An Empirical Analysis of Return, Volatility, Volume Relationship in an Emerging Stock Market:

An Empirical Analysis of 

Return, Volatility, Volume Relationship in an 

Emerging Stock Market:

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.

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 

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.

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.

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

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.

(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

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.

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:

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.

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.

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.

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:

( )

1

0 t t

t

a

bV

R

=

+

+

ε

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

( )

( )

(

1

)

100

×

−

₋

=

t t t

Ln

P

Ln

P

R

where

Ln

( )

P

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:

( )

(

(

1

)

100

×

−

₋

=

t t t

Ln

TV

Ln

TV

V

)

)

If the slope coefficient of the trading volume

( )

V

t 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:

( )

2

1 1 1

∑

∑

= − = −

+

+

+

=

n i t i t i m i i t i t

a

R

V

R

α

β

ε

( )

3 1 1 1

∑

∑

= − = − + + + = n i t i t i m i i t i t b R V V

γ

δ

η

in which and represent (log) return and (log) volume change respectively, and are autoregressive lag orders,

t

R

V

t m

n

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.

In equation (2), if the null hypothesis that the coefficients of 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

i t

V

₋

0

=

i

γ

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.

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

)

(

0,

)

(

4 ~ 5 1 1 t i t t i t i m i i t i t R D h N h R

∑

∑

= − = − + + + =

α

β

ϕ

ε

( )

5 1 1 2 0 + − + − = t t t h h

α

γε

δ

i t

R

₋

D

t−i t

h

_t

where are the ith lagged daily stock return, are the dummy variables representing the days of the week, is the conditional variance as a proxy for risk, and

ε

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

( )

V

_t 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:

(

0,

)

(

6 ~ 5 1 1 t i t t t i t i m i i t i t R D h V N h R

∑

∑

= − = − + + + + =

α

β

ϕ

η

ε

)

( )

5 1 1 2 0 + − + − = t t t h h

α

γε

δ

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.

is structured as follows:

)

(

0,

)

(

4 ~ 5 1 1 t i t t i t i m i i t i t R D h N h R

∑

∑

= − = − + + + =

α

β

ϕ

ε

( )

7

1 1 2 0 t t t t

h

V

h

=

α

+

γε

−

+

δ

₋

+

μ

By observing the above two equations, it is evidently that connects the conditional mean and conditional variance equations, which implies that volume has an indirect effect on return. If both

t

h

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 in the conditional variance equation, we can conclude a positive correlation between volatility and volume if

t

V

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

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 0 1000 2000 3000 4000 5000 6000 7000 2001 2002 2003 2004 2005 2006 2007 2008 CLOSING PRICE

whether and 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.

t

R

V

t

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 and in all three sub-periods. Therefore, it can be confirmed that stock return and logarithm change in trading volume are both stationary.

t

R

V

_t

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

4 Empirical Results and Analysis

4.1 Contemporaneous relationship between return and volume

(

Table 3 reports that the coefficients of regressing stock return

R

_t

)

on volume change

( )

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.

t

V

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)*

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 remain unchanged or fall significantly once trading volume is included in the conditional variance equation.

(γ + δ )

Equation (4) and (5) (without V)

Equation (6) and (5) (with V in mean equation)

Equation (4) and (7)

(with V in variance equation) 1. Concussive Market

Mean Equation

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 0 α _{6.372770 (0.3192) 0.628411 (0.5478) 4.285274 (0.0286)} 1 2 − t ε 0.076429 (0.1323) 0.029041 (0.4452) 0.042260 (0.3463) h2t-1 0.841144 (0.8775) 0.870799 (0.0000) 0.345597 (0.2656) Vt -- -- -- -- 0.108909 (0.0000)* 0.917573 -- -- -- 0.387857 -- γ + δ

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 remain unchanged or fall significantly once trading volume is included in the conditional variance equation.

(γ + δ )

Equation (4) and (5) (without V)

Equation (6) and (5) (with V in mean equation)

Equation (4) and (7)

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

( )

R

t has strong linear predictive

power on future volume change . 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.

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

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:

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.

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