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).
1
In Vayanos (2004), investors
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
k 1
k 1
QSPR j ,t  a j   b j ,k DAYk ,t   c j ,k MONTH k ,t  d j HOLIDAY t
(1)
 e j TICK1t  f j TICK 2 t  g t YEAR1t  ht YEAR 2 t  ASPR j ,t
In equation 1, the following variables are employed: (i) 4 day of the week dummies
(DAYk,t) for Monday through Thursday ; (ii) 11 month of the year dummies (MONTHk,t)
for February through December; (iii) a dummy for the trading days around holidays
(HOLIDAY,t); (iv) two tick change dummies (TICK1t and TICK2t) to capture the tick
change from 1/8 to 1/16 on 06/24/1997 and the change from 1/16 to decimal system on
01/29/2001 respectively; (v) a time trend variable YEAR1t
(YEAR2 t) is equal to the
difference between the current calendar year and 1988 (1997) or the first year when stock
j started trading on NYSE, whichever is later. The regression 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 TURN i ,t 1  ci ROIB i ,t 1  d i STDi ,t 1  f i PRC i ,t 2   i ,t 1
12
(2)
where Ri,t is the idiosyncratic return on stock i in month t and Rm,t is the month t return on
the CRSP value-weighted index. We run the time-series regression in equation (2) for
each individual stock to estimate the coefficients, and then report the mean and median of
the estimated regression coefficients, together with the percentage of statistically
significant ones (at 5% level), across all firms in our sample. Table 2 presents the
equally-weighted average coefficients across all individual stock regressions. Consistent
with the evidence in the previous literature, we find that high turnover predicts lower
spreads. Large order imbalance and volatile prices increase the market maker’s inventory
risks and hence, leads to larger spreads. In addition, the proportional spreads are also
higher for stocks with lower price levels.
More importantly, we find that both the lagged individual stock return and the lagged
market return have significant negative influence on liquidity, after controlling for the
firm specific factors. Consistent with the theoretical predictions in Kyle and Xiong
(2001) and Brunnermeier and Pedersen (2005), the wealth effect of a drop in market
prices is associated with a fall in liquidity. The evidence presented in Table 2 also shows
that prior market returns appear to have a higher impact on a stock’s liquidity than its
own lagged returns.
The models that link changes in market prices and liquidity in fact pose a stronger
prediction: the relation should be stronger for prior losses than gains. In particular, we
want to examine whether a drop in market prices have a differential effect than a similar
rise in prices.
Hence, we modify equation (3) to allow spread to react differentially to
positive and negative lagged returns:
ASPRi ,t  ai ASPRi ,t 1  bUP,i Ri ,t 1 DUP,i ,t 1  bDOW N,i Ri ,t 1 DDOW N, i ,t 1
 mUP,i Rm,t 1 DUP,m,t 1  m DOW N,i Rm,t 1 DDOW N, m,t 1
 vi TURN i ,t 1  ci ROIB i ,t 1  d i STDi ,t 1  f i PRC i ,t  2   i ,t 1
13
(3)
where DUP,i,t (DDOWN,i,t ) is a dummy variable that is equal to one if and only if Ri,t is
greater (less) than zero. DUP,m,t (DDOWN,m,t ) are similarly defined based on Rm,t. The
control variables are identical to those defined in equation (2).
The Panel B of Table 2 presents the empirical estimate of equation 3 for monthly
adjusted spreads. We find a significantly greater effect of negative lagged returns on
liquidity, at the market-level as well as individual stock level. Although both negative
and positive market returns affect liquidity, the estimated regression coefficient of
negative lagged market return on spread, which is -0.705 is significantly stronger than the
coefficient for lagged positive market return, which is -0.433. In order words, a drop in
the market valuation level over the past month leads to a bigger decline in the stock’s
liquidity when compared to the liquidity improvement following a rise in stock price.
While we find a similar pattern following a drop or rise in the stock own prices, there is a
clear effect of lagged market returns on liquidity. We have also considered additional
lagged returns (not reported here): while the effect of lagged returns declines as we move
to longer lags, the asymmetric effect of positive and negative returns remains prominent.
Additionally, we also examined the effect of lagged returns on liquidity over a shorter
interval, based on the effect on spreads in the first five days of each month. In unreported
results, we find that the effect of changes in aggregate market valuations on subsequent
liquidity is stronger in the first five days, indicating that the phenomenon is more
pronounced at the higher frequency.
As the next step, we examine whether the magnitude of lagged returns have
differential impact on liquidity. Thus, we run the regression as follows
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
 bDOW N, SMALL,i Ri ,t 1 DDOW N, SMALL, i ,t 1  bDOW N, LARGE,i Ri ,t 1 DDOW N, 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 DOW N, SMALL,i Rm,t 1 DDOW N, SMALL, m,t 1  m DOW N, LARGE,i Rm,t 1 DDOW N, LARGE,m,t 1
 vi TURN i ,t 1  ci ROIB i ,t 1  d i STDi ,t 1  f i PRC i ,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:
DLi , s  ai   i DL m.s   i.s
(5)
where DLi , s  ( ASPRi.s  ASPRi., s 1 ) / ASPRi.s 1 and DLm.s  ( ASPRm.s
 ASPRm.s 1 )
/ ASPRm.s 1 ) are the 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[ Rt2 /(1  Rt2 )] . We regress our comovement measure on market returns (Rmt) , taking
into account the sign and magnitude of market returns:
COMOVE t  a   Rm ,t   t
COMOVE t  a  b Rm,t DUP,t  c Rm,t DDOW N,t   t
(6)
(7)
COMOVE t  a  d Rm,t DDOW N, LARGE,t  e Rm,t DUP, LARGE,t
 fRm,t DDOW N, 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
liquidity commonality.
9
We, therefore, conclude that the increase in liquidity
commonality in down market states is related to adverse effects of a fall in the supply of
liquidity.
4.2 Commonality in Liquidity: Industry Spillover Effects
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  ( ASPRINDj .s  ASPRINDj , s 1 ) / ASPRINDj , s 1 is
the daily percentage change in the equally-weighted average of adjusted spreads across
all stocks in industry j 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
The industry classifications are obtained from K. French’s website at
http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html
3
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 RINDj ,t DUP, INDj ,t  c IND RINDj ,t DDOW N, INDj ,t
 bMKT RMKTj ,t DUP, MKTj ,t  cMKT RMKTj ,t DDOW N, MKT ,t   t
(11)
COMOVE INDj ,t  a  f IND RINDj ,t DUP, LARGE, INDj ,t  g IND RINDj ,t DDOW N, LARGE, INDj ,t
 hIND RINDj ,t DUP, SMALL, INDj ,t  j IND RINDj ,t DDOW N, SMALL, INDj ,t
 f MKT RMKTj ,t DUP, LARGE, MKTj ,t  g MKT RMKTj ,t DDOW N, LARGE, MKTj ,t
 hMKT RMKTj ,t DUP, SMALL, MKTj ,t  jMKT RMKTj ,t DDOW N, 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 ROIB i ,t Turni ,t / i 1 Ri ,t ROIB i ,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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Journal of Political Economy 111, 642-685.
Stoll, Hans R., 1978, The supply of dealer services in securities markets, Journal of
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:
QSPR j ,t
4
11
k 1
k 1
 a j   b j ,k DAYk ,t   c j ,k MONTH k ,t  d j HOLIDAY t
 e j TICK1t  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.
Year
Number
of
Securities
QSPR (Unadjusted Proportional
Quoted Spread)
ASPR (Adjusted Proportional
Quoted Spread)
Mean
Median
Coefficient
of Variation
Mean
Median
Coefficient
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 TURN i ,t 1  ci ROIB i ,t 1  d i STDi ,t 1  f i PRC i ,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  m DOW N,i Rm,t 1 DDOW N, m,t 1
 bUP,i Ri ,t 1 DUP,i ,t 1  bDOW N,i Ri ,t 1 DDOW N, i ,t 1 
 vi TURN i ,t 1  ci ROIB i ,t 1  d i STDi ,t 1  f i PRC i ,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 DOW N, LARGE,i Rm,t 1 DDOW N, LARGE, m,t 1  m DOW N, SMALL,i Rm ,t 1 DDOW N, 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
 bDOW N, LARGE,i Ri ,t 1 DDOW N, LARGE, i ,t 1  bDOW N, SMALL,i Ri ,t 1 DDOW N, SMALL,i ,t 1
 vi TURN i ,t 1  ci ROIB i ,t 1  d i STDi ,t 1  f i PRC i ,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
Statistics
Mean
Median
% of negative
% of positive
% positive
significant
Estimate
Statistics
Mean
Median
% of negative
% of positive
% negative
significant
Intercept
ASPR(i,t-1)
Ret(i,t-1)
Ret(m,t-1)
0.311***
0.240
0.736***
0.759
-0.312***
-0.222
97.4%
-0.553***
-0.344
95.2%
97.8%
88.8%
100.0%
99.8%
73.6%
55.4%
TURN(i,t-1)
ROIB(i,t-1)
STD(i,t-1)
PRC(i,t-1)
-0.002**
-0.001
59.9%
0.031***
0.014
0.058***
0.043
0.877***
0.536
56.6%
10.5%
57.9%
10.5%
76.3%
26.2%
10.2%
Panel B: Relation between Spread and the Signed Lagged Returns
Estimate
Statistics
Mean
Median
% of negative
% negative
significant
Ret(i,t-1) *
D(Up,i,t-1)
Ret(i,t-1) *
D(Down,i,t-1)
Ret(m,t-1) *
D(Up,m,t-1)
Ret(m,t-1) *
D(Down,m,t-1)
-0.220***
-0.139
79.3%
25.1%
-0.417***
-0.288
90.7%
48.7%
-0.433***
-0.242
78.7%
18.3%
-0.705***
-0.387
85.7%
28.9%
Panel C: Relation between Spread and the Magnitude of Lagged Returns
(a)
Estimate
Statistics
Mean
Median
% of negative
% negative
significant
(b)
(a)-(b)
Ret(m,t-1) *
Ret(m,t-1) *
D(Up,Large,m,t- D(Up,Small,m,t1)
1)
(c)
(d)
Ret(m,t-1) *
D(Down,Large,m,t1)
Ret(m,t-1) *
D(Down,Small,m,t1)
-0.533***
-0.253
66.5%
9.5%
-0.24***
(h)
(g)-(h)
-0.547***
-0.306
77.1%
17.1%
-0.386***
-0.227
72.5%
12.6%
-0.17***
56.2%
5.8%
-0.772***
-0.389
84.9%
29.7%
(e)
(f)
(e)-(f)
(g)
Estimate
Ret(i,t-1) *
Ret(i,t-1) *
Statistics D(Up,Large,i,t-1) D(Up,Small,i,t-1)
Mean
-0.226***
-0.205***
Median
-0.142
-0.142
% of negative
75.6%
73.2%
% negative
22.8%
15.9%
significant
(c)-(d)
58.2%
6.3%
Ret(i,t-1) *
Ret(i,t-1) *
D(Down,Large,i,t-1) D(Down,Small,i,t-1)
-0.020
48.8%
6.8%
36
-0.439***
-0.277
87.8%
41.7%
-0.395***
-0.262
83.4%
30.1%
-0.05**
52.5%
10.1%
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) *
D(Up,m,t-1)
Estimate
Statistics
High Volatility
Medium Volatility
Low Volatility
High - Low
-0.965***
-0.741***
-0.561***
-0.403**
Median
-0.710
-0.714
-0.451
-0.259
% of negative
% negative
significant
72.0%
17.8%
78.9%
16.5%
78.2%
17.3%
-0.587***
-0.479***
-0.218***
-0.369**
Median
-0.359
-0.408
-0.242
-0.117
Medium Size % of negative
% negative
significant
85.0%
13.1%
91.9%
20.7%
80.7%
22.9%
-0.262***
-0.217***
-0.171***
-0.091***
Median
-0.198
-0.155
-0.149
-0.048
% of negative
% negative
significant
83.6%
22.7%
88.3%
30.6%
92.7%
26.4%
High Volatility
Medium Volatility
Low Volatility
High - Low
-1.557***
-1.212***
-0.949***
-0.607**
Median
-1.151
-0.832
-0.873
-0.278
% of negative
% negative
significant
80.4%
27.1%
79.8%
21.1%
88.2%
41.8%
Mean
Small Size
Mean
Mean
Large Size
Ret(m,t-1) *
D(Down,m,t1)
Estimate
Statistics
Mean
Small Size
Mean
-0.832***
-0.534***
-0.409***
-0.423**
Median
-0.659
-0.429
-0.366
-0.293
Medium Size % of negative
% negative
significant
90.7%
32.7%
88.3%
31.5%
88.1%
33.0%
-0.295***
-0.251***
-0.211***
-0.083**
Median
-0.239
-0.156
-0.179
-0.061
% of negative
% negative
significant
85.5%
28.2%
82.0%
29.7%
90.9%
33.6%
Mean
Large Size
37
Ret(i,t-1) *
D(Up,i,t-1)
Estimate
Statistics
Mean
High Volatility
Medium Volatility
Low Volatility
High - Low
-0.437***
-0.452***
-0.321***
-0.116*
Median
-0.340
-0.309
-0.225
-0.116
% of negative
% negative
significant
83.2%
27.1%
83.5%
33.9%
77.3%
22.7%
-0.223***
-0.238***
-0.202***
-0.021
Median
-0.185
-0.211
-0.190
0.005
Medium Size % of negative
% negative
significant
82.2%
29.0%
88.3%
33.3%
80.7%
30.3%
-0.135***
-0.086***
-0.119***
-0.016
Median
-0.119
-0.062
-0.095
-0.024
% of negative
% negative
significant
85.5%
33.6%
81.1%
18.9%
83.6%
25.5%
High Volatility
Medium Volatility
Low Volatility
High - Low
-0.842***
-0.657***
-0.527***
-0.315**
Median
-0.759
-0.588
-0.450
-0.310
% of negative
% negative
significant
93.5%
54.2%
92.7%
47.7%
87.3%
38.2%
Small Size
Mean
Mean
Large Size
Ret(i,t-1) *
D(Down,i,t-1)
Estimate
Statistics
Mean
Small Size
Mean
-0.509***
-0.291***
-0.243***
-0.266**
Median
-0.435
-0.241
-0.263
-0.172
Medium Size % of negative
% negative
significant
97.2%
67.3%
89.2%
40.5%
87.2%
38.5%
-0.286***
-0.206***
-0.186***
-0.101**
Median
-0.250
-0.190
-0.158
-0.092
% of negative
% negative
significant
96.4%
71.8%
95.5%
59.5%
95.5%
50.9%
Mean
Large Size
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.
DLi.t  ai   i DLm.t   i.t
where DLi.t  ( ASPRi.t  ASPRi.t 1 ) / ASPRi.t 1 , the percentage change in adjusted daily proportional
spread for stock i;
DLm.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
Whole
Sample
Period
Sub-Periods
Positive
Market
Returns
Negative
Market
Returns
liquidity beta
0.74
0.83
R-square
0.074
0.080
liquidity beta
0.77
R-square
0.076
Large
Positive
Market
Returns
Small
Positive
Market
Returns
Small
Negative
Market
Returns
Large
Negative
Market
Returns
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:
DLi , s  ai   i DL m.s   i.s
where DLi , 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; DLm.s  ( ASPRm.s  ASPRm.s 1 ) ) / ASPRm.s 1 and ASPRm,s is the
cross-sectional, equally-weighted average of spreads across all stocks in the sample in day s.
For each
stock i , the above regression equation generates an R2i,t, for each month t. The cross-sectional average R2i,t,
denoted as Rt2, is used in the second stage monthly regression:
Model A: COMOVE t  a   Rm ,t   t
Model B: COMOVE t  a  b Rm,t DUP,t  c Rm ,t DDOW N,t   t
Model C: COMOVE t  a  g Rm ,t DDOW N, LARGE,t  e Rm ,t DUP, LARGE,t
 jRm,t DDOW N, 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
Intercept
Ret(m,t)
Ret(m,t) *
D(Down,m,t)
Ret(m,t) *
D(Up,m,t)
Ret(m,t) *
D(Down,Large,m,t)
Ret(m,t) *
D(Down,Small,m,t)
Ret(m,t) *
D(Up,Small,m,t)
Ret(m,t) *
D(Up,Large,m,t)
A
B
C1
C2
C3
-2.515
-127.78
-1.425
-3.18
-2.606
-81.60
-2.601
-74.11
-2.605
-68.35
-2.582
-59.58
-4.461
-4.59
-3.416
-2.54
1.093
1.22
-1.151
-0.47
-4.439
-4.99
-3.002
-1.66
1.540
1.41
0.013
0.01
-3.987
-4.37
-0.869
-0.29
0.531
0.34
0.669
0.74
-4.076
-4.74
1.087
1.31
Panel B: Liquidity Commonality and Market Returns
and other demand-side factors
41
Model
C2
C2
C2
-2.305
-11.34
-2.689
-54.11
-2.637
-31.34
Ret(m,t) *
D(Down,Large,m,t)
-3.772
-4.28
-3.007
-2.90
-4.285
-4.45
Ret(m,t) *
D(Down,Small,m,t)
-2.239
-1.27
-2.063
-1.13
-2.855
-1.55
Ret(m,t) *
D(Up,Small,m,t)
1.143
1.05
0.934
0.85
1.401
1.23
Ret(m,t) *
D(Up,Large,m,t)
-0.235
-0.22
-0.581
-0.54
-0.099
-0.09
Intercept
Ret(m,t)
Ret(m,t) *
D(Down,m,t)
Ret(m,t) *
D(Up,m,t)
Ret(m,t) *
D(Small,m,t)
Abs(ROIB)
ROIB
Comovement
ΔInstitutional
Holding
Market
Volatility
1.382
2.30
0.156
1.93
3.540
1.91
2.718
2.57
0.353
0.43
Idiosyncratic
Volatility
42
Table 6: Commonality in Liquidity, Industry and Market Returns
Each month, we estimate the following regression for stock i:
DLi,s  ai   i DLINDj ,.s   i.s
where DLi , s  ( ASPRi.s  ASPRi., s 1 ) / ASPRi.s 1 is the percentage change in adjusted daily proportional
spread for stock i from day s-1 to s; DL INDj .s  ( ASPRINDj .s  ASPRINDj , s 1 ) / ASPRINDj , 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:
COMOVEINDj ,t  a  bIND RINDj ,t  bMKT RMKTj ,t   t
Model B:
COMOVE INDj ,t  a  bIND RINDj ,t DUP, INDj ,t  c IND RINDj ,t DDOW N, INDj ,t
 bMKT RMKTj ,t DUP,MKTj ,t  cMKT RMKTj ,t DDOW N,MKT ,t   t
Model C:
COMOVE INDj ,t  a  f IND R INDj ,t DUP, LARGE, INDj ,t  g IND R INDj ,t DDOW N, LARGE, INDj ,t 
hIND R INDj ,t DSMALL, INDj ,t  f MKT RMKTj ,t DUP, LARGE, MKTj ,t  g MKT RMKTj ,t DDOW N, LARGE, MKTj ,t
 hMKT RMKTj ,t DSMALL, MKTj ,t   t
ere COMOVEINDj,t is defined as
2
ln[ R INDj
,t
wh
2
/(1  R INDj
,t )] ;
RINDj,t and RMKTj,t denote the month t return on
the value-weighted, industry j and market (excluding industry j) portfolios. The dummy variable DUP,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
Intercept
Ret(ind,t)
Ret(ind,t) *
D(Down,ind,t)
Ret(ind,t) *
D(Up,ind,t)
Ret(m,t)
A
B
C
-2.585
-483.78
-0.171
-1.42
-2.634
-280.21
-2.624
-218.5
-0.633
-2.86
0.170
0.94
-0.750
-4.76
Ret(m,t) *
D(Down,m,t)
Ret(m,t) *
D(Up,m,t)
Ret(ind,t) *
D(Down,Large,ind,t)
Ret(ind,t) *
D(Down,Small,ind,t)
Ret(ind,t) *
D(Up,Small,ind,t)
Ret(ind,t) *
D(Up,Large,ind,t)
Ret(m,t) *
D(Down,Large,m,t)
Ret(m,t) *
D(Down,Small,m,t)
Ret(m,t) *
D(Up,Small,m,t)
Ret(m,t) *
D(Up,Large,m,t)
-1.656
-5.69
0.159
0.61
-0.756
-3.17
-0.177
-0.49
0.048
0.19
0.116
0.58
-1.731
-5.77
-1.099
-1.99
0.243
0.74
-0.250
-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:
w p ,i ,t 
Ri ,t 1Turni ,t 1

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
Portfolio
t+1
0.74%
0.16%
0.58%
(6.35)
Loser
Winner
Loser minus Winner
(t-statistics)
Week
t+2
t+3
0.45%
0.40%
0.29%
0.36%
0.16%
0.04%
(2.20)
(0.58)
t+4
0.37%
0.38%
-0.01%
(-0.16)
Panel B: Contrarian Profits Conditional on Market Returns
Week t+1
Portfolio
Loser
Large Up
0.61%
Past Market Return
Small Up Small Down Large Down
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%
(1.13)
Week t+2
(4.91)
(2.84)
(2.97)
(t-statistics)
Portfolio
Loser
Large Up
0.88%
Winner
Loser minus Winner
(t-statistics)
45
Past Market Return
Small Up Small Down Large Down
0.47%
0.21%
1.04%
0.36%
0.41%
0.08%
0.22%
0.51%
(1.73)
0.06%
( 0.68)
0.14%
(1.05)
0.82%
(1.98)
Panel C: Contrarian Profits Conditional on Market Returns
and Liquidity Commonality
Portfolio
loser
winner
loser-winner
(t-stat)
Portfolio
loser
winner
loser-winner
(t-stat)
Large Up
Liquidity
Commonality
Week t+1
Past Market Return
Small Up
Small Down
Liquidity
Liquidity
Commonality
Commonality
Large Down
Liquidity
Commonality
High
Low
High
Low
High
Low
High
Low.
0.68%
(1.17)
0.62%
(0.62)
0.44%
(2.70)
0.66%
(4.30)
0.39%
(1.35)
0.57%
(3.23)
1.75%
(2.95)
0.61%
(1.15)
Large Up
Liquidity
Commonality
Week t+2
Past Market Return
Small Up
Small Down
Liquidity
Liquidity
Commonality
Commonality
Large Down
Liquidity
Commonality
High
Low
High
Low
High
Low
High
Low.
0.36%
(0.87)
0.67%
(1.54)
0.06%
(0.51)
0.06%
(0.45)
0.19%
(0.91)
0.08%
(0.53)
1.27%
(2.10)
0.38%
(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 ROIB i ,t 1Turni ,t 1 / i 1 Ri ,t 1 ROIB i ,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
Portfolio
Loser, Buy-Pressure
Loser Sell-Pressure
Winner, Buy-Pressure
Winner, Sell-Pressure
Loser, Buy-Pressure minus
Winner, Sell-Pressure
(t-statistics)
Loser, Sell-Pressure minus
Winner, Buy-Pressure
(t-statistics)
Portfolio
Loser, Buy-Pressure
Loser Sell-Pressure
Winner, Buy-Pressure
Winner, Sell-Pressure
Loser, Buy-Pressure minus
Winner, Sell-Pressure
(t-statistics)
Loser, Sell-Pressure minus
Winner, Buy-Pressure
t-statistics)
Unconditional
(Whole
Sample
Period)
0.68%
0.93%
Large Up
-0.23%
1.29%
Small Up
0.81%
1.00%
Small
Down
0.57%
0.42%
Large
Down
0.70%
2.20%
0.09%
0.43%
-0.25%
0.89%
0.18%
0.59%
-0.09%
0.10%
0.37%
0.16%
0.25%
(1.25)
-1.12%
(-1.25)
0.21%
(1.08)
0.46%
(0.93)
0.55%
(0.93)
0.84
(6.38)
1.54%
(3.86)
0.82%
(4.65)
Week t+2
0.51%
(2.47)
1.83%
(2.71)
Past Market Return
Unconditional
(Whole
Sample
Period)
0.50%
0.45%
Large Up
0.88%
0.72%
Small Up
0.51%
0.48%
Small
Down
0.31%
0.23%
Large
Down
0.96%
0.93%
0.27%
0.39%
0.34%
0.49%
0.39%
0.50%
0.06%
0.13%
0.11%
0.44%
0.12%
(1.16)
0.39%
(1.05)
0.01%
(0.10)
0.18%
(1.09)
0.52%
(0.81)
0.18
(2.14)
0.38%
(0.87)
0.10%
(0.94)
0.17%
(1.04)
0.82%
(1.83)
Past Market Return
47