Liquidity Variation and the Cross-Section of Stock Returns *

Transcription

1 Liquidity Variation and the Cross-Section of Stock Returns * Fangjian Fu Singapore Management University Wenjin Kang National University of Singapore Yuping Shao National University of Singapore Abstract Stock liquidity varies substantially over time. A significant decrease in liquidity is often followed by a sizable rebound, and vice versa. The month-to-month liquidity change predicts the cross-sectional stock returns in the following month. Caeteris paribus, a liquidity decrease predicts a low return and a liquidity increase predicts a high return. The results are not explained by other cross-sectional return determinants including the liquidity level. The results are consistent with the mean-reverting nature of liquidity and its variation being priced. A liquidity reduction predicts an expected liquidity increase and thus a lower expected return, and vice versa. Our research suggests liquidity variation as an important factor of asset pricing. Its effect is independent from the widely documented liquidity level effect. JEL Classification: G12 Keywords: Liquidity; Time-varying liquidity; Cross-sectional stock returns * Fangjian Fu, Lee Kong Chian School of Business, Singapore Management University, fjfu@smu.edu.sg, Phone: (+65) ; Wenjin Kang, National University of Singapore, bizkwj@nus.edu.sg; Yuping Shao, National University of Singapore, yuping.shao@nus.edu.sg. We thank Michael Brennan, Joey Engelberg, Allaudeen Hameed, and Tarun Chordia for their helpful comments.

2 1. Introduction Liquidity is important for asset pricing. Investors demand for compensation for holding illiquid assets caeteris paribus, expected returns on illiquid assets are higher than those on liquid assets. A number of studies have shown that the level of liquidity is priced in the cross-section of stock returns [e.g., Amihud and Mendelson (1986); Brennan and Subrahmanyam (1996); Datar, Naik, and Radcliffe (1998); Amihud (2002)]. However, the liquidity of a typical stock does not remain the same over time, and in fact, it is fairly volatile. For example, the average change in monthly liquidity for our sample stocks is as high as 45%. Although volatile, the time-series of liquidity is not random. The first-order autocorrelation of monthly liquidity changes is on average across our sample stocks. In other words, a typical stock s liquidity follows a mean-reverting process a decrease in liquidity is often followed by a sizable rebound and an increase in liquidity is followed by a drop. If liquidity is priced in stock returns, so should be the change in liquidity. If a stock incurs a significant reduction in liquidity in the previous month, according to the mean-reverting nature of liquidity, investors expect liquidity to improve in the current month. Due to the expected liquidity improvement, caeteris paribus, investors would offer a high price, or equivalently, demand a low return on this stock over the current month. The opposite is also true. If a stock experiences a significant liquidity improvement over the previous month, investors expect its liquidity to drop and thus, all else being equal, demand a high return for holding the stock over the current month. Our study provides strong supporting evidence for this liquidity change hypothesis. In each month from July 1963 to December 2010, we sort stocks listed on the NYSE and AMEX into deciles by their liquidity change in the previous month, and compute the current month return of the hedging portfolio, that is, long the decile of stocks that have experienced the largest liquidity improvement and short the decile of stocks that have incurred the largest liquidity reductions. The equal-weighted monthly return is on average 0.84% (0.56% if value-weighted) and statistically significant. The large hedging returns are not specific to certain sample periods and not explained by the Fama-French, momentum, and liquidity factors. In the standard Fama-MacBeth regressions of monthly stock returns, we control for other 1

3 determinants of cross-sectional returns, including size, book-to-market, momentum, and even the liquidity level, liquidity change in the previous month still survives as a significant predictor for the current month returns. The findings are robust to alternative model specifications, different measures of liquidity, and NASDAQ stocks. Our findings confirm the important role of liquidity in the cross-section of stock returns. We add to the literature by differentiating the persistent and transient components of liquidity and highlighting the independent effect of liquidity change (the transient component) on expected returns, apart from the widely documented effect of liquidity level (the persistent component). Our research calls for a better understanding of stock liquidity, such as the nature and causes, to improve our understanding of asset price dynamics. In an influential study, Gervais, Kaniel, and Mingelgrin (2001) find that stocks experiencing unusually high trading volume over a day tend to appreciate in the following month. They name this high-volume return premium and argue it consistent with the visibility hypothesis. A sudden increase in trading volume improves the stock s visibility to investors and an enlarged investor base increases the stock price. Their explanation depends on the assumptions of investor incomplete information (Merton, 1987) and short-sale constraint (Miller, 1977). Our study differs from theirs in two important aspects. First, the empirical findings of these two studies are distinct. They compare individual stock s daily trading volume against its past 50-day average and examine the top and bottom 10% outliers that experience trading volume shocks. Their sampling and design of research tend to capture the impact of a small number of sudden and significant changes in trading volume, while we focus on the more general variation in liquidity. Some of our liquidity measures, such as the bid-ask spread and the frequency of zero returns, are not related to stock visibility. More importantly, the visibility hypothesis does not seem able to explain our findings. First, we find similar results based on liquidity measures that are not related to stock visibility. Second, the visibility hypothesis has asymmetric implications because visibility appears a one-way traffic. A sudden and large increase in trading volume or liquidity attracts more investors attention on this stock and makes it visible to more investors. If the stock is short-sale constrained, its price reflects the view of the most optimistic 2

4 investors. As a result, a stock becoming visible to more investors leads to more purchases and a higher stock price. This might sound plausible for a relatively unknown stock with little trading ex ante. However, the opposite seems less credible: a sudden drop in trading activities makes this previously visible stock suddenly invisible to these attentive investors and due to the drop in investor base, the stock earns a low return in the subsequent month. In other words, the visibility hypothesis appears more sensible for increases in trading volume (as a proxy for investor attention) than for decreases in trading volume. However, our empirical results suggest the opposite. We find that liquidity decreases predict next month returns much stronger than liquidity increases do. Third, the visibility hypothesis relies on investor disagreement and short-sale constraint. We use analyst forecast dispersion as a proxy for investor disagreement and institutional ownership as a proxy for short-sale constraint, and interact them respectively with liquidity variation in the cross-sectional regression. We find that the positive effect of liquidity increase on the subsequent return is stronger in stocks with higher institutional ownership (which presumably are more visible and have less short-sale constraint), and is less significant in stocks with large analyst forecast dispersion. Both results go against the visibility hypothesis. The remainder of the paper proceeds as follows. Section 2 describes our data and key variables. Section 3 explores the time-series property of stock liquidity. In Section 4, we examine the cross-sectional relation between return and liquidity change, respectively, by the portfolio sorting approach and Fama-MacBeth regressions. We also investigate plausible explanations for the findings. Section 5 concludes the paper. 2. Data and Variables Our primary sample consists of common stocks listed on the NYSE and AMEX during July 1963 to December In the robustness tests we extend our analysis to NASDAQ stocks. We obtain the stock return and transaction data from the Center for Research in Security Prices (CRSP), and the company accounting information from the merged CRSP/Computstat database. We use Thomson Reuters I/B/E/S to retrieve measures of analyst earning forecasts and 13F filings for institutional ownership data. 3

5 Our primary measure of liquidity is Amihud s (2002) illiquidity ratio, which is defined as the absolute value of daily stock return scaled by the dollar trading volume of the stock on that day. Specifically, for stock i in month t, the Amihud ratio is estimated as, (1) where is the number of days with positive trading volume for stock i in month t, is the absolute value of the return of stock i on day, and is the dollar trading volume of stock i on day. A stock is defined as liquid if investors can trade it in large dollar volume without affecting the price much, i.e., the Amihud ratio is low. After obtaining the monthly Amihud ratio for each stock, we calculate a stock s liquidity change in month t as the log difference of its Amihud ratios between month t and t-1,. (2) A positive value suggests a decrease in liquidity and a negative value suggests an improvement in liquidity. Compared to transaction-based liquidity measures such as the bid-ask spread, the Amihud ratio has the virtue of not relying on intraday transaction data and therefore can be constructed over an extended sample period. Moreover, the Amihud ratio is shown to be highly correlated with transaction-based measures such as the bid-ask spread (see, e.g., Goyenko, Holden, and Trzcinka (2009), Hasbrouck (2009)). In the robustness tests, we also employ alternative liquidity measures including the bid-ask spread, turnover ratio, and the number of zero trading days. In the cross-sectional return tests, we control for firm characteristics that are documented by previous studies to explain returns. We follow Fama and French (1992) to construct size and book-to-market. In particular, a stock s market capitalization in June, as a measure of firm size, is used to explain monthly returns from July of the current year to June of the next year. The book-to-market ratio (B/M) is calculated as the stock s book value of equity in the previous fiscal yearend divided by its market capitalization in the previous calendar yearend. To capture the momentum effect (Jegadeesh and Titman, 1993), we compute the six-month compound return from month t-8 to t-3, where the return on month t is 4

6 to be explained. The liquidity level is measured as the average Amihud ratio from month t-8 to t-3. We follow Diether, Malloy, and Scherbina (2002) to define analyst forecast dispersion and the number of analysts following, based on I/B/E/S data. Institutional ownership, available since 1980, is the proportion of outstanding shares held by financial institutions in aggregate. In Table 1 Panel A, we report the time-series average of the cross-sectional variable summary statistics. The average number of stocks in each month is about 2500 during our sample period , under the constraint of non-missing return, market capitalization, and liquidity. The mean monthly return is 1.22% and the median 0.48% (following the convention, we exclude monthly returns over 300% to mitigate the effects of extreme value and potential data errors). On average, Amihud s illiquidity ratio decreases by about 1% per month, or 12% per year. This is consistent with the time trend of improving liquidity described in Chordia, Roll, and Subrahmanyam (2011) and Brennan, Huh, and Subrahmanyam (2012). More importantly, we find substantial variation of liquidity, as suggested by the absolute value of liquidity change ( ). On average, stock liquidity changes by as high as 45% from month to month. The median change is 35%. For our sample stocks since 1980, institutions on average hold 31% of outstanding shares. Since 1976, a typical stock in our sample is followed by 10 analysts, and their earnings forecast dispersion is around 16%. Panel B reports the time-series average of the cross-sectional simple correlations between variables. Consistent with the asset pricing literature, monthly returns are positively related to B/M (the value effect), the past six-month return (the momentum effect) and the level of Amihud illiquidity (the liquidity level effect), and are negatively related to market capitalization (the size effect) and analyst forecast dispersion (the divergence of opinion effect). Serving as a univariate test, the correlation between return and the lagged change in Amihud ratio is significantly negative. Stocks experiencing a liquidity increase in the previous month earn higher returns than stocks incurring a liquidity drop. It is worth mentioning that the correlation between return and the contemporaneous change in Amihud ratio is as high as and statistically significant at the 1% level. A positive return is often accompanied by an improvement in 5

7 liquidity while a negative return is concurrent with a decrease in liquidity. This has been documented by earlier studies such as Amihud (2002) and Hameed, Kang, and Viswanathan (2010). 3. Time-Series Property of Liquidity The summary statistics reported in Table 1 indicate substantial variation of stock liquidity from month to month. In this section, we examine whether the liquidity variation is completely random or predictable to some extent. We estimate the autocorrelation of monthly liquidity changes up to 12 lags. If the time-series of stock liquidity follows a random walk, the changes in liquidity are white noise and we expect no significant autocorrelations. However, we find a significantly negative correlation between two consecutive months liquidity changes. As reported in Table 2, the first-order autocorrelation is on average across all stocks. The autocorrelation decays quickly as time extends; it drops to for the second lagged month and becomes nearly zero for the latter months. The large first-order autocorrelation suggests the mean-reverting nature of stock liquidity. Stocks that have experienced a liquidity increase (decrease) in the previous month are expected to go through a liquidity decrease (increase) in the current month. Next, we examine if the patterns are different in stocks of different size. For each stock in each year, we adjust its yearend market capitalization by the Consumer Price Index (CPI) to be in 2010 dollars, and compute a time-series median market capitalization for each stock. We then divide stocks into small, medium, and large subsamples based on this median market capitalization, and compute the average autocorrelations across stocks in these three size subsamples. On average, the first-order autocorrelation is more negative in small stocks. 4. Liquidity Change and Stock Return 4.1. Portfolio Sorting Approach We first take the portfolio sorting approach to assess the effect of liquidity change on expected returns. At the beginning of month t, we sort the sample stocks into ten portfolios based on the change of 6

8 their Amihud illiquidity ratio in month t-1, that is, the log-difference of the Amihud ratios between month t-1 and t-2. The first portfolio, labeled Liquidity Decrease, contains stocks that have experienced the most positive changes in the Amihud illiquidity ratio, and the 10 th portfolio, labeled Liquidity Increase, consists of stocks that have experienced the most negative changes in the Amihud ratio. We calculate the equal- and value-weighted returns for each portfolio in month t, as well as the return spread between the two extreme portfolios (10 1). This return spread can be interpreted as the return for the hedging portfolio long stocks with the largest liquidity increase and short stocks with the largest liquidity decrease. Table 3 reports the portfolio return results. The results clearly suggest that liquidity change predicts stock returns in the next month. For example, the equal-weighted portfolio return monotonically increases from 0.80% for the largest liquidity decrease portfolio to 1.64% for the largest liquidity increase portfolio. The hedging portfolio earns an average monthly return of 0.84%, or an annual return of 10.08%. If we use value-weighted return, the hedging portfolio earns a monthly return of 0.56%, or an annual return of 6.72%. The hedging portfolio returns are significant both statistically and economically. Next we run a time-series regression of the hedging portfolio returns on Fama and French s (1993) three factors and estimate the regression intercept (alpha). The alphas are statistically significant and of similar magnitude as the raw hedging portfolio returns. The results suggest that the hedging portfolio returns are not explained by these common return factors. We also examine whether the return predictability of liquidity change is specific to certain sample periods. Figure 1 presents the hedging portfolio returns over our sample period To improve the visibility of the graph, we average monthly returns over each calendar year. It is clear that the hedging portfolio achieves positive returns in most years, though the magnitude varies. In only 2 out of 48 years in the sample, both the equal- and value-weighted hedging portfolio returns are negative. We further condition our portfolio sorting analysis on firm size. Many asset pricing anomalies are more evident in small stocks (see, e.g., Fama and French (2008)). The liquidity literature also suggests that the relation between liquidity and stock return is stronger in small stocks. For example, Brennan and 7

9 Subrahmanyam (1996) show that illiquid stocks outperform liquid stocks by a return of 1.69% per month for small stocks while the premium for illiquidity is 0.41% for large stocks, after adjusting for Fama-French three factors. Therefore, we explore whether our findings about liquidity change and stock return differ in stocks of different size. We employ a two-way dependent portfolio sorting approach. At the beginning of each month from July of the current year to June of the next year, we sort stocks based on their June market capitalization into three size portfolios (small, medium, and large). Within each size portfolio, we then sort stocks into ten portfolios based on their liquidity change in the previous month. We again compute the equal- and value-weighted portfolio returns and the hedging portfolio returns for each size group. In Table 3, the results suggest that the relation between liquidity change and stock return is significant in all three size portfolios, and it is stronger in smaller stocks. This is consistent with our findings in Table 2 that the first-order autocorrelation of liquidity changes is larger in smaller stocks Cross-Sectional Regression We further examine the relation between liquidity change and stock return using Fama-Macbeth regressions. The model is specified as follows: (3) where is the return of stock i in month t, is the liquidity change of stock i from month t-2 to month t-1, measured by the log difference of the Amihud ratios in these two months. Since the Amihud ratio is an illiquidity measure, if a liquidity increase (decrease) in month t-1 predicts a higher (lower) stock return in month t, we expect to observe a negative estimate of in the regression. We control for firm-specific characteristics that are documented by earlier studies to predict cross-sectional returns. They include firm size (ME), book-to-market ratio (B/M), and the past six-month compound return from month t-8 to t-3. More importantly, to ensure the impact of liquidity change on return that we observe is not a simple replication of the relation between return and liquidity level, we 8

10 also include stock liquidity level, estimated as the average Amihud ratio from month t-8 to t-3, in the regression. 1 In an alternative specification, we also control for analyst forecast dispersion, idiosyncratic volatility, the previous month return, and the maximum daily return in the previous month. The relation between return and liquidity change remains significant with these added control variables. Following the standard Fama-Macbeth (1973) method, we run a cross-sectional regression in each month. We then compute the time-series average of the coefficient estimates and evaluate the statistical significance based on the time-series standard errors of the estimates. The results are reported in Table 4. Consistent with the existing literature, we find that expected returns are positively related to the book-to-market ratio, past six-month return, and illiquidity. In other words, we confirm the value, momentum, and liquidity effects in our data. The coefficient estimate for firm size is positive but not statistically significant, so essentially the size-return relation is flat in our data (the relation becomes negative if we include Nasdaq stocks). More importantly, we find a strong negative coefficient for the liquidity change variable a decrease (an increase) in the Amihud illiquidity ratio predicts a higher (lower) stock return in the following month. The associated t-statistic is -8.74, which is higher than those for other cross-sectional return determinants. Caeteris paribus, stocks with liquidity improved in the previous month on average earn higher returns in the following month than stocks that have incurred a liquidity drop. The cross-sectional regression results are consistent with those based on portfolio sorting, and moreover, they confirm that the relation between return and liquidity change is robust after controlling for other cross-sectional return determinants. Next, we examine whether the relation exhibits any asymmetric pattern between liquidity increases and decreases. If an increase in liquidity causes or represents an improvement in stock visibility to investors, according to Gervais, Kaniel, and Mingelgrin (2001), greater visibility attracts more purchases of the stock and generates a higher return in the following period. This visibility story assumes investor 1 We use the time window of month t-8 to t-3 to measure the momentum return factor and stock liquidity level so that there is no time/information overlap with our liquidity change variable (measured as the change from month t-2 to t-1). However, even if we use the window of month t-6 to t-1 to measure these two variables, they have no impact on our main results. 9

11 incomplete information (Merton, 1987) and short-sale constraint (Miller, 1977) and therefore, is expected to work better for liquidity increases than for liquidity drops. Investors might get to know a stock because of other investors intensive trading of this stock. If some of them decide to buy this stock, the increased demand moves up its price. Investor attention might increase investor base, but a sudden drop in attention does not lead to a quick reduction of existing investor base. It is hard to believe that, because of a significant reduction in trading activities, investors who previously know this stock suddenly do not know this stock, i.e., the stock becomes invisible to them. We modify the regression in Equation (3) to be as follows: (4) where equals the liquidity change in month t-1 if it represents an increase in the liquidity (i.e., a decrease in the Amihud illiquidity ratio), and zero otherwise. The control variables are the same as in Equation (3). Under this specification, the predictive power of liquidity decrease is captured by the estimate of, and the predictability of liquidity increase is measured by the sum of estimates. Therefore, the estimate of captures if there exist asymmetric effects. The results of Model 3 in Table 4 suggest that although both liquidity increase and decrease predict expected returns in the next month, liquidity decrease has a predictive power twice as strong as liquidity increase. The difference, captured by the estimate for is statistically significant at the 1% level. This asymmetric predictability suggests that our key findings are not explained by the visibility story of Gervais, Kaniel, and Mingelgrin (2001). If any, the visibility story should predict an opposite asymmetric pattern. To further investigate the visibility story, we let the liquidity change variable interact with a non-extreme return dummy. It is known that liquidity increases (decreases) when stock price increases (decreases). The contemporaneous correlation between return and the change in Amihud ratio is as high as in our data. If we divide the sample into subsamples of liquidity increase versus decrease, the median contemporaneous return is 1.60% for the liquidity increase subsample and -0.61% for the liquidity 10

12 decrease subsample. The non-extreme return dummy is defined as follows. For stocks with a liquidity increase in the previous month, it equals 1 if the previous month return is lower than the median return of liquidity increase stocks and 0 otherwise. For stocks with a liquidity decrease in the previous month, the non-extreme return dummy is set to be 1 if the previous month return is higher than the median return of liquidity decrease stocks and 0 otherwise. If a significant change in trading volume (liquidity) captures investor attention, a corresponding big move in stock price would enhance such attention. Besides stocks with heavy trading, public media also like to cover biggest winners and losers stocks with extreme returns. In other words, if a stock s visibility improves due to a substantial change in trading activities, it would improve even more significantly for stocks that also experience extreme returns during the same period. Therefore, under the visibility story, the return predictability of liquidity change is expected to work better for stocks that have experienced extreme returns in the past month (i.e., non-extreme return dummy = 0). The results, presented under Model 4 and 5, do not support the visibility hypothesis. Once we include the interaction variable between the lagged liquidity change and the non-extreme return dummy, the coefficient estimate for the lagged liquidity change flips the sign and the coefficient estimate for the interaction variable remains negative and is three times as big in magnitude as the coefficient for the lagged liquidity change without the interaction variable (as reported under Model 2). This suggests that the return predictability of liquidity change is completely driven by stocks that have not incurred extreme returns. In Model 5, we differentiate between liquidity increase and decrease, and find that the lagged liquidity increase predicts a high return only when the stock does not realize an extremely positive return in the previous month. Likewise, the lagged liquidity decrease predicts a low return only when the stock does not incur an extremely negative return in the previous month The Liquidity Change Hypothesis We propose our results are consistent with the liquidity change hypothesis. Since liquidity is shown to be important in the cross-section of stock returns, investors would also care about the risk of liquidity 11

13 changes. All else being equal, investors demand return compensation for holding stocks whose liquidity is expected to drop; on the other hand, if a stock s liquidity is expected to improve, investors would give a high price (and thus expect a low return) for this stock. The mean-reverting nature of liquidity change, which we show in the previous section, is consistent with this hypothesis. Stocks that have experienced a significant increase (decrease) in liquidity are expected to decrease (increase) their liquidity in the next month, and accordingly, they are expected to earn high (low) expected returns in the next month. To test this hypothesis, we investigate if the lagged liquidity changes predict the cross-sectional variation of the current month liquidity changes. In Panel A of Table 5, we report the mean liquidity level in the lagged and current months (i.e., at month t-1 and t) and the mean liquidity change at month t (i.e., from month t-1 and t) for the ten portfolios sorted on the liquidity change at month t-1 (i.e., from month t-2 and t-1). The change in Amihud ratio at t -1, by construction, drops from 0.98 to from Portfolio 1 (Liquidity Decrease) to Portfolio 10 (Liquidity Increase). However, we do not find such a monotonic pattern for the liquidity level at either month t-1 or month t. Stocks in the two extreme portfolios (Portfolio 1 and 10) tend to have lower liquidity levels than those in the middle portfolios. This evidence suggests that liquidity change explains cross-sectional expected returns independently from the liquidity level effect, which is consistent with our Fama-MacBeth regression evidence that liquidity change predicts returns even after controlling for the liquidity level. More interestingly, we find a monotonically increasing pattern in the change of Amihud ratio at month t. It increases from for Portfolio 1 to 0.35 for Portfolio 10, yielding a statistically significant spread of This is consistent with the mean-reverting nature of liquidity change. A significant liquidity decrease (increase) in the lagged month predicts a significant liquidity increase (decrease) in the current month. The pattern holds for stocks of different size groups, while the liquidity change spread is the largest for small stocks. This is consistent with our findings of the largest return spread for small stocks, as reported in Table 3. Next, we run Fama-MacBeth regressions of the current month liquidity change on the lagged liquidity change. The results are reported in Table 5 Panel B, and can be summarized as follows. First, the 12

14 cross-sectional relation between the current and subsequent month liquidity changes is significantly negative. Past liquidity increases predict liquidity decreases in the following month, and vice versa. Second, this negative relation is stronger in stocks that have not realized extreme returns in the previous month. Third, this negative relation exists for both liquidity increase and decrease stocks, and in both scenarios, it is stronger in stocks that have experienced mild returns. The evidence is consistent with our return results and therefore, lends strong support to the liquidity change hypothesis. We check the robustness of our results by using alternative measures of liquidity, specifically the turnover ratio (constructed as trading volume divided by number of shares outstanding) and the bid-ask spread. In addition, we repeat our analyses for NASDAQ stocks. All the key results remain and in fact, become stronger in some scenarios. The Fama-MacBeth regression results for robustness checks are presented in Table Conclusion Liquidity is an important determinant of cross-sectional stock returns. All else being equal, investors expect higher returns for holding illiquid stocks. In this study, we find that, in addition to the level of liquidity, the change in liquidity has independent explanatory power for cross-sectional return variation. Stocks experiencing liquidity increases, on average, earn higher returns in the next month than stocks incurring liquidity drops. From the investment perspective, if investors long 10% of the NYSE/AMEX stocks that have experienced the largest liquidity increases in the previous month and short 10% of the largest liquidity decrease stocks, they expect to earn an equal-weighted monthly return of 0.84% (or 0.56% if value-weighted). This new empirical findings hold under different liquidity measures and after controlling for other known cross-sectional return determinants including the liquidity level, and are not explained by the popular common return factors. If investors care about the level of stock liquidity, they would also care about the expected change in liquidity. Further evidence suggests the expected liquidity change as a new determinant of expected returns. In general, liquidity of an individual stock follows a mean-reverting process. A substantial 13

15 increase (decrease) in liquidity is often followed by a sizable drop (rebound). Caeteris paribus, investors demand higher (lower) expected returns for stocks whose liquidity is expected to decrease (increase). We investigate alternative hypotheses but rule them out as valid explanations for our findings. Our research highlights the importance of other aspects of liquidity than just the level in asset pricing. 14

16 References Amihud, Yakov, 2002, Illiquidity and stock returns: Cross-section and time-series effects, Journal of Financial Markets 5, Amihud, Yakov, and Haim Mendelson, 1986, Asset pricing and the bid-ask spread, Journal of Financial Economics 17, Brennan, Michael J., Avanidhar Subrahmanyam, 1996, Market microstructure and asset pricing: On the compensation for illiquidity in stock returns, Journal of Financial Economics 41, Brennan, Michael, Sahn-Wook Huh, and Avanidhar Subrahmanyam, 2012, An analysis of the Amihud illiquidity premium, Working paper. Campbell, John Y., Sanford J. Grossman, and Jiang Wang, 1993, Trading volume and serial correlation in stock returns, Quarterly Journal of Economics 108, Chordia, Tarun, Richard Roll, and Avanidhar Subrahmanyam, 2000, Commonality in liquidity, Journal of Financial Economics 56, Chordia, Tarun, Richard Roll, and Avanidhar Subrahmanyam, 2011, Recent trend in trading activity and market quality, Journal of Financial Economics 101, Chordia, Tarun, Avanidhar Subrahmanyam, and Ravi Anshuman, 2001, Trading activity and expected stock returns, Journal of Financial Economics 59, Datar, Vinay T., Narayan Y. Naik, and Robert Radcliffe, 1998, Liquidity and stock returns: An alternative test, Journal of Financial Markets 1, Diether, Karl B., Christopher J. Malloy, Anna Scherbina, Differences of Opinion and the Cross Section of Stock Returns, Journal of Finance 57, Fama, Eugene F., and James MacBeth, 1973, Risk, return and equilibrium: Empirical tests, Journal of Political Economy 81, Fama, Eugene F., and Kenneth R. French, 1992, The cross section of expected stock returns, Journal of Finance 46, Fama, Eugene F. and Kenneth R. French, 1993, Common risk factors in the return on stocks and bonds, Journal of Financial Economics 33, Fama, Eugene F., and Kenneth R. French, 2008, Dissecting Anomalies, Journal of Finance 63, Gervais, Simon, Ron Kaniel, and Dan H. Mingelgrin, 2001, The high-volume return premium, Journal of Finance 56, Goyenko, Ruslan Y., Craig W. Holden, and Charles A. Trzcinka, 2009, Do liquidity measures measure liquidity?, Journal of Financial Economics 92, Hasbrouck, Joel, 2009, Trading costs and returns for US equities: Estimating effective costs from daily data, Journal of Finance, 64,

17 Hameed, Allaudeen, Wenjin Kang and S. Viswanathan, 2010, Stock market declines and liquidity, Journal of Finance 65, Jegadeesh, Narasimhan, and Sheridan Titman, 1993, Returns to buying winners and selling losers: Implications for stock market efficiency, Journal of Finance 48, Merton, Robert C., 1987, A simple model of capital market equilibrium with incomplete information, Journal of Finance 42, Miller, Edward M., 1977, Risk, uncertainty, and divergence of opinion, Journal of Finance 32, Pastor, Lubos, and Robert F. Stambaugh, 2003, Liquidity risk and expected stock returns, Journal of Political Economy 111,

18 The Liquidity Change Hedging Portflio Returns: Equal-Weighted Value-Weighted Figure 1: The liquidity change hedging portfolio returns: This figure depicts the time-series hedging portfolio returns. The hedging portfolio is constructed as follows. At the beginning of each month, we sort the sample stocks into deciles based on the previous month liquidity change. The first decile contains stocks that have experienced the largest liquidity decreases and the last decile contains stocks that have experienced the largest liquidity increases. The hedging portfolio is long on stocks in the last decile and short on stocks in the first decile. The hedging portfolio return is the difference in returns of the two extreme deciles (Decile 10 Decile 1). To improve the visibility of the graph, we present the average monthly return in each calendar year. 17

19 Table 1: Descriptive Statistics and Correlations of Variables Table 1 presents the descriptive statistics of our sample stocks. The sample consists of common stocks listed on the NYSE and AMEX during July 1963 to December Return is the monthly stock return in percentage. ln(me) and ln(b/m) are the log values of market capitalization and the book-to-market ratio. Following Fama and French (1992), for returns to be explained from this July to next June, market capitalization is measured at the end of this June. The book-to-market ratio is the previous fiscal year-end book value of equity divided by the previous calendar year-end market capitalization. ln(amihud) is the log value of the monthly Amihud illiquidity ratio. The variable construction follows Amihud (2002). Δln(Amihud) is the first-order difference of the monthly Amihud liquidity ratio and Δln(Amihud) is its absolute value. Institutional ownership is the proportion of outstanding shares held by financial institutions in aggregate. Analyst forecast dispersion is defined as the standard deviation of the analyst earnings forecasts scaled by the mean, following Diether, Malloy, and Scherbina (2002). The number of analyst following is the number of analysts that provide earnings forecasts for the firm. The institutional ownership data is only available since 1980 and the analyst forecast data is only available since Panel A reports the time-series average of the cross-sectional variable descriptive statistics. Panel B reports the time-series average of the cross-sectional Pearson correlations between these variables. The correlation coefficients in bold fonts are statistically significant at the 5% level. Panel A: Summary Statistics Variables Mean Median Standard Deviation Skewness Return (%) Δln(Amihud) (*100) Δln(Amihud) ln(me) ln(b/m) ln(amihud) Institutional ownership (since 1980) Analyst forecast dispersion (since 1976) Number of analysts following (since 1976) Panel B: Cross-Sectional Correlations Return ln(me) ln(b/m) Return (-3,-8) lnamihud (-3,-8) Lag (ΔlnAmihud) Institutional ownership ln(me) ln(b/m) Return(-3,-8) lnamihud(-3,-8) lag(δlnamihud) Institutional ownership Analyst Forecast dispersion

20 Table 2: The Time Series Property of Liquidity Change This table reports the autocorrelations of monthly liquidity changes. Liquidity is measured by the monthly Amihud illiquidity ratio, and liquidity change is the first-order difference of the monthly Amihud ratio. We estimate the autocorrelations of liquidity changes up to 12 lags for each stock, and then compute the average across stocks. The table reports the average autocorrelations up to 6 lagged months (autocorrelations beyond 6 lags are negligible). The column under All presents the average autocorrelations across all sample stocks. The other three columns present the average autocorrelations across small, medium, large firms, respectively. The size groups are classified as follows: for each stock in each year, we adjust its yearend market capitalization by the Consumer Price Index (CPI) to be in 2010 dollars. We then divide stocks into three size groups based on the stock s time-series median market capitalization. Autocorrelation of Liquidity Changes Lag of month All Small Medium Large firms firms firms

21 Table 3: Returns of Liquidity Change Portfolios This table presents returns of 10 portfolios sorted on the lagged liquidity change. In each month, we sort stocks into ten portfolios based on their liquidity change in the previous month. Portfolio 1 (10) includes the stocks whose liquidity decreases (increases) the most in the previous month, that is, the Amihud illiquidity ratio increase (decreases) the most. We then compute the equal-weighted and value-weighted portfolio returns respectively reported in Panel A and B. We also compute the hedging portfolio return (Portfolio 10 Portfolio 1), and run time-series regressions of the hedging portfolio returns on the Fama-French three factors to estimate alpha (the regression intercept). The corresponding t-statistics are reported in parentheses. Next we repeat the same analyses for small, medium, and large stocks, where size groups are formed based on the market capitalization in the previous month. 1 Liquidity Decrease Panel A: Equal-Weighted Portfolio Returns Liquidity Increase 10-1 (Raw Return) Fama-French three factor alpha All (7.89) (7.50) Small (6.67) (6.49) Medium (4.89) (5.18) Large (4.33) (4.56) 1 Liquidity Decrease Panel B: Value-Weighted Portfolio Returns Liquidity Increase 10-1 (Raw Return) Fama-French three factor alpha All (4.45) (4.33) Small (6.99) (6.94) Medium (4.30) (4.65) Large (3.46) (3.49) 20

22 Table 4: Fama-MacBeth Regression of Stock Return on Liquidity Change The Table presents the Fama-MacBeth regression results. In each month, we regress the returns of sample stocks on their previous month liquidity change (lagliqchange), as well as other firm characteristics including size (ln(me)), book-to-market ratio (ln(bm)), past six-month compound return (RET(-3,-8)), past six-month average stock illiquidity (lnamihud(-3,-8)). In some specifications, we separate lagliqchange into two variables, lagliqincrease and lagliqdecrease. Specifically, lagliqincrease equals the stock s previous month liquidity change if the Amihud illiquidity ratio decreases (it represents an improvement in liquidity), and 0 otherwise; lagliqdecrease equals the stock s previous month liquidity change if the Amihud illiquidity ratio increases (it represents a decrease in liquidity), and 0 otherwise. For stocks with an increase in liquidity in the previous month, non-extreme return dummy is defined as 1 if the previous month return is lower than the corresponding conditional median and 0 otherwise. For stocks with a decrease in liquidity in the previous month, non-extreme return dummy is defined as 1 if the previous month return is higher than the corresponding conditional median and 0 otherwise. We estimate the cross-sectional regression coefficients in each month, and report the time-series average of the regression coefficients. The corresponding t-statistics are reported in the parentheses. Model 1 Model 2 Model 3 Model 4 Model 5 ln(me) (0.91) (0.86) (0.90) (0.92) (0.97) ln(bm) (3.53) (3.51) (3.55) (3.61) (3.65) RET(-3,-8) (3.34) (3.49) (3.51) (3.57) (3.58) lnamihud(-3,-8) (2.91) (2.93) (3.08) (2.93) (3.07) lagliqchange (-8.74) (-7.59) (2.25) lagliqincrease (3.02) (3.14) lagliqdecrease 0.07 (0.79) lagliqchange * Non-extreme return dummy (-11.51) lagliqincrease * Non-extreme return dummy (-10.67) lagliqdecrease * Non-extreme return dummy (-9.36) Adjusted 3.93% 4.15% 4.19% 4.45% 4.52% 21

23 Table 5: Current and Lagged Liquidity Changes Panel A of this table presents the average liquidity and change in liquidity for 10 portfolios sorted on the lagged liquidity change. We also report the current month liquidity changes for small, medium, and large stocks respectively. Panel B reports the Fama-MacBeth regression results. In each month, we regress stocks current month liquidity change on their previous month liquidity change, interacted with the non-extreme return dummy. For stocks with liquidity improvement in the previous month, non-extreme return dummy is defined as 1 if the previous month return is lower than the corresponding conditional median and 0 otherwise. For stocks with liquidity decrease in the previous month, non-extreme return dummy is defined as 1 if the previous month return is higher than the corresponding conditional median and 0 otherwise. The time-series average of the cross-sectional regression coefficients and their corresponding t-statistics (in parentheses) are reported. Panel A: Average Liquidity and Liquidity Change in 10 Portfolios ΔlnAmihud at t-1 ln(amihud) at t-1 ln(amihud) at t ΔlnAmihud at t ΔlnAmihud at t: Small Medium Large 1 Liquidity decrease Liquidity increase 10-1 (t-stat) ( ) (-32.49) (-13.46) (96.07) (88.76) (82.21) (78.79) Panel B: Fama-MacBeth Regression of Liquidity Change Model 1 Model 2 Model 3 Model 4 Intercept (-1.54) (-1.49) (-3.18) (-3.34) lagliqchange ( ) (-70.80) lagliqchange * Non-extreme return dummy (-52.52) lagliqincrease (-76.34) (-52.01) lagliqdecrease (-78.50) (-49.29) lagliqincrease * Non-extreme return dummy (-45.51) lagliqdecrease * Non-extreme return dummy (-35.98) Adjusted 11.27% 12.66% 11.54% 13.02% 22

24 Table 6: Fama-MacBeth Regression of Stock Return on Liquidity Change: Robustness Check The table presents the robustness check results. In particular, Panel A reports the Fama-MacBeth regression results using turnover as the liquidity measure and Panel B reports the results using the bid-ask spread as the liquidity measure. Panel C reports the regression results on NASDAQ stocks, still using the Amihud ratio as the liquidity measure. Panel A: Turnover as the alternative measure of liquidity Model 1 Model 2 Model 3 Model 4 Model 5 ln(me) (-2.29) (-2.42) (-2.52) (-2.29) (-2.41) ln(bm) (3.21) (3.29) (3.30) (3.36) (3.39) RET(-3,-8) (3.29) (3.44) (3.45) (3.55) (3.58) Ln(Turnover(-3,-8)) (-2.57) (-2.36) (-2.42) (-2.31) (-2.31) lagliqchange (10.14) (7.59) (-2.17) lagliqincrease (-1.72) (-3.63) lagliqdecrease 0.08 (1.05) lagliqchange * 1.14 Non-extreme return dummy (11.61) lagliqincrease * 1.41 Non-extreme return dummy (10.42) lagliqdecrease * 0.79 Non-extreme return dummy (8.07) Adjusted 4.30% 4.44% 4.49% 4.72% 4.83% 23

25 Panel B: Bid-ask spread as the alternative measure of liquidity: Model 1 Model 2 Model 3 Model 4 Model 5 ln(me) (-0.18) (-0.10) (-0.15) (-0.05) (-0.11) ln(bm) (0.03) (0.41) (0.39) (0.40) (0.39) RET(-3,-8) (1.26) (0.87) (0.86) (0.87) (0.84) Spread(-3,-8) (1.99) (2.03) (2.07) (2.14) (2.15) lagliqchange (-0.58) (-1.40) (1.62) lagliqincrease (1.69) (3.23) lagliqdecrease (-0.21) lagliqchange * Non-extreme return dummy (-4.34) lagliqincrease * Non-extreme return dummy (-4.53) lagliqdecrease * Non-extreme return dummy (-2.16) Adjusted 3.00% 3.27% 3.34% 3.46% 3.58% 24

26 Panel C: NASDAQ stocks and Amihud ratio as the liquidity measure Model 1 Model 2 Model 3 Model 4 Model 5 ln(me) (0.47) (1.03) (1.04) (1.27) (1.33) ln(bm) (4.30) (4.48) (4.48) (4.78) (4.85) RET(-3,-8) (1.27) (1.62) (1.63) (1.69) (1.70) lnamihud(-3,-8) (1.87) (2.14) (2.27) (2.26) (2.43) lagliqchange (-6.02) (-6.84) (1.00) lagliqincrease (2.73) (1.41) lagliqdecrease 0.04 (0.49) lagliqchange * Non-extreme return dummy (-6.76) lagliqincrease * Non-extreme return dummy (-5.62) lagliqdecrease * Non-extreme return dummy (-6.60) Adjusted 2.41% 2.52% 2.56% 2.70% 2.76% 25