Institutional Investors and Short-Term Return Reversals

Transcription

1 Institutional Investors and Short-Term Return Reversals Qianqiu Liu, Ghon Rhee, and Hong Vo * This Draft: July 2012 * All authors are at Department of Financial Economics and Institutions, Shidler College of Business, University of Hawaii at Manoa, 2404 Maile Way, Honolulu, Hawaii, qianqiu@hawaii.edu (Liu); rheesg@hawaii.edu (Rhee); hongxv@hawaii.edu (Vo).

2 Institutional Investors and Short-Term Return Reversals Abstract We examine the impact of firm size on return reversals using weekly returns from January 1980 to December We find that return reversals are greater for large-firm stocks than for smallfirm stocks in the first half of the study period. However, the firm size effect on return reversals disappears in the second half of the study period. The difference in the intensity of return reversals between large- and small-firms is dictated by the market conditions. Return reversals of large-firm stocks are greater during the up market period than down market period. In contrast, there is no significant difference for small-firm stocks between up and down markets. A high institutional demand for large-firm stocks results in high demand for immediacy as well as strong return reversals for these stocks in the first half of the study period. After institutions shifted their preferences to stocks of smaller firms since the mid-1990s, return reversals for large-firm stocks became insignificantly different from small-size firms in the second half of the study period.

3 I. Introduction The short-term return reversal in the stock market has been a well established phenomena for more than 40 years and proven to be robust and of economic significance. Jegadeesh (1990), for example, documents profits of 2.49% per month over the period from a reversal strategy that buys loser and sells winner decile portfolios based on stock returns in the prior month and holds them for the next month. Similarly, Lehmann (1990) finds that the short-term contrarian strategy based on weekly stock returns generates 1.79% per week and positive profits in around 90% of the holding weeks from 1962 to In this paper we aim to advance our understanding of short-term reversal profits by investigating the pattern of serial correlation across different size groups with weekly returns. Jegadeesh (1990) shows stronger return reversals for small-firm stocks with monthly returns. This finding has been confirmed with the most recent data in the literature, such as Huang, Liu, Rhee, and Zhang (2010) and Da, Liu, and Schaumburg (2012). Contrary to the evidence from monthly returns, we document that large size stocks has stronger return reversals with the weekly returns from January 1980 to December This finding seems counterintuitive because large-firm stocks are very liquid, with low trading costs, and widely traded by institutions. However, it is consistent with the evidence first reported in Lehmann (1990) with the sample between 1962 and 1986, and recently in Gutierrez Jr. and Kelley (2008), where they find larger weekly return reversals for large stocks and stocks with high institutional ownership, high volatility, and high analyst coverage for the period from 1983 through The weekly returns of these stocks also have less momentum in the remaining of the year. 1

4 To further examine this pattern, we divide our sample into two equal-length subperiods. We find that return reversals are greater for large-firm stocks than for small-firm stocks in the first half of the sample, i.e, from January 1980 to December However, this difference disappears in the second half of the sample between January 1996 and December The difference in the intensity of return reversals is related to the market condition. We classify the markets as up and down markets depending on the market performance. When the market is up, we find that return reversals for large-firm stocks are much stronger than in down markets. The magnitude is also significantly greater than that of small-firm stocks in up markets. In contrast, the reversal difference is insignificant between up and down markets for small-firm stocks. Although return reversals for large-firm stocks are greater than for small-firm stocks in the first half of the sample, they are short-lived. The reversal for large firms does not last for more than two weeks on average. On the contrary, the duration for small size stocks is much longer it persists for one month. This also explains why the return reversal is much weaker on the large-firm stocks at the monthly frequency since 1980s. Our findings are robust when we exclude January and S&P 500 stocks from our sample and closely related to a large literature that examines the relation between institution investors and stock returns. Banz (1981) finds that adjusted returns of small-firm stocks, on average, are higher than those of large-firm stocks listed on NYSE for the period 1936 though However, Gompers and Metrick (2001) find the opposite evidence for common stocks listed on NYSE, AMEX, and NASDAQ from 1980 to According to them, institutional investors nearly doubled their shares of the stock market during this period. This compositional shift increases the demand for the stocks of large firms and decreases demand for the stocks of small firms, which explains the disappearance of the small-company stock premium partially. Further 2

5 analysis by Yan and Zhang (2009) indicates that the positive relation between institutional ownership and future stock returns is driven by short-term institutions, defined based on the portfolio turnover in the previous year. These short-term institutions are better informed and they trade actively to exploit their informational advantage. When institutions have private information about certain large-firm stocks, they will hurry up to trade immediately through aggressive orders rather than wait through limit orders because it is risky for them to wait (Grossman and Miller, 1988). To do so, institutions may pay some compensation to market markers or other liquidity providers to obtain these stocks earlier than others. Only investors with better information can trade the stocks of their preference when they initiate early. Institutions with less, or even no informational advantages or those coming later have to pay higher compensation (Griffiths, Smith, Turnbull, and White, 2000). A very strong continuous demand for large-firm stocks in a short time may push their value to depart from fundamentals, which will be followed by price reversals. However, large-firm stocks have low asymmetric information and are widely held by market markers as well as institutional investors. Hence, the reversals for large-firm stocks, if exist, last for a very short time. Institutions have shifted their preferences toward smaller, riskier securities since 1990s (Bennett, Sias, and Starks, 2003). This is also confirmed in Blume and Keim (2011), where they find that institutions, especially hedge funds, have increased their holdings of small stocks and decreased their holdings of large stocks over the period of 1980 through Their evidence indicates that although institutional investors have rapidly increased their percentage holdings of stocks over time, they now underweight the largest stocks and overweight the smallest stocks relative to their market weights. There are two possible reasons for the shift in institutional preferences: first, the demand shocks of the institutions have driven the valuations of large-firm 3

6 stocks too high and therefore make them unattractive; second, the increased institutionalization of large firm stocks have resulted in fewer opportunities for institutional investors to exploit their informational advantages. In contrast, stocks of smaller firms provide more opportunities for institutions to take advantage of their private information. We conduct further portfolio analysis and time-series regressions to show the important role of institutional holdings in explaining the significant reversal difference in the first half of the study period and the insignificance in the second half. The remainder of this study is organized as follows. In Section II we provide the details of the data sets used in our empirical analysis. Section III compares the return reversals between large-size stocks and small-size stocks from 1980 to We link these empirical findings to the institutional demand for large and small firm stocks in section IV. Section V presents our conclusions. II. Data Our data include NYSE, AMEX, and NASDAQ common stock daily returns and monthly returns from January 1980 to December We obtain daily and monthly returns data from the Center for Research in Security Prices (CRSP) and book values of individual stocks from COMPUSTAT. We use the daily value-weighted index return from CRSP as the market return. Weekly returns are calculated by compounding the daily returns from Thursday this week to Wednesday next week. 1 To mitigate bid-ask spread bias, our portfolio formation period is based on the four-day returns between the previous Thursday to this Tuesday, as in Lehman 1 We also construct weekly returns from Wednesday this week to Tuesday next week. Our empirical results are robust to the different methods to construct weekly returns. 4

7 (1990) and Avramov, Chordia, and Goyal (2006). We only include individual stocks with at least three years of data in the full sample. In addition, we exclude stocks with prices less than $5 at the end of each week. Our institution holding data is from the Thomson Financial Institutional 13F Ownership database. According to a 1978 amendment to the Securities and Exchange Act of 1934, all institutions are required to report their holdings to the Securities and Exchange Commission (SEC) if they have greater than $100 million of securities under discretionary management. 2 Holdings are reported quarterly on the SEC s form 13-F at the end of each March, June, September, and December back to 1980, where all common-stock positions greater than 10,000 shares or $200,000 must be disclosed. Our data include the quarterly reports from the first quarter of 1980 to the final quarter of Table I provides the summary statistics of our data set. Over the sample period from 1980 to 2011, the weekly return of the market index is 0.22%, which is equivalent to 11.44% at the annual level. The first half of the sample has a weekly return of 0.29%, which is 80% higher than that in the second half (0.16%). The stock market has a rapid growth during the sample period, with the market capitalization of all stocks 4.6 times in the second half ($12,719 billion) compared to the first half ($2,762 billion). Consistent with the trend in Gompers and Metrick (2001) that essentially overlaps our first half of the sample period, both the number of institutions with equity holdings and the percent of market owned by all institutions continue to grow in the second half of the sample period holdings. The number of institutions increases from 835 to 2121; the percent of market owned by these institutions increase substantially from less 2 Following Gompers and Metrick (2001), we also adjust the $100 million cutoff with the market index return. Our empirical results are qualitatively similar. These results are available upon request. 5

8 than 39.18% to 59.23%. The market capitalizations of the institution holdings have increased almost by seven folds, from $1,151 billion to $7,632 billion. Panel A of Figure 1 depicts the dynamics of the percentage of market capitalization owned by institutions. The percentage has been increasing over the sample period, except in the recent financial crisis. At the end of 2011, institutions hold around two-thirds of the total market cap. Panel B of Figure 1 shows that the fraction of shares outstanding held by institutions has been around 60% to 70% since 1990s. There is a sudden jump in 2004, when the fraction increases to about 80%. This pattern persists until the recent financial crisis. It dropped to below 60%, and then bounced back to about 70% at the end of the sample period. III. Short-Term Return Reversals The empirical regularity that individual stock returns exhibit negative serial correlation over a short horizon has been well known for a long time. Jegadeesh (1990) finds that the negative first-order correlation in monthly stock returns is highly significant, and he reports profits of about 2.49% per month from a contrarian strategy that buys loser stocks and sells winner stocks based on their formation month returns and holds them one month. Similarly, Lehmann (1990) finds that the short-term contrarian strategy based on a stock s one-week return generates 1.79% per week, and positive profits in 90% of the holding weeks. These findings are generally regarded as evidence of short-term return reversals of individual stocks. 3 3 In existing literature, there are different explanations for the source of short-term return reversals. Grossman and Miller (1988), Kaul and Nimalendran (1990), Conrad, Kaul and Nimalendran (1991) and Jegadeesh and Titman (1995a) argue that the return reversals are caused by market microstructure phenomena such as bid-ask spread or inventory effect. Lo and MacKinlay (1990) suggests that a size-dependent lead-lag market microstructure is an important source of contrarian profits. Jegadeesh and Titman (1995b) show that most of contrarian profits are due to stock price overreaction to firm-specific information instead of the lead-lag effect. 6

9 However, there is some difference in the pattern of return reversals with these two data frequencies. Jegadeesh (1990) shows stronger return reversals for small-firm stocks with monthly returns, which are also confirmed in the more recent studies, such as Huang, Liu, Rhee, and Zhang (2010) and Da, Liu, and Schaumburg (2012). In contrast, Lehmann (1990) document that the largest winners and losers experienced the largest subsequent reversals (pp. 19) with the weekly returns from 1962 to This finding is consistent with the evidence in Gutierrez Jr. and Kelley (2008), where they find larger return reversals in the first holding week and less momentum in the remaining of the year for large stocks. The difference seems puzzling, but has not received enough attention in the literature. We now focus on this issue in our empirical analysis. 3.1.Return reversals within size quintiles We examine the intensity of return reversals of weekly returns within different size groups from January 1980 to December Individual stocks are sorted into quintiles based on their market capitalizations at the end of the previous June, where NYSE breakpoints are adopted. Following the methodology of Bennett, Sias, and Starks (2003) and Sias (2004), we standardize both the independent and dependent variables, and compute the average β from the weekly cross-sectional Fama and Macbeth (1973) regressions within each size-based quintile: 4 4 We standardize all variables such that they have the mean value of zero and standard deviation of one within each size quintile per week. Therefore the intercept in Equation (1) is zero. The standardized regression coefficients are scale-free so that we can directly compare them across time. Our empirical results based on raw data are qualitatively similar. 7

10 (1) The intensity of return reversal is measured by the regression coefficient, β. 5 We also report the average of the difference between β of stocks in the largest size quintile and that of smallest size quintile. The t-statistics are computed using Newey-West (1987) correction method. Panel A of Table II shows strong evidence of return reversals as β is significant at the 1% level among all quintiles for the whole period between 1980 and The return reversal for large-firm stocks is It is the strongest as the absolute value is the largest among the size quintiles. The return reversal for small-firm stocks is , which is the weakest. The difference in the return reversals between these two groups is and it is significant at the 1% level. We divide the whole sample period into two equal-length subperiods: and In the first subperiod, the return reversals for small-firm and large-firm stocks are and , respectively. The difference in return reversals between the two groups is and the return reversal of the large-firm stocks is significantly stronger than that of the small stocks at the 1% level. The return reversal declined in the second period for all the size groups, except for the smallest size quintile. The return reversal for small-firm stocks increases from to , while the return reversal for large-firm stocks declines from to This decline is significant at the 1% level. Although the return reversal for large-firm stocks is still greater than that of small-firm stocks in the second period , the 5 Under the assumption that the independent variable is unrelated with the residual in Equation (1), the regression coefficient β is equal to the first-order autocorrelation of individual stocks. Since it is negative in most cases, we use the magnitude of β to measure the intensity of return reversal hereafter. 8

11 difference does not show statistical significance any longer. Therefore, larger return reversals for large-firm stocks in the whole period are driven by the first period from 1980 to In Panels B, C, and D of Table II, we examine the performance of the size quintiles in the next 2-4 weeks after their formation. The evidence indicates that return reversals are very shortterm, especially for large-firm stocks. Although the coefficient is still significantly negative in the second week for these large-firm stocks in the full sample, the intensity is much weaker ( ) compared to that in the first week ( ). The return reversal disappears in the third and fourth weeks as the coefficients are positive in the full sample period and the two subperiods. The only exception is the fourth week in the first subperiod between 1981 and 1996, in which the return reversal for large stocks exists, but indistinguishable from zero statistically. In contrast, return reversals for the small-firm stocks last much longer. They are significant until the third week after the portfolio formation in the full sample and the first subperiod Return reversals still exist for small stocks in the fourth week although they are not significant. In the first period and the whole period, return reversals are larger for small-firm stocks than for large-firm stocks in the second until the fourth week. In short, return reversals for large-firm stocks almost disappear after holding for two weeks and hence are short-lived, while return reversals for small-firm stocks are stronger than those of large-firm stocks for weeks 2-4 after the portfolio formation. The evidence in Table II also explains why returns reversals of large-firm stocks are weaker than those of the small-firm stocks at the monthly level. We examine return reversals for size quintiles using monthly data in Table III. Table III shows that the coefficients of monthly return reversals for large-firm stocks are , , and in the periods , , and , respectively. None of them is significant. However, monthly return 9

12 reversals for stocks from quintiles 1-4 are all significant at the 1% level in the first period and the whole period, except quintile 4 in the full sample period, which is also significant at the 5% level. The intensity of monthly return reversals deceases with size. Therefore, the difference of the return reversals between small and large-firm stocks is the largest, and it is significant at the 1% level in the full and first period. In the most recent sample, the difference of monthly return reversals between these two size quintiles is smaller and significant at the 10% level. In Table II, we have shown that return reversals for large-firm stocks are stronger than those of the small-firm stocks based on weekly returns, especially in the first subperiod from 1980 to However, return reversals for large-firm stocks are short-lived and mainly exist in the first week after portfolio formation. As the weekly return reversals for small-firm stocks last longer, monthly return reversals are larger for small-firm stocks. This pattern exists in both of the subperiods, and is stronger in the first half of our sample period. 3.2.Robustness of weekly return reversals Jegadeesh (1990) finds that the monthly return reversal is stronger in the month of January, especially for small-size stocks. As a robustness check, we examine the weekly return reversals after removing January from the sample in Table IV. The results are quite close to those in Table II. In general, we find that the return reversal of the large stocks is significantly stronger than that of the small stocks at the 1% level in the first half of the sample; the return reversal for large-firm stocks is still greater in the second period from 1996 to 2011, but the difference is no longer significant. As in Table II, larger return reversals for large stocks in the 10

13 full sample period are driven by the first period from 1980 to 1995, even after January is excluded. The evidence also shows that return reversals are very short-term, especially for large stocks. They disappear in the third and fourth weeks as the coefficients are usually positive. Return reversals are larger for small stocks than for large stocks in the second until the fourth week. They are significant until the third week. Return reversals still exist for small stocks in the fourth week although they are not significant. Da and Schaumburg (2011) construct a contrarian strategy on S&P 500 stocks and show that the resulting profits are economically and statistically significant. As institutions, especially index funds, hold very large ratios of S&P 500 stocks, we redo the exercise in Table II with these stocks excluded from the largest size quintile. The results reported in Table V are consistent with our earlier findings. In general, we document stronger return reversal of large stocks than that of small stocks in the first week. The difference is extremely significant in the first half of the sample, but weakens and becomes insignificant in the second period from 1996 to We also confirm that return reversals are larger for small stocks in the third and fourth weeks as they disappear for large stocks in these horizons. There is one different pattern though when S&P 500 stocks are removed from the sample. The return reversal of large stocks is stronger than that of small stocks in the second week of the portfolio holding period. For example, the coefficients of monthly return reversals for large-firm stocks are , , and in the full sample, and the two subperiods, respectively, while the corresponding numbers for small stocks are , , and However, the difference is not significant at the conventional confidence intervals. 11

14 In sum, these robustness tests demonstrate that return reversals are very short-term, especially for large stocks. They are stronger in the first week, but weaker than that of small stocks in the second half of a month Return reversals in different market states Several studies of return anomalies examine lead-lag effects (McQueen, Pinegar, and Thorley, 1996 and Hameed and Kusnadi, 2004) and momentum (Cooper, Gutierrez Jr., and Hameed, 2004) in different market states. They find that cross-autocorrelations and momentum profits are asymmetric in different market states. In this study, we also examine whether return reversals are asymmetric for small- and large-firm stocks in different market states. In Table VI, we compare return reversals of large- and small-firm stocks in up and down market states in the full sample and the two subperiods, and We define market states according to the sign of the return on the value-weighted market return at the portfolio formation week: UP means that market return is nonnegative; DOWN means that market return is negative. We examine return reversals in the UP and DOWN markets for both large and small-firm stocks to see where the return reversals come from. We run Fama-MacBeth (1973) cross-sectional regressions as in Equation (1) for the size quintiles in the UP and DOWN states. Panel A of Table VI shows that in the first holding week return reversals for large-firm stocks in up markets are much stronger than those in down markets, while the reversals are similar for small stocks in both up and down markets. For 6 We also investigate other settings, such as excluding NASDAQ stocks, or removing the top 1% and bottom 1% stocks in terms of their market capitalization from our sample. The results from these additional tests are consistent what we document in Table II. 12

15 example, during the sample period from 1980 to 2011, return reversals for large-firm stocks in the up markets are , while in down markets they are only This difference is highly significant at the 1% level. In fact, we find stronger reversals in up markets than in down markets for all size quintile portfolios. It is only in the smallest size quintile where the difference of the reversal intensity is insignificant between up and down markets. We also note that the reversal difference between large and small firms only happens in up markets since the difference is insignificant in the down markets. Similar patterns also exist in the two half sample periods; return reversals in up markets are much stronger than in down markets, especially for large stocks. There is a slight difference in the first sample period from 1980 to 1995, when return reversals of large stocks are also significant higher than those of small stocks in the down markets. However, the difference ( ) is still much smaller when compared with the up market ( ). The evidence in the two half sample periods shows that with the time the reversal is weaker for all size quintiles except the smallest quintile, as the magnitudes of reversals in the four larger size quintiles are much smaller in the second half of the sample period between 1996 and The reversals for small stocks are similar in the two subperiods; their difference is insignificant in both up and down markets. Panel B of Table VI shows that the reversal difference is much smaller and insignificant between the up and down markets in the second holding week. The difference between large and small stocks is insignificant either in both up and down markets although return reversals of small stocks are still significant in the second week no matter that the market is up or down in the formation week, the magnitude of return reversal for large stocks drops a lot in the second week, which reduces the reversal difference between these two size quintiles. This is also consistent with our findings in Table II. 13

16 In sum, our results show stronger return reversals for large-firm stocks in up markets than small-firm stocks, especially in the first period. The difference in down markets is much smaller. The reversal in the second period is much weaker for large stocks, which also shorten the distance from the reversal of small stocks. These findings combined together indicate that the extremely strong reversal for large stocks in the up markets of the first period is a main root of the finding documented in the previous subsection, i.e., return reversals are larger for large-firm stocks than for small-firm stocks in the first subperiod, as well as in the whole period. IV. Return Reversals and Institutional Investors We have documented that return reversals are stronger for large-firm stocks than for small-firm stocks from 1980 to The difference is no longer significant since mid-1990s. Our findings are closely related to the literature that examines the relation between institutional investors and stock returns. In their sample from 1980 to 1996, Gompers and Metrick (2001) find that institutional investors nearly doubled their shares of the stock market, and this compositional shift increases the demand for the stocks of large firms and decreases demand for the stocks of small firms. They argue that the demand of institutional investors causes the disappearance of the size premium since 1980s. Yan and Zhang (2009) further show that the positive relation between institutional ownership and future stock returns is driven by short-term institutions, defined based on the portfolio turnover in the previous year. These short-term institutions are better informed and they trade actively to exploit their informational advantage. Panel A of Table VII shows that institutions continue to increase their percentage holdings of stocks since 1990s. In the first sample period, 41.98% of large stocks are owned by institutional investors, and the ratio of institutional holdings for large stocks increases to 59.08% 14

17 in the second period. This represents a 14.3% increase. The change of the percentage holdings of small stocks is more remarkable: institutions own 21.91% of the small stocks from 1980 to 1995, and the percentage increases to 49.06% from 1996 to Compared with the first period, the percentage holdings increases by 224% in the second half of the sample period. Although the average percentage of institution holdings for large stocks is still higher than for small stocks from 1996 to 2011, Panel A of Figure 2 shows that small stocks have caught up with large stocks in terms of institution holdings in the last five years since More importantly, we find that large stocks are overweighted in the first sample period, but underweighted in the second period. This is shown in Panel B of Table VII, where we calculate the weight of a stock as the difference between its weight in institutions relative to its market weight following Blume and Keim (2011). In the sample period from 1980 to 1995, the average weight for large stocks is 2.89%. It changes to be negative at -1.89% in the second period from 1996 to In contrast, the average weight for small stocks changes from -2.05% to -0.52% during these two subperiods. These findings are consistent with Bennett, Sias, and Starks (2003) and Blume and Keim (2011), which report that institutions have shifted their preferences toward smaller, riskier securities since 1990s. Panel B of Figure 2 illustrates dynamics of institutional weights relative to market weights for size quintiles. It is clear to see the relative weight for large stocks have been declining, from 8% in 1980 to -3% in The weight for small stocks has been increasing gradually over time, from -3% to close to zero at the end of the sample period. Their evidence indicates that although institutional investors have rapidly increased their percentage holdings of stocks over time, they now underweight the largest stocks and overweight the smallest stocks relative to their market weights. There are two possible reasons for the shift in institutional preferences: first, the demand shocks of the institutions have driven the valuations 15

18 of large-firm stocks too high and therefore make them unattractive; second, the increased institutionalization of large firm stocks have resulted in fewer opportunities for institutional investors to exploit their informational advantages. In contrast, stocks of smaller firms provide more opportunities for institutions to take advantage of their private information. Very large trades (block trades) of institutions may be over the supply capacity of any market marker (Grossman and Miller, 1988) and need long trading durations (Keim and Madhavan, 1995). Chan and Lakonishok (1995) find that over a half of institutions packages in their sample need at least four days to complete. Thus, if the demand curve for stocks is not perfectly elastic and institutions trade large positions on stocks, share prices will change. Sias, Starks, and Titman (2006) show that institutional trading includes both temporary liquidity effects, which are reversed later and permanent effects, in which the share price will continue. Thus, the price change, when institutions trade large positions, includes both the temporary price effect and the permanent price effect. The temporary price effect of large trades of institutions comes from the demand for immediacy. Kraus and Stoll (1972) and Grossman and Miller (1988) argue that in the incompletely competitive world, the temporary price effect may exist in the short-run even there exist both willing buyers and willing sellers because they have to pay for the market markers and other liquidity suppliers a price concession when they want to sell or a price premium when they want to buy immediately Two-way dependent sorting: cross-sectional evidence 7 Refer to Llorente et al. (2002), Kaniel, Saar, and Titman (2008), and Campbell, Ramdorai, and Schwartz (2009). 16

19 To investigate whether institution holdings play an important role in short-term reversals, we conduct the following two-way sorting in Table VIII. We sort the stocks based on their number of institutional holdings, then within each quintile further sort stocks into quintiles based on the firm size. According to Akins, Ng, and Verdi (2012), the number of institutional investor ownership can be used as a proxy for competition, which measures the rivalry among informed investors to acquire and trade profitably on private information in the facing of information asymmetry. They find that the pricing of information asymmetry decreases when there is more competition. The competition also leads to high demand for immediacy, which causes short-term reversals. Table VIII indicates that after controlling for the number of institutions, there is no return reversal intensity difference between large-firm stocks and small-firm stocks in most of the cases. Especially in the portfolio with high number of institutions, we document much stronger return reversals than in other subgroups. However, the reversal difference between large and small stocks is insignificant in this group in the full sample and the first period. The average reversal difference is insignificant either across the five institutional holdings portfolios in the full sample and two subperiods. 4.2 Time-series regressions Institutions may have different levels of demand for immediacy in different market states. According to Brennan et al. (2011), institutions are more likely to have higher demand for immediacy with large sells than large buys in both up and down markets. 8 They use monthly data and confirm their hypothesis. However, Chiyachantana et al. (2004) find that because institutions 8 Large sells ( large buys ) means that institutions buy (sell) in large quantity and hence may affect the share price. 17

20 trade large positions and pay higher compensation for the other trading side when they trade on the same side of the market, what institutions buy in up markets and what institutions sell in down markets have stronger demand for immediacy and hence may have larger reversals of returns. Since institutions that overweigh stocks have higher demand of immediacy, we calculate the difference between the percentage of institutions that overweigh large stocks and small stocks (DIO). Figure 3 shows that the fraction of institutions that overweigh large stocks is very high at 62% in the beginning of the sample; it has been declining and is around 45% at the end of the sample. In contrast, the percentage of institutions that overweigh small stocks has been increasing. It has increased from 15% to 35% over the full sample period 1980 to With this factor to proxy the time-variation of institutional holdings, we run the following time-series regressions to investigate whether the time-variation of reversal difference between large-firm stocks and small-firm stocks can be explained by the difference of institutional holdings between these size portfolios over time: (2) where week t, are the average reversal coefficients of the largest and smallest size quintiles at is the difference between the percentage of institutions that overweigh larges stocks and small stocks as defined above, includes systematic factors, such as the market, size and book-to-market factors as in Fama and French (1993) and momentum factor as in Carhart (1997). Table IX shows that DIO is highly significant in all the specifications in the full sample and the first half of sample period when we have documented significant reversal difference 18

21 between large and small stocks. The coefficient on DIO is also positive in these periods, which indicates that the reversal of large stocks is much higher than that of small stocks when there are more institutions that overweigh large stocks than small stocks. This is exactly the pattern we have found in Tables II and VII. With this factor to explain the time-variation institutional holdings, the size factor is not significant. Although DIO is not significant in the second half of sample period, it is in a period when the reversal difference is insignificant between large and small stocks. This is also the time when DIO is much smaller. In summary, we have provide portfolio and regression analyses to show that institutions contribute to return reversals. Institutions hold much more large stocks than small stocks in the period 1980 to 1995, when we document much stronger return reversals for large-firm stocks. There is a shift of preferences to hold small-firm stocks by institutions in the second period, which may explain the insignificant reversal difference from 1996 to V Conclusions We examine return reversals in size quintiles with weekly returns from January 1980 to December The sample is divided into two equal-length subperiods. We find that return reversals are greater for large-firm stocks than for small-firm stocks in the first half of the sample, i.e, from January 1980 to December However, this difference disappears in the second half of the sample between January 1996 and December The difference in the intensity of return reversals is related to the market condition. We classify the markets as up and down markets depending on the market return in the previous week. When the market is up, we find that return reversals for large-firm stocks are significantly stronger than in down markets, 19

22 and they are also much stronger than those of small stocks in up markets. In contrast, there is no significant difference between return reversals for large-firm stocks and small-firm stocks in down markets. Although return reversals for large-firm stocks are greater than for small-firm stocks in the first half of the sample, they are short-lived. The reversal for large firms does not last for more than two weeks on average. On the contrary, the duration for small size stocks is much longer it persists for one month. This also explains why the return reversal is much weaker for large-firm stocks at the monthly frequency. We argue that high institutional demand for large-firm stocks may result in high demand for immediacy as well as return reversals for these stocks in the period 1980 though mid 1990s. Institutions shift their preferences to stocks of smaller firms since then. The market efficiency has improved and the degree of market efficiency is greater for large-firm stocks than smallfirm stocks (Chordia, Roll, and Subrahmanyam, 2008). Hence, institutions may demand less and are ready to pay less for demand for immediacy for large-firm stocks. As a result, return reversals for large-firm stocks are smaller since the mid-1990s. Understanding the causes of short-term return reversal and the role of institutional investors have important implications for empirical asset pricing tests, and more generally for the limits of market efficiency. Our work sheds new light and helps researchers better understand this anomaly and its relation with institutional ownership. 20

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27 Table I Summary Statistics This table reports the summary statistics of our sample data set. Our sample period is from January 1980 to December We construct weekly returns for this period, and report the mean, median, standard deviation of the variables for the full sample and two subsamples form 1980 to 1995, and 1996 to The variables include: weekly returns of the market index (in percentage), the total market capitalizations (in billions of dollars), the numbers of institutional investors, the total number of stocks with institutional holdings, fraction of shares outstanding held by institutions, the market capitalizations of all institutional holdings, and the percent of market capitalization by institutional holdings relative to the total market capitalization (%) Mean Median Standard deviation Mean Median Standard deviation Mean Median Standard deviation Weekly market returns (%) Total market cap (Bil.) Number of Institutions Number of stocks institutions hold Fraction of shares outstanding owned institutions (%) Market Cap of institutional holding (Bil.) Percent of market capitalization by institutional holdings (%)