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					                           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.




                                                 1
                                      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.




                                             2
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

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
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


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
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

    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
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.



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


                                                       6
    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




                                              7
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




                                             8
    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.




                                                9
   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:
                 4                11
QSPRj ,t  a j   b j ,k DAYk ,t   c j ,k MONTHk ,t  d j HOLIDAYt
                k 1             k 1                                       (1)
         e j TICK1t  f j TICK 2 t  g t YEAR t  ht YEAR2 t  ASPRj ,t
                                              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



                                             10
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



3.1 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


                                            11
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:

ASPRi ,t  ai ASPRi ,t 1  bi Ri ,t 1  mi Rm,t 1
           vi TURNi ,t 1  ci ROIBi ,t 1  d i STDi ,t 1  f i PRCi ,t 2   i ,t 1   (2)




                                                          12
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:

ASPRi ,t  ai ASPRi ,t 1  bUP,i Ri ,t 1 DUP,i ,t 1  bDOWN,i Ri ,t 1 DDOWN, i ,t 1
            mUP,i Rm,t 1 DUP,m,t 1  mDOWN,i Rm,t 1 DDOWN, m,t 1                        (3)

            vi TURNi ,t 1  ci ROIBi ,t 1  d i STDi ,t 1  f i PRCi ,t 2   i ,t 1




                                                           13
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




                                             14
ASPRi ,t  ai ASPRi ,t 1  bUP, SMALL,i Ri ,t 1 DUP, SMALL,i ,t 1  bUP, LARGE ,i Ri ,t 1 DUP, LARGE ,i ,t 1
            bDOWN, SMALL,i Ri ,t 1 DDOWN, SMALL, i ,t 1  bDOWN, LARGE ,i Ri ,t 1 DDOWN, LARGE ,i ,t 1

            mUP, SMALL,i Rm,t 1 DUP, SMALL,m,t 1  mUP, LARGE ,i Rm,t 1 DUP, LARGE ,m ,t 1                     (4)

            m DOWN, SMALL,i Rm ,t 1 DDOWN, SMALL, m ,t 1  m DOWN, LARGE ,i Rm ,t 1 DDOWN, LARGE ,m ,t 1

            vi TURNi ,t 1  ci ROIBi ,t 1  d i STDi ,t 1  f i PRCi ,t  2   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 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




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 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.
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.


                                                              15
   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.


                                              16
   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.


4 Comovement in Liquidity

4.1. 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



                                            17
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:

    DL i , s  ai   i DL m.s   i.s   (5)

    where DL i , s  ( ASPRi.s  ASPRi., s 1 ) / ASPRi.s 1 and DL m.s  ( ASPR m.s    ASPRm.s 1 )

/ ASPRm.s 1 ) 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).



                                                 18
   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

= ln[ Rt /(1  Rt )] . We regress our comovement measure on market returns (Rmt) , taking
        2        2



into account the sign and magnitude of market returns:
  COMOVE t  a   Rm ,t   t                                           (6)
  COMOVE t  a  b Rm ,t DUP,t  c Rm ,t DDOWN,t   t                   (7)
  COMOVE t  a  d Rm ,t DDOWN, LARGE ,t  e Rm,t DUP, LARGE ,t
                   fR m ,t DDOWN, SMALL,t  gRm ,t DUP, SMALL,t   t   (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


                                                   19
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


                                             20
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.


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.


                                                    21
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
                             9
liquidity commonality.           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




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.


                                                    22
    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 ( DLi , s ), within each month:

     DLi ,s  ai   i DL INDj,.s   i.s                                     (9)

where the industry-liquidity factor DL INDj.s  ( ASPR INDj.s  ASPR INDj, s 1 ) / ASPRINDj, s 1 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 R 2 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

3
 The industry classifications are obtained from K. French’s website at
http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html



                                                   23
independent effects of changes in the value of the industry and market portfolios on

liquidity comovement:
     COMOVE INDj,t  a  bIND RINDj,t  bMKT RMKTj ,t   t                                (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:
    COMOVE INDj,t  a  bIND R INDj,t DUP, INDj,t  c IND R INDj,t DDOWN, INDj,t
         bMKT RMKTj ,t DUP, MKTj ,t  cMKT RMKTj ,t DDOWN, MKT ,t   t                   (11)
     COMOVE INDj,t  a  f IND R INDj,t DUP, LARGE , INDj,t  g IND R INDj,t DDOWN, LARGE , INDj,t
         hIND R INDj,t DUP, SMALL, INDj,t  j IND RINDj,t DDOWN, SMALL, INDj,t
         f MKT RMKTj ,t DUP, LARGE , MKTj ,t  g MKT RMKTj ,t DDOWN, LARGE , MKTj ,t
         hMKT RMKTj ,t DUP, SMALL, MKTj ,t  jMKT RMKTj ,t DDOWN, SMALL, MKTj ,t   t    (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 RMKTj ,t 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 RMKTj ,t is a significant

-0.750 while the coefficient for RINDj ,t 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


                                                      24
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.


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. 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



                                             25
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: wi , p ,t 1   Ri ,t Turni ,t / i 1 Ri ,t Turni ,t , where p denotes winner
                                                         Npt



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  p ,t k  i 1 wit 1 Ri ,t k , which can be
                                                                     Np



interpreted as the return to a $1 investment in each portfolio. The combined contrarian


                                                  26
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


                                             27
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:
     p ,t 1  i 1 [ Ri ,t ROIBi ,t Turni ,t / i 1 Ri ,t ROIBi ,t Turni ,t ]Ri ,t 1
                   N pt                               Np



   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


                                                           28
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



                                             29
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.




                                            30
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Morck, R., B. Yeung, and W. Yu, 2000, the Information Content of Stock Markets: Why
  Do Emerging Markets Have Synchronous Stock Price Movements?, Journal of
  Financial Economics 59, 215-260.

Morris, Stephen, and Hyun Song Shin, 2004, Liquidity Black Holes, Review of Finance
  8, 1-18.

Naik, Narayan, and Pradeep Yadav, 2003, Risk Management with Derivatives by Dealers
   and Market Quality in Government Bond Markets, Journal of Finance 5, 1873-1904.

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                                           32
Pastor, Lubos, and Robert F. Stambaugh, 2003, Liquidity risk and expected stock returns,
   Journal of Political Economy 111, 642-685.

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    Finance 33, 1133-1152.

Vayanos, Dimitri, 2004, Flight To Quality, Flight to Liquidity and the Pricing of Risk,
   NBER working paper.




                                            33
                 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, ASPR j, using the
following regression model:

                         4              11
QSPR j ,t    a j   b j ,k DAY k ,t   c j ,k MONTH k ,t  d j HOLIDAY t
                      k 1              k 1

             e j TICK 1t  f j TICK 2 t  g t YEAR1t  ht YEAR 2 t  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 in the panel below.


                             QSPR (Unadjusted Proportional              ASPR (Adjusted Proportional
   Year      Number                Quoted Spread)                            Quoted Spread)
               of
            Securities
                                                      Coefficient                               Coefficient
                             Mean         Median      of Variation     Mean         Median      of Variation
   1988        1040          1.28%           1.04%        0.636        1.37%         1.10%         0.661
   1989        1098          1.14%           0.91%        0.694        1.27%         1.00%         0.729
   1990        1149          1.42%           1.09%        0.728        1.59%         1.24%         0.748
   1991        1228          1.32%           1.02%        0.710        1.52%         1.17%         0.722
   1992        1319          1.25%           0.98%        0.715        1.49%         1.18%         0.705
   1993        1445          1.21%           0.92%        0.808        1.50%         1.19%         0.710
   1994        1504          1.16%           0.90%        0.731        1.51%         1.23%         0.664
   1995        1567          1.06%           0.82%        0.758        1.47%         1.19%         0.669
   1996        1643          0.98%           0.74%        0.818        1.42%         1.18%         0.662
   1997        1707          0.77%           0.59%        0.814        1.35%         1.09%         0.694
   1998        1698          0.78%           0.57%        0.844        1.38%         1.10%         0.712
   1999        1577          0.85%           0.61%        0.840        1.39%         1.13%         0.692
   2000        1452          0.93%           0.61%        0.949        1.42%         1.17%         0.682
   2001        1308          0.54%           0.31%        1.217        1.41%         1.17%         0.650
   2002        1226          0.40%           0.21%        1.290        1.30%         1.07%         0.672
   2003        1190          0.26%           0.13%        1.262        1.16%         0.96%         0.707




                                                     34
               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  ai ASPRi ,t 1  mi Rm,t 1  bi Ri ,t 1
            vi TURNi ,t 1  ci ROIBi ,t 1  d i STDi ,t 1  f i PRCi ,t 2   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  ai ASPRi ,t 1  mUP,i Rm,t 1 DUP,m,t 1  mDOWN,i Rm,t 1 DDOWN, m,t 1
            bUP,i Ri ,t 1 DUP,i ,t 1  bDOWN,i Ri ,t 1 DDOWN, i ,t 1 

            vi TURNi ,t 1  ci ROIBi ,t 1  d i STDi ,t 1  f i PRCi ,t 2   i ,t 1
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:
ASPRi ,t  ai ASPRi ,t 1  mUP, LARGE ,i Rm,t 1 DUP, LARGE ,m ,t 1  mUP, SMALL,i Rm ,t 1 DUP, SMALL,m ,t 1
           m DOWN, LARGE ,i Rm ,t 1 DDOWN, LARGE , m ,t 1  m DOWN, SMALL,i Rm ,t 1 DDOWN, SMALL,m ,t 1

           bUP, LARGE ,i Ri ,t 1 DUP, LARGE ,i ,t 1  bUP, SMALL,i Ri ,t 1 DUP, SMALL,i ,t 1

           bDOWN, LARGE ,i Ri ,t 1 DDOWN, LARGE , i ,t 1  bDOWN, SMALL,i Ri ,t 1 DDOWN, SMALL,i ,t 1

           vi TURNi ,t 1  ci ROIBi ,t 1  d i STDi ,t 1  f i PRCi ,t  2   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 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).




                                                                     35
                    Panel A: Relation between Spreads and Lagged Returns
      Estimate
                               Intercept             ASPR(i,t-1)           Ret(i,t-1)          Ret(m,t-1)
      Statistics
               Mean            0.311***               0.736***            -0.312***            -0.553***
            Median              0.240                  0.759               -0.222               -0.344
      % of negative                                                        97.4%                95.2%
      % of positive              97.8%                100.0%
         % positive              88.8%                 99.8%                73.6%                55.4%
         significant
      Estimate
                              TURN(i,t-1)            ROIB(i,t-1)          STD(i,t-1)           PRC(i,t-1)
      Statistics
               Mean            -0.002**               0.031***             0.058***             0.877***
            Median              -0.001                 0.014                0.043                0.536
      % of negative             59.9%
      % of positive                                    56.6%                57.9%                76.3%
        % negative               10.2%                 10.5%                10.5%                26.2%
         significant

          Panel B: Relation between Spread and the Signed Lagged Returns
       Estimate               Ret(i,t-1) *          Ret(i,t-1) *         Ret(m,t-1) *        Ret(m,t-1) *
       Statistics             D(Up,i,t-1)          D(Down,i,t-1)         D(Up,m,t-1)        D(Down,m,t-1)
             Mean              -0.220***              -0.417***           -0.433***            -0.705***
            Median              -0.139                 -0.288              -0.242               -0.387
      % of negative             79.3%                  90.7%               78.7%                85.7%
        % negative              25.1%                  48.7%               18.3%                28.9%
         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
                 D(Up,Large,m,t- D(Up,Small,m,t-                    D(Down,Large,m,t-   D(Down,Small,m,t-
  Statistics           1)              1)                                  1)                  1)
       Mean          -0.547***           -0.386***      -0.17***        -0.772***           -0.533***         -0.24***
      Median          -0.306              -0.227                         -0.389              -0.253
% of negative         77.1%               72.5%          56.2%           84.9%               66.5%            58.2%
  % negative          17.1%               12.6%           5.8%           29.7%                9.5%             6.3%
   significant
                        (e)                  (f)          (e)-(f)           (g)                 (h)            (g)-(h)
  Estimate      Ret(i,t-1) *     Ret(i,t-1) *                           Ret(i,t-1) *       Ret(i,t-1) *
  Statistics D(Up,Large,i,t-1) D(Up,Small,i,t-1)                    D(Down,Large,i,t-1) D(Down,Small,i,t-1)
        Mean   -0.226***         -0.205***               -0.020         -0.439***           -0.395***         -0.05**
      Median     -0.142           -0.142                                 -0.277              -0.262
% of negative    75.6%             73.2%                 48.8%           87.8%               83.4%            52.5%
  % negative     22.8%             15.9%                  6.8%           41.7%               30.1%            10.1%
   significant




                                                         36
       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.


  Ret(m,t-1) *         Estimate
                                    High Volatility     Medium Volatility      Low Volatility     High - Low
  D(Up,m,t-1)          Statistics
                          Mean         -0.965***            -0.741***            -0.561***          -0.403**
                        Median          -0.710                 -0.714             -0.451            -0.259
   Small Size    % of negative          72.0%                  78.9%               78.2%
                   % negative           17.8%                  16.5%               17.3%
                    significant
                          Mean         -0.587***            -0.479***            -0.218***          -0.369**
                        Median          -0.359                 -0.408             -0.242            -0.117
 Medium Size % of negative              85.0%                  91.9%               80.7%
               % negative               13.1%                  20.7%               22.9%
                significant
                          Mean         -0.262***            -0.217***            -0.171***         -0.091***
                        Median          -0.198                 -0.155             -0.149            -0.048
   Large Size    % of negative          83.6%                  88.3%               92.7%
                   % negative           22.7%                  30.6%               26.4%
                    significant
 Ret(m,t-1) *
                       Estimate
 D(Down,m,t-                        High Volatility     Medium Volatility      Low Volatility     High - Low
                       Statistics
     1)
                          Mean         -1.557***            -1.212***            -0.949***          -0.607**
                        Median          -1.151                 -0.832             -0.873            -0.278
   Small Size    % of negative          80.4%                  79.8%               88.2%
                   % negative           27.1%                  21.1%               41.8%
                    significant
                          Mean         -0.832***            -0.534***            -0.409***          -0.423**
                        Median          -0.659                 -0.429             -0.366            -0.293
 Medium Size % of negative              90.7%                  88.3%               88.1%
               % negative               32.7%                  31.5%               33.0%
                significant
                          Mean         -0.295***            -0.251***            -0.211***          -0.083**
                        Median          -0.239                 -0.156             -0.179            -0.061
   Large Size    % of negative          85.5%                  82.0%               90.9%
                   % negative           28.2%                  29.7%               33.6%
                    significant




                                                          37
 Ret(i,t-1) *       Estimate
                                 High Volatility   Medium Volatility   Low Volatility   High - Low
 D(Up,i,t-1)        Statistics
                        Mean       -0.437***          -0.452***          -0.321***       -0.116*
                      Median        -0.340               -0.309           -0.225         -0.116
 Small Size     % of negative       83.2%                83.5%            77.3%
                  % negative        27.1%                33.9%            22.7%
                   significant
                        Mean       -0.223***          -0.238***          -0.202***        -0.021
                      Median        -0.185               -0.211           -0.190          0.005
Medium Size % of negative           82.2%                88.3%            80.7%
              % negative            29.0%                33.3%            30.3%
               significant
                        Mean       -0.135***          -0.086***          -0.119***        -0.016
                      Median        -0.119               -0.062           -0.095         -0.024
 Large Size     % of negative       85.5%                81.1%            83.6%
                  % negative        33.6%                18.9%            25.5%
                   significant

 Ret(i,t-1) *       Estimate
                                 High Volatility   Medium Volatility   Low Volatility   High - Low
D(Down,i,t-1)       Statistics
                        Mean       -0.842***          -0.657***          -0.527***       -0.315**
                      Median        -0.759               -0.588           -0.450         -0.310
 Small Size     % of negative       93.5%                92.7%            87.3%
                  % negative        54.2%                47.7%            38.2%
                   significant
                        Mean       -0.509***          -0.291***          -0.243***       -0.266**
                      Median        -0.435               -0.241           -0.263         -0.172
Medium Size % of negative           97.2%                89.2%            87.2%
              % negative            67.3%                40.5%            38.5%
               significant
                        Mean       -0.286***          -0.206***          -0.186***       -0.101**
                      Median        -0.250               -0.190           -0.158         -0.092
 Large Size     % of negative       96.4%                95.5%            95.5%
                  % negative        71.8%                59.5%            50.9%
                   significant




                                                    38
                              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.
DL i.t  ai   i DL m.t   i.t
where DL i.t  ( ASPRi.t  ASPRi.t 1 ) / ASPRi.t 1 , the percentage change in adjusted daily proportional
spread for stock i;     DL m.t  ( ASPRm.t  ASPRm.t 1 ) / ASPRm.t 1 ) 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.

                                      Sub-Periods                               Sub-Periods
                   Whole                                      Large        Small         Small          Large
                                   Positive   Negative
                   Sample                                    Positive     Positive      Negative       Negative
                                   Market      Market
                   Period                                    Market       Market         Market         Market
                                   Returns    Returns
                                                             Returns      Returns       Returns        Returns

 liquidity beta       0.77
  R-square            0.076
 liquidity beta                     0.74         0.83
  R-square                         0.074        0.080
 liquidity beta                                               0.70          0.75          0.79           0.96
  R-square                                                   0.070         0.074         0.075          0.101




                                                        39
                   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:
DL i , s  ai   i DL m.s   i.s
where DL i , s  ( ASPRi.s  ASPRi., s 1 ) / ASPRi.s 1 , the percentage change in adjusted daily proportional
spread for stock i from day s-1 to s; DL m.s  ( ASPR m.s  ASPR m.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
                                                           2
stock i , the above regression equation generates an R i,t, for each month t. The cross-sectional average R2i,t,
denoted as Rt2, is used in the second stage monthly regression:
Model A: COMOVE t  a   Rm ,t   t
Model B: COMOVE t  a  b Rm ,t DUP,t  c Rm ,t DDOWN,t   t
Model C: COMOVE t  a  g Rm ,t D DOWN, LARGE ,t  e Rm ,t DUP, LARGE ,t
                                jR m ,t D DOWN, SMALL,t  kRm ,t DUP, SMALL,t   t
where COMOVEt is defined as ln[ Rt2 /(1  Rt2 )] . 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




                                                         40
     Model             A        B         C1       C2       C3
Intercept            -2.515   -2.606     -2.601   -2.605   -2.582
                    -127.78   -81.60     -74.11   -68.35   -59.58
Ret(m,t)             -1.425
                      -3.18
Ret(m,t) *                    -4.076
D(Down,m,t)                    -4.74
Ret(m,t) *                     1.087
D(Up,m,t)                       1.31
Ret(m,t) *                               -4.461   -4.439   -3.987
D(Down,Large,m,t)                         -4.59    -4.99    -4.37
Ret(m,t) *                               -3.416   -3.002   -0.869
D(Down,Small,m,t)                         -2.54    -1.66    -0.29
Ret(m,t) *                                1.093    1.540    0.531
D(Up,Small,m,t)                            1.22     1.41     0.34
Ret(m,t) *                               -1.151    0.013    0.669
D(Up,Large,m,t)                           -0.47     0.01     0.74
            Panel B: Liquidity Commonality and Market Returns
                       and other demand-side factors




                                    41
       Model          C2       C2       C2
 Intercept           -2.305   -2.689   -2.637
                     -11.34   -54.11   -31.34
 Ret(m,t)

 Ret(m,t) *
 D(Down,m,t)
 Ret(m,t) *
 D(Up,m,t)
 Ret(m,t) *          -3.772   -3.007   -4.285
 D(Down,Large,m,t)    -4.28    -2.90    -4.45
 Ret(m,t) *          -2.239   -2.063   -2.855
 D(Down,Small,m,t)    -1.27    -1.13    -1.55
 Ret(m,t) *          1.143    0.934    1.401
 D(Up,Small,m,t)     1.05     0.85     1.23
 Ret(m,t) *          -0.235   -0.581   -0.099
 D(Up,Large,m,t)      -0.22    -0.54    -0.09
 Ret(m,t) *
 D(Small,m,t)
 Abs(ROIB)           1.382
                     2.30
 ROIB                0.156
 Comovement
ΔInstitutional       1.93
Holding              3.540
                     1.91
 Market                       2.718
 Volatility                   2.57
 Idiosyncratic                         0.353
 Volatility                            0.43




                              42
         Table 6: Commonality in Liquidity, Industry and Market Returns
Each month, we estimate the following regression for stock i:
DLi , s  a i   i DL INDj,.s   i.s

where DL i , 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; DL INDj.s  ( ASPR INDj.s  ASPR INDj, s 1 ) /               ASPR INDj , s 1 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:
      COMOVE INDj,t  a  bIND R INDj,t  bMKT RMKTj ,t   t
Model B:
      COMOVEINDj,t  a  bIND RINDj,t DUP, INDj,t  c IND RINDj,t DDOWN, INDj,t
       bMKT RMKTj ,t DUP,MKTj ,t  cMKT RMKTj ,t DDOWN,MKT ,t   t
Model C:
      COMOVE INDj,t  a  f IND R INDj,t DUP, LARGE , INDj,t  g IND R INDj,t DDOWN, LARGE , INDj,t 
      hIND R INDj,t DSMALL, INDj,t  f MKT RMKTj ,t DUP, LARGE , MKTj ,t  g MKT RMKTj ,t DDOWN, LARGE , MKTj ,t
       hMKT RMKTj ,t DSMALL, MKTj ,t   t
                                                                                                                              wh
ere COMOVEINDj,t is defined as
                                              2
                                         ln[R INDj,t   /(1  R INDj,t )] ;
                                                               2
                                                                             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.




                                                                  43
       Model            A              B         C
                       -2.585         -2.634   -2.624
 Intercept
                      -483.78        -280.21   -218.5
 Ret(ind,t)            -0.171
                        -1.42
 Ret(ind,t) *                        -0.633
 D(Down,ind,t)                        -2.86
 Ret(ind,t) *                         0.170
 D(Up,ind,t)                           0.94
 Ret(m,t)             -0.750
                       -4.76
 Ret(m,t) *                          -1.656
 D(Down,m,t)                          -5.69
 Ret(m,t) *                           0.159
 D(Up,m,t)                             0.61
 Ret(ind,t) *                                  -0.756
D(Down,Large,ind,t)                             -3.17
 Ret(ind,t) *                                  -0.177
D(Down,Small,ind,t)                             -0.49
 Ret(ind,t) *                                   0.048
 D(Up,Small,ind,t)                               0.19
 Ret(ind,t) *                                   0.116
 D(Up,Large,ind,t)                               0.58
 Ret(m,t) *                                    -1.731
 D(Down,Large,m,t)                              -5.77
 Ret(m,t) *                                    -1.099
 D(Down,Small,m,t)                              -1.99
 Ret(m,t) *                                     0.243
 D(Up,Small,m,t)                                 0.74
 Ret(m,t) *                                    -0.250
 D(Up,Large,m,t)                                -0.78




                                44
                                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:
                 Ri ,t 1Turni ,t 1
 w p ,i ,t 
               
                   Np
                 i 1
                        Ri ,t 1Turni ,t 1
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
                                                                           Past Market Return
                              Portfolio
                                                         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
                                                                           Past Market Return
                                Portfolio
                                                         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)




                                                        45
             Panel C: Contrarian Profits Conditional on Market Returns
                            and Liquidity Commonality

                                                  Week t+1
                                             Past Market Return
                    Large Up          Small Up             Small Down         Large Down
                     Liquidity         Liquidity             Liquidity          Liquidity
 Portfolio                           Commonality          Commonality         Commonality
                   Commonality

                 High      Low      High          Low     High      Low     High      Low.
loser
winner
loser-winner     0.68%    0.62%    0.44%         0.66%    0.39%    0.57%    1.75%    0.61%
(t-stat)         (1.17)   (0.62)   (2.70)        (4.30)   (1.35)   (3.23)   (2.95)   (1.15)

                                                  Week t+2
                                             Past Market Return
                    Large Up          Small Up             Small Down         Large Down
                     Liquidity         Liquidity             Liquidity          Liquidity
 Portfolio                           Commonality          Commonality         Commonality
                   Commonality

                 High      Low      High          Low     High      Low     High      Low.
loser
winner
loser-winner     0.36%    0.67%    0.06%         0.06%    0.19%    0.08%    1.27%    0.38%
(t-stat)         (0.87)   (1.54)   (0.51)        (0.45)   (0.91)   (0.53)   (2.10)   (0.67)




                                            46
            Table 8: Contrarian Profits, Market Returns and Order Imbalance
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:
w p ,i ,t  Ri ,t 1 ROIBi ,t 1Turni ,t 1 / i 1 Ri ,t 1 ROIBi ,t 1Turni ,t 1
                                                Np


where Turnit is the turnover and ROIBit the relative order imbalance for stock i in week t. Post-formation
contrarian profits for week t+1 and t+2 are reported for the whoe sample period and sub-periods conditional
on market returns. Large Up (Large Down) refers to cumulative market returns from week t-4 to t-1 being
above (below) 1.5 return standard deviation. Small Up (Small Down) market refers to cumulative market
returns between zero and 1.5 (-1.5) standard deviation. We also report separately for stocks whose ROIB is
positive (buy pressure) and negative (sell pressure).
                                                                    Week t+1
                                             Unconditional                              Past Market Return
                                               (Whole
                                               Sample                                               Small    Large
 Portfolio                                     Period)                Large Up         Small Up     Down     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, Sell-Pressure                            0.25%                -1.12%           0.21%       0.46%    0.55%
 (t-statistics)                                   (1.25)               (-1.25)          (1.08)      (0.93)   (0.93)
 Loser, Sell-Pressure minus
 Winner, Buy-Pressure                              0.84                 1.54%           0.82%       0.51%    1.83%
 (t-statistics)                                   (6.38)                (3.86)          (4.65)      (2.47)   (2.71)
                                                                                      Week t+2
                                             Unconditional                              Past Market Return
                                               (Whole
                                               Sample                                               Small    Large
 Portfolio                                     Period)                Large Up         Small Up     Down     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, Sell-Pressure                            0.12%                 0.39%           0.01%       0.18%    0.52%
 (t-statistics)                                   (1.16)                (1.05)          (0.10)      (1.09)   (0.81)
 Loser, Sell-Pressure minus
 Winner, Buy-Pressure                              0.18                 0.38%           0.10%       0.17%    0.82%
 t-statistics)                                    (2.14)                (0.87)          (0.94)      (1.04)   (1.83)




                                                                   47

				
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