dynamical relation between return trading volume and volatility

8/2/2019 Dynamical Relation Between Return Trading Volume and Volatility

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FinancialheReviewEFA

EasternFinance

Association The Financial R eview 38 (2001) 153-174

The Dynamic Relation Between StockReturns, Trading Volume, and Volatility

Gong-meng ChenMichael Firth*Oliver M. RuiThe Hong Kong Polytechnic University

AbstractWe examine the dynamic relation between returns, volume, and volatility of stock

indexes. The data come from nine national markets and cover the period from 1973 to 2000.The results show a positive correlation between trading volume and the absolute value ofthe stock price change. Granger causality tests dem onstrate that for some coun tries, returnscause volume and volume causes returns.Our results indicate that trading volume con tributessome information to the returns process. The resu lts also show persistence in volatility evenafter we incorporate contemporaneous and lagged volume effects. The results are robustacross the nine national markets.Keywords: stock index returns, trading volume, volatility, EGARCHJEL Classification: G15

1. IntroductionOur purpose in this paper is to empirically examine the dynamic (causal)

relation betw een sto ck marke t returns, trading volume, and volatility in n ine majornational stock markets. M ost previous empirical research has used data from theUnited States,but relatively little wo rk has been cond ucted on oth er national m arkets.Ou r study see ks to remed y this situation.*Corresponding aurhor: Departme nt of A ccountancy, The Hong Kong Polytechnic University, HungHom, Hong Kong, China; Phone: (852) 276670 62;Fax: (852)23309845;Email:[email protected]. Ru i gratefully acknowledges the financial support from the Hong Kong Polytechnic University(Account No. G-YC26).The au thors thank an anonym ous referee for helpful comments.

153


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154 G. Chen, M. irth, 0.Rui/The Financial Review 38 (2001)153-1 74Our initial analysis centers on the volume and price change relation. Clark

(1973) and Lamoureux and Lastrapes (1990, 1994) link price volatility with theunderlying information flow in the markets, and use volume as a measure of theinformation flow. These studies form the basis of our first hypothesis, which exam-ines the reasons for the volume and stock return relation.We test a second hypothesis in which the formation of returns is conditionalon various inform ation arrivals that all affect trading volum e in the same way. Thenine markets we examine are among the largest in terms of market capitalizationand turnover. We use EG ARC H techniques to examine the returns, trading volume,and a conditional volatility relation, and com pare and contrast the results from thesemarkets.The paper proceeds as follows. In Section 2 we provide an overview of theprevious research on the relation between trading volum e, price change, and volatil-ity. Section 3 describes our data set. In Section 4, we discuss the m ethodology andpresent the empirical results. Section 5 summarizes and concludes.

2. Literature rev iewStudying the relation between stock returns and trading volume has absorbedfinancial economists for many years. Karpoff (1986) provides three reasons forthis. First, the returnshrading volume relation provides insight into the structure of

financial markets. Second, the returndtrading volume relation is important for eventstudies that use a combination of stock returns and trading volume data to drawinferences. Third, the returndtrading volume relation is critical to the debate overthe empirical distribution of specu lative prices.Beginning with Osborne (1959), researchers have studied the returndvolumerelation from a variety of perspectives. For example, previous empirical investiga-tions have included the relation between price indexes and aggregate exchangetrading volum e (Granger and M orgenstern, 1963), between contemporaneous abso-lute price change and trading volume (Crouch, 1970), between price change andtrading volume (Westerfield, 1977; Tauchen and Pitts, 1983; Rogalski, 1978), be-tween the variance of price change and trading volum e (Epps and Epps, 1976), andbetween squared price change and trading volum e (Harris, 1986; Clark, 1973). Fromthese research studies two em pirical relations emerge as stylized facts: the correlationbetween trading volume (V) and the absolute value of the stock price change (lopl)is positive, and the correlation between trading volume and the stock price change(Ap) is also positive (Karpoff, 1987).Gallant, Rossi, and Tauchen (1992) point out that much of the previous empiricalwork on the return-volume relation focuses primarily on the contemporaneous rela-tion between price changes and volume. Although som e models use cross correlationsto imply a dynamic relation between returns and volume, these studies do notnecessarily examine causal relations. For example, Hiemstra and Jones (1994) uselinear and nonlinear Granger causality tests to investigate the dynamic relation


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G. Chen, M . Firth, 0.Rui/The Financial Review 38 (2001) 153-174 155between stock returns and percentage changes in trading volume. Foster and Viswa-nathan (1995) derive a speculative trading model with endogenous informed tradingthat yields a conditionally heteroskedastic time series for volume and volatility.Andersen (1996) develops an empirical return volatility/volumemodel from a micro-structure framework.We believe that in a dynamic context, an important issue should be whetherinformation about trading volume is useful in improving forecasts of price changes(i.e., returns) and return volatility. Prior empirical research can be classified intofour categories. Below, we briefly review studies in each category. The empiricalstudies we review use data from the United States. Comparatively few studies havebeen done outside of the U.S.2.1. Trading volume and the absolute value of price changes

There is an old Wall Street adage that It takes trading volume to make pricesmove. There are numerous empirical findings to support what we call a positivetrading volume-absolute price change correlation.Crouch (1970) finds positive correlations between the absolute values of dailyprice changes and daily trading volume for both market indexes and individualstocks. Clark (1973) finds a positive relation between the square of a measure ofthe price change and aggregated trading volume using daily data from the cottonfutures market. Using four-day intervals and monthly data for a total of 51 stocks,Morgan (1976) finds that in all cases, the variance of price change is positivelyrelated to trading volume. Westefield (1977) finds the same relation in a sampleof daily price change and trading volume for 315 common stocks, as do Tauchenand Pitts (1983), who use daily data from the Treasury Bill futures market.Epps and Epps (1976), using transactions data from 20 stocks, find a positiverelation between the sample variances of price changes and the trading volumelevels. Wood, McInish, and Ord (1985) also report a positive correlation betweentrading volume and the magnitude of the price change at the transactions level. Jainand Joh (1988), using data from a market index, find a similar correlation over one-hour intervals.There are four theoretical explanations for the positive relation between theabsolute price changes and trading volumes: a sequential arrival of information(SAI) model, a mixture of distributions (MD) model, a rational expectation assetpricing (REAP) model, and a differences of opinion (DO) model.Studies by Copeland (1976), Morse (1980), Jennings, Starks, and Fellingham(1981), and Jennings and Barry (1983) develop and extend the SAI model. In theirversion, new information is disseminated sequentially to traders, and traders whoare not yet informed cannot perfectly infer the presence of informed trading. Conse-quently, the sequential arrival of new information o the market generates both tradingvolume and price movements, both of which increase during periods characterized bynumerous information shocks.


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156 G. Chen, M. Firth, 0. Rui/The Financial Review 38 (2001) 153-174One explanation for the positive volatility/trading volume correlation comes

from research into the distribution of speculative prices (Clark, 1973; Epps andEpps, 1976). According to the MD hypothesis, price volatility and trading volumeshould be positively correlated because they jointly depend on a common underlyingvariable. This variable could be interpreted as the rate of information flow to themarket. In other words, both the price and trading volume change contemporaneouslyin response to new information.Clark (1973) assumes the daily price change is the sum of a random numberof within-day price changes. Thus the variation in the daily price change is a randomvariable with a mean proportional to the mean number of daily transactions. Clarkargues that trading volume is related positively to the number of within-day transac-tions, therefore the trading volume is related positively to the variability of the pricechange.Epps and Epps (1976) examine the mechanics of within-day trading. The changein the market price on each within-day transaction is the average of the changes inall of the traders reservation prices. Epps and Epps assume there is a positive relationbetween the extent to which traders disagree when they revise their reservation pricesand the absolute value of the change in the market price. That is, an increase in theextent to which traders disagree can indicate a larger absolute price change. There-fore, the price variabilitykrading volume relation arises because the volume oftrading is positively related to the extent to which traders disagree when they revisetheir reservation prices.Speculative trading stems from disagreements among traders over the relationbetween the announcement and the ultimate performance of the assets in question.Such disagreements can arise either because speculators have different private infor-mation, or because they interpret public data differently.

Rational expectations models show disagreement generated by private informa-tion. These models generally involve trading among privately informed traders,uninformed traders, and liquidity or noise traders. Wang (1994) develops an equilib-rium model of stock trading in which investors are heterogeneous in their informationand private investment opportunities, and trade rationally for both informationaland non-informational reasons. In his model, trading is always accompanied byprice changes, since investors are risk-averse. For example, when a group of investorssells their shares to rebalance their portfolios, to induce other investors to buy, theprice of the stock must drop. As information asymmetry increases, the uninformedinvestors demand higher discounts in price when they buy the stock from theinformed investors. Thus, these investors are able to cover the risk of trading againstprivate information. Therefore, trading volume is always positively correlated withabsolute price changes, and the correlation increases with information asymmetry.Harris and Raviv (1993) assume that traders receive common information.However, traders differ in the way in which they interpret this information, andeach trader believes absolutely in the validity of his interpretation. Harris and Ravivrefer to this as the assumption that traders have differences of opinion, and assume


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G. Chen, M. irth, 0.Rui/The Financial Review 38 (2001) 153-174 157that traders start with common prior beliefs about the returns to a particular asset.As information about the asset becomes available, each trader uses his own modelof the relation between the news and the assets returns to update his beliefs aboutreturns. Harris and Raviv (1993) assume that there are two types of risk-neutral,speculative traders who they term responsive and unresponsive. The two types agreeon whether a given piece of information is favorable or unfavorable, but theydisagree on the extent to which the information is important. When they receivefavorable (unfavorable) information, speculators in the responsive group greatlyincrease (decrease) their probability expectation of high returns. Speculators in theunresponsive group do not. Therefore, when the cumulative impact of the pastinformation is favorable, the responsive speculators value the asset more highly andwill own all of it. But when the cumulative impact of the past information isunfavorable, the unresponsive speculators value the asset more highly and will ownall of it. Trading will occur when, and only when, cumulative information switchesfrom favorable to unfavorable, or vice versa. Thus, the Harris and Raviv modelpredicts that absolute price changes and trading volume are positively correlated.2.2. Trading volume and price chang e

Studies by Epps and Epps (1976), Harris (1986), Morgan (1976), Rogalski(1978), and Smirlock and Starks (1985) imply a positive correlation between tradingvolume and the price change per se. Jennings, Starks, and Fellingham (1981) extendCopelands (1976) SAI model to incorporate real world margin constraints and shortselling, and provide an alternate theory consistent with the correlation between andV and Ap. Their argument is that short positions are possible but are more costlythan long positions. The costliness of short positions implies that the quantitydemanded by an investor with a short position is less responsive to price changesthan is the quantity demanded by an investor with a long position. Jennings, Starks,and Fellingham are able to show that in many cases, when a previously uninformedtrader interprets the new information pessimistically, the trading volume that resultsis less than when the trader is an optimist. Since price decreases with a pessimistand increases with an optimist, the authors argue that trading volume is relativelyhigh when the price increases and low when the price decreases.Karpoff (1986) constructs a model that depends on asymmetries in the costsof going long or short. Costly short sales restrict some investors from acting ontheir information, so the effect is to decrease their demands. This effect decreasesthe variance of interperiod shifts in transaction supply relative to that for transactiondemand. In turn, this shift creates a positive covariance between trading volumeand price change over the period.2.3. Causal relation between trading volume and stock price changes

Some theoretical studies explicitly investigate the dynamic relation betweentrading volume and stock returns, a relation that might have some causal relation


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158 G. Chen,M. irth, 0.Rui/The Financial Review 38 (2001) 153-174implications. Campbell, Grossman, and Wang (1993) develop a model in whichone implication is that price changes accompanied by high volume will tend to bereversed, and that this reversal will be less true of price changes on days with lowvolume.Blume, Easley, and OHara (1994) present a model in which traders can learnvaluable information about a security by observing both past price and past volumeinformation. In their model, volume provides data on the quality or precision ofinformation about past price movements. Thus, traders who include volume measuresin their technical analysis perform better in the market than those who do not.Wang (1994) analyzes dynamic relations between volume and returns basedon a model with information asymmetry. His model shows that volume may provideinformation about expected future returns. In their study, He and Wang (1995)develop a rational expectations model of stock trading in which investors havedifferent information concerning the underlying value of the stock. They examinethe way in which trading volume relates to the information flow in the market, andhow investors trading reveals their private information.Chordia and Swaminathan (2000) examine the interaction between tradingvolume and the predictability of short-term stock returns. They find that daily returnsof stocks with high trading volume lead daily returns of stocks with low tradingvolume. They attribute this empirical result to the tendency of high volume stocksto respond promptly to market-wide information. Chordia and Swaminathan con-clude that trading volume plays a significant role in the dissemination of market-wide information.Although these studies have some implications for causal relations betweentrading volume and stock returns, there has been no rigorous study of empiricalcausal relations between volume and returns to confirm or reject these implications.In this study, we empirically examine causal relations between stock market tradingvolume and stock returns.2.4. Trading volume and conditional volatility

The Engle (1982) autoregressive conditional heteroskedasticity (ARCH) pro-cess provides a good fit for many financial return time series. The ARCH modelallows the conditional variance to change over time as a function of past squarederrors. The strength of the ARCH technique is that by using established and wellspecified models for economic variables, the conditional means and variances canbe estimated jointly. The autocorrelation in the time-varying rate of informationarrival leads to time-series dependencies n conditional volatility that can be modeledas GARCH processes. This research design is rooted in a class of theoretical modelsin which trading volume and price volatility are driven by exogenous informationinnovations. Lamoureux and Lastrapes (1990) use this econometric framework totest whether there are GARCH effects remaining after the conditional volatilityspecification expands to include the contemporaneous trading volume, which is a


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G. Chen,M. irth, 0.Rui/The Financial Review 38 (2001)153-174 159proxy for inform ation arrival. They find that for individual stocks, volatility persis-tence falls significantly once contemporaneous trading volume is included.

The data set comprises daily market price index and trading volume series fornine of the largest stock exchanges: New York, Tokyo, London, Paris, Toronto,Milan, Zurich, Amsterdam, and Hong Kong. We choose these markets because theyare large, well established, well regulated, and have sufficient data for our statisticaltests. Also, because they have many foreign investors, these markets have a globalinterest. Table 1 lists our specific indexes, the sample period, and the total numberof observations, for each national market. Our sample does not include the dateswhen trading volume is not available. We value-weight all indexes. The indexesrepresent a large coverage (greater than 50%of total market capitalization) of stockswithin each market. Data are collected from Datastream. We match all series ofindexes and trading volumes.Table 1 also presents the basic statistics relating to the returns and tradingvolume of each index. The statistics show that returns are negatively skewed,although the skewness statistics are not large. The negative skewness implies thatthe return distributions of the shares traded on these exchanges have a heavier tailof large values and hence a higher probability of earning negative returns. In allbut three of the markets, the kurtosis values are very much larger than three. Thisresult shows clearly that for most series, the distribution of returns have fat tailscompared with the normal distribution. It implies that much of the non-normalityis due to leptokurtosis.Previous studies report strong evidence of both linear and nonlinear time trendsin trading volume series (e.g., Gallant, Rossi, and Tauchen, 1992). We test trendstationarity in trading volume by regressing the series on a deterministic functionof time. To allow for a nonlinear time trend and a linear trend, we include a quadratictime trend term:

where V , is raw trading volume in each stock market.Panel B of Table 1 shows the coefficients (with t-statistics in parentheses) thatresult from regressing trading volume on linear and nonlinear time trend variables.In general, the coefficients for both the linear and the quadratic terms are statisticallysignificant and the model fit is high. Therefore, we use trading volumes adjustedfor both linear and nonlinear time trends for all nine markets. The detrended tradingvolumes are the residuals from equation (1).To test for a unit root (or the difference stationary process), we use the aug-mented Dickey-Fuller (1979) test:


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162 G. Chen, M. irth, 0.Rui/The Financial Review 38 (2001) 153-174

where x is stock return or detrended volume.The test results reported in Table 1, panel C, show that the null hypothesisthat the stock return series and detrended trading volume series are nonstationary(i.e., have a unit root) is strongly rejected.This result confirms that detrended tradingvolume and stock return series are both stationary.

4. Empirical results4.1. Trading volume and stock price changes

We first examine whether the stylized facts relating to returns-volume relationsfit the data for the nine markets, by testing for the contemporaneous correlation.To do so , we use two alternative forms of the stock price change (return), as shownin the following regressions:V, =a + bR, + ut

V, = a + blR,l + ut(3 )(4)

where the dependent variable (V) is detrended volume, and the independent variableis the natural logarithm of the price relative or its absolute value.Table 2 shows the results of these regressions. Equations (3) and (4) aredisplayed in panels A and B, respectively. In panel A, the coefficients for Japan,Switzerland, the Netherlands, and Hong Kong are significant at the 1% level, andthe coefficient for France is significant at the 5%level. Therefore, there is a positivecontemporaneous relation between trading volume and returns in Japan, Switzerland,the Netherlands, Hong Kong, and France. We find no significant relations for theU.S. , the U.K., Canada, and Italy. The result for the U.S. market contrasts withprevious studies. In panel B, the coefficients from regressing absolute returns ontrading volume are statistically significant at the 1% level in all nine markets.

4.2 . Causal relation between trading volume and stock price changesOur empirical procedures test whether trading volume precedes stock returns,or vice versa This is the notion behind causality testing in Granger (1969), and itis based on the premise that the future cannot cause the present or the past. If aneventn occurs before an eventy , then we can say that x causesy . Formally, according

to Granger (1969), if the prediction of y using past x is more accurate than theprediction without using past x in the mean square error sense [i.e., if a2(y, I It-l)< a2(yt It.l - x,), where It is the information set], then x Granger-causesy .


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164 G. Chen, M.Firth, 0.Rui/The Financial Review 38 (200 1) 1.53-174We use the following bivariate autoregressions to test for causality between

the two variables trading volume and stock returns:F F

F F

In equation (3,f the pjcoefficients are statistically significant, --en including bothpast values of return and past history of volume yields a better forecast of futurevolume. Therefore, we say returns cause volume. If a standard F-test does not rejectthe hypothesis that pj= 0 for all j , then returns do not cause volume.In equation (6), if causality runs from volume to returns, then the 8, coefficientswill jointly be different from zero. If both p and 6 are different from zero, there isa feedback relation between returns and trading volume. For the estimation of thevector autoregression (VAR), we use five lags based on both the Akaike informationcriterion (AIC) and the Schwarz criterion. These lags amount to allowing for week-long information in the regression.Table 3 presents the results of causal relation tests based on a bivariate model.F-statistics and corresponding significance levels are also shown. Panel A showsthe results of the test of the null hypothesis that returns do not Granger-causevolume. The F-statistic is significant at the 1% level for the the U.S. , Japan, theU.K., Italy, and Hong Kong, significant at the 5% level for the Netherlands, andsignificant at the 10% level for France and Switzerland.Panel B, Table 3, shows that in the test of the null hypothesis, volume doesnot Granger-cause return. The F-statistics are significant at the 5% level for Switzer-land and the Netherlands, and significant at the 10%level for Canada and HongKong. This finding implies that in the presence of current and past returns, tradingvolume adds some significant predictive power for future returns in these countries.These results agree with some theoretical models that imply information content ofvolume for future returns. The results from panels A and B imply a feedback systemin Switzerland, the Netherlands, and Hong Kong. In these three countries, returnsare influenced by volume and volume is influenced by returns. Overall, the modelfits are better for equation ( 5 ) than for equation (6).The evidence indicates strongerevidence of returns causing volume than volume causing returns.4.3. Trading volume and conditional volatility

Table 1 shows that for most series, the distribution of returns is fat tailedcompared with the normal distribution. Hence, a GARCH application is more appro-priate than standard statistical models. Pagan and Schwert (1990) and Nelson (1991)develop the exponential GARCH (EGARCH) model. There are advantages of


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G. Chen, M. irth, 0.Rui/The Financial Review 38 (2001) 153-174 167EGARCH over GARCH (see, for example, Cumby, Figlewski, and Hasbrouck,1993). First, by using the exponential formulation, the restrictions of positive con-straints on the estimated coefficients in A RCH and GA RCH are no longer necessary.Second, a weakness of the G ARCH model is that the cond itional variance dependson the magnitude of the d isturbance term, but not its sign. GARCH fails to capturethe negative asymmetry apparent in many financial time series. The EGARCHmodel lessens this problem by modeling the standardized residual as a movingaverage (MA ) regressor in the variance equation while preserving the estimation ofthe magnitude effect.The A RCW GAR CH approach to m odeling changing volatility also precludesthe testing of Black's (1976 ) leverage effect. How ever, the EGARCH class of modelscaptures the tendency for negative shocks to be associated with increased volatility.We use the following EGARCH(1,l) model to estimate stock return volatility:

Table 4 eports the results of the EGARCH model in equation (7). We obtain theparameter estimates by maximizing the log-likelihood using the Bem dt, Hall, Hall,and Hausman (197 4) algorithm.Our results agree with those of other empirical studies on time-varying volatility.First, the log-likelihood statistics are very large. This result implies that the EGA RC Hmodel is an attractive representation of daily return behavior that successfullycaptures the temporal dependence of return volatility. Second, the EGARCH param e-terization is statistically significant. Third, the p coefficient in each conditionalvariance equation is considerably larger than a,mplying that large market su rprisesinduce relatively small revisions in future volatility. Fourth, the leverage factor yis positive. The results support the n egative leverage factors suggested by Nelson(1991).Finally, the persistence of the co nditional variance process, which we measureby a+p, is high and often close to unity. As the sum of the a and j3 coefficientsapproach one ( l ) , the greater is the persistence of shocks to volatility (Lamoureuxand Lastrapes, 199 0; Najand and Yung, 1991). Along with the observation that p >a,he fact that (a j3) is sligh tly less than unity suggests the processes are stationary(Bollerslev, 1987; Engle and Bollerslev, 1986). These results imply that currentinformation is relevant in predicting future volatility over a very long horizon. Asa model specification test we report the Ljung-Box statistics for 24'h-order serialcorrelation in the level and squared standard ized residua ls. Both Ljung-Box statisticsindicate that the residuals do not show any significant serial correlation. Thus, theestimated models fit the data very w ell. To examine the hyp othesis that the flow


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G.Chen,M . Firth, 0.Rui/The Financial Review 38 (2001)153-174 169of information to the market helps explain the volatility of returns, we use tradingvolume as a proxy for information innovations. We choose daily trading volumeas a measure of the amount of daily information that flows into the market. Themodel is given by the following equation:

The mixture model predicts that x > 0. Furthermore, in the presence of volumewith x > 0, if daily volume is serially correlated, a and p will be small andstatistically insignificant. The persistence of variance as measured by(a p) shouldbecome negligible if accounting for the uneven flow of information (V) explainsthe presence of EGARCH in the data.Strictly speaking, we can make inferences from equation (8) only if volumeis exogenous (Najand and Yung, 1991; Bessembinder and Seguin, 1993). Thereforewe use lagged volume (Vt-l) in the model specification. Lagged volume can beinterpreted as a predetermined variable. Najand and Yung (1991) find that withlagged volume the GARCH effect is consistently significant in all calendar periods.They observe a statistically meaningful positive correlation between price variabilityand volume for their sample. Bessembinder and Seguin (1993), using a range ofdifferent futures contracts, demonstrate that the conditional volatility exhibits strongpersistence even when they include unexpected and expected volume and openinterest in the specification. These results are at odds with the results of Lamoureuxand Lastrapes (1990).We find that the EGARCH coefficients a and p are statistically significant forreturn series in the nine stock markets, as reported in Table 5. x is also statisticallysignificant except for Canada and Switzerland. The sums (a p) are close to one,indicating the persistence of past volatility in explaining current price volatility.The EGARCH effect remains significant when lagged volume is included inthe model. However, the persistence in volatility as measured by(a p) is marginallysmaller when we do so. Trading volume as a proxy for information innovationsdoes not reduce the importance of a and p in explaining persistence in volatilityof returns in the nine stock markets.Our results suggest that volatility is better explained by previous volatility thanby volume. The significant coefficients(x) n V in Table 5 indicate that volume isan endogenous variable in the system, and that there is a positive association betweenreturn variance and lagged trading volume.

We repeat the analyses, using contemporaneous trading volume (V,) instead oflagged volume (Vt-l) in equation (8). Our results are similar to those in Table 5 andtherefore are not separately tabulated. One interpretation of the results is that volume


18/21

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G.Chen, M.Firth, 0. ui/The Financial Review 38 (2001) 153-174 171is not a proxy for information. This result agrees with the interpretation of B lume,Easley, and OHara (1994) that volume provides information about the qualityof information signals, rather than representing the information signal itself. Analternative interpretation is that volume is a proxy for information. How ever, infor-mation does not explain the volatility that is due to noise trading in the market.

5. SummaryOur study uses Granger causality tests to examine whether returns explainvolume or volume explains returns. Our data com prise index returns and tradingvolume from the U.S., Japan, the U.K, France, Canada, Italy, Switzerland, theNetherlands, and Hong Kong. Our results show a positive correlation betweentrading volume and the absolute value of the stock price change in all nine markets.These results agree with the findings from U.S. studies. Our Granger causalityresults show that returns cause volume and, although to a lesser extent, that volumecauses returns.Our results suggest the EGA RCH models reflect an appropriate representationof the returns in stock index data. Our evidence indicates that trading volumecontributes some information to the returns processes of stock indexes. How ever,in contrast to Lamoureux and Lastrapes (1990), we find that the persistence in

volatility remains even after incorporating contemporaneous and lagged volumeeffects (both of w hich are proxies for information flow).Our findings suggest that more can be learned about the stock market throughstudying the joint dynam ics of stock prices and trading volume than by focusingonly on the univariate dynamics of stock prices. We find that ou r results are robustacross all nine m ajor stock markets, implying that there are similar returns, tradingvolume, and volatility patterns across these markets.

ReferencesAndersen, T. G . , 1996. Return volatility and trading volume: An information flow interpretation ofBerndt, E.R., B.H. Hall, R.E. Hall, and J.A. Hausman, 1974. Estimation and inference in nonlinearBessembinder, H. and R.J. Seguin, 1993. Price volatility, trading volume, and market depth: EvidenceBlack, F., 1976. Studies of stock price volatility changes, Proceedings of the American StatisticalBlume, L., D. Easley , and M. OHara, 1994. Market statist ics and technical analysis: The role of volum e,Bollerslev, T., 1987. A conditionally heteroskedastic time series model for speculative prices and ratesCampbell, J . Y. ,S . J. Grossman, and J. Wang, 1993. Trading volum e and serial correlation in stockChordia, T. and B. Swaminathan, 2000. Trading volume and cross-autocorrelations in stock returns,

stochastic volatility, Journal o Finance 51, 169-204.structural models, Annals o Economic and Social Measurement 4, 653-665.from futures markets, Journal o Financial and Qu antitative Ana lysis 28, 21-39.Association, Business and Economics Srutistics Section, 177-181.Journal of Finance 4 91 , 153-182.of return, Journal of Econometrics 31, 307-327.returns, Quarterly Journal o Economics 108, 905-939.Journal of Finance 55,913-935.


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172 G. Chen, M. Firth, 0.Rui/The Financial Review 38 (2001) 153-174Clark, P.K., 1973. A subordinated stochastic process model with finite variance for speculative prices,Copeland, T. E., 1976. A m odel of asset trading under the a ssum ption of sequen tial information arr ival,Crouch, R. L., 1970. The volume of transac tions and price changes on the New York S tock Exchange,Cumby , R., S . Figlewski, and J. Hasbrou ck, 1993. Forecasting volatility and correlations with EGARCHEngle, R. F., 1982. Autoregressive conditional heteroskedasticitywith estim ates of the variance of U.K.Engle, R.F. and T. B ollerslev, 1986. Mo deling the persisten ce of co nditional variance, EconometricEpps, T. W. and M . L. Epps, 1976. The stochas tic dependence of security pr ice chang es and transactionFos ter, F. D. and S . Visw anathan, 1995. Can speculative trading explain the volume-volatility relation ?Gallan t, A. R., P.E . Rossi, and G . Tauche n, 1992. Stock prices and volume, Review ojFinancia1 StudiesGranger, C.W .J., 1969. Investigating causal relations by econom etric models and cro ss-spectralmethods,

Econometrica 41, 135-55.Journal of Finance 31, 1149-1168.Financial Analysts Journal 26, 104-109.models, Journal of Derivatives, Winter, 21-63.inflation, Econometrica 50, 987-1008.Reviews 5, 1-50.volumes: Implications for the mixture-of-distributionshypothesis, Econometrica 44, 305-21.Journal of Business & Economic Statistics, 13, 379-396.5, 199-242.Econometrica 37. 424-438.Granger, C.W.J. an dO . Morgen stern, 1963. Spectral analysis of New York stock market prices, Kyklos16, 1-27.Harris, L., 1986. Cross-security tests of the mixture of distributions hypothes is, Journal of Financial

Harris, M. and A. Raviv, 1993. Differences of opinion make a horse race, Review of Financial StudiesHe, H. and J. Wang, 1995. Differential information and dynamic behavior of stock trading volume,Hiemstra, C. and J.D. Jones, 1994. Testing for linear and nonlinear Granger causality in the stock pnce-Jain, P.C. and G.H. Soh, 1988. The dependence between hourly prices and trading volume, Journal ofJennings, R.H., L. S tarks, and J . Fellingham, 1981. An equ ilibrium model of asse t trading with sequentialJennings, R.H. and C . B arry, 1983. Information dissemination and p ortfolio choice,Journal of FinancialKarpoff, J.M., 1986. A theory of trading volume, Journal ofFinance 41, 1069-1088.Karpoff, J.M., 1987. The relation between price changes and trading volume: A survey, Journal ofLamoureux, C.G. and W .D. Lastrape s, 1990. Hete roskedas ticity in stock return data: Volume versusLamoureux, C.G. and W.D. Lastrapes, 1994. Endogenous rading volume and momentum in stock- returnMorgan, I.G., 1976. Stock prices and heteroskedasticity,Journal of Business 49, 496-508.Morse, D., 1980 .Asymmetrical information n sec uritiesmarkets and trading volume, Journal ofFinancialNajand, M. and K. Yung, 1991. A GA RCH exam ination of the relationship between volume and priceNelson, D. B., 1991. Conditional heteroskedasticity n asset returns: A new a pproach, Econometrica 59 ,Osb orne , M.F.M., 1959. Brownian motion in the stock market, Operations Research 7, 145-173.Pagan, A.R. and G.W. S chwert, 1990. Alternative models for conditional stock volatility, Journal ofRogalski, R.J., 1978. The dep ende nce of prices and volume, Review of Economics and Statistics 60 ,Smirlock, M. and L. Starks, 1985. A further exam ination of stock price chang es and transaction volume,

and Quantitative Analysis 21, 39-46.6, 473-506.Review of Financial Studies 8, 919-972.volume relation, Journal of Finance, 49, 1639-1664.Financial and Quantitative Analysis 23, 269-283.information arrival, Journal of Finance 36, 143-161.and Quantitative Analysis 18, 1-19.

Financial and Quantitative Analysis 22, 109-126.GARCH effects, Journal of Finance 45, 221-229.volatility, Journal of Business and Econom ic Statistics 12, 253-260.

and Quantitative Analysis 15, 1129-1148.variability in futures markets, Journal of Futures Markets 11, 613-621.323-370.

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G. Chen, M. Firth, 0.Rui/The Financial Review 38 (2001) 153-174 173Tauchen, G. E. and M. Pitts, 1983. The price variability-volume relationship on speculative markets,Wang, J ., 1994.A model of competitive stock trading volume,Journal of Political Economy 102, 127- 168.Westerfield, R., 1977. The distribution of common stock price changes: An application of transactions

time and subordinated stochastic models, Journal of Financial and Quantitative Analysis 12,743-765.Wood, R.A., T.H. Mclnish, and J.K. Ord, 1985. An investigation of transactions data for NYSE stocks,Journal of Finance 60, 723-739.

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dynamical relation between return trading volume and volatility

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