Essay I: What Kind of Trading Drives Return Autocorrelation
4. Empirical Results
4.2 Robustness Checks
When we test the significance of the average coefficient in Tables 2 and 3, we assume zero correlations between coefficients. This assumption is not correct if the error terms from the 1st step time-series regressions are correlated across stocks. To reduce the cross-sectional correlation between error terms, we follow Jorion (1990) to add the market return (MR) and the industry return (IR) to the time-series regressions as follows:
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 + C3 MRt+1 +C4 IRt+1+ εt+1.. (8)
Column (1) of Table 4 reports the coefficient estimates of model (8). The coefficients on market return and industry return are both significantly positive, but their significance does not change the significance of institutional trading. Results in Table 4 are very similar to Table 2. Therefore, our inferences are not driven by the cross-sectional correlation.
Results in Table 4 also suggest that trading by foreigners and mutual funds are based on firm-specific information rather than market or industry wide information.
Including the market and industry returns in the regression scarcely changes the coefficients on institutional trading. For example, the coefficient on foreigner (mutual fund) buying is 0.0195 (0.0487) in Table 2, and 0.0136 (0.0406) when market and industry returns are included with regressions in Table 4.
Including the market and industry returns in the regression does not guarantee the
Table 4: Autocorrelation Regarding Firm-specific Returns and Volumes
We perform the following time-series regression for each stock.
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 + C3 MRt+1 +C4 IRt+1+ εt+1, where Vt is defined as ln(turnovert+0.00000255) and is detrended by its past-200-days average. Dt[R>0]
= 1 if Rt>0 and 0 otherwise, Dt[R≦0] = 1 if Rt≦0 and 0 otherwise; DtFB=1 if VtFB is higher than its past-200-days average, and DtFB= 0 otherwise. DtFS , DtMB, DtMS, DtDB, and DtDS are similarly defined.
VtFB (VtFS), VtMB (VtMS), and VtDB (VtDS) are the daily buy (sell) turnover of foreigner, mutual fund, and dealers trading, respectively. MRt+1 is the market return, and IRt+1 is the industry return. The sample includes 1,049 stocks for which there are at least 750 daily observations and that were listed on the Taiwan Stock Exchange and the Gre Tai Securities Market. The sample period is from 2000/12/12 to 2007/3/30. From the time-series regression estimates, we calculate and report the cross-sectional robust mean for each size group. * denotes significance at the 10% level, ** denotes significance at the 5% level, and *** denotes significance at the 1% level.
(1) (2) (3)
Remove market component from institutional turnovers
NO NO YES
isolation of the firm-specific volume. As an alternative, we follow LMSW to estimate firm-specific returns and volumes and use them in the regression model (6). The firm-specific returns and volumes are residuals of market models for returns and the detrended log turnover. The market return is defined as the change in the log of the
Taiwan Stock Exchange Value-weighted Index. The market turnover used in the market model is the detrended natural logarithmic (as in equation (2)) of the market turnover, which equals the total value of shares traded on the Taiwan Stock Exchange divided by the total market capitalization. We report results using firm-specific returns and volumes in columns (2) and (3) of Table 4.
The difference between columns (2) and (3) is in the definition of the dummy variables that measure the extent of institutional trading. The definition used in column (2) is the same as the one used in Table 2. Take the dummy variable for foreigners' buy as an example: foreigners' buy is heavy if the buy turnover is greater than its 200-day moving average. The definition used in column (3) is the firm-specific component of foreigners' buy. We first estimate a market model by regressing foreigners' buy turnover against the market turnover. Foreigners' buy is heavy if the residual of the market model is greater than its 200-day moving average. As mentioned earlier, we do not use the log of institutional turnover to define dummy variables because that will reduce the power of our tests.
The qualitative results in columns (2) and (3) of Table 4 are similar to results in Table 2. Take the coefficient on mutual fund buying as an example: it is 0.0487 in Table 2, 0.0402 in column (2), and 0.0295 in column (3). Therefore, the effect of institutional trades on autocorrelation is mainly driven by firm-specific information.
The next question we address is whether the autocorrelated return on the next day reflects public or private information. Suppose the information is positive. The positive return on the next day can reflect private information revealed by more purchase on the next day from institutions. The same institution can split its orders into several days to reduce the price impact (Kyle, 1985). Several institutions may receive noisy private signals of the same underlying information sequentially and trade on them (Hirshleifer,
Subrahmanyam, and Titman, 1994). In either scenario, positive autocorrelations occur when institutions make heavy purchase consecutively.
On the other hand, if institutions receive private information and trade on it just prior to its public announcement, then the return on the next day will reflect the public announcement. In the LMSW model, the public announcement on the next day will cause the informed trader to trade on the opposite side.6 Suppose the good information becomes public on date t+1, the uninformed traders will revise upward their expectation of the fundamental value and increase their demand. The price will go up. Given that the price is higher, the informed traders who have the same expectation of the fundamental value on date t and t+1 will reduce their demand on date t+1. Therefore, informed traders will buy the stock on date t and sell it on date t+1.
To distinguish between the public and private information stories, we expand the regression model (6) to the following one (9),
Rt+1 = C0 + C1 Rt + C2Vt Rt +
(CFB + CFBB Dt+1FB+ CFBSDt+1FS
) DtFB Dt[R>0] VtRt + (CFS + CFSS Dt+1FS+ CFSBDt+1FB
) DtFS Dt[R≦0] Vt Rt + (CMB + CMBB Dt+1MB+ CMBSDt+1MS
) DtMB Dt[R>0] Vt Rt + (CMS + CMSS Dt+1MS+ CMSBDt+1MB
) DtMS Dt[R≦0] Vt Rt +
CDB DtDBDt[R>0]Vt Rt+ CDSDtDSDt[R≦0] Vt Rt + εt+1. (9)
We decompose the coefficients on dummy variables into three parts depending on the trading direction on the next day. Take the heavy buy from mutual funds as an
6 We would like to thank an anonymous referee for pointing this out.
example. In regression model (6), the coefficient on the dummy variable DtMB
that captures heavy buys from mutual funds is CMB. Now we have three coefficients: CMB, CMBB, and CMBS. The first part CMB is the same as before. The second part CMBB captures the days when a heavy buy is followed by another heavy buy from mutual funds. Under the private information story CMBB is positive. The third part CMBS captures the days when a heavy buy is followed by a heavy sale from mutual funds. CMBS is positive under the public information story. We apply the same decomposition to buy and sell from foreigners and mutual funds. For the trading from dealers, we do not decompose the coefficients because it is not information driven.
Table 5 reports the coefficient estimates. The first thing to notice is that the autocorrelation coefficients are almost always negative (CFB,CMB, and CMS) when a heavy trade is not followed by another heavy trade. It suggests that heavy trade for only one day is more likely to be allocation trade than information trade.
When a heavy trade is followed by another heavy trade on the same directions, the autocorrelation coefficients are significantly higher, that is, CFBB, CFSS, CMBB, and CMSS
are significantly positive. By contrast, when trading on the next day is on the opposite direction most of the coefficients (CFSB, CMBS, CMSB) are significantly negative. The evidence is consistent with the private information story and the significance of the positive autocorrelation primarily reflects private information revealed by trading on t+1. However, without detailed data, we cannot determine whether this trading is caused by order splitting from the same institutions or by trading from different institutions.
Another issue of concern is whether applying the same one-day estimation interval for all stocks is reasonable. In LMSW’s model, the positive autocorrelation reflects partial information revealed in trading and its further revelation in the future. Therefore, the appropriate interval is the one which includes enough trades to partially reflect the
Table 5: Autocorrelation Regarding Contemporaneous Trading
We perform the following time-series regression for each stock.
Rt+1 = C0 + C1 Rt + C2Vt Rt +(CFB + CFBB Dt+1FB+ CFBSDt+1FS
) DtFB Dt[R>0] VtRt + (CFS + CFSS Dt+1FS+ CFSBDt+1FB) DtFS Dt[R≦0] Vt Rt + (CMB + CMBB Dt+1MB+ CMBSDt+1MS) DtMB Dt[R>0] Vt Rt + (CMS + CMSS Dt+1MS+ CMSBDt+1MB) DtMS Dt[R≦0] Vt Rt + CDB DtDBDt[R>0]Vt Rt+ CDSDtDSDt[R≦0] Vt Rt + εt+1, where Vit is defined as ln(turnoverit+0.00000255) and is detrended by its past-200-days average.
Dt[R>0] = 1 if Rit>0 and 0 otherwise, Dt[R≦0] = 1 if Rit≦0 and 0 otherwise; DitFB=1 if VitFB is higher than its past-200-days average, and DitFB= 0 otherwise. DitFS , DitMB
, DitMS, DitDB, and DitDS are similarly defined. VitFB (VitFS), VitMB (VitMS), and VitDB (VitDS) are the daily buy (sell) turnover of foreigner, mutual fund, and dealers trading, respectively. The sample includes 1,049 stocks for which there are at least 750 daily observations and that were listed on the Taiwan Stock Exchange and the Gre Tai Securities Market. The sample period is from 2000/12/12 to 2007/3/30. From the time-series regression estimates, we calculate and report the cross-sectional robust mean for each size group. * denotes significance at the 10% level, ** denotes significance at the 5% level, and *** denotes significance at the 1% level
All firms 1st Quartile The Smallest
2nd Quartile 3rd Quartile 4th Quartile The Largest C0 (Constant) 0.0778*** 0.0460*** 0.0765*** 0.0873*** 0.0966***
C1 (Rt) 0.0541*** 0.0335*** 0.0609*** 0.0651*** 0.0454***
information, but not too long to fully reflect the information within the interval. For an illiquid stock, a one-day interval may not include enough trades to reflect information.
On the other hand, for a liquid stock, a multiple-day interval can reduce the magnitude and the significance of the autocorrelation coefficient if the interval used is longer than the number of days required to fully reflecting information.
To allow the estimation interval differ across stocks we follow the idea used by LMSW: more days will be included in the estimation interval for low turnover stocks.
We first calculate the median daily turnover for each stock, and sort all stocks into three groups based on the median turnover. The cross-sectional median of the median turnover for the three groups are 0.1058%, 0.3507%, and 0.9011%, respectively. As a result, we estimate the regression model (6) by using a one-day interval for high turnover stocks, a three-day interval for middle turnover, and an eight-day interval for low turnover stocks. For a multiple-day interval, the return is compounded daily return and the turnover is the sum of daily turnover.
Table 6 reports the estimation results. When the measurement interval is lengthened, there is less evidence of a higher autocorrelation during heavy institutional trading. Compared with Table 2, what remains unchanged is the positive autocorrelation coefficient during heavy buying from mutual funds. The point estimate 0.0246 is smaller than the number in Table 2 (0.0487), but is significant at a 1% level. For foreign investors, the effect of heavy buying on autocorrelation is not significant for the whole sample, but it is still significant for large firms. The smaller autocorrelation coefficients suggest that, for some stocks, the multiple-day interval is longer than the number of days required to fully reflect information.
On the other hand, the autocorrelation coefficients on days when foreigners or mutual funds sell heavily are not significantly different from other days when we move
Table 6: Measurement Interval Depends on Turnover
We perform the following time-series regression for each stock.
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,
where Vt is defined as ln(turnovert+0.00000255) and is detrended by its past-200-days average. Dt[R>0]
= 1 if Rt>0 and 0 otherwise, Dt[R≦0] = 1 if Rt≦0 and 0 otherwise; DtFB=1 if VtFB is higher than its past-200-days average, and DtFB= 0 otherwise. DtFS , DtMB, DtMS, DtDB, and DtDS are similarly defined.
VtFB (VtFS), VtMB (VtMS), and VtDB (VtDS) are the daily buy (sell) turnover of foreigner, mutual fund, and dealers trading, respectively. The sample includes 1,049 stocks for which there are at least 750 daily observations and that were listed on the Taiwan Stock Exchange and the Gre Tai Securities Market.
The sample period is from 2000/12/12 to 2007/3/30. From the time-series regression estimates, we calculate and report the cross-sectional robust mean for each size group. * denotes significance at the 10% level, ** denotes significance at the 5% level, and *** denotes significance at the 1% level. We calculate the median daily turnover for each stock over the sample period (MedTurn) and assign all stocks into three groups according to their median turnover. The cross-sectional averages of MedTurn for the three groups are 0.1060%, 0.3615%, and 1.0414%, respectively. The cross-sectional medians of MedTurn for the three groups are 0.1058%, 0.3507%, and 0.9011%, respectively. We use the one-day interval for the high MedTurn stocks (350 stocks), the three-day interval for the median MedTurn stocks (349 stocks), and the eight-day interval for the low MedTurn stocks (350 stocks).
to a multiple-day interval. This suggests that the effect of information-based selling is quick to be fully reflected in the price.
There is evidence that, for two small size quartiles, the average autocorrelations are
significantly negative when foreigners buy heavily. It is not consistent with our ex-ante identification that foreigners are informed traders. However, these stocks are very small.
The total market capitalization of the two small size quartiles is less than 5% of the aggregate market capitalization. Given the small size, the purchase from foreigners may cause a temporary impact and price reversal.
To summarize, we find evidence that is consistent with the LMSW model’s prediction that information trading generates positive autocorrelations. We also find that, due to short-sale constraints imposed on foreigners and mutual funds, their selling has less information content and causes smaller autocorrelations.