2 - Weatherhead School of Management



Stock Market Decline and Liquidity*

Allaudeen Hameed

Wenjin Kang

and

S. Viswanathan

This Version: February 27, 2006

* Hameed and Kang are from the Department of Finance and Accounting, National University of Singapore, Singapore 117592, Tel: 65-6874-3034, 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, David Hsieh, Pete Kyle, Ravi Jagannathan, Christine Parlour, David Robinson, Avanidhar Subrahmanyam, Sheridan Titman and participants at the NBER 2005 microstructure conference for their comments.

ABSTRACT

Recent theoretical work suggests that commonality in liquidity and variation in liquidity levels 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. 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 correlation between short-term price reversals on heavy trading volume and market states. These results cannot be explained by imbalances in buy-sell orders, institutional trading and market volatility which may proxy for changes in demand for liquidity.

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. In 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 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 papers 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]

Recent research suggests an empirical link between changes in aggregate value of assets and liquidity. For instance, Chordia, Roll and Subrahmanyan (2001, 2002) show that negative market returns predict higher market-wide daily spreads. Our paper takes this evidence much further. First, we ask how aggregate stock and industry returns affect individual stock liquidity at a monthly frequency (we also look at the liquidity in the first five days of the month to consider other frequency). We examine the cross-sectional differences in the effect of negative market returns for stocks sorted on size and volatility.

Second, we pursue the idea that large drop in market valuations 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 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.[4] However, the extant empirical literature does not consider whether the 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). As we will see below, our analysis of comovement is much more comprehensive. We carefully relate our findings to theories of market making that focus on capital constraints and attempt to sufficiently distinguish between the effects due to demand and supply of liquidity.

Third, we utilise the framework provided by Campbell, Grossman and Wang (1993) to investigate the inter-temporal changes in the compensation for supplying liquidity. In their model, 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. Following Lehmann (1990), Conrad, Hameed and Niden (1994) and Avramov, Chordia, Goyal (2005), we adopt the contrarian investment strategy to quantify the association between changes in aggregate market valuations and the cost of providing liquidity.

Our empirical approach is as follows. We use proportional quoted spread (as a proportion of the stock price) as one of our key variables[5]. 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 (2001). The adjusted proportional spread represents the key variable for our analysis.

We find that quoted spreads (as a proportion of the stock prices) are negatively related to lagged market returns and lagged own returns. Further, lagged negative market returns and lagged negative own returns have much larger effects than positive returns. Using the buy-sell imbalance to proxy for the demand effect, we show that the negative effect of market returns persists after inclusion of the buy-sell imbalance. Our results are robust to the inclusion of the lagged quoted spread, turnover, volatility, one over the price, and other control measures. We findings are stronger when we use the returns in the first five days of the month, i.e, the time magnitude seems to be in weeks rather than months. When we sort the securities into size and volatility groups, our findings are strongest for smaller firms and firms with high volatility – here the large negative return has the biggest punch.

Next, we investigate the hypothesis that large negative returns affect the supply of market making by looking at the comovements in liquidity. We first regress the individual firm spreads on the equally weighted market spread and find that the correlation (liquidity beta) to be higher with negative returns. This suggests that large negative price movements induce market illiquidity in all stocks. We use the R2 statistic from the market model regression of the stock liquidity on the market liquidity as our input in comovement regressions. Since the seminal work of Roll (1988), a high R2 in market model regressions have been used to measure synchronicity in returns. We use a similar idea here in context of liquidity. If aggregate market liquidity does not explain individual stock liquidity much, the comovement in liquidity is low and each stock’s liquidity is determined by its individual characteristics. However, if the comovement in liquidity is high (the liquidity of all stocks tends to move together), the cross-securities average R2 will be high.

We regress the average R2 against lagged market returns and find that large negative market returns dramatically increase the liquidity comovement. This is consistent with the view that large negative market shocks increase market illiquidity across all stocks. Our finding is robust to the inclusion of changes in demand for liquidity measured by order imbalance, changes in institutional holdings and market and idiosyncratic return volatility. We also consider whether the comovement is due to industry effects or market effects. An increase in comovement caused by a negative industry return could show up as a market wide effect. We show that when we include the industry return and the market return (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 suggest 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 returns drop.

Our evidence is strengthened by the finding that short-term price reversals on heavy trading volume, which proxy for the cost of supplying liquidity, are greatest following large market downturns. A simple zero-cost contrarian investment strategy yields a economically significant 1.19 percent per week when conditioned on large negative market returns, and is significantly higher than the profits of between 0.48 and 0.65 percent observed under other market conditions. The contrarian profits in large down markets are even higher when it coincides with periods of high liquidity commonality and high imbalance between sell and buy orders in the market. Hence, supply of liquidity falls after large negative stock market movements 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 contrarian portfolio investment strategy is 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 $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 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 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:

[pic] (1)

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 residual provides us the adjusted proportional quoted spread (ASPR), which is used in our subsequent analyses. 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 average bid-ask spreads are higher on Fridays and in January to April and October and around holidays. 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 1.28% in 1988 to 0.26% 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 deterministic time-series trend in stock spreads.

3. Liquidity and Past Returns

1. Time Series Analysis

In order to examine the impact of lagged market returns on spreads, 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-specific returns (Ri,t-1) are defined by the difference between monthly raw individual stock and market returns.

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 rate reduce inventory risk per trade and thus should lead to smaller spreads. Hence we add the monthly turnover rate (TURNi), measured by total trading volume divided by shares outstanding for firm i, into the regression to control for the spread changes due to the market maker’s inventory concern, although such inventory concerns are likely to be temporary and not dominant at monthly horizon.

In addition to turnover, liquidity may also be affected by the 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 Subrahmanyam (2002) report that order imbalances are correlated with spread width 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 correlations.

The adjusted spreads for each firm is regressed on lagged returns and other firm characteristics:

[pic] (2)

where Ri,t is the idiosyncratic return on stock i in month t and Rm,t is the month t return on the CRSP value-weighted index. 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 are also higher for stocks with lower price levels.

More importantly, we find that both the lagged individual stock return and the lagged market return have significant negative influence on liquidity, after controlling for the firm specific factors. Consistent with the theoretical predictions in Kyle and Xiong (2001) and Brunnermeier and Pedersen (2005), the wealth effect of a drop in market prices is associated with a fall in liquidity. The evidence presented in Table 2 also shows that prior market returns appear to have a higher impact on a stock’s liquidity than its own lagged returns.

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:

[pic] (3)

where DUP,i,t (DDOWN,i,t ) is a dummy variable that is equal to one if and only if Ri,t is greater (less) than zero. DUP,m,t (DDOWN,m,t ) are similarly defined based on Rm,t. The control variables are identical to those defined in equation (2).

The Panel B of Table 2 presents the empirical estimate of equation 3 for monthly adjusted spreads. We find a significantly greater effect of negative lagged returns on liquidity, at the market-level as well as individual stock level. Although both negative and positive market returns affect liquidity, the estimated regression coefficient of negative lagged market return on spread, which is -0.705 is significantly stronger than the coefficient for lagged positive market return, which is -0.433. In order words, a drop in the market valuation level over the past month leads to a bigger decline in the stock’s liquidity when compared to the liquidity improvement following a rise in stock price. While we find a similar pattern following a drop or rise in the stock own prices, there is a clear effect of lagged market returns on liquidity. We have also considered additional lagged returns (not reported here): while the effect of lagged returns declines as we move to longer lags, the asymmetric effect of positive and negative returns remains prominent. Additionally, 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. In unreported results, we find that the effect of changes in aggregate market valuations on subsequent liquidity is stronger in the first five days, indicating that the phenomenon is more pronounced at the higher frequency.

As the next step, we examine whether the magnitude of lagged returns have differential impact on liquidity. Thus, we run the regression as follows

[pic] (4)

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 rest dummy variables DUP,,SMALL,,i,,t (DDOWN,,SMALL,,i,,t ) and DUP,,LARGE,,i,,t (DDOWN,,LARGE,,,i,,t ) are similarly defined based on return on stock i, Ri,t.

The results presented in Table 2, Panel C highlights the distinct asymmetric effect of large, negative market returns: large negative market returns exert the biggest drop in liquidity. On the other hand, the magnitude of a stock’s own lagged return does not exhibit similar predictive power on spreads. Hence, the evidence that liquidity dries up following large negative market returns supports the wealth effects argument proposed in the recent theoretical models.[6] [7]

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 firm-specific returns, although the coefficients are smaller in magnitude. 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 0.08 and 0.61 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, 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 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.

3. . Commonality in Liquidity

ity. tical developments explaining variation in liquidityd returns and liquidity and report thatis iComovement in Liquidity

1. Comovement in Liquidity and Market Returns

The funding constraint models suggest that large negative return reduce the pool of capital and the supply of market making and hence reduces the market liquidity. In particular, these 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 the first step, we use a single-factor market model to compute the commonality in daily liquidity. Daily individual stock proportional quoted spreads (ASPRi,s) are regressed on the market-wide average 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:

[pic] (5)

where[pic]and[pic][pic] [pic]) are the percentage change in adjusted daily proportional quoted spread from day s-1 to s for stock i and the market respectively. Thus, for each stock i with at least 15 valid daily observations in month t, the market model regression yields an R2 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. For each month t, the degree of commonality in liquidity, denoted as Rt2, is obtained by taking an equally-weighted average of R2i,t. A high Rt2 reflects a strong common component in liquidity changes, and hence, high comovement in liquidity. We report the average liquidity betas and R2 separately for months when the returns on the market index is positive and negative as well as when the market returns are large and small. Positive returns on the market index is classified as large (small) if the returns are more than 1.5 standard deviation above (below) its unconditional mean returns. Large and small negative returns are similarly defined, consistent with our specification in equation (4).

As reported in Table 4, the average monthly liquidity-beta coefficient and the regression R2 in equation (5) across all stocks is 0.77 and 7.6 percent respectively. We find that the average beta increases (decreases) to 0.83 (0.74) in down (up) market states. As one would expect, the percentage of variation in individual firm liquidity explained by the market liquidity is also higher at 8 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 0.96 as well as R2 of 10.1 percent. Hence, large, negative market returns decrease the liquidity of all stocks in the market and increase liquidity commonality.

Next, we explore the time-series relation between liquidity commonality and market returns. Since the Rt2 values are constrained to be between zero and one by construction, we define liquidity comovement as the logit transformation of Rt2, COMOVEt =[pic]. We regress our comovement measure on market returns (Rmt) , taking into account the sign and magnitude of market returns:

[pic] (6)

[pic] (7)

[pic]

[pic] (8)

where, DUP,t (DDOWN,t ) is a dummy variable that captures positive (negative) market returns, and DUP,LARGE,t (DDOWN,LARGE,t ) is the dummy variable that is equal to one when positive (negative) market returns (Rm,t) are higher (lower) than z standard deviations from its mean. DUP,SMALL,t (DDOWN,SMALL,t ) is a dummy variable that is equal to one if and only if Rm,t is greater (less) than 0 and less (greater) than z standard deviation above (below) its mean return. We consider three values of z: 2.0, 1.5 and 1.0 standard deviations from the mean to check the robustness of our results.

Table 5 presents the empirical estimates of the relation between comovement and market returns. As shown in the first column of Panel A in Table 5, the comovement in liquidity is significantly negatively related to market returns. When we independently evaluate positive and negative market returns using equation (7), we find that the effect of market returns on liquidity comovement is confined to down markets. The asymmetric effect of market returns indicates that individual stock liquidity comovement is linked to drop in aggregate market valuations. Estimates of equation (8) shows that the liquidity comovement is strongest when there is a large drop in market prices and the latter finding is robust to different cut-off values used to identify large negative market return states.

Together, our 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.

We also consider other factors that may affect the inter-temporal variation in liquidity commonality. Vayanos (2004) specifies stochastic market volatility as a key state variable that 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.[8]

Finally, 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 absolute value of the relative order imbalance (or abs(ROIB)) defined in Section 3.1 as our measure of level of order imbalance. To measure commonality in order imbalances, we estimate the R2 from a single-factor regression model of individual firm order imbalance on market (average) order imbalance, similar in spirit to the liquidity commonality measure using proportional spreads in equation (5). In addition, we construct a measure of order flow imbalance arising from institutional trading. We obtain quarterly institutional holding data for all firms in our sample from Thompson Financial/Spectrum Institutional Holdings database for the time period 1988 to 2003. First, we compute the quarterly percentage change in institutional holdings for each security. Second, for each quarter, we average the percentage change in holdings across all stocks to measure the net change in institutional holdings, and denote its absolute value as ΔInstitutionalHolding. A large value of ΔInstitutionalHolding implies that there is substantial amount of imbalance in institutional trading.

Table 5, Panel B shows 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. Therefore, the results are consistent with the prediction in Vayonas (2004) that uncertainty in the market increases investor demand for liquidity. Extreme shifts in the aggregate order imbalance, both in terms of the level as well as degree of comovement in order imbalance, has significant positive effects on liquidity commonality. Furthermore, large variations in equity holdings by institutional investors add to liquidity commonality. These results illustrate two major findings. First, liquidity commonality is driven by changes in demand for liquidity, proxied by the above variables. Second, and more importantly, these demands factors cannot explain the asymmetric effect of market returns on liquidity. In all the above specifications, we continue to find that large drop in market index is associated with significant increase in liquidity commonality.[9] We, therefore, conclude that the increase in liquidity commonality in down market states is related to 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. 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. 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.

We begin by estimating the following industry-factor model for daily change in liquidity for security i ([pic]), within each month:

[pic] (9)

where the industry-liquidity factor [pic][pic][pic] is the daily percentage change in the equally-weighted average of adjusted spreads across all stocks in industry j in day s. Similar to our approach in estimating market-wide liquidity commonality in equation (5), we aggregate the regression R2 from equation (9) 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 COMOVEINDj,t. We form 17 industry-wide comovement measures using the SIC classification derived by Fama-French.[10] COMOVEINDj,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:

[pic] (10)

We also investigate the asymmetric effect of positive and negative industry and market returns on liquidity comovement, as well as the effect of large and small industry and market returns:

[pic]

[pic] (11)

[pic]

[pic][pic]

[pic] (12)

where the dummy variables are defined in the same way as in equations (7) and (8). The regression coefficient associated with the independent variable [pic] provides a 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 liquidity comovement on industry 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 [pic] is a significant -0.750 while the coefficient for [pic] is -0.171 and statistically insignificant at conventional levels. When we separate the returns according to their magnitude, large negative market returns turn out to have the biggest impact on liquidity movements. For example, large negative industry portfolio return is associated with an increase in the industry liquidity comovement by 0.756 while a large negative market return deepens the industry-wide comovement by more than twice the magnitude at 1.731. These results strongly support the idea that when 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.

4. 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. Hence, the price reversal 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.

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 of the market.

The weekly contrarian investment strategy that we employ is similar in spirit to the formulation in Lehmann (1990), Conrad, Hameed and Niden (1994) and Avramov et al. (2005). First, 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: [pic], where p denotes winner or loser portfolio. Consistent with the contrarian investment strategy, we long the loser securities and short the winner securities, with weights depending positively on the magnitude of returns. Since the weights are also proportional to the stock’s turnover, the scheme places greater absolute portfolio weights on securities with high 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 [pic], which can be interpreted as the return to a $1 investment in each portfolio. The combined contrarian profits are obtained by taking the difference in profits from the loser and winner portfolios.

To the extent that the contrarian profits reflect the cost of supplying liquidity, we expect the price reversals on heavy volume to be negatively (positively) related to changes in aggregate market valuations (liquidity commonality). 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. Finally, we further divide the four market states into two equal sub-periods based on liquidity commonality (as defined in Section 4.1).

Table 7, Panel A reports significant contrarian profit of 0.58 percent in week t+1 (t-statistics is 6.35) for the full sample period. A large portion of the profits comes from the loser portfolio with a return of 0.74 percent, suggesting that price reversals on heavy volume are stronger after an initial price decline. The contrarian profit at 2 week lag is small at 0.16 percent, but is statistically significant (t statistics is 2.20). The contrarian profit declines rapidly and insignificant as we move to longer lags. Since the contrarian profits and price reversals appear to lasts for up to two weeks, we stop our subsequent analyses at 2 weeks lag.

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 to 1.19 percent compared to profits of between 0.48 and 0.65 percent in the other three market states. We find similar profit pattern in week t+2, although the magnitude falls quickly. It is also noteworthy that the loser portfolio shows the largest profit (above 1.0 percent) following large negative market returns, consistent with the hypothesis that price reversals on heavy selling pressure are related to compensation for liquidity provision. Finally, Panel C of Table 7 reveals that state of the market return as well as the degree of liquidity commonality affect contrarian profits. We observe a dramatic increase in the contrarian profits in week t+1 (t+2) to 1.75 (1.27) percent following periods of high liquidity commonality and large decline in market valuations. These profit figures are more than double the profits of between 0.39 and 0.68 percent observed for the other market states in week t+1. The cumulative evidence in Table 8 indicates that in periods when the market makers face the tightest funding constraints and highest cost of providing liquidity, stocks experience the biggest price reversals on heavy trading, especially, loser stocks.

In Campbell, Grossman and Wang (1993), price reversals occur as market makers accommodate selling pressure. High trading volume, on the other hand, does not account for the direction of trade, although we assume that high volume on price decline are mostly seller-initiated trades. It is natural to check if our results hold when we separate buyer and seller initiated trades. To do this, we compute order imbalance for stock i at week t, ROIBit as the difference between buyer and seller initiated trades scaled by the dollar trading volume. A large positive (negative) ROIBit indicates strong buy (sell) pressure. According to Campbell, Grossman and Wang, price reversals for loser securities would be most intensive when sell pressure is dominant. We examine contrarian profits conditional on loser and winner securities facing buy or sell pressure, giving us four different portfolios. The computation of contrarian profits for each of these four portfolios is also modified to allow the weights to vary in proportion to the absolute value of ROIBit:

[pic]

where NPt represents the number of securities in the portfolio of losers with buy pressure, losers with sell pressure, winners with buy pressure or winners with sell pressure. For example, the securities with the biggest weight in the losers with net sell pressure would be those which have large negative returns, heavy trading volume as well as seller-initiated trades far exceeding buyer-initiated ones.

Table 8 presents the results for the four portfolios sorted on past returns and net buy or sell order imbalance. The unconditional contrarian profits for the four portfolios reveals that the loser portfolio with net sell pressure registers the biggest contrarian profits of 0.93 percent in week t+1 while winner securities with net buy pressure has the lowest profits of 0.09 percent. A zero-investment portfolio consisting of a long position in the loser, sell pressure portfolio and a short position in the winner, buy pressure portfolio generates a significant weekly profit of 0.84 percent. When we condition the contrarian profits on market states, we find a striking effect on large down markets: the loser, net sell pressure portfolio shows the biggest reversal profit of 2.20 percent. The combined portfolio of loser, sell pressure minus winner, buy-pressure generates significant profits of 1.83 percent per week, conditional on large negative market returns. A similar pattern emerges in week t+2, although the magnitude is smaller. The short-term price reversals are consistent with increase in expected returns required to compensate liquidity providers as they accommodate heavy selling pressure. This cost of supplying liquidity is greatest following large decline in aggregate market valuations, providing support to our contention that supply side liquidity effects are most important when funding constraints are binding.

6. Conclusion

This paper shows that liquidity responds asymmetrically to changes in asset market values. Large negative 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. 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. The economic significance of the price reversal is strongest when the large fall in market prices are accompanied by high liquidity commonality and large imbalance between investor buy and sell orders. 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 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.

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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 seasonally adjusted spreads, ASPRj, using the following regression model:

[pic]

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 in the panel below.

[pic]

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:

[pic]

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:

[pic]

where 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: [pic]

where DUP,LARGE,,m,t (DDOWN,LARGE,m,t ) is a dummy variable that is equal to one if and only if R,m,t is above 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).

Panel A: Relation between Spreads and Lagged Returns

[pic]

Panel B: Relation between Spread and the Signed Lagged Returns

[pic]

Panel C: Relation between Spread and the Magnitude of Lagged Returns

[pic]

Table 3: Relation between Spread and Signed Lagged Returns: Coefficients based on two-way dependent sorts on firm size and volatility

The regression model and the definition of variables are identical to Panel B in Table 2, except that the estimates are reported separately for nine portfolios formed by a two-way dependent sorts based on firm size and historical return volatility.

[pic]

[pic][pic]

[pic]

[pic][pic]

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.

[pic]

where [pic], the percentage change in adjusted daily proportional spread for stock i; [pic]) and ASPRm,t is the cross-sectional, equally-weighted average of daily spreads across all stocks. The regression generates a monthly series of liquidity betas and regression R2 .The panel below reports the cross-sectional average beta and R2 for the whole sample period as well as sub-periods defined by the sign and magnitude of market returns in month t. Lage and small market returns are defined based on whether the returns are above or below 1.5 standard deviation from zero returns.

[pic]

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:

[pic]

where[pic], the percentage change in adjusted daily proportional spread for stock i from day s-1 to s; [pic])[pic] 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:

Model A: [pic]

Model B: [pic]

Model C: [pic]

[pic]

where COMOVEt is defined as [pic]. The dummy variable DUP,t (DDOWN,t ) is equal to one if and only if the return on the CRSP value-weighted market index in month t (Rm,t ) is positive (negative). DUP,LARGE,t (DDOWN,LARGE,t ) is equal to one if Rm,t is greater (less) than z standard deviation above (below) its mean return. DUP,SMALL,t (DDOWN,SMALL,t ) is equal to one if and only if Rm,t is between 0 and z (-z) standard deviation from its mean. We consider three values of z: 2.0, 1.5 and 1.0 corresponding to models C1, C2, and C3. The t-statistics are reported in italic. In Panel B, we add the following monthly variables to model C2: (a) ROIB, the average relative order imbalance; (b) commonality in ROIB, similar to the COMOVE measure for liquidity we use above; (c) percentage change in institutional holdings; (d) market-wide volatility; and (e) average idiosyncratic volatility.

Panel A: Liquidity Commonality and Market Returns

[pic]

Panel B: Liquidity Commonality and Market Returns

and other demand-side factors

[pic]

Table 6: Commonality in Liquidity, Industry and Market Returns

Each month, we estimate the following regression for stock i:

[pic]

where [pic] is the percentage change in adjusted daily proportional spread for stock i from day s-1 to s; [pic] [pic] is the percentage change of the cross-sectional, equally-weighted average of spreads across all stocks in the industry j in day s, ASPRINDj,s. The above regression generates R2i,t, for each month t. The cross-sectional average R2i,t within industry j for month t is denoted as RINDj,t2, which is used in the second stage monthly regression :

Model A:

[pic]

Model B:

[pic]

Model C:

[pic]where COMOVEINDj,t is defined as [pic]; 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,INDj,,t (DDOWN,INDj,,t ) is equal to one if and only if RINDj,t is positive (negative). 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. The corresponding market dummy variables are similarly defined. The t-statistics are reported in italic.

[pic]

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 weights on stock I in week t is given by:

[pic]

where Turnit is stock I turnover in week t-1. Post-formation contrarian profits for week t+k, for k=1,2,3 and 4 is reported in Panel A. In Panel B, contrarian profits for sub-periods 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 zero. Small Up (Small Down) market refers to cumulative market returns between zero and 1.5 (-1.5) standard deviation. In Panel C, we further split the market return sub-period based on whether liquidity commonality is above (below) the median.

Panel A: Unconditional Contrarian Profits

| |Week |

|Portfolio |t+1 |t+2 |t+3 |t+4 |

|Loser |0.74% |0.45% |0.40% |0.37% |

|Winner |0.16% |0.29% |0.36% |0.38% |

|Loser minus Winner |0.58% |0.16% |0.04% |-0.01% |

|(t-statistics) |(6.35) |(2.20) |(0.58) |(-0.16) |

Panel B: Contrarian Profits Conditional on Market Returns

|Week t+1 |

|Portfolio |Past Market Return |

| |Large Up |Small Up |Small Down |Large Down |

|Loser |0.61% |0.81% |0.45% |1.43% |

|Winner |-0.03% |0.27% |-0.03% |0.24% |

|Loser minus Winner |0.65% |0.55% |0.48% |1.19% |

|(t-statistics) |(1.13) |(4.91) |(2.84) |(2.97) |

|Week t+2 |

| Portfolio |Past Market Return |

| |Large Up |Small Up |Small Down |Large Down |

|Loser |0.88% |0.47% |0.21% |1.04% |

|Winner |0.36% |0.41% |0.08% |0.22% |

|Loser minus Winner |0.51% |0.06% |0.14% |0.82% |

|(t-statistics) |(1.73) |( 0.68) |(1.05) |(1.98) |

Panel C: Contrarian Profits Conditional on Market Returns

and Liquidity Commonality

| |Week t+1 |

|Portfolio |Past Market Return |

| |Large Up |Small Up |Small Down |Large Down |

| |Liquidity Commonality |Liquidity Commonality |Liquidity Commonality |Liquidity Commonality |

| |High |

|Portfolio |Past Market Return |

| |Large Up |Small Up |Small Down |Large Down |

| |Liquidity Commonality |Liquidity Commonality |Liquidity Commonality |Liquidity Commonality |

| |High |

| |Unconditional (Whole|Past Market Return |

| |Sample Period) | |

| | |Large Up |Small Up |Small Down |Large Down |

|Loser, Buy-Pressure |0.68% |-0.23% |0.81% |0.57% |0.70% |

|Loser Sell-Pressure |0.93% |1.29% |1.00% |0.42% |2.20% |

|  | |  | | |  |

|Winner, Buy-Pressure |0.09% |-0.25% |0.18% |-0.09% |0.37% |

|Winner, Sell-Pressure |0.43% |0.89% |0.59% |0.10% |0.16% |

|Loser, Buy-Pressure minus Winner, | |-1.12% |0.21% |0.46% |0.55% |

|Sell-Pressure |0.25% | | | | |

|(t-statistics) |(1.25) |(-1.25) |(1.08) |(0.93) |(0.93) |

|Loser, Sell-Pressure minus Winner, | |1.54% |0.82% |0.51% |1.83% |

|Buy-Pressure |0.84 | | | | |

|(t-statistics) |(6.38) |(3.86) |(4.65) |(2.47) |(2.71) |

|Portfolio |Week t+2 |

| |Unconditional (Whole|Past Market Return |

| |Sample Period) | |

| | |Large Up |Small Up |Small Down |Large Down |

|Loser, Buy-Pressure |0.50% |0.88% |0.51% |0.31% |0.96% |

|Loser Sell-Pressure |0.45% |0.72% |0.48% |0.23% |0.93% |

|  | | | | | |

|Winner, Buy-Pressure |0.27% |0.34% |0.39% |0.06% |0.11% |

|Winner, Sell-Pressure |0.39% |0.49% |0.50% |0.13% |0.44% |

|Loser, Buy-Pressure minus Winner, | |0.39% |0.01% |0.18% |0.52% |

|Sell-Pressure |0.12% | | | | |

|(t-statistics) |(1.16) |(1.05) |(0.10) |(1.09) |(0.81) |

|Loser, Sell-Pressure minus Winner, | |0.38% |0.10% |0.17% |0.82% |

|Buy-Pressure |0.18 | | | | |

|t-statistics) |(2.14) |(0.87) |(0.94) |(1.04) |(1.83) |

-----------------------

[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.

[2] The work of Eisfeldt (2004) suggests that assets could be more liquid during certain periods relative to others.

[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] 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 affect illiquid assets. Sadka (2005) documents that the earnings momentum effect is partly due to higher liquidity risk.

[5] We repeat the analysis with raw and effective proportional spreads and find similar results.

[6] 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 µjt. The across security correlations are estimated using the following relation: µj+1,t = ³0 + ³1,t µj,t + ¾j,t. The cross-equation dependence is measured by the average slope coefficient ³1 and the associated tεjt. 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. These results suggest that the mean cross-equation dependence in the residuals are not significant and do not materially affect our results.

[7] The negative relation between lagged returns and liquidity remains robust when we replace adjusted spreads with raw spreads and effective spreads.

[8] Another candidate variable that may affect time variation in commonality in liquidity is aggregate funds flow. For example, investors in Vayanos (2004)’s model are fund managers who are subject to withdrawals when the fund’s performance falls below an exogenous threshold. When the funds performance fall sufficiently, withdrawals become more likely and managers are less willing to hold illiquid assets. This argument can be extended to link flow of funds from the mutual fund industry to time variation in demand for liquidity, and hence, liquidity commonality. A large value of FundFlow implies that there is a substantial amount of institutional money flowing into or out of the equity market. We plan to include this variable in the next version.

[9] We also examine if order imbalance comovement is endogeneously determined. Our 2SLS analyses (not reported here)confirm that strong influence of large negative market return on liquidity comovement is not biased by concerns about endogeniety.

3 The industry classifications are obtained from K. French’s website at

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