Stock Market Decline and Liquidity*

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, and . Viswanathan is from the Fuqua School of Business, Duke University , Tel: 1-919-660-7782, Fax: 1-919-660-7971, . We thank Yakov Amihud, Michael Brandt, Markus Brunnermeier, David Hsieh, Pete Kyle, Ravi Jagannathan, Christine Parlour, David Robinson, Avanidhar Subrahmanyam, Sheridan Titman and participants at the NBER 2005 microstructure conference for their comments.

ABSTRACT

Recent theoretical work suggests that commonality in liquidity and variation in liquidity levels can be explained by supply side shocks affecting the funding available to financial intermediaries. Consistent with this prediction, we find that liquidity levels and commonality in liquidity respond asymmetrically to positive and negative market returns. Stock liquidity decreases while commonality in liquidity increases following large negative market returns. We document that a large drop in aggregate value of securities creates greater liquidity commonality due to the inter-industry spill-over effects of capital constraints. We also show that the cost of supplying liquidity is highest following market downturns by examining the correlation between short-term price reversals on heavy trading volume and market states. These results cannot be explained by imbalances in buy-sell orders, institutional trading and market volatility which may proxy for changes in demand for liquidity.

1. Introduction

In recent theoretical research, the idea that market returns endogenously affect liquidity has received attention. For example, in Brunnermeier and Pedersen (2005), market makers obtain significant financing by pledging the securities they hold as collateral. Alarge decline in aggregate market value of securities reduces the collateral value and imposes capital constraint, leading to a sharp decrease in the provision ofliquidity. Liquidity dry-ups arise when the worsening liquidity leads to call for higher margins, and feedback into further funding problems.[1]Since this supply of liquidity effect affects all securities, Brunnermeier and Pedersen also predict larger commonality in liquidity following market downturns. Anshuman and Viswanathan (2005), on the other hand, present a slightly different model where investors are asked to provide collateral when asset values fall and decide to endogenously default, leading to liquidation of assets. Simultaneously, market makers are able to finance less in the repo market leading to higher spreads, and possibly greater commonality in liquidity.

Several other recent papers link changes in asset value to liquidity. In Morris and Shin (2003), traders sell when they hit price limits (which are correlated across traders) and liquidity black holes emerge when prices fall enough (the model in analogous to a bank run). Their model emphasizes the feedback effect of one trader’s liquidation decision on other traders. In Kyle and Xiong (2001), a drop in stock prices leads to reduction in holdings of risky assets because investors have decreasing absolute risk aversion, resulting in reduced market liquidity (see also Gromb and Vayonos (2002) for a model of capital constraints and limits to arbitrage). In Vayanos (2004), investors withdraw their investment in mutual funds when asset prices (fund performance) fall below an exogenously set level. Consequently, when mutual fund managers are close to the trigger price, they care about liquidity, especially during volatile periods. Hence, these theoretical models also emphasize shifts in demand for liquidity with changes in asset prices as liquidation of assets generates more selling pressure.[2]Additionally, some of the above papers also suggest cross-sectional differences in the liquidity effects: a drop in asset value has a greater impact on the liquidity of stocks with greater volatility exposure, a phenomenon related to flight to liquidity (see e.g. Anshuman and Viswanathan (2005), Vayanas (2004) and Acharya and Pedersen (2004)).[3]

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

Second, we pursue the idea that large drop in market valuations reduces the aggregate collateral of the market making sector which feeds back as higher comovement in market liquidity. While there is some research on comovements in market liquidity in stock and bond markets (Chordia, Roll, Subrahmanyam (2000), Hasbrouck and Seppi (2001), Huberman and Halka (2001) and others) and evidence that market making collapsed after the stock market crisis in 1987 (see the Brady commission report on the 1987 crisis), there is little empirical evidence that focus on the effect of stock market movements on commonality in liquidity. Two recent papers consider the effect of capital constraints on liquidity. Using daily data and specialist stock information, Coughenour and Saad (2004) ask whether changes in the market return affect stock liquidity at a daily frequency. In an interesting paper on fixed income markets, Naik and Yadav (2003) show that Bank of England capital constraints affect price movements.[4]However, the extant empirical literature does not consider whether the comovement of liquidity increases dramatically after large market drops in a manner similar to the finding that stock return comovement goes up after large market drops (see the work of Ang, Chen and Xing (2004) on downside risk and especially Ang and Chen (2002), for work on asymmetric correlations between portfolios). As we will see below, our analysis of comovement is much more comprehensive. We carefully relate our findings to theories of market making that focus on capital constraints and attempt to sufficiently distinguish between the effects due to demand and supply of liquidity.

Third, we utilise the framework provided by Campbell, Grossman and Wang (1993) to investigate the inter-temporal changes in the compensation for supplying liquidity. In their model, risk-averse market makers require payment for accommodating heavy selling by liquidity traders. This cost of providing liquidity is reflected in the temporary decrease in price accompanying heavy sell volume and the subsequent increase as prices revert to fundamental values. Following Lehmann (1990), Conrad, Hameed and Niden (1994) and Avramov, Chordia, Goyal (2005), we adopt the contrarian investment strategy to quantify the association between changes in aggregate market valuations and the cost of providing liquidity.

Our empirical approach is as follows. We use proportional quoted spread (as a proportion of the stock price)as one of our key variables[5]. Since spreads trend downward over time and there are regime changes corresponding to tick size changes, we adjust spreads using a regression that accounts for these effects and the day of the week, holiday and other effects, following Chordia, Roll and Subrahmanyam (2001). The adjusted proportional spread represents the key variable for our analysis.

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

Next, we investigate the hypothesis that large negative returns affect the supply of market making by looking at the comovements in liquidity. We first regress the individual firm spreads on the equally weighted market spread and find that the correlation (liquidity beta) to be higher with negative returns. This suggests that large negative price movements induce market illiquidity in all stocks.We use the R2statistic from the market model regression of the stock liquidity on the market liquidity as our input in comovement regressions. Since the seminal work of Roll (1988), a high R2 in market model regressions have been used to measure synchronicity in returns. We use a similar idea here in context of liquidity. If aggregate market liquidity does not explain individual stock liquidity much, the comovement in liquidity is low and each stock’s liquidity is determined by its individual characteristics. However, if the comovement in liquidity is high (the liquidity of all stocks tends to move together), the cross-securities average R2 will be high.

We regress the average R2 against lagged market returns and find that large negative market returns dramatically increase the liquidity comovement. This is consistent with the view that large negative market shocks increase market illiquidity across all stocks.Our finding is robust to the inclusion of changes in demand for liquidity measured by order imbalance, changes in institutional holdings and market and idiosyncratic return volatility. We also consider whether the comovement is due to industry effects or market effects. An increase in comovement caused by a negative industry return could show up as a market wide effect. We show that when we include the industry return and the market return (without that particular industry), large negative shocks to both returns increase comovement in liquidity. However, the market effect is much bigger in magnitude than the industry effect. This suggest that spillover effects across securities after negative market shocks are important and provides strong support for the idea that market liquidity drops across all assets at the same time when market returns drop.

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

The remainder of the paper is organised as follows. Section 2 provides a description of the data and key variables. The methodology and results pertaining to the relation between past returns and liquidity is presented in Section 3 while Section 4 presents the same with respect to commonality in liquidity. The formulation and results from the contrarian portfolio investment strategy is produced in Section 5. Section 6 concludes the paper.

1. Data

The transaction-level data are collected from the New York Stock Exchange Trades and Automated Quotations (TAQ) and the Institute for the Study of Securities Markets (ISSM). Thedaily 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, whichmatches a trading record to the most recent quote preceding this trade by at least five seconds. If a price is closer to the ask quote, it is classified as a buyer-initiated trade, and if it is closer to the bid quote it is classified as a seller-initiated trade. If the trade is at the midpoint of the quote, we use a “tick-test” to classify it as buyer- (seller-) initiated trade if the price is higher (lower) than the price of the previous trade. The anomalous transaction records are deleted according to the following filtering rules: (i) Negative bid-ask spread; (ii) Quoted spread > $5; (iii) Proportional quoted spread > 20%; (iv) Effective spread / Quoted spread > 4.0.

In this paper, we use bid-ask spread as the measure of liquidity. We compute the proportional quoted spread (QSPR)by dividing the difference between ask and bid quotes by the midquote. We repeat our empirical tests with the proportional effective spread, which is two times the difference between the trade execution price and the midquote scaled by the midquote, and find similar results (unreported). The individual stock daily spread is constructed by averaging the spread for all transactions for the stock on any given trading day. During the last decade, spreads have narrowed with the fall in tick size and growth in trading volume. Thus, to ascertain the extent to which the change of spread is caused by past returns, we adjust spreadsfor 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:

(1)

In equation 1, thefollowing 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 stockj started trading on NYSE, whichever is later. The regression residual provides us the adjusted proportional quoted spread (ASPR), which is used in our subsequent analyses.The time series regression equation 1 is estimated for each stock in our sample. Unreported cross-sectional average of the estimated parameters show seasonal patterns in quoted spread: the average bid-ask spreads are higher on Fridays and in January to April and October and around holidays. The tick-size change dummies also pick up significant drop in spread width after the change in tick rule on NYSE. Our results comports well with the seasonality in liquidity documented in Chordia et al. (2005). After adjusting for the seasonality in spreads, wedo not observe any significant time trend. In Table 1,the un-adjusted spread(QSPR)exhibits a clear time trend with theannual 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 adjustedspread (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.

1. Liquidity and Past Returns

3.1Time 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.