoretical frameworks developed by Copeland (1976) and Epps and Epps (1976).

This may suggest undetected non-linear causality between return and volume. Thirdly, there is a strong positive correlation between return volatility and volume change in all cases. It also represents a substantial reduction in the persistence of volatility in both bull and bear market in supportive with Lamoureax and Lastrapes (1990), by incorporating volume change into the conditional variance equation. In contrast, the persistence of volatility remains unchanged in concussive market of sub-period 1. This can be interpreted in a way that trading volume is not a good proxy for the arrival of new information.

Although the financials system in China is still not well-established and related governmental regulations and supervision are far from perfect, China has already become one of the biggest stock market in the world. It is interesting to see that the findings are in common with most of the empirical results documented for U.S. and other developed stock markets. It shed the light on the fact that China is emerging rapidly on the track of international practices and the stock market in China has become more efficient.

The empirical evidence in this paper also enhances our understanding on the micro-structure and operational efficiency in Chinese stock market. For further research, it is recommended to undertake both liner and non-linear causality tests to capture the underlying non-liner causal relation between return and volume change. For the GARCH effect in concussive market, it leaves the possibility to decompose the logarithm change of trading volume or choose another variable as a proxy for the rate of information flow to test the degree of volatility persistence.

Ming Zhang Master’s Thesis

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Ming Zhang Master’s Thesis

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