This paper finds that trading volume is a significant determinant of the lead-lag patterns observed in stock returns. Daily and weekly returns on high volume portfolios lead returns on low volume portfolios, controlling for firm size. Nonsynchronous trading or low volume portfolio autocorrelations cannot explain these findings. These patterns arise because returns on low volume portfolios respond more slowly to information in market returns. The speed of adjustment of individual stocks confirms these findings. Overall, the results indicate that differential speed of adjustment to information is a significant source of the cross-autocorrelation patterns in short-horizon stock returns. BOTH ACADEMICS AND PRACTITIONERS HAVE LONG BEEN interested in the role played by trading volume in predicting future stock returns. 1 In this paper, we examine the interaction between trading volume and the predictability of short horizon stock returns, specifically that due to lead-lag cross-autocorrelations in stock returns. Our investigation indicates that trading volume is a significant determinant of the cross-autocorrelation patterns in stock returns. 2 We find that daily or weekly returns of stocks with high trading volume lead daily or weekly returns of stocks with low trading volume. Additional tests indicate that this effect is related to the tendency of high volume stocks to respond rapidly and low volume stocks to respond slowly to marketwide information.  This paper is closely related to the literature on cross-autocorrelations initiated by Lo and MacKinlay~1990!. Lo and MacKinlay find that positive autocorrelations in portfolio returns are due to positive cross-autocorrelations among individual security returns. Specifically, they find that the correlation between lagged large firm stock returns and current small firm returns is higher than the correlation between lagged small firm returns and current large firm returns. Our results show that trading volume has important information about cross-autocorrelation patterns beyond that contained in firm size. The explanations that have been proposed for these cross-autocorrelation patterns~see Mech~1993!! can be classified into three groups. The first group of explanations claims that cross-autocorrelations are the result of time-varying expected returns~see Conrad and Kaul~1988!!. A variant of this explanation suggests that cross-autocorrelations are simply a restatement of portfolio autocorrelations and contemporaneous correlations~see Hameed~1997! and Boudoukh, Richardson, and Whitelaw~1994!!. Once account is taken of portfolio autocorrelations, according to this explanation, portfolio cross-autocorrelations should disappear. The second group of explanations~see Boudoukh et al.! suggests that portfolio autocorrelations and cross-autocorrelations are the result of market microstructure biases such as thin trading. The final explanation for the lead-lag cross-autocorrelations claims that these lead-lag effects are due to the tendency of some stocks to adjust more slowly~underreact! to economy-wide information than others~see Lo and MacKinlay~1990! and Brennan, Jegadeesh, and Swaminathan~1993!!. 3 We refer to this explanation as the speed of adjustment hypothesis. Why do these lead-lag patterns not get arbitraged away? Most likely because of the high transaction costs that any trading strategy designed to exploit these short-horizon patterns would face~see Mech~1993!!. Our empirical tests are designed to take into account the issues raised by the first two explanations. First, we conduct vector autoregressions involving pairs of high and low volume portfolio returns. Holding firm size constant, we examine whether lagged high volume portfolio returns can predict current low volume portfolio returns controlling for the predictive power of lagged low volume portfolio returns. We use both daily and weekly returns in our empirical tests and take other precautions to minimize the impact of nonsynchronous trading on our results. We find that high volume portfolio returns significantly predict low volume portfolio returns even in the largest size quartile. We also find that these results are robust in the post-1980 time period. These results show that own autocorrelations and nonsynchronous trading cannot fully explain the observed lead-lag patterns in stock returns. 3 Others who have provided similar explanations include Badrinath, Kale, and Noe~1995!, McQueen, Pinegar, and Thorley~1996!, and Connolly and Stivers~1997!. The Journal of Finance Next, in order to examine the source of these cross-autocorrelations, we conduct Dimson market model regressions~see Dimson~1979!! using returns on zero investment portfolios that are long in high volume portfolios and short in low volume portfolios of approximately the same size. The results indicate that the lead-lag effects are related to the tendency of low volume stocks to respond more slowly to marketwide information than high volume stocks. Finally, we use a speed of adjustment measure based on lagged betas from Dimson regressions to examine the ex ante firm characteristics of a subset of stocks that contribute the most~or the least! to portfolio autocorrelations and cross-autocorrelations. The evidence indicates that there are striking differences in trading volume across stocks that contribute the most and the least to portfolio autocorrelations and cross-autocorrelations. Specifically, stocks that contribute the most have 30 percent to 50 percent lower trading volume. The key conclusions are as follows. Returns of stocks with high trading volume lead returns of stocks with low trading volume primarily because the high volume stocks adjust faster to marketwide information. This is consistent with the speed of adjustment hypothesis. Thus, trading volume plays a significant role in the dissemination of marketwide information. Thin trading can explain some of the lead-lag effects, but it cannot explain all of them. The lead-lag effects are also not explained by own autocorrelations. The rest of the paper is organized as follows. Section I discusses the data and the empirical tests and Section II discusses the empirical results. Section III provides additional evidence using individual stock data and Section IV concludes. I. Data and Empirical Tests Since Lo and MacKinlay~1990! document that large firm returns lead small f irm returns, we control for size effects in examining the crossautocorrelation patterns between high volume and low volume stocks. We do this by forming a set of 16 portfolios based on size and trading volume, using turnover as our measure of trading volume. Most previous studies~see Jain and Joh~1988! and Campbell, Grossman, and Wang~1993!! have used turnover, defined as the ratio of the number of shares traded in a day to the number of shares outstanding at the end of the day, as a measure of the trading volume in a stock. Moreover, using turnover disentangles the effect of firm size from trading volume. Raw trading volume and dollar trading volume are both highly correlated with firm size. In our sample, the crosssectional correlations between firm size and raw trading volume and firm size and stock price are 0.78 and 0.72 respectively; the correlation between size and turnover is 0.15 and the correlation between turnover and raw vol- 915 ume is 0.60. Thus, turnover is highly correlated with raw volume but more or less uncorrelated with firm size, which is exactly what we seek from this variable. 4 For the period from 1963 to 1996, four size quartiles are formed at the beginning of each year by ranking all firms in the CRSP NYSE0AMEX stock file by their market value of equity as of the December of the previous year, and then dividing them into four equal groups. Only firms with ordinary common shares are included in these portfolios. Additionally, all closed-end funds, real estate investment trusts, American Depositary Receipts, and Americus trust components are excluded from these portfolios. Firms in each size quartile are further divided into four equal groups based on their average daily trading volume over the previous year. To be included in one of these 16 portfolios, a firm must have at least 90 daily observations of trading volume available in the previous year. Once portfolios are formed in this manner at the beginning of each year, their composition is kept the same for the remainder of the year. Daily and weekly equal-weighted portfolio returns are computed for each portfolio by averaging the non-missing daily or weekly returns of the stocks in the portfolio. Foerster and Keim~1998! report that the likelihood of a NYSE0AMEX stock going without trading for two consecutive days is 2.24 percent and for five consecutive days it is only 0.42 percent. Therefore, in order to minimize the effect of nonsynchronous trading on cross-autocorrelations, returns of stocks that did not trade at date t or t Ϫ 1 are excluded from the computation of portfolio returns for date t. This ensures that the daily returns of any stock that did not trade for two consecutive days are excluded from the computation of portfolio returns for those two days and for the following day. As is common in the literature, we measure weekly returns from Wednesday close to the following Wednesday close. 5 The use of weekly returns should further alleviate concerns of nontrading. Daily and weekly stock returns, average trading volume, and annual firm size are all obtained from CRSP from January 1963 through December 1996. Table I presents descriptive statistics on the 16 size-volume portfolios. The mean portfolio returns suggest a negative cross-sectional relationship between trading volume and average stock returns. 6 The daily means for 4 Henceforth, unless otherwise stated, trading volume refers to this specific definition of trading volume. 5 Seasonal patterns in weekly autocorrelations have been examined in detail by Keim and Stambaugh~1984!, Bessembinder and Hertzel~1993!, and Boudoukh et al.~1994!. Bessembinder and Hertzel find, for example, that the patterns in autocorrelations across weekdays are related to the importance of weekend returns versus nonweekend returns in autocorrelation patterns and are robust to alternative market microstructures. Though this is an interesting issue, as far as our paper is concerned we simply want to show that our results are robust to these patterns. In order to check the robustness of the weekly results, we repeat all of our analysis using weekly returns computed from Friday close to the following Friday close and Tuesday close to the following Tuesday close. The results are similar. 6 See Brennan, Chordia, and Subrahmanyam~1998! and Datar, Naik, and Radcliffe~1998!. The Journal of Finance Table I Summary Statistics for Size-Volume Portfolios Summary statistics for size-volume portfolios are computed over . Pij refers to a portfolio of size i and volume j. i ϭ 1 refers to the smallest size portfolio and i ϭ 4 refers to the largest size portfolio. Similarly j ϭ 1 refers to the lowest volume and j ϭ 4 refers to the highest volume portfolio. EW is an equal-weighted market index of NYSE0AMEX firms. Summary statistics for returns are computed using both daily returns and nonoverlapping weekly returns. Each week ends on a Wednesday. For comparison, we also report autocorrelations computed using weekly returns with weeks ending on Tuesday and Friday. The columns titled Wednesday, Tuesday, and Friday refer to weeks defined with those ending days. Statistics of portfolio size and volume are obtained as follows: First, the cross-sectional statistics~median and mean! of size and volume are computed for each portfolio for each year. Then the yearly cross-sectional statistics of each portfolio are averaged over time and reported below. N refers to the average number of firms in each portfolio each day or each week over . The number of daily returns for all portfolios from 1963 to 1996 is 8,560. The number of nonoverlapping weekly returns over the same time period is 1,774. r k refers to the kth order autocorrelation. S k refers to the sum of first k autocorrelations. The size figures are in billions of dollars. The volume numbers represent average daily percentage turnover.
Choueifaty and Coignard REF show that trading volume is a significant determinant of the lead-lag patterns observed in stock returns.
Trading volume and cross-autocorrelations in stock returns
Journal of Finance
Economics