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  • 1. Stock Market Declines and Liquidity* Allaudeen Hameed Wenjin Kang and S. Viswanathan This Version: November 25, 2006 * Hameed and Kang are from the Department of Finance and Accounting, National University of Singapore, Singapore 117592, Tel: 65-6516-3034 and 65-6516-3194, Fax: 65-6779-2083, allaudeen@nus.edu.sg and bizkwj@nus.edu.sg. Viswanathan is from the Fuqua School of Business, Duke University , Tel: 1-919-660-7782, Fax: 1-919-660-7971, viswanat@duke.edu. We thank Yakov Amihud, Michael Brandt, Markus Brunnermeier, Doug Foster, Joel Hasbrouck, David Hsieh, Pete Kyle, Ravi Jagannathan, Christine Parlour, David Robinson, Avanidhar Subrahmanyam, Sheridan Titman and participants at the NBER 2005 microstructure conference, National University of Singapore, University of Evry (France), University of Texas (Austin), University of Alberta, for their comments. 1
  • 2. ABSTRACT Recent theoretical work suggests that variation in liquidity can be explained by supply side shocks affecting the funding available to financial intermediaries. Consistent with this prediction, we find that liquidity levels and commonality in liquidity respond asymmetrically to positive and negative market returns. Stock liquidity decreases while commonality in liquidity increases following large negative market returns. The asymmetric liquidity commonality results cannot be explained by indexing, market volatility and commonality in order flows which may be related to changes in demand for liquidity. We document that a large drop in aggregate value of securities creates greater liquidity commonality due to the inter-industry spill-over effects of capital constraints. We also show that the cost of supplying liquidity is highest following market downturns by examining the returns to zero investment trading strategies capitalizing on short-term price reversals on heavy trading volume. 2
  • 3. 1. Introduction In recent theoretical research, the idea that market returns endogenously affect liquidity has received attention. For example, in Brunnermeier and Pedersen (2005), market makers obtain significant financing by pledging the securities they hold as collateral. A large decline in aggregate market value of securities reduces the collateral value and imposes capital constraint, leading to a sharp decrease in the provision of liquidity. Liquidity dry-ups arise when the worsening liquidity leads to call for higher margins, and feedback into further funding problems.1 Since this supply of liquidity effect affects all securities, Brunnermeier and Pedersen also predict larger commonality in liquidity following market downturns. Anshuman and Viswanathan (2005), on the other hand, present a slightly different model where investors are asked to provide collateral when asset values fall and decide to endogenously default, leading to liquidation of assets. Simultaneously, market makers are able to finance less in the repo market leading to higher spreads, and possibly greater commonality in liquidity. Several other recent papers link changes in asset value to liquidity. In Morris and Shin (2003), traders sell when they hit price limits (which are correlated across traders) and liquidity black holes emerge when prices fall enough (the model in analogous to a bank run). Their model emphasizes the feedback effect of one trader’s liquidation decision on other traders. According to Kyle and Xiong (2001), a drop in stock prices leads to reduction in holdings of risky assets because investors have decreasing absolute risk aversion, resulting in reduced market liquidity (see also Gromb and Vayonos (2002) for a model of capital constraints and limits to arbitrage). In Vayanos (2004), investors 1 This spiral effect of drop in collateral value is also emphasized in the classic work of Kiyotaki and Moore (1997), where lending is based on the value of land. 3
  • 4. withdraw their investment in mutual funds when asset prices (fund performance) fall below an exogenously set level. Consequently, when mutual fund managers are close to the trigger price, they care about liquidity, especially during volatile periods. Hence, these theoretical models also emphasize shifts in demand for liquidity with changes in asset prices as liquidation of assets generates more selling pressure.2 Additionally, some of the above models also suggest cross-sectional differences in the liquidity effects: a drop in asset value has a greater impact on the liquidity of stocks with greater volatility exposure, a phenomenon related to flight to liquidity (see e.g. Anshuman and Viswanathan (2005), Vayanas (2004) and Acharya and Pedersen (2004)).3 In this paper, we investigate the empirical link between changes in aggregate value of assets and liquidity, taking into account endogenous effects of changes in demand and supply of liquidity. Using proportional spread (as a proportion of stock price) as one of our key variables measuring liquidity, we find that average monthly spreads are negatively related to lag market returns.4 Moreover, large negative market returns have much stronger impact on spreads than positive returns, and this relation is robust to the inclusion of lagged own stock returns, turnover, volatility, inverse of price, and other control variables. Specifically, the average spread increases by 3.6 (7.8) basis points after a (large) market decline. We also consider controlling for demand effects, using buy-sell 2 The work of Eisfeldt (2004) suggests that market liquidity varies with the states of the world, where assets are more liquid during good times and high productivity. 3 The impact of collateral constraints and flight to quality are also emphasized in a strand of literature in macroeconomics and banking. The seminal paper on collateral is due to Kiyotaki and Moore (1997), who argue that the ability to borrow depends on the collateral value, which is endogenous. Caballero and Krishnamurthy (2005) show that flight to liquidity episodes amplify collateral shortages, leading to macroeconomic problems. In Diamond and Dybvig (1983), depositors’ concern about liquidity shortages lead to bank runs, see also Diamond and Rajan (2005). 4 Since spreads trend downward over time and there are regime changes corresponding to tick size changes, we adjust spreads using a regression that accounts for these effects and the day of the week, holiday and other effects, following Chordia, Roll and Subrahmanyam (2005). We repeat the analysis with raw and effective proportional spreads as well as dollar spreads and qualitatively similar results. 4
  • 5. order imbalance as a proxy, and show that the negative effect of market returns persists. Our findings are strengthened when we examine the spreads in the first five days of the month, indicating that the time magnitude seems to be in weeks rather than months. In cross-sectional analyses, when we sort the securities into size and volatility groups, the empirical relation is strongest for smaller firms and firms with high volatility, consistent with the arguments that drop in valuations having a bigger impact on these risky firms. While our results are consistent with Chordia, Roll and Subrahmanyan (2001, 2002), we argue that a large fall in aggregate market valuations affects the supply of liquidity. Next, we investigate the idea that huge market-wide decline in prices reduces the aggregate collateral of the market making sector which feeds back as higher comovement in market liquidity. While there is some research on comovements in market liquidity in stock and bond markets (Chordia, Roll, Subrahmanyam (2000), Hasbrouck and Seppi (2001), Huberman and Halka (2001) and others) and evidence that market making collapsed after the stock market crisis in 1987 (see the Brady commission report on the 1987 crisis), there is little empirical evidence that focus on the effect of stock market movements on commonality in liquidity. Two recent papers consider the effect of capital constraints on liquidity. Using daily data and specialist stock information, Coughenour and Saad (2004) ask whether changes in the market return affect stock liquidity commonality at a daily frequency. In an interesting paper on fixed income markets, Naik and Yadav (2003) show that Bank of England capital constraints affect price movements.5 However, the extant empirical literature does not consider whether the 5 Other related work include Pastor and Stambaugh (2003) who show that liquidity is a priced state variable; and Amihud and Mendelson (1986) who show that illiquid assets earn higher returns. In Acharya and Pedersen (2005), a fall in aggregate liquidity primarily affects illiquid assets. Sadka (2005) documents that the earnings momentum effect is partly due to higher liquidity risk. 5
  • 6. comovement of liquidity increases dramatically after large market drops in a manner similar to the finding that stock return comovement goes up after large market drops (see the work of Ang, Chen and Xing (2004) on downside risk and especially Ang and Chen (2002), for work on asymmetric correlations between portfolios). We document that the correlation between individual firm spreads and market average spreads increases during periods of market declines (higher liquidity beta). We also find that large negative market returns increases liquidity comovement, measured by R2 statistic from the market model regression of the stock spreads on the market (average) spread. Specifically, the average R2 (liquidity beta) increases to 10.1 per cent (1.07) during periods when the market has experienced a large drop in valuations, compared to an unconditional mean value of 7.7 percent (0.93). When we separately examine S&P and non S&P index stocks, both groups of stocks exhibit significantly larger liquidity beta and liquidity commonality when market returns are most negative. These findings are consistent with the view that large negative market shocks increase market illiquidity across all stocks and that the liquidity correlations are not due to indexing effects. We also address the issue of whether variation in liquidity commonality is due to correlated movement in demand for liquidity across stocks. We do this by jointly estimating the commonality in buy and sell order imbalance, our proxy for commonality in demand for liquidity. We find that the commonality in order-imbalance is lower in rising markets and is significantly affected by aggregate flow of funds out of the equity market. More importantly, the impact of market returns on liquidity commonality cannot by explained by correlated order imbalances. 6
  • 7. We show that when we include returns on the industry and market (without that particular industry), large negative shocks to both returns increase comovement in liquidity. However, the market effect is much bigger in magnitude than the industry effect. This suggests that spillover effects across securities after negative market shocks are important and provides strong support for the idea that market liquidity drops across all assets at the same time when market declines. Finally, we use the short-term price reversals on heavy trading as our measure of the cost of supplying liquidity and examine if the cost varies with state of market returns. For example, in Campbell, Grossman and Wang (1993), risk-averse market makers require payment for accommodating heavy selling by liquidity traders. This cost of providing liquidity is reflected in the temporary decrease in price accompanying heavy sell volume and the subsequent increase as prices revert to fundamental values. We use the returns to two trading strategies to empirically gauge the cost of supplying liquidity: contrarian investment strategy (Conrad, Hameed and Niden (1994) and Avramov, Chordia, Goyal (2005); and limit-order trading strategy (Handa and Swartz (1996)). A simple zero-cost contrarian investment strategy that captures the price reversals on heavy trading yields an economically significant return of 1.18 percent per week when conditioned on large negative market returns, and is much higher than the unconditional return of 0.58 percent. The stronger price reversals in large down markets lasts up to two weeks, is higher in periods of high liquidity commonality and cannot be explained by standard Fama-French risk factors. A limit order trading strategy of placing limit buy (sell) orders on price declines (increases) captures the idea of return to liquidity provision. For example, a strategy that places a buy (sell) limit order at the beginning of 7
  • 8. each week after a 5 percent drop (rise) in stock prices, generates an unconditional buy- minus-sell portfolio weekly return of 0.71 percent. Again, the returns to this limit order strategy is most profitable after a large fall in the market, where the return increases to 1.56 percent per week. These dramatic price reversals after large market declines are statistically and economically significant. Overall, our results provides empirical support to the idea that supply of liquidity falls after large negative stock market returns and is consistent with the “collateral” based view of liquidity that has been espoused in recent theoretical papers. The remainder of the paper is organised as follows. Section 2 provides a description of the data and key variables. The methodology and results pertaining to the relation between past returns and liquidity is presented in Section 3 while Section 4 presents the same with respect to commonality in liquidity. The formulation and results from the investment strategy based on short-term price reversals are produced in Section 5. Section 6 concludes the paper. 2. Data The transaction-level data are collected from the New York Stock Exchange Trades and Automated Quotations (TAQ) and the Institute for the Study of Securities Markets (ISSM). The daily and monthly return data are retrieved from the Center for Research in Security Prices (CRSP). The sample stocks are restricted to NYSE ordinary stocks from January 1988 to December 2003. We exclude Nasdaq stocks because their trading protocols are different. ADRs, units, shares of beneficial interest, companies incorporated outside U.S., Americus Trust components, close-ended funds, preferred stocks, and REITs are also excluded. To be included in our sample, the stock’s price must be within 8
  • 9. $3 and $999. This filter is applied to avoid the influence of extreme price levels. The stock should also have at least 60 months of valid observations during the sample period. After all the filtering, the final database includes more than 800 million trades across about one thousand five hundred stocks over sixteen years. The large sample enables us to conduct a comprehensive analysis on the relation among liquidity level, liquidity commonality, and market returns. For the transaction data, if the trades are out of sequence, recorded before the market open or after the market close, or with special settlement conditions, they are not used in the computation of the daily spread and other liquidity variables. Quotes posted before the market open or after the market close are also discarded. The sign of the trade is decided by the Lee and Ready (1991) algorithm, which matches a trading record to the most recent quote preceding this trade by at least five seconds. If a price is closer to the ask quote, it is classified as a buyer-initiated trade, and if it is closer to the bid quote it is classified as a seller-initiated trade. If the trade is at the midpoint of the quote, we use a “tick-test” to classify it as buyer- (seller-) initiated trade if the price is higher (lower) than the price of the previous trade. The anomalous transaction records are deleted according to the following filtering rules: (i) Negative bid-ask spread; (ii) Quoted spread > $5; (iii) Proportional quoted spread > 20%; (iv) Effective spread / Quoted spread > 4.0. In this paper, we use bid-ask spread as the measure of liquidity. We compute the proportional quoted spread (QSPR) by dividing the difference between ask and bid quotes by the midquote. We repeat our empirical tests with the proportional effective spread, which is two times the difference between the trade execution price and the midquote scaled by the midquote, and find similar results (unreported). The individual stock daily spread is constructed by averaging the spread for all transactions for the stock on any given trading day. During the last decade, spreads have narrowed with the fall in tick size and growth in trading volume. Thus, to ascertain the extent to which the change of spread is caused by past returns, we adjust spreads for deterministic time-series 9
  • 10. variations such as changes in tick-size, time trend, and calendar effects. Following Chordia, Sarkar and Subrahmanyam (2005), we regress QSPR on a set of variables known to capture seasonal variation in liquidity: 4 11 QSPR j ,t = ∑ d j ,k DAYk ,t + ∑ e j ,k MONTH k ,t + f1, j HOLIDAYt k =1 k =1 (1) + f 2, j TICK1t + f 3, j TICK 2t + f 4, j YEAR1t + f 5, j YEAR2t + ASPR j ,t In equation 1, the following variables are employed: (i) 4 day of the week dummies (DAYk,t) for Monday through Thursday ; (ii) 11 month of the year dummies (MONTHk,t) for February through December; (iii) a dummy for the trading days around holidays (HOLIDAY,t); (iv) two tick change dummies (TICK1t and TICK2t) to capture the tick change from 1/8 to 1/16 on 06/24/1997 and the change from 1/16 to decimal system on 01/29/2001 respectively; (v) a time trend variable YEAR1t (YEAR2 t) is equal to the difference between the current calendar year and 1988 (1997) or the first year when stock j started trading on NYSE, whichever is later. The regression residuals, including the intercept, provide us the adjusted proportional quoted spread (ASPR). The time series regression equation 1 is estimated for each stock in our sample. Unreported cross- sectional average of the estimated parameters show seasonal patterns in quoted spread: the bid-ask spreads are typically higher on Fridays and around holidays; spreads are lower from May to September relative to other months. The tick-size change dummies also pick up significant drop in spread width after the change in tick rule on NYSE. Our results comports well with the seasonality in liquidity documented in Chordia et al. (2005). After adjusting for the seasonality in spreads, we do not observe any significant time trend. In Table 1, the un-adjusted spread (QSPR) exhibits a clear time trend with the annual average spread decreasing from 1.26 percent in 1988 to 0.26 percent in 2003, but the trend is removed in the time series of the seasonally adjusted spread (ASPR) annual averages. We also plot the two series, QSPR and ASPR, in Figure 1, which comfortingly reveals that our adjustment process does a reasonable job in controlling for the 10
  • 11. deterministic time-series trend in stock spreads. 3. Liquidity and Past Returns 3.1 Time Series Analysis In order to examine the impact of lagged market returns on liquidity, we first aggregate the daily adjusted spreads for each stock to obtain average monthly adjusted spreads. The monthly adjusted proportional spread for each firm i (ASPRi,t) is regressed on the lagged market return (Rm,t-1), proxied by the CRSP value-weighted index. We test the key prediction of the underlying theoretical models that liquidity is affected by lagged market returns, particularly, large negative returns. At the same time, it is possible that liquidity is affected by lagged firm specific returns, since large changes in firm value may have similar wealth effects. Firm i’s idiosyncratic returns (Ri,t) are defined as the difference between month t returns on stock i and the market index.6 We also introduce a set of firm specific variables that may affect the intertemporal variation in liquidity. Market microstructure models in Demsetz (1968), Stoll (1978) and Ho and Stoll (1980) suggest that large trading volume and high turnover reduce inventory risk per trade and thus should lead to smaller spreads. We add monthly turnover (TURNi), measured by total trading volume divided by shares outstanding for firm i, into the regression to control for the spread changes arising from the market maker’s inventory concern, although such concerns are likely to be temporary and not likely to dominate at monthly horizon. In addition to turnover, liquidity may also be affected by order imbalance. Heavy selling or buying may amplify the inventory problem, causing market makers to adjust their quotes to attract more trading on the other side of the market. Chordia, Roll and 6 Our results are unchanged when idiosyncratic returns are computed as the excess returns from a market model specification: Rit – (ait + bit Rmt). 11
  • 12. Subrahmanyam (2002) report that order imbalances are correlated with spread and conjecture that this could arise because of the specialist’s difficulty in adjusting quotes during periods of large order imbalances. To control for this effect, we add the absolute value of relative order imbalance (ROIBit), measured by the absolute value of the difference between the dollar amount of buyer- and seller-initiated orders standardized by the dollar amount of trading volume over the same month. It is also well known that individual firm spreads are positively affected by the return volatility. Hence, we include the monthly volatility (STDi,t) of returns on stock i using the method in French, Schwert and Stambaugh (1987). We add a price level control to ensure that the predictability in spread is not a manifestation of variations in the price level. Since the price level is used in the computation of proportional spread, we add the inverse of the stock price for firm i obtained in the beginning of the month t-2 (1/Pt-2), and denote this variable as PRCi,t-2. Finally, we include the lagged value of spread to account for serial correlation in spreads. The adjusted spreads for each firm is regressed on lagged returns and other firm characteristics: ASPRi ,t = α i + β i Rm,t −1 + γ i Ri ,t −1 + cv ,iTURN i ,t −1 + cIB ,i ROIBi ,t −1 + cSD ,i STDi ,t −1 + cPRC ,i PRCi ,t −2 + φi ASPRi ,t −1 + ε i ,t −1 (2) It should be noted that we use lagged values of the independent variables to account for any endogeneity issues in the specification. We run the time-series regression in equation (2) for each individual stock to estimate the coefficients, and then report the mean and median of the estimated regression coefficients, together with the percentage of statistically significant ones (at 5% level), across all firms in our sample. Table 2 presents the equally-weighted average coefficients across all individual stock regressions. Consistent with the evidence in the previous literature, we find that high turnover predicts lower spreads. Large order imbalance and volatile prices increase the market maker’s inventory risks and hence, leads to larger spreads. In addition, the proportional spreads 12
  • 13. are also higher for stocks with lower price levels. More importantly, we find that negative lagged market return (as well as negative idiosyncratic return) worsens stock liquidity, after controlling for the firm specific factors. Consistent with the theoretical predictions in Kyle and Xiong (2001) and Brunnermeier and Pedersen (2005) and others, the wealth effect of a market-wide drop in asset prices is associated with a fall in liquidity. It should be noted that the sensitivity of spreads to lagged market returns cannot be attributed to idiosyncratic shocks in stock prices, which also affects spreads. The models that link changes in market prices and liquidity in fact pose a stronger prediction: the relation should be stronger for prior losses than gains. In particular, we want to examine whether a drop in market prices have a differential effect than a similar rise in prices. Hence, we modify equation (3) to allow spread to react differentially to positive and negative lagged returns: ASPRi ,t = α i + βUP ,i Rm,t −1 DUP ,m,t −1 + β DOWN ,i Rm,t −1 DDOWN ,m,t −1 + γ UP ,i Ri ,t −1 DUP ,i ,t −1 + γ DOWN ,i Ri ,t −1 DDOWN ,i ,t −1 (3) + cv ,iTURN i ,t −1 + cIB ,i ROIBi ,t −1 + cSD ,i STDi ,t −1 + cPRC ,i PRCi ,t −2 + φi ASPRi ,t −1 + ε i ,t −1 where Rt −1 denotes absolute returns, DUP,m,t (DDOWN,m,t ) is a dummy variable that is equal to one if and only if Rm,t is greater (less) than zero. DUP,i,t (DDOWN,i,t ) are similarly defined based on Ri,t. The control variables are identical to those defined in equation (2). Panel B of Table 2 presents the empirical estimate of equation 3. We find a significantly greater effect of negative market returns on liquidity: regressing spreads on lagged market returns gives an average coefficient of 0.696 (-0.436) when the market is DOWN (UP). There is also an asymmetric relation between spreads and lagged idiosyncratic returns, with a greater sensitivity to negative returns. While we find a similar pattern following a drop or rise in the stock own prices, there is a clear 13
  • 14. asymmetric effect of lagged market returns on liquidity. As the next step, we examine whether the magnitude of lagged returns have differential impact on liquidity. Thus, we run the regression as follows ASPRi ,t = α i + βUP ,SMALL,i Rm ,t −1 DUP ,SMALL ,m ,t −1 + βUP ,LARGE ,i Rm ,t −1 DUP ,LARGE ,m,t −1 + β DOWN ,SMALL ,i Rm,t −1 DDOWN ,SMALL,m ,t −1 + β DOWN ,LARGE ,i Rm ,t −1 DDOWN , LARGE ,m ,t −1 + γ UP ,SMALL ,i Ri ,t −1 DUP ,SMALL,i ,t −1 + γ UP ,LARGE ,i Ri ,t −1 DUP , LARGE ,i ,t −1 (4) + γ DOWN ,SMALL ,i Ri ,t −1 DDOWN ,SMALL ,i ,t −1 + γ DOWN , LARGE ,i Ri ,t −1 DDOWN ,LARGE ,i ,t −1 + cv ,iTURN i ,t −1 + cIB ,i ROIBi ,t −1 + cSD ,i STDi ,t −1 + cPRC ,i PRCi ,t −2 + φi ASPRi ,t −1 + ε i ,t −1 where DUP,SMALL,m,t (DDOWN,SMALL,m,t ) is a dummy variable that is equal to one if and only if Rm,t is between zero and 1.5 standard deviation above (below) its unconditional mean return. DUP,LARGE,m,t (DDOWN,LARGE,m,t ) is a dummy variable that is equal to one if and only if Rm,t is greater (less) than 1.5 standard deviation above (below) its mean return. The other dummy variables DUP,SMALL,i,t (DDOWN,SMALL,i,t ) and DUP,LARGE,i,t (DDOWN,LARGE,i,t ) are similarly defined based on the idiosyncratic return on stock i, Ri,t. The results presented in Table 2, Panel C highlights the distinct asymmetric effect of large, negative market returns: bid-ask spreads are most sensitive to market returns when there is large negative market returns. The average value of the regression coefficient associated with lagged negative market returns increase (reduce) to 0.773 (0.529) for large (small) negative returns. The difference in the effects of large and small negative market returns on spreads is also statistically significant at conventional levels. On the other hand, the magnitude of a stock’s own lagged return does not exhibit similar predictive influence on spreads.7 Hence, the evidence that liquidity dries up following 7 Following Chordia et al. (2000) and Coughenour and Saad (2004), we examine the effect of cross- equation correlations on the standard errors of the estimated coefficients. Each month t, the residual from the estimated equation (2), (3), or (4) for stock j are denoted as εjt. The across security correlations are estimated using the following relation: εj+1,t = γ0 + γ1,t εj,t + ξj,t. The cross-equation dependence is measured by the average slope coefficient γ1 and the associated t-statistics. The average slope coefficient (t-statistics) for equations (2), (3) and (4) are -0.0012 (-0.043), -0.0013 (-0.047) and -0.0017 (-0.060) respectively. 14
  • 15. large negative market returns supports the wealth effects argument proposed in the recent theoretical models. Although not reported in the tables (but available upon request from authors), additional analyses of the relation between spreads and market returns provide more insights. First, we find that the average adjusted spread in months following a negative market return is higher than positive market returns by 3.6 basis points, after controlling for other determinants of spreads in equation (3). Likewise, the average adjusted spread in large (small) down market states is higher than the spreads in small up market states by 7.8 (2.5) basis points. These changes in adjusted spreads are statistically significant and are of economic importance compared to the base level average adjusted spreads of about 1 percent. In order words, a drop in the market valuation level over the past month leads to bigger spreads when compared to spread changes following a rise in stock price, and a large drop in market valuations exerts the biggest drop in liquidity. Second, we considered additional lagged returns: while the effect of lagged returns declines as we move to longer lags, the asymmetric effect of positive and negative returns remains prominent. Third, we also examined the effect of lagged returns on liquidity over a shorter interval, based on the effect on spreads in the first five days of each month. We find that the effect of changes in aggregate market valuations on subsequent liquidity is stronger in the first five days: using equation (3), the regression coefficient for down (up) market returns increases (decreases) to 1.08 (-0.53). Similarly, the corresponding estimate using equation (4) also shows a higher impact of large negative market returns in the first week of the month. The adjusted spreads goes up by 11 basis points following large negative market returns when compared to small, positive market return states. The latter findings indicate that the phenomenon is more pronounced at the weekly frequency. Finally, the negative relation between lagged market returns and liquidity is robust to These results suggest that the mean cross-equation dependence in the residuals are not significant and do not materially affect our results. 15
  • 16. replacing proportional spreads as our measure of liquidity, with alternatives such as effective proportional spreads, dollar spreads or the price impact measure used in Brennan and Subrahmanyam (1996). 3.2 Liquidity and Past Returns: Cross-sectional Evidence The theoretical models (e.g. Brunnermeier and Pederson (2005) and Vayanos (2004)) on the effect of funding constraints on liquidity suggest that the reduction in liquidity following a down market would be dominant in high volatility stocks. This is based on the idea that high volatility stocks require greater use of capital as they are more likely to suffer higher haircuts (margin requirements) when funding constraints bind. In this sub- section, we examine the cross-sectional differences in the relation between lagged returns and spreads among stocks that differ in historical volatility, controlling for firm size. The parameter estimates from equation (3) are grouped into nine portfolios formed by a two- way dependent sort on firm size and historical stock return volatility. We first sort the sample stocks according to their average market value during the middle of the sample period (1996 to 1998), and form three size-portfolios (small, medium and large). Within each size portfolio, we sort the stocks by their average monthly volatility during the same three-year period and form three volatility-portfolios (high, medium and low volatility). The mean and median individual stock’s coefficient estimates from the regression of equation (3) are reported for each size-volatility portfolio. The main findings in Table 3 can be summarized as follows. First, we continue to find stronger impact of negative market returns on liquidity for each of the nine size- volatility portfolios. Second, stock liquidity is more sensitive to changes in market returns for small capitalization stocks and stocks with high volatility, particularly following periods of market decline. Third, we find similar pattern of sensitivity of liquidity to lagged negative firm-specific returns, although the coefficients are smaller in magnitude. 16
  • 17. Fourth, lagged market returns have significantly higher impact on the liquidity of stocks which are more volatile, within each size portfolio. For example, a one percent drop in the aggregate market value increases the average spread of high volatility stocks between 0.07 and 0.63 basis points more than stocks with low volatility. The latter results support the supply side argument that a stock’s liquidity is adversely affected by a drop in collateral value of assets, especially for volatile stocks. The above findings on the asymmetric effect of lagged market returns on liquidity is consistent with the other recent empirical work. For example, Chordia, Roll and Subrahmanyam (2002) show that at the aggregate level, daily spreads increase dramatically following days with negative market return but decrease only marginally on positive market daily returns. They indicate that the asymmetric relation between spread and lagged daily returns may be caused by that the inventory accumulation concerns (high specialist inventory levels) are more binding in down markets. Our paper builds on the important work by Chordia, Roll and Subrahmanyam (2001, 2002) which predates the recent theoretical explanations on the variation in liquidity. We extend the findings in Chordia, Roll and Subrahmanyam in several ways. First, we show that market and firm-specific returns forecast future liquidity at monthly horizon. Second, we document the asymmetric response of liquidity to positive and negative returns at the firm level, with significant drop in liquidity following large negative market returns. Third, the relation between decline in aggregate market value and subsequent liquidity is strongest for small and volatile stocks. Collectively, these findings are consistent with the wealth effects and funding constraints arising from a drop in asset values. On the other hand, they are less likely to be driven by market maker’s immediate inventory concerns which are less important at monthly frequency. Comovement in Liquidity 4.1. Comovement in Liquidity and Market Returns 17
  • 18. When market makers and other intermediaries are constrained by their capital base, a large negative return reduce the pool of capital that is tied to marketable securities and, hence, reduces the supply of liquidity. In particular, the theoretical models predict that the funding liquidity constraints in down market states increases the commonality in liquidity across securities and its comovement with market liquidity. In this section, we pursue this idea further and investigate whether the commonality in liquidity increases when there is a negative market return, especially large negative market return. We adopt a measure that is commonly used to capture stock price synchronicity to analyze comovement in liquidity. The R2 statistic from the market model regression has been extensively used to measure comovement in stock prices (e.g. Roll (1988), Morck, Yueng and Yu (2000)). A high R2 indicates that a large portion of the variation is due to common, market-wide movements. As a first step, we use a single-factor market model to compute the commonality in daily liquidity. Changes in daily adjusted proportional spreads for firm i on day s (ASPRi,s) are regressed on changes in the market-wide average adjusted spreads (ASPRm,s), where ASPRm,s is obtained by equally-weighting all firm level adjusted spreads, excluding firm i. Following Chordia, Roll and Subrahmanyam (2001), we estimate the linear regression: DLi , s = ai + β LIQ ,i DLm, s + ε i , s (5) where DLi ,s = ( ASPRi ,s − ASPRi ,s −1 ) / ASPRi ,s −1 and DLm,s = ( ASPRm,s − ASPRm,s−1 ) / ASPRm, s −1 ) are the changes in adjusted spreads from day s-1 to s for stock i and the market respectively. For each stock i with at least 15 valid daily observations in month t, the market model regression yields a liquidity beta, βi,t , and a regression r-square denoted as R2i,t. A high R2i,t suggests that a large portion of the daily variations in liquidity for stock i in month t can be explained by market-wide liquidity variations. For each month t, the degree of commonality in liquidity, denoted as R2t, is obtained by taking an equally- weighted average of R2i,t. A high R2t reflects a strong common component in liquidity 18
  • 19. changes, and hence, high comovement in liquidity. We report the average liquidity betas and R2s separately for months when the returns on the market index are positive and negative as well as when the market returns are large and small. Positive returns on the market index are classified as large (small) if the returns are greater than 1.5 standard deviation above its mean (between zero and 1.5 standard deviation above its mean). Large and small negative returns are similarly defined, consistent with our specification in equation (4). In unreported results, we also consider large and small market states defined based on market index returns that are one standard deviation away from the mean and the results are qualitatively identical. As reported in Table 4, the average monthly liquidity-beta coefficient and the regression R2 in equation (5) across all stocks is 0.93 and 7.7 percent respectively. We find that the average beta increases (decreases) to 0.98 (0.91) in down (up) market states. As expected, the percentage of variation in individual firm liquidity explained by the market liquidity is also higher at 8.0 percent in down markets. In addition, the increase in liquidity commonality is greatest in large down market states as reflected in both an average liquidity beta of 1.07 as well as R2 of 10.1 percent. The liquidity betas in other market states are significantly smaller at between 0.81 and 0.96. Similarly, the average liquidity commonality measured by R2t in other market states are also significantly lower between 7.0 and 7.5 percent. Hence, market returns decrease the liquidity of all stocks in the market and increase liquidity commonality.8 8 We also analyse the conditional correlations in liquidity between size sorted portfolios. Starting with the average (equally-weighted) daily adjusted spreads (ASPR) for each portfolio, we fit a GARCH(1,1) model for the liquidity variable. The conditional correlations between the GARCH residuals for each pair of portfolios are allowed to vary over time, following the dynamic conditional correlations (DCC) methodology introduced by Engle (2002). The estimates of average conditional correlation between the liquidity of the small and large size portfolios monotonically increase from 0.226 following large up market states to 0.307 after large market declines. Our findings indicate that the conditional correlations in liquidity are significantly higher following large market declines, across all pairs of size portfolios. We find similar results when we consider portfolios of stocks consisting of S&P and non-S&P constituent stocks. These results underscore the main idea that asset liquidity becomes more correlated following market declines, consistent with the systemic effect arising from constraints in supply of liquidity. Details are furnished in Appendix I. 19
  • 20. The common variation could also arise from correlated demand for liquidity by index-linked funds or index arbitrageurs. For example, Harford and Kaul (2005) find that indexing leads to common effects in the intra-day (fifteen minute) order flow and (to a lesser extent) trading costs for S&P 500 constituent stocks, the most widely followed index. To ascertain if indexing is the primary source of the common liquidity effects, we segregated the stocks in our sample into two groups depending on whether the stock is an S&P 500 stock or not. Data on S&P membership is obtained from Standard and Poor’s records and the membership information is updated annually. In Panel C, Table 4, we separately report the average liquidity beta and commonality for the two groups of stocks. Although market liquidity explains a smaller portion of the variation in non-index stocks, we find that liquidity beta for non-S&P stocks are higher than index stocks in all market states. The liquidity beta of non-S&P (S&P) stocks rises from 0.91 (0.55) to 1.19 (0.82) when we compare the estimates associated with large positive and large negative market returns. More importantly, similar to the estimates in Panel B, both groups of firms exhibit significantly larger liquidity beta and liquidity commonality when market returns are most negative. The evidence implies that indexing alone cannot explain the correlated liquidity movements we find in our paper. In addition, the increased liquidity correlations on large negative market is a market-wide phenomenon, affecting both index and non- index stocks. These results on the effect of drop in market valuations on liquidity commonality is highly consistent with the supply-side arguments presented in Kyle and Xiong (2001), Anshuman and Viswanathan (2005) and Brunnermeier and Pedersen (2005). When there is a huge decline in market prices, the capital constraint faced by the market making sector becomes more binding and reduces their ability to provide liquidity and hence, the commonality in liquidity increases. On the other hand, periods of rising market valuations of similar magnitude do not affect commonality in liquidity. The inter-temporal variation in liquidity commonality may also be affected by other factors. Vayanos (2004) specifies stochastic market volatility as a key state variable that 20
  • 21. affects liquidity in the economy. In his model, investors become more risk averse during volatile times and their preference for liquidity is increasing in volatility. Consequently, a jump in market volatility is associated with higher demand for liquidity (also termed as flight to liquidity) and, conceivably increases liquidity commonality. On the other hand, if liquidity is not a systematic factor and is primarily determined by firm specific effects, then changes in liquidity should be related to variation in idiosyncratic volatility. Hence, we examine if changes in liquidity commonality is related to market or firm-specific volatility. Stock market volatility is computed using the method described in French, Schwert and Stambaugh (1987). Specifically, we sum the squared daily returns on the value-weighted CRSP index to obtain monthly market volatility, taking into account any serial covariance in market returns. Monthly idiosyncratic volatility for each firm is obtained by taking the standard deviation of the daily residuals from a one-factor market model regression. The firm-specific residual volatility is averaged across all stocks to generate our idiosyncratic volatility measure. Large differences between buy and sell orders for a particular security has the effect of reducing liquidity. Extreme aggregate order imbalance is likely to increase the demand on the liquidity provision by market makers and also increase the inventory concern faced by maker makers as shown by Chordia, Roll and Subrahmnayam (2002). If high levels of aggregate order imbalance impose similar pressure on the demand for liquidity across securities, we expect to see a positive relation between order imbalance and commonality in spreads. In addition, if the effect of order imbalance on aggregate stock liquidity is due to correlated shifts in demand by buyer or seller initiated trades, commonality in liquidity may be attributed to the commonality in order imbalance. Hence, we explore the impact of both the level and commonality in order imbalance on liquidity comovement. Since we are interested in the magnitude of order imbalance, we use the cross-sectional mean relative order imbalance (ROIB) defined in Section 3.1 as our measure of level of order imbalance. To measure commonality in order imbalances, 21
  • 22. we estimate the R2 from a single-factor regression model of individual firm order imbalance on market (equally-weighted average) order imbalance, similar in spirit to the liquidity commonality measure using proportional spreads in equation (5). We introduce these additional variables that affect liquidity commonality using a regression framework in Table 5. Since the R2t values are constrained to be between zero and one by construction, we define liquidity comovement as the logit transformation of R2t, LIQComt = ln[R2t /(1−R2t)]. We regress our comovement measure on market returns (Rmt) , taking into account the sign and magnitude of market returns: LIQComt = a + θUP ,SMALL Rm,t DUP ,SMALL,t + θUP ,LARGE Rm ,t DUP ,LARGE ,t + θ DOWN ,SMALL Rm ,t DDOWN ,SMALL,t + θ DOWN ,LARGE Rm,t DDOWN ,LARGE ,t + controls + ε t (6) where, the return and dummy variables are defined in Section 3.1. As shown in the first column of estimates in Table 5, liquidity comovement is strongest when there is a large drop in market prices. Consistent with the main findings in Table 4, we consider other cut-offs of 2.0 and 1.0 standard deviations from the mean to identify large negative market return states and obtain similar results (but not reported here). Shifts in the order imbalance co-movement, which we interpret as a measure of correlation in demand for liquidity, are positively associated with liquidity commonality. In other words, periods of large systematic movement in liquidity is associated with periods of high systematic movement in imbalance in buy and sell orders. In the next columns in Table 5, we report a significant positive relation between market volatility and liquidity commonality, separate from the effect of market returns. On the other hand, changes in the level of idiosyncratic volatility do not affect the degree of comovement in liquidity among stocks. These results are consistent with the prediction in Vayonas (2004) that uncertainty in the market increases investor demand for liquidity and subsequently increasing liquidity commonality. Extreme shifts in the aggregate order imbalance (ROIB), in addition to market volatility, also have significant positive effects on liquidity commonality. Nevertheless, adding these demand measures does not 22
  • 23. eliminate the significant asymmetric effect of market returns on liquidity commonality. To the extent that comovement in order imbalance across securities picks up correlation in demand for liquidity, it would be interesting to document the sources that drive the common variations in order flow. The next column in Table 5 reports the determinants of order imbalance commonality. Unlike the evidence on liquidity commonality, we do not find a similar jump in order imbalance comovement after a large drop in market valuations. Order imbalances across stocks have a smaller systematic component, particularly after a rise in aggregate market prices. This is not surprising since market returns and constraints on aggregate capital are not expected to affect liquidity demand in the same way. We also consider several other factors that may affect the time variation in commonality in liquidity demand. Flow of cash into and out of equity mutual funds can create correlated imbalances in order flows. For example, when there is a large withdrawal of funds by mutual fund owners in aggregate, fund managers are less willing and able to hold (particularly illiquid) assets, creating correlated demand for liquidity across stocks. New flow of funds into the mutual fund companies, on the other hand, does not create an immediate buy pressure and hence, may not affect the correlation in liquidity demand. We obtain data on monthly net flow of funds into U.S. equity mutual funds for our sample period from 1984 to 2004 from Investment Company Institute. We divide the net fund flow by the total assets under management by U.S. equity funds to generate our monthly time series of net mutual fund flow. As expected, net mutual fund flows significantly reduce the order imbalance comovement. On the other hand, common correlations in order flow are positively associated with market volatility and liquidity commonality. There appears to be a significant association between the two comovement measures, and that both variables may affect each other simultaneously. In this case, the endogeneity problem is likely to cause the parameter estimates to be biased and 23
  • 24. inconsistent. We therefore estimate the coefficients based on two-stage least squares (2SLS) estimation. As shown in the last column of Table 5, our finding that liquidity commonality increases only in large, down market states remains robust. At the same time, order imbalance commonality drops significantly in months with positive market returns. Overall, the results presented so far show that while liquidity commonality is driven by changes in supply as well as demand for liquidity, the demand factors cannot explain the asymmetric effect of market returns on liquidity. On the other hand, the increase in liquidity commonality in down market states is consistent with the adverse effects of a fall in the supply of liquidity. 4.2 Commonality in Liquidity: Industry Spillover Effects Our findings on liquidity commonality arising from the supply-side comport with those in Coughenour and Saad (2004). Coughenour and Saad (2004) provide evidence of covariation in liquidity arising from specialist firms providing liquidity for a group of firms and sharing a common pool of capital, inventory and profit information. In this section, we broaden the investigation by addressing an unexplored issue of whether liquidity commonality within an industry is significantly affected by aggregate market declines. If the common effects of market returns on liquidity commonality are due to correlated industry events, then, stocks in the same industry will exhibit common reaction to industry-wide information flow. Conversely, if the liquidity commonality is driven by constraints in the ability of the market making sector to supply liquidity in the aggregate, we ought to observe that a fall in aggregate market value generates liquidity spillover effects across industries. Specifically, we examine if industry-wide comovement in liquidity is affected by a decrease in the valuation of stocks from other industries, beyond the effect of its own industry returns. We begin by estimating the following industry-factor model for daily change in 24
  • 25. liquidity for security i ( DLi , s ), within each month: DLi , s = ai + β LIQ , i DLINDj , s + ε i , s (7) where the industry-liquidity factor DL INDj.s = ( ASPRINDj .s − ASPRINDj , s −1 ) / ASPRINDj ,s −1 is the daily percentage change in the equally-weighted average of adjusted spreads across all stocks in industry j on day s. Similar to our approach in estimating market-wide liquidity commonality in equation (5), we aggregate the regression R2 from equation (7) for each month t, across all firms in industry j. To obtain an industry-wide measure of commonality in liquidity for each month, we perform a logit transformation of the industry level average RINDj,t2, denoted as LIQComINDj,t. We form 17 industry-wide comovement measures using the SIC classification derived by Fama-French.9 LIQComINDj,t, is regressed on the monthly returns on the industry portfolio j (RINDj,t) and the returns on the market portfolio, excluding industry portfolio j (RMKTj,t) to examine the independent effects of changes in the value of the industry and market portfolios on liquidity comovement: LIQComINDj ,t = a + δRINDj ,t + θRMKTj , t + ε t (8) We also investigate the asymmetric effect of positive and negative industry and market returns on liquidity comovement, as well as the effect of the magnitude of these returns: LIQComINDj ,t = a + δ UP ,SMALL RINDj ,t DUP ,SMALL ,INDj ,t + δ UP ,LARGE RINDj ,t DUP ,LARGE ,INDj ,t + δ DOWN ,SMALL RINDj ,t DDOWN ,SMALL ,INDj ,t + δ DOWN ,LARGE RINDj ,t DDOWN ,LARGE ,INDj ,t (9) + θUP ,SMALL RMKTj ,t DUP ,SMALL ,MKTj ,t + θUP ,LARGE RMKTj ,t DUP ,LARGE ,MKTj ,t + θ DOWN ,SMALL RMKTj ,t DDOWN ,SMALL ,MKT ,t + θ DOWN ,SMALL RMKTj ,t DDOWN ,LARGE ,MKTj ,t + ε t where the dummy variables are defined in the same way as in equation (6). The regression coefficient associated with the independent variable RMKTj ,t provides a 93 The industry classifications are obtained from K. French’s website at http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html 25
  • 26. measure liquidity spillover effects. The results are reported in Table 6. We find that industry portfolio returns, especially large, negative returns, have a significant effect on liquidity commonality while positive industry returns do not affect liquidity comovement. More interestingly, we find that the return on the market portfolio (excluding own industry returns) exert a strong influence on comovements in industry-wide liquidity. In the basic formulation, the market portfolio returns dominate the industry returns in terms of its effect of industry-wide liquidity movements. The regression coefficient estimate for RMKTj ,t is a significant -0.65 while the coefficient for RINDj ,t is smaller at -0.27. When we separate the returns according to their magnitude, large negative market returns turn out to have the biggest impact on industry level liquidity movements. For example, large negative industry portfolio return is associated with an increase in the industry liquidity comovement by 0.91 while a large negative market return deepens the industry-wide comovement by almost twice the magnitude at 1.73. These results strongly support the idea that when large negative market returns occur, spillovers due to capital constraints broaden across industries, increasing the commonality in liquidity at the market-level. Overall, we show that liquidity of stocks within an industry exhibits the greatest commonality when the aggregate market experience a huge decline in market valuations, emphasizing the importance of the spillover effect across industries that arises from the market-level funding constraint faced by the market making sector.10 10 Recent behavioral models argue that a positive relation between past returns and firm liquidity could arise from an increase in supply of overconfident individual traders following price run-ups (Gervais and Odean (2001)), overreaction to sentiment shocks ((Baker and Stein (2004)) or disposition effects (Shefrin and Statman (1985)). We examine this possibility using the percentage of small trades, defined as trades below $5000, as a proxy for uninformed, behaviorally biased trades by individuals (see Lee (1992), Lee and Radhakrishna (2000), Barber, Odean and Zhu (2006)). While we find an increase in the percentage of small trades following positive returns, we do not find any evidence of decreases in small trades following negative returns. Hence, the asymmetric effect on market returns on liquidity cannot be explained by these behavioral biases. Detailed results are available form the authors. 26
  • 27. 5 Liquidity and Short-term Price Reversals Another approach to measure the effect of market declines on liquidity provision is to examine the degree of short-term price reversals following heavy trading activity. In Campbell, Grossman, and Wang (1993), for example, fluctuations in aggregate demand from liquidity traders is accommodated by risk-averse, utility maximising market makers who require compensation for supplying liquidity. In their model, heavy volume is accompanied by large price decreases as market makers require higher expected returns to accommodate the heavy liquidity (selling) pressure. Their model implies that these stock prices will experience a subsequent reversal, as prices go back to their fundamental value. Using a parallel motivation based on price reversals following heavy volume, Pastor and Stambaugh (2003) suggest a role for a liquidity factor in an empirical asset pricing model. Hence, the price reversal following high volume (liquidity shortages) and the implied short-term predictability in returns can be viewed as a “cost of supplying liquidity”. Conrad, Hameed, and Niden (1994) provide empirical support to this prediction by documenting that high-transaction NASDAQ stocks exhibit significant reversal in weekly returns. Similarly, Avramov, Chordia, and Goyal (2005) find that weekly return reversals for NYSE/AMEX stocks with heavy trading volume is more significant for less liquid stocks. Recent evidence in Kaniel, Saar and Titman (2006) suggest that individual investors act as liquidity providers to other investors that require immediacy and that the short-term price reversals are related to illiquidity. The empirical evidence presented in this paper so far indicates that the market making sector’s capacity to accommodate liquidity needs varies over time. In particular, large losses in the value of market makers’ collateral, which is linked to the value of the underlying securities, imposes tight funding constraint and restricts the supply of liquidity. Hence, we examine if the short-term price reversals on heavy volume associated with increased compensation for providing liquidity is dependent on the state 27
  • 28. of the market. We examine the extent of price reversals in different market states using two empirical trading strategies: contrarian and limit-order trading strategies. The first approach relies on the weekly contrarian investment strategy formulation in Conrad, Hameed and Niden (1994) and Avramov et al. (2005). We construct Wednesday to Tuesday weekly returns for all NYSE stocks in our sample for the period 1988 to 2003. Skipping one day between two consecutive weeks avoids the potential negative serial correlation caused by the bid-ask bounce and other microstructure influences. Next, we sort the stocks in week t into positive and negative return portfolios. For each week t, return on stock i (Rit) which is higher (lower) than the median return in the positive (negative) return portfolio is classified as a winner (loser) securities. We focus our analysis on the behavior of weekly returns for securities in these extreme winner and loser portfolios. The number of securities in the loser and winner portfolio in week t is denoted as NLt and NWt respectively. As Campbell, Grossman and Wang (1993) argue, variations in aggregate demand of liquidity traders generate large amount of trading together with a high price pressure. We use stock i’s turnover in week t (Turnit), which is the ratio of weekly trading volume and the number of shares outstanding, to measure the amount of trading. The contrarian portfolio weight of stock i in week t+1 within the winner and loser portfolios is given by: wi , p ,t +1 = −Ri ,t Turni ,t / ∑i =1 Ri ,t Turni ,t , where p denotes winner Npt or loser portfolio. The contrarian investment strategy is long on the loser securities and short on the winner securities, with weights depending positively on the magnitude of returns and turnover. The sum of weights for each portfolio is 1.0 by construction. The contrarian profit for the loser and winner portfolio for week t+k is: π p ,t +k = ∑i =1 wit +1 Ri ,t +k , which can be interpreted as the return to a $1 investment in Np each portfolio. The combined zero-investment profits are obtained by taking the difference in profits from the loser and winner portfolios. 28
  • 29. To the extent that the contrarian profits reflect the cost of supplying liquidity, we expect the price reversals on heavy volume to be negatively related to changes in aggregate market valuations. We investigate the effect of lagged market returns on the above contrarian profits by conditioning the profits on cumulative market returns over the previous four weeks. Specifically, we examine contrarian profits over four market states: large up (down) market is defined as market return being 1.5 standard deviation above (below) mean returns; and small up and down market refers to market return being between zero and 1.5 standard deviations around the mean returns. In the second approach, we follow Handa and Schwartz (1996) in devising a simple limit-order trading strategy to measure the profits to supplying liquidity. By submitting a limit buy order below the prevailing bid price, the investor provides liquidity to the market. If short-term price variations are due to arrival of liquidity traders, we should observe subsequent price reversals which are the compensation for liquidity provision. At the same time, the limit order trader expects to lose from the trade upon arrival of informed traders, in which case the price drop would be permanent and irreversible (ie. limit buy order imbeds a free put option). Our maintained hypothesis that liquidity dries up after a dive in aggregate market values implies that the expected profits to supplying liquidity is highest following large down markets. The limit-order strategy is implemented as follows. At the beginning of each week t, a limit buy order is placed at x% below the opening price(Po).We will consider three values of x, i.e. 3%, 5%, and 7%. If the transaction price falls to or below Po (1- x%) within week t (week t is the trading window), the limit order is executed and the investment is held for a period of k weeks. We consider holding periods of k equal to 1 and 2 weeks. If the limit order is not executed in week t, we assume that the order is withdrawn. A similar strategy is employed to execute limit sell orders if prices reach or exceed Po (1+ x%). The above procedure is applied to each stock in our sample to generate buy and sell limit-order weekly returns For each week t+1, we construct the 29
  • 30. cross-sectional average weekly returns (for buy and sell orders), weighting each stock i by its turnover in week t wi ,t +1 = Turni ,t / ∑i =1 Turni ,t . Again, we investigate if the Npt payoff to the limit order trading strategy is dependent on market states, which are defined by cumulated market returns over weeks t-4 to t-1. Table 7 and 8 report the results for the contrarian and limit-order trading strategies respectively. Table 7, Panel A reports significant contrarian profit of 0.58 percent in week t+1 (t-statistics is 5.38) for the full sample period. A large portion of the profits comes from the loser portfolio with a return of 0.75 percent, suggesting that price reversals on heavy volume are stronger after an initial price decline. The contrarian profit declines rapidly and becomes insignificant as we move to longer lags. Since the contrarian profits and price reversals appear to lasts for at most two weeks, we limit our subsequent analyses to the first two weeks after the portfolio formation period. As shown in Panel B of Table 7, lagged market returns significantly affect the magnitude of contrarian profits, with largest profit registered in the period following large decline in market prices. Week t+1 profit in the large down market increases noticeably to 1.18 percent compared to profits of between 0.52 and 0.64 percent in the other three market states. We find similar profit pattern in week t+2, although the magnitude falls quickly. It is noteworthy that the loser portfolio shows the largest profit (above 1.0 percent per week) following large negative market returns, consistent with the hypothesis that price reversals on heavy selling pressure are related to compensation for liquidity provision. To ascertain if the difference in loser and winner portfolio returns can be explained by loadings on risk factors, we estimate the alphas from a Fama-French three factor model. We regress the contrarian profits on the three factors representing the market (return on the value-weighted market index), size (difference in returns on small and large market capitalization portfolios) and book-to-market (difference in returns on value and growth 30
  • 31. portfolios).11 As shown in Panel B, the risk-adjusted profits are little changed when adjusted for these factor loadings. The profits in large down markets remain economically large at 1.16 percent per week, indicating that these risk factors cannot explain the price reversals.12 13 Table 8, Panel A shows that our limit order trading generates significant profits for all three values filter rules of 3, 5 and 7 percent, with weekly buy-minus-sell portfolio expected returns ranging from 0.37 percent to 0.97 percent in the first week. These returns become economically small in magnitude beyond one week. For example, a limit order strategy of buying (selling) when prices fall (rise) by 5 percent in week t gives a significant average return of 0.71 percent in week t+1, which decreases to 0.10 percent in week t+2. Consistent with the liquidation provision argument, the bulk of the expected returns comes from gains due to the limit buy investment. In Panel B, we examine if these returns are different across market states. The buy-minus-sell portfolio returns are similar in all the market states, except for large down states. For example, the 5 percent limit order trading rule generates a buy-minus-sell returns of between 0.63 to 0.68 percent per week in almost all market states, close to the unconditional returns. The striking exception is in the large down markets, where the buy-minus-sell portfolio weekly returns more than doubles to 1.56 percent. Hence, the evidence on limit order investment portfolio returns provides corroborative evidence that high returns to supplying liquidity in large down markets are linked to liquidity dry ups due to tightened 11 The weekly returns on the three Fama-French factors are constructed using daily portfolio returns downloaded from Ken French’s data library. 12 In unreported results, we find that the contrarian profits jumps to 1.73 percent following periods of high liquidity commonality (as defined in Section 4.1) and large decline in market valuations, consistent with funding constraints increasing the expected return to liquidity provision. 13 We also consider the effects of order imbalance by implementing the contrarian strategy separately on stocks with net buyer initiated and net seller initiated orders (not reported here). The augmented strategy yields higher profits of 1.64 percent in large down markets when we long loser, sell pressure portfolio and short the winner, buy pressure portfolio. In particular, the biggest price rebound occurs for loser stocks with high sell pressure. This is consistent with our contention that liquidity suppliers require highest compensation (to accommodate selling pressure) following large market declines when funding constraints are binding. 31
  • 32. capital constraints. 6. Conclusion This paper documents that liquidity responds asymmetrically to changes in asset market values. Consistent with the models of wealth effects on supply of liquidity, large negative market returns decrease liquidity much more than positive returns increase liquidity, particularly for high volatility firms. We explore the commonality in liquidity and show a drastic increase in commonality after large negative market returns. We also document a spillover effect of liquidity commonality across industries. Liquidity commonality within an industry increases significantly when the market returns (excluding the specific industry) are large and negative. These spillover and commonality in liquidity as aggregate market value declines confirms the supply of liquidity effect affecting all securities. Finally, we use the idea in Campbell, Grossman and Wang (1993) that short-term stock price reversals on heavy sell pressure reflect compensation for supplying liquidity and examine if liquidity costs varies with large changes in aggregate asset values. Indeed, we find that the cost of providing liquidity is highest in periods with large market declines. A zero investment strategy based on either the portfolio weights in Avaramov, Chordia and Goyal (2005) or a limit order trading strategy produces economically significant returns (between 1.18 percent and 1.56 percent per week) only after a large fall in aggregate market prices. Taken together, these are strong evidence of a supply effect considered in Brunnermeier and Pedersen (2005), Anshuman and Viswanathan (2005), Kyle and Xiong (2001), and Vayanos (2004). Overall, we believe that our paper presents strong evidence of the collateral view of 32
  • 33. market liquidity: market liquidity falls after large negative market returns because aggregate collateral of financial intermediaries fall and many asset holders are forced to liquidate, making it difficult to provide liquidity precisely when the market demands it. References Acharya, Viral V., and Lasse Heje Pedersen, 2005, Asset Pricing with Liquidity Risk, Journal of Financial Economics 77, 375-410. Amihud, Yakov and Haim Mendelson, 1986, Asset Pricing and the Bid-Ask Spread, Journal of Financial Economics 17, 223-249. Ang, Andrew, and Joe Chen, 2002, Asymmetric correlations in Equity Portfolios, Journal of Financial Economics 63, 443-494. Ang, Andrew, Joe Chen, and Yuhang Xing, 2006, Downside Risk, Review of Financial Studies, forthcoming. Anshuman, Ravi and S. Viswanathan, 2005, Market Liquidity, Working Paper, Duke University. Avramov, Doron, Tarun Chordia, and Amit Goyal, 2005, Liquidity and Autocorrelation of Individual Stock Returns, forthcoming, Journal of Finance. Baker, Malcolm and Jeremy C. Stein, 2004, Market Liquidity as a Sentiment Indicator, Journal of Financial Markets, Volume 7, Issue 3 , June 2004, 271-299 Barber, Brad, Terrance Odean, and Ning Zhu, 2006, Do Noise Traders Move Markets?, Working Paper, University of California, Berkeley. Brennan, Michael J., and Avanidhar Subrahmanyam, 1995, Investment analysis and price formation in securities markets, Journal of Financial Economics 38, 361-381. Brunnermeier, Markus and Lasse Pedersen, 2005, Market Liquidity and Funding Liquidity, Working Paper, Princeton University. 33
  • 34. Caballero, Ricardo, and Arvind Krishnamurthy, 2005, Financial System Risk and the Flight to Quality, Northwestern University working paper. Cappiello Lorenzo, Robert Engle, and Kevin Sheppard, 2003, Asymmetric Dynamics in the Correlations of Global Equity and Bond Returns, Working Paper, European Central Bank. Campbell, John Y., Sanford J. Grossman and Jiang Wang, 1993, Trading Volume and Serial Correlation in Stock Returns, The Quarterly Journal of Economics, Vol. 108(4), 905-939. Chordia, Tarun, Richard Roll, and Avanidhar Subrahmanyam, 2000, Commonality in liquidity, Journal of Financial Economics 56, 3-28. Chordia, Tarun, Richard Roll, and Avanidhar Subrahmanyam, 2001, Market liquidity and trading activity, Journal of Finance 56, 501-530. Chordia, Tarun, Richard Roll and Avanidhar Subrahmanyam, 2002, Order imbalance, liquidity and market returns, Journal of Financial Economics 65, 111-130. Chordia, Tarun, Asani Sarkar, and Avanidhar Subrahmanyam, 2005, An Empirical Analysis of Stock and Bond Market Liquidity, Review of Financial Studies 18, 85-129. Conrad, Jennifer, Allaudeen Hameed, and Cathy Niden, 1994, Volume and Autocovariances in Short-Horizon Individual Security Returns, Journal of Finance, 49, 1305-1329. Coughenour, Jay and Mohsen Saad, 2004, Common market makers and commonality in liquidity, Journal of Financial Economics, 37-69. Demsetz, Harold, 1968, The Cost of Transaction, Quarterly Journal of Economics 82, 33-53. Diamond, Douglas, and Philip Dybvig, 1983, Bank Runs, Deposit Insurance and Liquidity, Journal of Political Economy, 91, 401-419. Diamond, Douglas, and Raghuram Rajan, 2005, Liquidity Shortages and Banking Crisis, forthcoming, Journal of Finance. Eisfeldt, Andrea, 2004, Endogenous Liquidity in Asset Markets, Journal of Finance 59, 1-30. Engle, Robert, 2002, Dynamic conditional correlation: A simple class of multivariate generalized autoregressive conditional heteroskedasticity models, Journal of Business & Economic Statistics 20, 339-350. French, Kenneth, G. William Schwert, and Robert Stambaugh, 1987, Expected Stock 34
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  • 37. Appendix I: Dynamic Conditional Correlation of Spreads and Market Returns In this appendix, we examine the relationship between market returns and the conditional correlations in stock liquidity, measured by the dynamic conditional correlation (DCC) method proposed by Engle (2002). The DCC model relies on the parsimonious univariate GARCH estimates of liquidity for each asset and has the computational advantage over the multivariate GARCH model. The estimation starts with first obtaining a series of liquidity shocks from univariate GARCH specification of the liquidity variable and, in the second stage, we estimate the conditional correlation between asset liquidity shocks. We follow Engle (2002) and Cappiello et al. (2003), who use a similar methodology to estimate the time-varying correlation between the stock and the bond market returns. We use the DCC methodology to model the liquidity movements between a pair of portfolios. We consider pairs of size sorted portfolios (small, medium and large size portfolios) and also the correlation in liquidity between S&P and non-S&P constituent stocks. We sort the stocks in our sample into three size portfolios (or S&P and non-S&P portfolios) and take the equally-weighted average daily adjusted spread as the portfolio daily spread. As spreads tend to be highly autocorrelated, we fit an AR(1) model for average spreads and use the residuals as our liquidity variable. We obtain weekly dynamic correlation estimates between a pair of portfolio liquidity shocks by taking the average of all the daily DCC estimates in a week. Finally, we report the weekly dynamic correlations for each market state based on the magnitude and sign of market returns, as defined in the text in Section 3. Table A1 presents the conditional correlations in liquidity between size portfolios for each market state. The average DCC estimate of the correlation in spreads between large and small stock portfolios increases from 0.25 to 0.31 after a large negative market return. A large drop in market prices has a similar effect on conditional correlations between other pairs of size portfolios. The conditional correlation between liquidity of S&P and non-S&P constituent stocks exhibit a parallel behavior: the conditional 37
  • 38. correlation between these two portfolio spreads increases after a large negative market returns from 0.38 to 0.44. The DCC confirms that the sharp increase in commonality in spreads following large market declines. Table A1: DCC Estimates Conditional on Market Returns The sample stocks are sorted into three size portfolios (or the S&P and non-S&P constituent portfolios). The portfolio daily spread is equally-weighted average of the stock daily adjusted spread in the portfolio. We obtain the residual of the first-order auto-regression on the portfolio spreads and apply the DCC with mean-reverting model on various pairs of the portfolio spread residuals. The daily DCC estimates are averaged into the weekly dynamic correlation estimates. The weekly dynamic correlation conditional on market states is reported below. Market states are defined based on the cumulative CRSP value-weighted return from week t-4 to week t-1. Large Up (Large Down) refers to cumulative market returns being 1.5 standard deviation above (below) the mean. Small Up (Small Down) market refers to cumulative market returns between zero and 1.5 (-1.5) standard deviation. The DCC differences that are significant at 99%, 95%, and 90% confidence level are labelled with ***, **, and * respectively. Past Market Return DCC Estimates (a): Large (b): Small (c): Small (d): Large (e): Average (d) - (e) Up Up Down Down excluding (d) DCC between small and 0.226 0.243 0.260 0.307 0.248 0.060*** large size portfolios DCC between small and 0.394 0.399 0.405 0.451 0.401 0.051*** medium size portfolios DCC between medium and 0.423 0.467 0.497 0.537 0.474 0.063*** large size portfolios DCC between S&P and 0.362 0.372 0.393 0.442 0.378 0.063*** non-S&P portfolios 38
  • 39. Table 1: Descriptive Statistics: Raw and Adjusted Spreads The proportional quoted bid-ask spread for firm j, QSPRj, is defined as (ask quote – bid quote) / [(ask quote + bid quote)/2]. Daily QSPRj is generated by averaging the spread of all the transactions within a day. The daily quoted spreads are adjusted for seasonality to obtain the adjusted spreads, ASPRj, using the following regression model: 4 11 QSPR j ,t = ∑ d j ,k DAYk ,t + ∑ e j ,k MONTH k ,t + f1, j HOLIDAYt k =1 k =1 + f 2, j TICK1t + f 3, j TICK 2t + f 4, j YEAR1t + f 5, j YEAR2t + ASPR j ,t where we employ (i) 4 day of the week dummies (DAYk,t) for Monday through Thursday ; (ii) 11 month of the year dummies (MONTHk,t) for February through December; (iii) a dummy for the trading days around holidays (HOLIDAY,t); (iv) two tick change dummies (TICK1t and TICK2t) to capture the tick change from 1/8 to 1/16 on 06/24/1997 and the change from 1/16 to decimal system on 01/29/2001 respectively; (v) a time trend variable YEAR1t (YEAR2 t) is equal to the difference between the current calendar year and the year 1988 (1997) or the first year when the stock is traded on NYSE, whichever is later. The summary statistics of the annual average of the daily quoted spread (QSPR) and adjusted spread (ASPR) for the sample period January 1988 to December 2003 are reported below. QSPR (Unadjusted Proportional ASPR (Adjusted Proportional Year Number Quoted Spread) Quoted Spread) of Coefficient Coefficient Securities Mean Median Mean Median of Variation of Variation 1988 1027 1.26% 1.04% 0.618 1.33% 1.08% 0.641 1989 1083 1.13% 0.91% 0.671 1.24% 0.98% 0.708 1990 1146 1.41% 1.09% 0.720 1.56% 1.23% 0.748 1991 1224 1.32% 1.02% 0.712 1.50% 1.16% 0.723 1992 1320 1.25% 0.98% 0.714 1.47% 1.17% 0.703 1993 1430 1.18% 0.92% 0.736 1.45% 1.17% 0.692 1994 1497 1.14% 0.90% 0.717 1.47% 1.20% 0.657 1995 1562 1.06% 0.82% 0.741 1.43% 1.17% 0.657 1996 1641 0.97% 0.74% 0.769 1.38% 1.15% 0.649 1997 1709 0.77% 0.59% 0.812 1.31% 1.07% 0.670 1998 1709 0.78% 0.57% 0.834 1.32% 1.07% 0.692 1999 1607 0.85% 0.62% 0.822 1.34% 1.11% 0.679 2000 1482 0.93% 0.62% 0.930 1.38% 1.15% 0.666 2001 1328 0.55% 0.32% 1.213 1.38% 1.15% 0.648 2002 1243 0.39% 0.21% 1.266 1.26% 1.06% 0.657 2003 1200 0.26% 0.13% 1.251 1.13% 0.95% 0.692 39
  • 40. Table 2: Relation Between Spread and Lagged Market Returns Monthly average adjusted spreads for each security is regressed on lagged market returns and idiosyncratic stock returns. The idiosyncratic stock returns (Ri,t) are calculated as individual stock returns minus market returns. Panel A uses the following regression specification: ASPRi ,t = α i + β i Rm,t −1 + γ i Ri ,t −1 + cv ,iTURN i ,t −1 + cIB ,i ROIBi ,t −1 + cSD ,i STDi ,t −1 + cPRC ,i PRCi ,t −2 + φi ASPRi ,t −1 + ε i ,t −1 where ASPRi,t refers to stock i’s seasonally adjusted, daily proportional spread averaged across all trading days in month t; Ri,t is the idiosyncratic return on stock i in month t; Rm,t is the month t return on the CRSP value-weighted index; TURNi,t refers to the number of shares traded each month divided by the total shares outstanding; ROIBi,t is the absolute value of the monthly difference in the dollar value of buyer- and seller- initiated transactions (standardized by monthly dollar trading volume); STDi,t is the volatility of stock i’s returns in month t; PRCi,t-2 is equal to (1/Pi,t-2), where Pi,t-2 is the stock price at the beginning of month t-2. Panel B is based on the modified regression: ASPRi ,t = α i + βUP ,i Rm ,t −1 DUP ,m ,t −1 + β DOWN ,i Rm ,t −1 DDOWN ,m,t −1 + γ UP ,i Ri ,t −1 DUP ,i ,t −1 + γ DOWN ,i Ri ,t −1 DDOWN ,i ,t −1 + cv ,iTURN i ,t −1 + cIB ,i ROIBi ,t −1 + cSD ,i STDi ,t −1 + cPRC ,i PRCi ,t −2 + φi ASPRi ,t −1 + ε i ,t −1 Where |Rm,t| ( |Ri,t| ) denotes the absolute market (idiosyncratic) returns, DUP,m,,t (DDOWN,m,t ) is a dummy variable that is equal to one if and only if Rm,t is greater (less) than zero; DUP,i,t (DDOWN,i,t )are similarly defined based on Ri,t . Panel C uses the following specification: ASPRi ,t = α i + βUP ,SMALL,i Rm,t −1 DUP ,SMALL,m,t −1 + βUP ,LARGE ,i Rm,t −1 DUP ,LARGE ,m,t −1 + β DOWN ,SMALL,i Rm,t −1 DDOWN ,SMALL,m,t −1 + β DOWN ,LARGE ,i Rm,t −1 DDOWN ,LARGE ,m,t −1 + γ UP ,SMALL,i Ri ,t −1 DUP ,SMALL,i ,t −1 + γ UP ,LARGE ,i Ri ,t −1 DUP ,LARGE ,i ,t −1 + γ DOWN ,SMALL,i Ri ,t −1 DDOWN ,SMALL,i ,t −1 + γ DOWN ,LARGE ,i Ri ,t −1 DDOWN ,LARGE ,i ,t −1 + cv ,iTURN i ,t −1 + cIB ,i ROIBi ,t −1 + cSD ,i STDi ,t −1 + cPRC ,i PRCi ,t −2 + φi ASPRi ,t −1 + ε i ,t −1 where DUP,LARGE,m,t (DDOWN,LARGE,m,t ) is a dummy variable that is equal to one if and only if Rm,t is greater (less) than 1.5 standard deviation above (below) its mean return. DUP,SMALL,m,,t (DDOWN,SMALL,m,t ) is a dummy variable that is equal to one if and only if Rm,t is between zero and (negative) 1.5 standard deviation form its mean return. DUP,SMALL,i,t (DDOWN,SMALL,i,t ) and DUP,LARGE,i,t (DDOWN,LARGE,i,t) are similarly defined based on Ri,t . Cross-sectional mean and median of the coefficient estimates are reported in the row labelled as “Mean” and “Median”. The averages that are significant at 99%, 95%, and 90% confidence level are labelled with ***, **, and * respectively. “% of positive (negative)” and “% of positive (negative) significant” refer to the percentage of the positive (negative) coefficient estimates and the percentage of the coefficient estimates with t-statistics greater than +1.645 (-1.645). 40
  • 41. Panel A: Relation between Spreads and Lagged Returns Estimate Statistics Intercept ASPR(i,t-1) Ret(m,t-1) Ret(i,t-1) Mean 0.310*** 0.737*** -0.554*** -0.312*** Median 0.238 0.758 -0.343 -0.221 % positive (negative) 97.8% 100.0% (95.3%) (97.4%) % positive (negative) 88.9% 99.9% (55.7%) (74.0%) significant Estimate Statistics TURN(i,t-1) ROIB(i,t-1) STD(i,t-1) PRC(i,t-1) Mean -0.002** 0.031*** 0.059*** 0.875*** Median -0.001 0.014 0.041 0.540 % positive (negative) (60.0%) 56.8% 58.0% 76.7% % positive (negative) (10.0%) 10.3% 10.8% 26.2% significant Panel B: Relation between Spread and Signed Lagged Returns |Ret(m,t-1)| * |Ret(m,t-1)| * |Ret(i,t-1)| * |Ret(i,t-1)| * Estimate Statistics D(Up,m,t-1) D(Down,m,t-1) D(Up,i,t-1) D(Down,i,t-1) Mean -0.437*** 0.696*** -0.219*** 0.412*** Median -0.248 0.381 -0.139 0.288 % positive (negative) (79.1%) 85.5% (78.7%) 90.8% % positive (negative) (19.0%) 28.2% (25.1%) 49.1% significant Panel C: Relation between Spread and the Magnitude of Lagged Returns (a) (b) (a)-(b) (c) (d) (c)-(d) |Ret(m,t-1)| * |Ret(m,t-1)| * |Ret(m,t-1)| * |Ret(m,t-1)| * Estimate Statistics D(Up,Large,m,t-1) D(Up,Small,m,t-1) D(Dow n,Large,m,t-1) D(Dow n,Small,m,t-1) Mean -0.564*** -0.382*** -0.18*** 0.773*** 0.529*** 0.25*** Median -0.317 -0.222 0.387 0.245 % positive (negative) (77.2%) (72.0%) (56.8%) 84.8% 66.3% 58.5% % positive (negative) (17.7%) (12.1%) (6.0%) 29.4% 9.4% 6.3% significant (e) (f) (e)-(f) (g) (h) (g)-(h) |Ret(i,t-1)| * |Ret(i,t-1)| * |Ret(i,t-1)| * |Ret(i,t-1)| * Estimate Statistics D(Up,Large,i,t-1) D(Up,Small,i,t-1) D(Dow n,Large,i,t-1) D(Dow n,Small,i,t-1) Mean -0.224*** -0.207*** -0.02 0.434*** 0.383*** 0.05** Median -0.139 -0.148 0.280 0.264 % positive (negative) (77.8%) (71.4%) (49.1%) 87.7% 83.2% 52.8% % positive (negative) (23.9%) (15.3%) (6.5%) 40.6% 30.5% 9.6% significant 41
  • 42. Table 3: Relation between Spread and Signed Lagged Returns: Coefficients based on two-way dependent sorts on firm size and volatility Monthly adjusted proportional spread of each security is regressed on signed lagged market returns and idiosyncratic stock returns. ASPRi ,t = α i + βUP ,i Rm,t −1 DUP ,m ,t −1 + β DOWN ,i Rm ,t −1 DDOWN ,m ,t −1 + γ UP ,i Ri ,t −1 DUP ,i ,t −1 + γ DOWN ,i Ri ,t −1 DDOWN ,i ,t −1 + cv ,iTURN i ,t −1 + cIB ,i ROIBi ,t −1 + cSD ,i STDi ,t −1 + cPRC ,i PRCi ,t −2 + φi ASPRi ,t −1 + ε i ,t −1 The definition of variables is identical to Panel B in Table 2. The regression coefficient estimates are reported separately for nine portfolios, which are formed by a two-way dependent sort based on the average of firm size and historical return volatility of the years 1995, 1996, and 1997. |Ret(m,t-1)| * High Volatility Medium Volatility Low Volatility High - Low D(Up,m,t-1) Small Size -1.052*** -0.740*** -0.649*** -0.403** Medium Size -0.557*** -0.467*** -0.239*** -0.318*** Large Size -0.272*** -0.217*** -0.170*** -0.102** |Ret(m,t-1)| * High Medium Low High - Low D(Down,m,t-1) Volatility Volatility Volatility Small Size 1.593*** 1.220*** 0.962*** 0.631*** Medium Size 0.853*** 0.543*** 0.420*** 0.433*** Large Size 0.290*** 0.250*** 0.223*** 0.067* Ret(i,t-1) * High Volatility Medium Volatility Low Volatility High - Low D(Up,i,t-1) Small Size -0.462*** -0.438*** -0.320*** -0.142** Medium Size -0.228*** -0.256*** -0.192*** -0.037 Large Size -0.134*** -0.083*** -0.118*** -0.016 Ret(i,t-1) * High Medium Low High - Low D(Down,i,t-1) Volatility Volatility Volatility Small Size 0.853*** 0.646*** 0.553*** 0.300*** Medium Size 0.500*** 0.287*** 0.269*** 0.231*** Large Size 0.299*** 0.205*** 0.185*** 0.114** 42
  • 43. Table 4: Liquidity Betas and Market Returns Each month, the percentage change in adjusted daily proportional spread for each stock i is regressed on the percentage change in the aggregate market spreads. DLi , s = ai + β LIQ , i DLm, s + ε i , s where DLi , s = ( ASPRi ,s − ASPRi ,s −1 ) / ASPRi ,s −1 is the percentage change in adjusted daily proportional spread for stock i; DLm, s = ( ASPRm ,s − ASPRm,s −1 ) / ASPRm,s −1 and ASPRm,s is the cross-sectional equally-weighted average of daily spreads across all stocks. The regression generates a monthly series of liquidity betas and regression R 2. The panel below reports the cross-sectional average beta and R2 for the whole sample period as well as conditional on market returns in month t. In Panels B and C, large and small market returns are defined based on whether the returns are above or below 1.5 standard deviation from its mean returns. Panel C reports the estimates for S&P and non-S&P constituent stocks. All t-statistics are based on White’s correction. Panel A Unconditional Conditional on Market Returns (a) Positive (b) Negative (b) Market Market minus Returns Returns (a) Liquidity beta 0.08 0.93 0.91 0.98 (t-statistics) (2.39) R-Square (%) 0.6 7.7 7.4 8.0 (t-statistics) ( 1.80) Number of Monthly 192 122 70 Observations Panel B Conditional on Large and Small Market Returns (a) Large (b) Small (c) Small (d) Large (a) (c) (d) Positive Positive Negative Negative minus minus minus Market Market Market Market (b) (b) (b) Returns Returns Returns Returns Liquidity beta -0.11 0.04 0.16 0.81 0.92 0.96 1.07 (t-statistics) (-1.68) (1.23) (4.12) R-Square (%) -0.4 0.1 2.6 7.0 7.5 7.5 10.1 (t-statistics) (-1.53) (0.23) (2.82) Number of Monthly 10 112 56 14 Observations Panel C Conditional on Large and Small Market Returns (a) Large (b) Small (c) Small (d) Large (a) (c) (d) Positive Positive Negative Negative minus minus minus Market Market Market Market (b) (b) (b) Returns Returns Returns Returns S&P index stocks Liquidity beta -0.05 0.05 0.22 0.55 0.60 0.65 0.82 (t-statistics) (-0.42) (0.80) (2.60) R-Square (%) -0.1 0.5 4.8 7.6 7.7 8.2 12.6 (t-statistics) (-0.26) (0.94) (3.66) Non-S&P index stocks Liquidity beta -0.14 0.05 0.14 0.91 1.05 1.10 1.19 (t-statistics) (-1.68) (1.01) (2.55) R-Square (%) -0.6 -0.1 1.7 6.8 7.3 7.2 9.0 (t-statistics) (-2.21) (-0.46) (1.83) 43
  • 44. Table 5: Commonality in Liquidity and Market Returns Commonality in liquidity is based on the r-square (R2i,t) from the following regression for stock i within each month t: DLi , s = ai + β LIQ ,i DLm, s + ε i , s where DLi , s = ( ASPRi ,s − ASPRi , s −1 ) / ASPRi , s −1 is the percentage change in adjusted daily proportional spread for stock i from day s-1 to s; DLm,s = ( ASPRm,s − ASPRm,s −1 ) / ASPRm,s −1 and ASPRm,s is the cross- sectional equally-weighted average of spreads across all stocks in the sample in day s. For each stock i, the above regression equation generates an R2i,t, for each month t. The cross-sectional average R2i,t, denoted as Rt2, is used in the second-stage monthly regression: LIQComt = a + θUP ,SMALL Rm ,t DUP,SMALL,t + θUP ,LARGE Rm ,t DUP ,LARGE ,t + θ DOWN ,SMALL Rm ,t DDOWN ,SMALL ,t + θ DOWN ,LARGE Rm ,t DDOWN ,LARGE ,t + controls + ε t where LIQComt is defined as ln[ Rt /(1 − Rt )] . The dummy variable DUP,LARGE,m,t (DDOWN,LARGE,m,t ) is equal to 2 2 one if Rm,t is greater (less) than 1.5 standard deviation above (below) its mean return. DUP,SMALL,m,t (DDOWN,SMALL,m,t ) is equal to one if Rm,t is between 0 and 1.5 (-1.5) standard deviation from its mean. The White’s corrected t-statistics are reported in italic. We add the following monthly control variables to the analysis: (a) ROIB, the average relative order imbalance; (b) commonality in ROIB, similar to the COMOVE measure for liquidity we use above; (c) equity mutual fund flows as a proportion of total mutual fund investment ; (d) market-wide volatility; and (e) average idiosyncratic volatility. 44
  • 45. OLS 2SLS Dependent Liquidity Comovement ROIB Liquidity ROIB Variables Comovement Comovement Comovement Intercept -2.140 -2.035 -2.079 -0.601 -2.433 -0.502 -9.91 -7.06 -5.49 -2.52 -7.52 -0.81 |Ret(m,t)| * 3.983 2.710 3.382 -0.770 2.663 -0.865 D(Down,Large,m,t) 4.14 2.37 3.11 -1.22 2.73 -1.02 |Ret(m,t)| * 2.271 1.077 1.703 -0.164 0.921 -0.180 D(Down,Small,m,t) 1.10 0.51 0.82 -0.15 0.52 -0.16 |Ret(m,t)| * 1.551 0.527 0.962 -2.572 -0.112 -2.594 D(Up,Small,m,t) 1.62 0.52 1.00 -3.76 -0.10 -3.76 |Ret(m,t)| * 0.092 -1.010 -0.554 -1.422 -1.440 -1.407 D(Up,Large,m,t) 0.15 -1.45 -0.83 -1.94 -1.30 -2.06 Market 0.106 0.089 0.131 0.086 Volatility 2.15 2.97 2.63 2.26 Idiosyncratic 0.075 Volatility 0.78 ROIB 1.274 1.292 1.696 Level 1.73 1.75 2.53 ROIB 0.186 0.088 0.149 -0.109 Comovement 2.16 0.97 1.53 -0.80 Liquidity 0.098 0.137 Comovement 1.91 0.59 ROIB 0.487 0.492 Comovement (t-1) 7.59 7.41 Mutual Fund -0.696 -0.669 Flow -3.07 -2.49 45
  • 46. Table 6: Commonality in Liquidity, Industry and Market Returns Each month, we estimate the following regression for stock i: DLi , s = ai + β LIQ ,i DLINDj , s + ε i , s where DLi , s = ( ASPRi ,s − ASPRi ,s −1 ) / ASPRi , s −1 is the percentage change in adjusted daily proportional spread for stock i from day s-1 to s; DLINDj , s = ( ASPR INDj , s − ASPRINDj , s −1 ) / ASPR INDj , s −1 is the percentage change of the equally-weighted average of spreads across all stocks in the industry j in day s, ASPRINDj,s. The above regression generates R2i,t, for every stock i in each month t. The cross-sectional average R2i,t within industry j for month t is denoted as R2INDj,t, which is used in the second stage monthly regression : Model A: LIQComINDj , t = a + δRINDj , t + θRMKTj , t + ε t Model B: LIQComINDj ,t = a + δ UP ,SMALL RINDj ,t DUP ,SMALL , INDj ,t + δ UP , LARGE RINDj ,t DUP , LARGE , INDj ,t + δ DOWN , SMALL RINDj ,t DDOWN ,SMALL , INDj ,t + δ DOWN , LARGE RINDj ,t DDOWN ,LARGE , INDj ,t + θUP , SMALL RMKTj ,t DUP ,SMALL , MKTj ,t + θUP , LARGE RMKTj ,t DUP , LARGE , MKTj ,t + θ DOWN , SMALL RMKTj ,t DDOWN , SMALL , MKT ,t + θ DOWN , SMALL RMKTj ,t DDOWN ,LARGE ,MKTj ,t + ε t 2 2 where LIQComINDj,t is defined as ln[ R INDj ,t /(1 − R INDj ,t )] ; RINDj,t and RMKTj,t denote the month t return on the value-weighted, industry j and market (excluding industry j) portfolios. The dummy variable DUP,LARGE,INDj,t (DDOWN,LARGE,INDj,t ) is equal to one if RINDj,t is greater (less) than 1.5 standard deviation above (below) its mean return. DUP,SMALL,INDj,t (DDOWN,SMALL,INDj,t ) is equal to one if RINDj,t is between 0 and 1.5 (-1.5) standard deviation from its mean. The corresponding market dummy variables for RMKTj,t are similarly defined. White’s heteroskedasticity consistent t-statistics are reported in brackets. Model A B -2.382 -2.425 Intercept -441.62 -219.48 Ret(ind,t) -0.272 -2.25 Ret(mk t,t) -0.649 -4.09 |Ret(ind,t)| * 0.910 D(Down,Large,ind,t) 3.33 |Ret(ind,t)| * 0.386 D(Down,Small,ind,t) 1.09 |Ret(ind,t)| * 0.064 D(Up,Small,ind,t) 0.27 |Ret(ind,t)|* 0.040 D(Up,Large,ind,t) 0.23 |Ret(mk t,t)| * 1.735 D(Down,Large,mk t,t) 5.4 |Ret(mk t,t)| * 0.916 D(Down,Small,mk t,t) 1.66 |Ret(mk t,t)|* 0.228 D(Up,Small,mk t,t) 0.77 |Ret(mk t,t)| * 0.190 D(Up,Large,mk t,t) 0.63 46
  • 47. Table 7: Contrarian Profits and Market Returns Weekly stock returns are sorted into winner (loser) portfolios if the returns are above (below) the median of all positive (negative) returns in week t. Contrarian portfolio weight on stock i in week t is given by: Ri ,t −1Turni ,t −1 w p ,i ,t = ∑ Np i =1 Ri ,t −1Turni ,t −1 where Ri,t and Turni,t is stock i’s return and turnover in week t. Post-formation contrarian profits for week t+k, for k=1,2,3 and 4 are reported in Panel A. Panel B reports contrarian profits conditional on market returns. Large Up (Large Down) refers to cumulative market returns from week t-4 to t-1 being 1.5 standard deviation above (below) the mean. Small Up (Small Down) market refers to cumulative market returns between zero and 1.5 (-1.5) standard deviation. Factor-adjusted returns represent the alphas from regressing the returns on Fama-French 3 factors: i.e. market, size and book-to-market factors. Newey-West autocorrelation corrected t-statistics are given in brackets. Panel A: Unconditional Contrarian Profits Week Portfolio t+1 t+2 t+3 t+4 Loser 0.75% 0.43% 0.39% 0.37% Winner 0.17% 0.29% 0.37% 0.41% Loser minus Winner 0.58% 0.14% 0.03% -0.04% (t-statistics) (5.38) (1.69) (0.38) (-0.52) Panel B: Contrarian Profits Conditional on Market Returns Week t+1 Past Market Return Portfolio Large Up Small Up Small Down Large Down Loser 0.54% 0.83% 0.48% 1.37% Winner -0.10% 0.29% -0.04% 0.19% Loser minus Winner 0.64% 0.54% 0.52% 1.18% (t-statistics) (0.93) (4.07) (2.51) (3.01) Loser minus Winner 0.57% 0.48% 0.50% 1.16% (adjusted for French-French factors) (t-statistics) (0.83) (3.83) (2.41) (2.90) Week t+2 Past Market Return Portfolio Large Up Small Up Small Down Large Down Loser 0.86% 0.44% 0.21% 0.97% Winner 0.43% 0.40% 0.09% 0.07% Loser minus Winner 0.43% 0.03% 0.12% 0.90% (t-statistics) (1.21) (0.33) (0.88) (1.93) Loser minus Winner 0.34% -0.01% 0.12% 0.84% (adjusted for Fama-French factors) (t-statistics) (0.88) (-0.09) (0.87) (1.88) 47
  • 48. Table 8: Limit Order Trading Profits At the beginning of each week, stocks are sorted into the sell (buy) portfolios if its price hit x% above (below) its opening price. If the stock price hits the limit, the stock is added to the buy or sell portfolios, with stocks weights proportional to its turnover in ranking week, i.e. weight for firm i in week t is Turni,t / ∑ Np Turni ,t −1 , where Turni,t is stock i’s turnover in week t. We consider x equal to 3, 5, and 7 percent and i =1 holding periods of one (t+1) and two (t+2) weeks. Post-formation contrarian profits for week t+1 and t+2 are reported in Panel A. Panel B reports contrarian profits conditional on market returns. Large Up (Large Down) refers to cumulative market returns from week t-4 to t-1 being 1.5 standard deviation above (below) the mean returns. Small Up (Small Down) market refers to cumulative market returns between zero and 1.5 (-1.5) standard deviation. Newey-West autocorrelation corrected t-statistics are given in brackets. Panel A: The Unconditional Profits of Limit Order Contrarian Strategy Open Price +/- 3% Open Price +/- 5% Open Price +/- 7% Week Week Week Portfolio t+1 t+2 t+1 t+2 t+1 t+2 Limit Buy 0.70% 0.40% 0.93% 0.39% 1.07% 0.39% Limit Sell 0.33% 0.30% 0.21% 0.29% 0.10% 0.29% Buy-minus-Sell 0.37% 0.10% 0.71% 0.10% 0.97% 0.09% (t-statistics) (7.69) (2.59) (10.47) (1.64) (9.65) (1.02) 48
  • 49. Panel B: The Profits of Limit Order Contrarian Strategy Conditional on Market Returns Criteria = Open Price +/- 3% Week t+1 Past Market Return Portfolio Large Up Small Up Small Down Large Down Limit Buy 0.58% 0.72% 0.62% 0.90% Limit Sell 0.24% 0.41% 0.29% -0.06% Buy-minus-Sell 0.33% 0.31% 0.34% 0.96% (t-statistics) (1.51) (5.70) (4.05) (4.16) Criteria = Open Price +/- 5% Week t+1 Past Market Return Portfolio Large Up Small Up Small Down Large Down Limit Buy 0.68% 0.96% 0.79% 1.36% Limit Sell 0.04% 0.33% 0.12% -0.21% Buy-minus-Sell 0.64% 0.63% 0.68% 1.56% (t-statistics) (1.81) (7.52) (5.52) (5.17) Criteria = Open Price +/- 7% Week t+1 Past Market Return Portfolio Large Up Small Up Small Down Large Down Limit Buy 0.76% 1.12% 0.86% 1.73% Limit Sell -0.10% 0.24% -0.01% -0.40% Buy-minus-Sell 0.86% 0.88% 0.87% 2.13% (t-statistics) (1.75) (6.72) (5.36) (4.89) 49
  • 50. Figure 1: A Time Series Plot of the Average Raw and Adjusted Quoted Spreads The figures below show the cross-sectional mean of the raw and adjusted proportional quoted spreads for a constant sample of stocks that have valid observations throughout the full sample period. Unadjusted Spread 1.80 1.60 1.40 1.20 QSPR% 1.00 0.80 0.60 0.40 0.20 0.00 Date Jan-88 Jan-91 Jan-92 Jan-95 Jan-96 Jan-98 Jan-99 Jan-01 Jan-02 Jan-03 Jan-89 Jan-90 Jan-93 Jan-94 Jan-97 Jan-00 Adjusted Spread 1.80 1.60 1.40 1.20 QSPR% 1.00 0.80 0.60 0.40 0.20 0.00 Jan-88 Jan-89 Jan-90 Jan-91 Jan-92 Jan-93 Jan-94 Jan-95 Jan-98 Jan-99 Jan-00 Jan-03 Jan-96 Jan-97 Jan-01 Jan-02 Date 50