Wermers (1999) found significant differences of abnormal return between stocks in the buy- and sell-herding. However, the differences decrease in the long-run. A temporary price adjustment reveals the destabilization of stock price by the herding. However, a permanent impact would indicate that herding plays a more beneficial role in stock markets by increasing the speed of price adjustment to new information.
Table 9 Herding statistics by mutual fund performance quintile under binomial distribution
Herding statistics
performance quintiles Herding measure (HM)
Note 1. The values in parentheses are t-statistics.
2. (*) and (**) are denoted significant at 5% and 1% level, respectively.
Table 10. Herding statistics by mutual fund performance quintile under trinomial distribution
Herding statistics
Performance quintiles Herding measure (H ′M )
2. (*) and (**) are denoted significant at 5% and 1% level, respectively.
We group the sample into several portfolios by ranking buy-herding measures and sell-herding measures. That is, stocks in the buy-herding subgroup are ranked by , and quintile portfolios are formed. Thus, the top quintile portfolio (BHM1) contains stocks that lightly buy in herds, and the bottom portfolio (BHM5) contains stocks that strongly buy. This procedure is repeated for stocks in the sell-herding subgroup and is ranked by following the formation of quintile portfolios. In other words, the top portfolio (SHM1) contains stocks that slightly sell in herds, and the bottom portfolio (SHM5) contains stocks that strongly sell. Therefore, we form 10 portfolios. Then we calculate the abnormal returns of 10 portfolios during the period.
t ,
BHMi
t ,
SHMi
Table 11 shows the abnormal returns for portfolios BHM1 through SHM1 from January 2001 to March 2005. For example, the abnormal return shown for portfolio BHM1 in the period T represents the monthly average abnormal return that would accrue to investing on January 2001. In other words, we hold an equal-weighted portfolio of stocks that most lightly buy in herds and then rebalancing to hold this portfolio during the following months. This process is repeated until the end of March 2005. Similarly, same processes are calculated for portfolios form by SHMi,t.
From Table 11, last two rows, (B5-S5) and ((B1~B5)-(S1-S5)), show that there are significant differences of abnormal returns between stocks in the buy- and sell-herding. However, the differences of abnormal return will decrease gradually. Therefore, the herding doesn’t increase the stock market volatility that is consistent with Sias and Starks (1997). Consequently, the seventh hypothesis is proved in Table 11.
Table 11 Market stabilization and herding behavior
T-4 T-3 T-2 T-1 T T+1 T+2 T+3 T+4 BHM1 4.298 4.196 3.995 3.981 4.002 3.849 3.706 3.582 3.583 (Light
buying) (8.172)** (8.200)** (7.923)** (8.740)** (8.630)** (8.257)** (7.861)** (7.338)** (7.151)**
BHM2 4.125 3.927 3.729 3.894 3.843 3.838 3.869 3.687 3.639 (5.358)** (5.133)** (4.711)** (4.887)** (4.796)** (4.681)** (4.623)** (4.485)** (4.444)**
BHM3 4.924 4.366 3.991 3.957 4.004 4.146 4.087 4.057 4.027 (4.642)** (6.299)** (5.399)** (5.637)** (3.444)** (5.278)** (4.904)** (4.751)** (4.817)**
BHM4 3.59 3.258 2.759 2.822 3.037 2.883 2.951 2.883 3.013 (2.032)* (1.681) (1.323) (1.576) (1.968)* (2.180)* (2.086)* (1.969)* (2.054)*
BHM5 3.618 3.270 2.648 2.822 3.024 3.033 3.063 3.206 2.902 (Heavy
buying) (3.521)** (3.472)** (2.139)* (2.690)** (3.207)** (3.019)** (2.907)** (2.859)** (2.381)*
SHM1 -1.661 -1.629 -1.530 -1.518 -1.438 -1.368 -1.257 -1.118 -0.98 (Light
selling) (-6.725)** (-6.166)** (-5.486)** (-5.399)** (-4.996)** (-4.776)** (-4.129)** (-3.727)** (-3.181)**
SHM2 -1.015 -0.955 -0.915 -0.723 -0.562 -0.583 -0.444 -0.221 -0.024 (-1.406) (-1.586) (-1.391) (-1.140) (-1.015) (-1.067) (-0.894) (-0.770) (-0.563) SHM3 -0.596 -0.910 -0.931 -0.863 -0.525 -0.465 0.014 0.062 0.099
(0.398) (-0.131) (-0.120) (-0.562) (-0.401) (-0.563) (0.662) (0.662) (0.715) SHM4 -0.871 -1.524 -2.072 -1.976 -1.600 -1.549 -1.357 -0.891 -0.674
(0.078) (-0.627) (-2.006)* (-2.748)** (-2.344)* (-2.282)* (-1.936) (-0.924) (-1.158) SHM5 -0.637 -1.132 -1.577 -1.408 -1.064 -1.069 -0.843 -0.872 -0.696 (Heavy
selling) (-0.062) (-1.090) (-1.384) (-2.538)* (-2.070)* (-2.088)* (-1.727) (-2.070)* (-1.847) B5-S5 4.255 4.402 4.225 4.230 4.088 4.102 3.906 4.078 3.598
(2.951)** (3.523)** (2.357)* (2.553)* (2.899)** (2.725)** (2.456)* (2.338)* (1.839) (B1~B5) - 5.067 5.033 4.829 4.793 4.620 4.557 4.313 4.091 3.888 (S1~S5) (6.872)** (6.533)** (7.168)** (6.988)** (7.032)** (7.242)** (6.563)** (6.124)** (5.893)**
Note 1.BHM1 (BHM5) contains stocks that slightly (strongly) buy in herd. Similarly, SHM1 (SHM5) contains stocks that slightly (strongly) sell in herd.
2. B5-S5 represents the abnormal return of BHM5 portfolio minus the abnormal return of SHM5 portfolio.
3. (B1~B5)-(S1~S5) represents abnormal returns that equally weights long position in BHM1 through BHM5 and equally weights short positions in SHM1 through SHM5.
4. T is average 51 monthly abnormal returns starting on January 2001 and reinvest until March 2005.
5. The values in parentheses are t-statistics. On the other hand, (*) and (**) are denoted significant at 5%
and 1% level, respectively.
7. Conclusions
This paper extends traditional binomial distribution to trinomial distribution, including buy, sell and hold, to investigate the manager’s herding behavior. We analyze the herding behavior by grouping the sample into several subgroups that are ranked by firm size, stock returns and mutual fund performance. Finally, we analyze whether the manager’s herding behavior stabilize or destabilize stock market.
For the first empirical result, we find significant herding behavior of managers from 2001 to 2005 in Taiwan, especially for buy-herding. Since the economy state enter a boom, the buy-herding is more significant than sell-herding for equity funds. Second, the herding statistics estimated by trinomial distribution are smaller than those statistics estimated by binomial distribution as a result of disregarding another trade direction - hold. Thus, we infer that herding statistics under binomial distribution may overestimate managers’ herding behavior. Third, for small firms, managers will follow other managers’ trading strategy because small firms disclose less information and stocks are usually illiquidity. Fourth, herding on the buy-side is strongest in high current-return stocks and herding on the sell-side is strongest in low current-return stocks. In other words, managers adopt positive-feedback trading strategy to buy past winners and sell past losers.
However, there are no significant relationship between past stock returns and herding behavior. Fifth, for funds with worse performance, managers have more significant herding behavior due to the reputation and sharing-the-blame.
Finally, we form 10 portfolios by grouping stocks in the buy- and sell-herding and they are ranked by BHM and SHM. We find that there are significantly different abnormal returns between stock in buy-herding subgroups and sell-herding subgroups. However, these differences will decrease gradually. Therefore, managers’ herding behavior doesn’t destabilize stock market. In contrast, the manager’s herding behavior can increase the speed of price adjustment to a reasonable price.
The trade direction, hold, is always ignored in previous studies, which only consider two trade directions: buy and sell. This paper develops a test of herding to test the manager’s herding behavior by postulating and proving seven hypotheses under trinomial distribution, including three trade directions: buy, sell and hold. Consequently, we hope that this paper can help investors to understand mutual funds market more deeply.
Acknowledgements
The authors would like to thank the editor, anonymous referees, Professor Yi-Chun Huang and Ying-Feng Chen for their helpful comments, suggestions and corrections in revising this paper.
8. Reference
Banerjee, A. V. (1992), “A Simple Model of Herd Behavior,” Quarterly Journal
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