Empirical Method

The regression model starts from the following specification:

Rt+1 = C0 + C1 Rt + β ^{Vt Rt + εt+1.,} (1)

where Rt is the daily return and Vt is the daily total volume at time t. We follow LMSW to define Vt as the detrended natural logarithmic of the daily turnover (number of total shares traded divided by the number of outstanding shares). Before taking the log we first add a small number (0.00000255) to the turnover to avoid zero trading volume. We then detrend the series by subtracting a 200-day moving average:

).

Equation (1) allows the first-order autocorrelation coefficient of returns, C1+ β ^Vt, to be a function of trading volume. We call β the marginal autocorrelation coefficient since it represents the change in the return autocorrelation that arises when Vt changes by one unit. If, on average, investors trade on information, then β will be positive, whereas if investors trade to hedge, then βwill be negative. LMSW test their model by examining the cross-sectional relation between β and firm variables that measure the degree of information asymmetry.

We propose to test the LMSW model by allowing β to be time-varying and using institutional trading volumes to identify periods of intensive information trading. The first specification uses only dummy variables as follows:

β^{t = C2 + CFB DtFBDt[R>0] + CFSDtFSDt[R≦0] + CMBDtMBDt[R>0] + CMSDtMSDt[R≦0] +}

CDBDtDBDt[R>0] + CDSDtDSDt[R^≦0]. (3)

Dt[R>0] (Dt[R^≦0]) is a dummy variable that equals one if Rt >0 (Rt≦0). DtFB

is a dummy variable that equals one if the daily buy turnover (buy volume, which we denote by the superscript B, divided by the number of shares outstanding) from foreigners (superscript F) is higher than its 200-day moving average. DtFS

, DtMB, DtMS

, DtDB

, and DtDS

are defined similarly, where superscript S denotes sell volume, M denotes mutual funds, and D denotes dealers. In contrast to total volume, we do not use log turnover to define dummy variables. Taking logs here will reduce the importance of large institutional

volumes, which we use to test the LMSW's predictions, and reduce the power of our tests.

Our specification assumes a different autocorrelation coefficient of returns only if the direction of heavy institutional trades is the same as the direction of returns, that is, when the daily return is positive and institutional buy is heavy or when the daily return is negative and institutional sell is heavy. This specification follows the LMSW model that trading based on good information drives up the price while trading based on bad information causes the price to drop. For brevity, in the rest of the paper when I say heavy buy, I mean heavy buy on a positive-return day. Similarly, when I say heavy sell, I mean heavy sell on a negative-return day.

Given that, on average, foreigners and mutual funds trade on information, trading is more likely driven by information when foreigners or mutual funds trade more extensively. Therefore, when the trading volume of foreigners or mutual funds is high relative to its moving average, the autocorrelation coefficient is higher. The coefficients CFB, CFS, CMB, and CMS in equation (3) should be positive, in accordance with the LMSW model.

The second hypothesis that we test stipulates that the buy volumes of foreigners and mutual funds generate a more positive autocorrelation than sell volume because the short-sale constraint will make sell volume contain less information (Hong and Stein, 2002). If the buy volume is more information driven than the sell volume, then CFB

should be greater than CFS and CMB should be greater than CMS.

On the other hand, dealers are less likely to trade on information. Thus, the autocorrelation coefficient on days of heavy trading from dealers is lower than the coefficient on days of heavy trading from foreigners or mutual funds. The coefficients CDB and CDS in equation (3) should be less than coefficients CFB,CFS, CMB, and CMS, in

accordance with the LMSW model.

The second specification that we use directly employs institutional trading volume by decomposing total volume into its components as in the following:

β^{tVt = C2VtO + CFBQtFBDt[R>0] + CFSQtFSDt[R 0]≦ + CMBQtMBDt[R>0] + CMSQtMSDt[R 0]≦ +} CDBQtDBDt[R>0] + CDSQtDSDt[R 0]≦ , (4)

where VtO

is the natural logarithmic of the daily turnover from investors other than foreigners, mutual funds, and dealers, and is detrended by its past-200-days average.

QtFB

is the daily buy turnover from foreigners divided by turnover from othersand is detrended by its past-200-days average. QtFS

, QtMB

, QtMS

, QtDB

, and QtDS

are defined similarly. Notice that we define VtO

and Q differently: the former as the log of volumes and the latter as the ratio of volumes. The reason is because the log of the sum of volumes is not equal to the sum of log volumes.

To obtain the decomposition in (4), we use the following approximation (before detrending):

Taking logs of both sides of the approximation (5) gives us the decomposition:

Vt = ln(turnovert)≈ VtO+QtFB+QtFS+QtMB+QtMS+QtDB+QtDS

.

Substituting equations (3) or (4) into (1) gives the regression models (6) and (7):

Rt+1 = C0 + C1Rt + C2VtRt + CFBDtFBDt[R>0]VtRt + CFSDtFSDt[R^≦0]VtRt + CMBDtMBDt[R>0]VtRt+ CMSDtMSDt[R^≦0]VtRt + CDBDtDBDt[R>0]VtRt+

CDSDtDSDt[R^≦0]VtRt + εt+1, (6)

Rt+1 = C₀ + C₁Rt + C₂VtORt + CFBQtFBDt[R>0]Rt + CFSQtFSDt[R^≦0]Rt + CMBQtMBDt[R>0]Rt+ CMSQtMSDt[R^≦0]Rt + CDBQtDBDt[R>0]Rt+ CDSQtDDt[R^≦0]Rt + εt+1. (7)

We use a two step procedure to estimate coefficients in models (6) and (7). The first step is to run time-series regression for each stock to get the OLS estimate of coefficients. When any one group of institutional investors does not trade a given stock at all, its dummy variable is removed from the regression. We then estimate a cross-sectional average of the coefficients by running a robust regression that has only the intercept term. We use the STATA software rreg command to estimate the intercept.

A robust regression estimate is designed to deal with extreme observations with statistical validity. It is a form of weighted least-squares that first drops the most influential observations and then imposes smaller weights on observations with larger absolute residuals (Baker and Hall, 2004; Li, 1985). We have also estimated the mean with winsorizing or trimming at the 5^th and 95^th percentiles, the results are very similar.