Market Crashes

Maria Kasch

Jose Gonzalo Rangel

Moritz Weigand*

First Draft: January 2010 This Version: April 2011

Abstract

This paper studies cross-sectional determinants of stock returns and order flow around five recent episodes of market crashes in the United States during the period from 1998 to 2008. Stocks with high volatility, turnover, and market beta are consistent losers during crashes and winners during recoveries. Trading activity in times of crashes is subject to flight to size. Recoveries are characterized by flights to stocks with large crash-period losses, low crash-period volatility and turnover, and small stocks. Overall, the evidence suggests that cross-sectional returns in crisis periods are determined by (i) stocks’ “market sensitivity” characteristics and (ii) re-allocation of resources in the market. Keywords: stock market crashes; post-crash recoveries; order imbalance; flight to size, flight to quality; flight to liquidity ______________________________________ This paper was previously distributed under the title “Market Crashes, Order Imbalance and Stock Returns: Evidence from NYSE”. For helpful comments and suggestions, we are grateful to Viral Acharya, Alessandro Beber, Tarun Chordia, John Griffin, Allaudeen Hameed, Paolo Pasquariello, Lasse Pedersen, Stefan Ruenzi, Asani Sarkar, Laura Starks, Avanidhar Subrahmanyam, Erik Theissen, Sheridan Titman, and participants at seminars at the University of Mannheim and Financial Management Association 2010 European meeting. * Kasch: University of Mannheim, Department of Finance (kasch@uni-mannheim.de) and University of Texas at Austin, McCombs School of Business, Department of Finance (maria.kasch@mccombs.utexas.edu). Rangel: Bank of Mexico, Economic Studies (jgrangel@banxico.org.mx). Weigand: PPI AG (moritz.weigand@ppi.de).

1

A number of episodes of severe market declines in the recent decades have led to a surge of

theoretical studies that describe market mechanisms characterizing periods of market

crashes.1 While the details of the individual mechanisms differ, many of them make similar

cross-sectional predictions related to changes in investor preferences for holding assets with

specific characteristics and reallocation of resources in the market, often termed as flights,

reflecting agents’ disengagement from risky investments in favor of safety, certainty, and

liquidity. Trading pressures associated with these flights are expected to explain a significant

portion of price movements in crash periods. Consequently, the analysis of the characteristics

of order flow and the inter-relation between order flow and returns in times of crashes is of

high relevance for understanding the market mechanisms characterizing these periods. The

present paper provides such analysis, following a broader goal of exploring the cross-

sectional determinants of returns and trading activity in the stock market during crisis events.

Our study is the first to present evidence on systematic cross-sectional patterns that

characterize trading activity and returns in the U.S. stock market around times of crisis by

studying five recent episodes of market crashes and subsequent recoveries during the period

1998 – 2008. The results suggest that cross-sectional returns in the studied periods are

determined by (i) stocks’ “market sensitivity” characteristics and (ii) re-allocation of

resources (flights) in the market specific to the periods of crashes and recoveries.

We find that stock characteristics such as volatility, turnover, and market beta

determine the losers during crashes and the winners during recoveries. Stocks with high

volatility, turnover, and beta experience consistently greater losses in times of market

downturns. The highly significant negative relation between turnover and crash returns that

repeats in all five analyzed periods is particularly noteworthy, since the market crises

literature does not make any explicit predictions on the role of turnover as a determinant of 1 For instance, Easley and O’Hara (2010), Brunnemeier and Pedersen (2009), Caballero and Krishnamurthy (2008), Garleanu and Pedersen (2007), Morris and Shin (2004) Vayanos (2004), Bernardo and Welch (2003), Gromb and Vayanos (2002), Kyle and Xiong (2001) and Xiong (2001), to mention a few.

2

stock price movements in these periods. In times of market recoveries, following the crashes,

the relation of returns to volatility, turnover, and market beta reverses to positive.

Furthermore, crash and recovery returns are positively associated with contemporaneous

changes in order imbalance.2 While the source of the order imbalance - return relation reflects

the mapping of changes in trading patterns of market participants into returns3, one may think

of two major sources of the relation of crash and recovery returns to stock characteristics like

volatility, turnover and the market beta.

First, to the extent that some of these stock variables are associated with common

factors in stock returns, their levels may imply more or less exposure to systematic risk. The

beta – return relation is an obvious example. In times of crashes (recoveries), when market

drops (rises), the stocks with higher market beta will experience greater losses (gains), ceteris

paribus. Similarly, it might be expected that in periods of high market volatility

characterizing market downturns, stocks with greater volatility are subject to greater excess

downside volatility, and hence, to particularly low average returns, ceteris paribus. The

volatility - return relation is in excess of stocks’ exposure to systematic risk as measured by

market beta, since there is evidence that volatility is a risk factor itself (Ang, Hodrick, Xing,

and Zhang (2006)). Following the same argument, it might be expected that in periods of

recovery, high volatility stocks particularly enjoy the benefits of the high market activity

driven by the flow of positive news that characterize these periods. With regard to the return -

2 The relation between order flow and prices is one of the central predictions of theoretical microstructure models. This relation has received a strong empirical support. Hasbrouck (1988, 1991a and 1991b) provides analysis of the order flow – price relation at the intraday transaction data frequency; Hasbrouck and Seppi (2001) demonstrate that commonality in the order flow explains about half of the commonality in returns at fifteen-minute intraday frequency. A number of studies document the order flow – price relation at the lower data frequencies. For example, Edelen and Warner (2001) and Chordia, Roll and Subrahmanyam (2002) study this relation at the aggregate market level using daily data. Chordia and Subrahmanyam (2004) present evidence of cross-sectional relation of order imbalance and returns of individual stocks. Evans and Lyons (2002) document the order flow - price relation in foreign exchange market and Kurov and Lasser (2004) in futures market. 3 Beber, Brandt and Kavajecz (2011) discuss conditions under which order flow may contain less, the same, or more value relevant information than asset price changes. They employ order flow data to study aggregate portfolio rebalancing across industry sectors at different stages of business cycle.

3

turnover relation, it can be argued that in times of high selling (buying) activity typical of

market downturns (recoveries)4, the feature of high trading intensity may imply more selling

(buying), ceteris paribus. Specifically, it may be expected that stocks with greater trading

volume are those that are being massively sold (bought) during crash (recovery) periods.

These trading pressures may lead to particularly strong price declines (rises).5 The discussed

relations between stock characteristics and returns capture stocks’ sensitivity to market trends.

The importance of the described effects is emphasized by the fact that one might reasonably

assume that in times of crises, the changes in prices of individual stocks are, to a large extent,

driven by a re-evaluation of the overall market level rather than information specific to

individual firms.

The second source of association between stock characteristics and crash and

recovery returns is related to changes in investor preferences for holding stocks with specific

features. The changes in preferences are reflected in changes in the premium demanded for

holding these stocks and adjustments in their market supply and demand, i.e. flights. Our

paper is the first to provide direct evidence on flights in the stock market during recent crises

events by studying the cross-sectional determinants of changes in order imbalance in these

periods.

The results uncover a compelling evidence of an increase in relative supply of small

stocks during all five crash periods. We term this phenomenon as flight to size. 6 The

phenomenon of flight to size has not been discussed before in the extant literature. The

4 The empirical evidence in this paper shows significant increases in the proportion of sell-initiated trades in times of market crashes and a reversal in the order flow direction in times of recoveries. 5 To make this point clear, consider an example of two stocks A and B with different trading intensity; say while stock A is traded on average once a month, stock B is traded on average thousand times a month. Now, if the period under consideration is characterized by unusual selling activity (as during market crashes), then it can be argued that during that period stock B will remain as a more traded asset and then it may be more exposed to selling pressures than stock A, ceteris paribus. A similar argument applies to the periods of recovery where stock B is expected to be more exposed to buying pressures. 6 The described phenomenon can alternatively be termed as flight away from small stocks. However, to make it comparable to the notions of flight to quality and fight to liquidity discussed in the literature, we use the term flight to size. The flight to size/quality/liquidity might be driven by a considerable increase in supply of small/volatile/illiquid stocks or a considerable increase in demand for large/low-volatility/liquid stocks, or both.

4

literature rather suggests mechanisms generating the effects of flight to quality and flight to

liquidity. In principle, given that size is strongly associated with both liquidity and volatility,

the significant effect of size might be interpreted as being the result of flights to liquidity

and/or quality. Our result, however, is robust to controlling for liquidity and volatility

variables, as well as for further stock characteristics and systematic market factor loadings.

Furthermore, while the phenomenon of flight to size characterizes all market crashes,

regardless of their special features and economic background, some other forms of

reallocation of resources are specific to individual crises. For instance, during the crash

period of 2008, we find evidence of an increase in relative supply of high-volatility stocks

(consistent with flight to quality) that is significant and robust to adding the effect of various

control variables. In addition, we find evidence of a surge in relative supply of low-turnover

stocks for three crash periods. To the extent that turnover reflects a dimension of assets’

liquidity this result may be interpreted as evidence of flight to liquidity.

The described results support, as an empirical fact, that flight to size is a general

characteristic of the market behavior under conditions of uncertainty associated with market

crashes. Developing a theoretical framework to explain this empirical phenomenon is beyond

the aims of this paper. Nevertheless, we discuss some possible explanations that might

motivate further research on this topic. For example, Zhang (2006) argues that information

uncertainty of a firm’s value is inversely related to its size.7 In a context of crisis periods, this

phenomenon may be exacerbated and investors may avoid stocks that post a higher

uncertainty on future returns (Caballero and Krishnamurthy (2008)). Alternatively, our results

are consistent with the finding that small stocks are more sensitive to cash flow news

(Campbell and Vuolteenaho (2004), Da and Warachka (2009), Campbell, Polk and

7 The higher information uncertainty of small firms relative to large firms might be attributed to the fact that small firms (i) are less diversified, (ii) have less information available for the market e.g. due to lower analyst and media coverage, (iii) are more likely to be subject to limits of arbitrage e.g. due to higher trading costs and short sale constraints (in particular, direct constraints attributed to limited supply of lendable shares (Nagel (2005)).

5

Vuolteenaho (2010)). Indeed, since crisis periods are associated with (current or expected)

bad economic states and increases in risk aversion, small stocks that are characterized by

higher cash flow betas may be perceived by investors as highly exposed to negative cash flow

shocks, and investors may find large stocks as valuable hedges against changes in the set of

investment opportunities and/or realizations of negative consumption growth.8

The results for the recovery changes in order imbalance show a number of systematic

patterns. There is a strong evidence of flights to the stocks with large crash-period losses.

This is consistent with the intuition that during recoveries the high demanded stocks are those

that may be perceived as undervalued. However, the results also indicate that investors

remain cautious about buying the stocks that were volatile and heavily traded during the

preceding crash period. Specifically, the evidence suggests flights to the low crash-period

volatility stocks (flight to quality) and flights to the low crash-period turnover stocks. We

also find evidence of an increase in relative demand for small stocks in most of recoveries

studied in the paper.

Our analysis is related to the early work by Blume, MacKinlay and Terker (1989), and

Lauterbach and Ben-Zion (1993), who study returns and order imbalance around the market

crash of October 1987.9 The recent three decades have been characterized by significant

changes in market structures, and the mechanisms specific to recent crashes are expected to

be in many respects different from those during the crash on Black Monday in 1987. Our

paper contributes to the understanding of market mechanisms characterizing the U.S. stock

market during crisis events by presenting evidence on determinants of cross-sectional returns 8 In this regard, the results of Parker and Julliard (2005) suggest that small stocks have higher exposure to consumption risk because they pay poorly before and early in recessions. Jagannathan and Wang (2007) also support that smaller firms are exposed to higher consumption risk compared to larger firms. For the literature that grounds variation in firms’ systematic risks in relation to the operating risks they are likely to face, see Berk, Green, and Naik (1999), Gomes, Kogan, and Zhang (2003), Carlson, Fisher, and Giammarino (2004, 2006), Zhang (2005), and Novy-Marx (2010). These studies argue that a combination of growth options, irreversible investment, and operating leverage will make large, growth companies less risky than small, value companies. 9 Blume et al. analyze the behavior of the U.S. market on October 19th and 20th. Lauterbach and Ben-Zion examine the Israeli market (stocks traded on Tel Aviv Stock Exchange) during the days surrounding the crash.

6

and order flow during five recent episodes of market crashes. Several of the empirical

patterns we identify are new, and have not been considered in the existing empirical or

theoretical literature. For instance, the findings related to the role of turnover as cross-

sectional determinant of returns in times of crashes and recoveries, or the compelling

evidence of flight to size characterizing crashes could motivate further research aiming to

explain these phenomena.

The paper proceeds as follows. Section I reviews the theoretical literature on market

mechanisms that characterize periods of financial crisis, specifically, the so-called

amplification mechanisms. Section II defines the crisis periods and describes the data

employed in the analysis. Section III presents cross-sectional analysis of crash-period returns

and changes in order imbalance. Section IV presents similar analysis for the recovery periods.

Section V concludes.

I. Literature on Market Mechanisms Characterizing Crashes

There is a large theoretical literature on amplification mechanisms that provide an

explanation for strong price declines in times of market crashes. Krishnamurthy (2009)

suggests a distinction between two broad categories of amplifiers: (i) balance sheet amplifiers

related to shortages of capital/liquidity and to tight credit conditions and (ii) information

amplifiers related to uncertainty in the markets, in particular, the Knightian uncertainty

(Knight, 1921).

While literature suggests different forms of the balance sheet amplifiers, their general

mechanism can be summarized as follows. The (initial) asset price decline generates tighter

balance-sheet constraints that lead to asset liquidations. This situation causes further decline

in prices – then the mechanism repeats and generates a downward price spiral. Based on

Shleifer and Vishny (1997), in times when market specialists’ financiers cannot distinguish

7

between losses due to demand driven shocks from losses due to the specialists’ lack of skill,

they eventually withdraw their capital and induce forced liquidations that amplify existing

losses. In the models of Kyle and Xiong (2001) and Xiong (2001), the risk-bearing capacity

of convergence traders is correlated with their wealth. Under regular market conditions, when

trading by noise traders moves prices away from fundamentals, convergence traders take

advantage of arbitrage opportunities, and stabilize prices. However, when the wealth effect

associated with initial losses dominates the substitution effect (Campbell and Kyle, 1993),

convergence traders liquidate their positions in risky assets in response to increased noise

trading and, therefore, trade into the same direction as noise traders amplifying the effect of

the original shock.

A number of studies emphasize that funding constraints faced by market makers do

not need to be binding for the loss spiral to arise. The mere fear of a future binding constraint

can be sufficient to prevent market makers from providing liquidity. For example, Shleifer

and Vishny (1997) demonstrate how arbitrageurs avoid investments in highly volatile assets

that feature high profit opportunities but would expose them to a disproportional high risk of

forced liquidations. A further amplifying channel which is based on anticipated consequences

of loss limits is presented by Morris and Shin (2004).10 In their model, short-term traders

have to liquidate their positions when hitting a loss limit. Therefore, traders that anticipate

further losses rush to immediately liquidate their assets. The downward dynamic of the model

arises when traders are aware that other traders face similar trading constraints without

knowing the exact loss limits. Observing losses raises the fear of a downward spiral and

triggers fire sales, causing a self-fulfilling prophecy similar to bank runs. The authors term

this mechanism liquidity black hole, the deterioration of assets prices in the absence of

changes to the fundamentals.

10 See also Bernardo and Welch (2003).

8

An amplification of losses in the context of leveraged investments is discussed by

Brunnermeier (2009). Facing a fixed leverage ratio, investors can be forced to unwind large

positions in assets in response to relatively small losses. Similar to the case of capital

outflows initial losses are thus amplified by forced subsequent sales. As convergence traders

typically make extensive use of leverage, the described mechanism is very relevant in

reflecting their trading behavior.

Vayanos (2004) studies the changes in investors’ risk aversion in times of market

downturns. In his model, the link between liquidity and returns is established via an

increasing risk aversion towards illiquidity in reaction to price drops. Under regular market

conditions stylized fund managers act as long-term investors being affected little by asset

volatility or costs of trading. However, when asset prices approach a threshold associated

with a forced liquidation of the fund, fund managers’ risk aversion towards illiquidity as well

as towards volatility increases. In addition, risk aversion increases in the level of volatility,

which further influences the probability of forced liquidations. In consequence, the model

predicts that in times of market turmoil illiquid and volatile stocks are more susceptible to

losses as investors become increasingly reluctant to hold assets associated with these risk

attributes.

In addition to loss spirals, the literature predicts that the so-called margin spirals play

an important role in the periods of market downturns (e.g. Brunnermeier and Pedersen

(2009)). When margin requirements depend on market conditions such as liquidity and

volatility, decreases in liquidity can lead to a self-amplifying dynamic. Increasing margin

requirements limit the trading abilities of market specialists to offset unmatched trading needs,

which eventually trigger forced liquidations. The original sell pressure is amplified, leading

to further losses and increases in volatility. Further, the exit of market specialists leads to a

higher illiquidity which again affects margin requirements. Margin requirements being

9

dependent on market conditions are expected to be observed when investors’ financiers

cannot observe the origin of price movements and therefore rely on measures like Value-at-

Risk when setting margins. In this context, Brunnermeier and Pedersen predict the

phenomenon of flight to quality in times of market downturns, as volatile assets are more

funding intensive and consequently, less attractive when funding is tight. Further, these

authors demonstrate that the loss and margin spirals are mutually reinforcing each other in

amplifying losses during market downturns. In their model, margin requirements and

investors funding determine the level of market liquidity. At the same time both factors are

affected by liquidity fluctuations.

While the amplification mechanisms discussed above emphasize liquidation

externalities, the literature also suggests existence of amplifiers attributed to Knightian

uncertainty (immeasurable risk). Following Caballero and Krishnamurthy (2008) and

Krishnamurthy (2009), in times of crises market participants may often face risks they do not

well understand due to lack of historical record to refer to. Standard valuation and hedging

models therefore do not apply to these new market conditions and market participants have

little time to re-define them. In this context, Caballero and Krishnamurthy cite Alan

Greenspan (2004): “…When confronted with uncertainty, especially Knightian uncertainty,

human beings invariably attempt to disengage from medium to long-term commitments in

favor of safety and liquidity…”. Indeed, the model of Caballero and Krishnamurthy predicts

that in times characterized by Knightian uncertainty, agents shed risky financial claims in

favor of safety and certainty, while financial intermediaries hoard liquidity. 11

The reviewed literature describes market mechanisms that lead to significant price

declines largely unrelated to the worsening of firm fundamentals. Since these price declines

are not driven by firm idiosyncratic information, the exposure to systematic risk is expected

11 See also Easley and O’Hara (2010) who draw on the insights of Knightian uncertainty to explain the lack of trading in a variety of financial assets affected by the sub-prime crisis.

10

to be an important determinant of cross-sectional returns in crash periods. At the same time,

the literature predicts a number of cross-sectional patterns related to changes in supply and

demand for stocks with specific characteristics in times of crisis. In particular, as emphasized

in Caballero and Krishnamurthy (2008), the implications of balance sheet amplifiers and

uncertainty amplifiers in times of financial crises are similar in the sense that both predict

disengagement from different types of risk in favor of safe assets. While theoretical studies

have a consensus about this general prediction, there is very little empirical work that

provides a direct analysis of cross-sectional changes in supply and demand (i.e. flights) and

their implication for asset prices in the stock market around crisis events.12 Our study fills this

gap in the literature.

II. Crisis Periods and Data

A. Definition of the crisis periods

We analyze the following five recent episodes of stock market crashes associated with13:

- The 1998 Russian financial crisis

- September 11, 2001

- The burst of the dot-com bubble in 2002

- The beginning of the subprime mortgage crisis in 2007

- The financial crisis of 2008

There is not a generally accepted approach in the literature to definition of time

intervals associated with market crashes, in particular, to the definition of turning points that 12 As noted in the introduction, Blume et al (1989) is the only study which analyzes the effects of order imbalance in the US market during a crash event. 13 In an earlier version of this paper, we also analyzed the 1997 market downturn associated with the Asian crisis. However, this period was characterized by weak signals of crisis and recovery in the US based on the aggregate stock market data. It is possible that the short-term effects of this global financial turmoil on the US were offset by the strong domestic demand in this country during this period or that the largest effects were of long-term nature and not immediately evident. For example, Harrigan (2000) argues that the impact of the 1997 Asian crisis on US industries was small and localized, and that only one sector, the steel industry, experienced falling prices and output in the wake of the crisis.

11

distinguish pre-crash, crash and post-crash (recovery) periods. The market crises analyzed in

this paper span different time lengths, have different economic background, and special

features in the development of market conditions. The literature which analyzes the crash of

October 1987 faces a less challenging task in the definition of the studied periods. For

instance, in Blume et al. (1989) who analyze returns and order imbalance during the crash of

October 1987, the crash is the Black Monday (October 19th) and October 20th is considered

as the day of (partial) market recovery.

INSERT FIGURE 1 HERE

Figure 1 illustrates the behaviour of the S&P 500 index, the market volatility index

VIX, and the average absolute quoted spread of the NYSE common stocks (denoted

Illiquidity) during the years in which the analyzed crises events took place. Note that at the

beginning of each year the aggregate illiquidity is normalized to be equal to the

corresponding level of the VIX. For each market crisis, with the exception of that in 2008,

three intervals are defined: a benchmark (pre-crash), a crash and a recovery interval. We do

not define a recovery interval for the crash of 2008, as market volatility remained high for a

number of months following this crash, there was a further market decline in February 2009

and the signs of recovery were weak during the rest of 2009. Our general approach is to

define the crash interval as a distinguishable time period with pronounced negative market

returns related to the crisis under consideration. The recovery interval is a distinguishable

time period immediately following the crash featured by a reversal of the negative crash-

interval market trend to a positive trend.

Due to the heterogeneity of the development of each crisis, it is not possible to apply

exactly the same procedure to the definition of intervals for all studied periods. Our approach

is to start with a common procedure to the definition of intervals, and then make adjustments

on a crisis-by-crisis basis when particular features of individual events make problematic the

12

application of this common procedure. A conceptual sketch of the intervals is depictured in

the Figure 2 below.

Figure 2. Stylized crisis / definition of intervals

The common procedure to the definition of the crash interval is as follows: 1) Identify

the day with the largest negative return during the respective crisis (day t in Figure 2); 2) The

start of the crash period is chosen as the day with the highest level of the S&P 500 index

during the time interval of 30 days prior to day t; 3) The end of the crash is set to be the day

with lowest level of the S&P 500 index between day t and the following 30 trading days. This

approach is applied to the definition of the crash intervals in 1998, 2007 and 2008. Since the

crash of 2001 was triggered by the events of September 11, the first day of the crash period is

defined as the first day when market opened after this date (i.e. September 17).14 The crash of

2002 spanned a more prolonged time period than other cases. Indeed, the crash interval in

2002 covers 100 days and is defined directly by studying the development of the S&P 500

index.

14 We have also set as the first day of the 2001 crash the day before September 11 (i.e. September 10 instead of September 17). Further, noting that the period immediately preceding the September 11 is characterized by a relatively strong downward market trend, we have additionally produced estimates with the first day of the crash period defined using the common procedure described above. In both cases, the cross-sectional results are qualitatively similar to those presented in the paper and are available upon request.

Time

Period 2: Crash

Period 3: Recovery

Period 1: Benchmark

t

max. 30 days

max. 30 days

20 days

Aggregate price level

13

For all five stock market crashes, the pre-crash benchmark interval is defined as the

interval of 100 days that ends 20 days before the crash. We next turn to the definition of the

recovery periods. As noted above, we do not define a recovery interval for 2008. For all other

periods the recovery intervals are defined as intervals following directly after the last day of

the respective crash. The end of each recovery period is defined as the day with the highest

value of the S&P 500 during the subsequent 30 trading days. As a robustness check we have

also defined the recovery intervals uniformly across the analyzed periods in 1998-2007 as the

time period of two months after the last day of the respective crash. The cross-sectional

evidence based on this alternative definition of the recovery intervals is qualitatively similar

to that presented in the paper and is available upon request.15

INSERT TABLE I HERE

Table I presents exact dates and lengths of the individual benchmark, crash and

recovery intervals. The defined crash and recovery intervals are indicated in Figure 1 by the

vertical lines. While crash periods are associated with increasing market volatility and

illiquidity, recoveries show a reversal of these variables to lower levels. It is important to note

the persistence in the level of the volatility index VIX. Even though volatility declines during

recoveries, on average it is significantly higher than its pre-crash level. Another interesting

observation is that changes in the level of aggregate illiquidity around crisis events are

typically smaller in magnitude and are not as persistent as in the case of the VIX.

Under the described changing market conditions associated with crash and recovery

periods, the cross-sectional patterns of returns and trading activity may show important

15 Other possibilities to estimate turning points in market trends may include the application of statistical filtration methods that could capture variations in the long-term trend of the index (e.g., the Hodrick and Prescott (1997) and the Baxter and King (1999) filters). However, this approach may also post drawbacks due to the lack of consensus on the appropriate assumptions to control for the degree of smoothness to approximate the unobserved trend (which needs to be pre-defined to assess the accuracy of this type of methods) and the possibility of unstable patterns at the extremes of the time series. We leave this analysis for future research.

14

differences. In the following two sub-sections we describe the data and stock variables which

will be employed in the analysis of returns and order imbalance in sections III and IV.

B. Data Sample

For each crisis period, our initial sample consists of all common stocks (share codes

10 and 11) traded on the NYSE in the respective period. To be included in the analyzed

sample, a stock has to satisfy the following criteria. First, it should have sufficient data

available from CRSP to calculate returns, turnover and market size in the benchmark period.

Second, it should have at least 12 monthly return observations in the 36 months preceding a

crash (this is the minimum number of observations considered to estimate a stock’s market

beta). Third, the data on book value of equity for the fiscal year preceding a crash has to be

available from COMPUSTAT in order to calculate book-to-market ratio (B/M) of a stock at

the end of that fiscal year. Further, to reduce the influence of outliers and potential data errors

on our analysis, we exclude from the sample stocks with average price in the benchmark

period exceeding $999, B/M<0, B/M>10, estimated market beta exceeding 40 (in absolute

value), and return standard deviation in the benchmark period exceeding 30%. The resulting

sample is merged with the order imbalance (OIB) data calculated from NYSE TAQ database.

Hence, the sample is further restricted to stocks with available OIB data in the analyzed

periods. The universe of stocks covered by the OIB data as well as the procedure of the

construction of the order imbalance variables from transaction data based on the Lee and

Ready (1991) algorithm is provided in Chordia and Subrahmanyam (2004, section 3.1).

15

C. Definition of the Variables and Descriptive Statistics

In this section, we describe the cross-sectional variables employed in the analysis of

returns and order imbalance around crisis events. Since flight to quality and flight to liquidity

are some of the central cross-sectional predictions of the literature on market crisis (e.g.

Vayanos (2004), Brunnermeier and Pedersen (2009), Caballero and Krishnamurthy (2008))

our list includes variables related to stock volatility and liquidity.16 Furthermore, our list

includes the risk characteristics of Fama and French (1992) (denoted henceforth as FF3) and

the return momentum of Jegadeesh and Titman (1993). We use subscript “1” to denote the

benchmark (pre-crash) period, “2” to denote the crash period, and “3” to denote the recovery

period. We define the following cross-sectional variables:

• RET2 and RET3 – cumulative returns in the crash and recovery periods;

• ∆OIB1:2 and ∆OIB2:3 – difference between order imbalance in crash and pre-crash

periods, and difference between order imbalance in recovery and crash periods. Order

imbalance in period t is defined as t tt

t t

Buys -SellsOIB =

Buys +Sells, where Buys and Sells

denote the total number of bought and sold stocks;

• VOLA1, VOLA2 and VOLA3 – volatility in the benchmark, crash and recovery

periods, where volatility is measured as the standard deviation of daily returns;

• log(TURN1), log(TURN2) and log(TURN3) – natural logarithm of average daily

turnover in the benchmark, crash and recovery periods;

• BETA – the CAPM beta, measured in the period of the 36 months prior to a crash;

• log(SIZE) – natural logarithm of the market size measured on the last day of the

benchmark interval;

16 In our cross-sectional analysis of returns and order imbalance around crisis events we considered bid-ask spread and share turnover as explanatory variables proxying for stock liquidity. While turnover showed statistical significance in the estimated specifications, bid-ask spreads (based on either absolute or relative measures) did not. The specifications including spreads are therefore not reported in the paper, but they are available upon request.

16

• B/M – book-to-market ratio, measured as a ratio of book value of a firm at the end of

the fiscal year preceding the crash and average market size in the last month of that

fiscal year.

• RET1 – cumulative return in the period of six months preceding a crash.

INSERT TABLE II HERE

Table II presents summary statistics of the variables listed above. For each variable

we report its cross-sectional mean and standard deviation. Additionally, for the variables that

represent changes in the levels of price and order imbalance, we report t-test statistics for

equality of these changes to zero.

The evidence for the crash and recovery period returns is as expected. We document a

highly significant negative mean return in all five crash periods. Clearly, the strongest price

decline occurs during the 2008 crash with the sample stocks losing about 50% of their market

value. The mean returns during the studied market recoveries are positive and highly

significant.

Similar to the case of returns, we observe pronounced differences between crash and

recovery period changes in order imbalance. While these changes are negative in crash

periods (implying an increase in stock supply), there is a reversal effect during market

recoveries, with changes in OIB being positive and highly significant in all four studied

recoveries. This is consistent with the observed patterns in returns. The recovery of 2007

appears to be the weakest in comparison with other periods in terms of both return and OIB

changes, perhaps due to the uncertainty in the US market and the state of economy.

Next we turn to the analysis of volatility and turnover around crisis events. The table

reports the levels of these variables in the benchmark, crash and recovery intervals. We do

not show the estimates of the formal tests for changes in volatility and turnover across the

intervals, but we do discuss if these changes are statistically significant (based on t-tests for

17

equality of the paired changes to zero) when describing the results below.17 As expected, the

estimates indicate a significant rise in the standard deviation of returns during the crash

periods relative to the benchmark periods for all five studied events. It is noteworthy that the

level of stock volatility is considerably higher during the crash of 2008 than in the other

periods; the sample average standard deviation of returns in the 2008 crash is 0.065, at least

twice as high as in most of the other periods.18 Recovery volatilities are typically lower than

crash volatilities but still exceed the benchmark levels. This is consistent with the pattern

observed in Figure 1 with the VIX index reverting slowly to the lower long-term level during

market recoveries.

Turning to analysis of stock turnover, there is a significant increase in trading

intensity for the 2001, 2002, 2007 and 2008 crash events. In contrast, in 1998 we do not find

significant changes in turnover from the benchmark to the crash period. Further, estimates

indicate that, as compared to the crash numbers, the average levels of turnover experience

significant declines during the recoveries of 2001 and 2007, but remain unchanged in those of

1998 and 2002.

The estimates of market beta indicate that the average beta of the analyzed NYSE

sample is below 1 for three out of the five crisis periods. In more recent periods, 2007 and

2008, the average betas are above 1, which may indicate structural changes in the profile of

systematic risk of the analyzed NYSE stocks across crisis periods.19 The average firm size in

the analyzed samples is relatively stable across the first three crisis periods, but increases in

2007 and 2008. The B/M ratio reaches its highest level in 2001 and its lowest level in 2007.

Finally, our momentum variable, measured as a return in the six months preceding a crash,

shows a consistent pattern across all the five periods. This variable is positive in all periods,

17 The results of these tests are available upon request. 18 Indeed, during the crash of 2008 the volatility index VIX reaches its historical maximum. 19 The cross-sectional medians show the same pattern, indicating that the patterns observed in 2007 and 2008 are not a consequence of individual outliers in the data sample.

18

and significant in four out of five periods (1998 being an exception). This pattern is

consistent with a positive market trend preceding crash events.

III. Market Crashes – Cross-sectional Evidence In this section, we present empirical analyses of the cross-sectional determinants of returns

and changes in order imbalance during periods of market crashes.

A. Returns

INSERT TABLE III HERE

Table III presents univariate and multivariate cross-sectional analyses of crash returns.

The univariate evidence in Panel A reveals systematic patterns characterizing returns during

market crashes. There is a highly significant negative relation between the benchmark

volatility, turnover, the market beta of a stock and its crash return for all the events

considered.

Market size shows a statistically significant impact in the cross-section of crash

returns for four out of five market crashes. However, the sign of the effect is not consistent

across the individual periods. While larger stocks show greater losses in 2002, an opposite

pattern is observed during the 1998, 2007 and 2008 crashes, where the smaller stocks

experience greater price declines. The estimates indicate a negative relation between B/M and

crash returns during the last four crisis periods (2001, 2002, 2007 and 2008) 20, implying

greater loses for the value stocks. With respect to the momentum variable, RET1, we find a

positive and significant effect in 2008 only. Finally, regarding the crash-period change in

order imbalance, 1:2OIB∆ , we find a positive sign that is statistically significant for the

crashes of 2001, 2007 and 2008. This positive sign is expected and consistent with the

intuition that an excess of supply tends to decrease prices and returns.

20 This relation is however statistically insignificant in 2002.

19

Next we turn to multivariate analyses of the cross-section of crash-period returns in

Panel B of Table III. We report estimates of the following two specifications:

2, 0 1 1, 2 1, 3 1:2,log( )i i i i iRet VOLA TURN OIBβ β β β ε= + + + ∆ + (1)

2, 0 1 1, 2 1, 3 4 5 6 1, 7 1:2,log( ) log( ) /i i i i i i i i iRet VOLA TURN BETA SIZE B M Ret OIB uγ γ γ γ γ γ γ γ= + + + + + + + ∆ + (2)

The first specification includes stock volatility, turnover, and order imbalance as

explanatory variables of crash returns. The second one controls for the FF3 characteristics

and return momentum.

Overall, the results from the multivariate specifications are qualitatively similar to the

univariate results in Panel A. The effect of benchmark turnover is negative and significant for

both specifications in all periods. The coefficient on benchmark volatility is negative in all

cases too. For specification (1), the negative coefficient on volatility remains significant in all

periods; for specification (2), the negative coefficient is insignificant at the conventional

levels in 2001 and 2007 (the t-statistic in 2001 is, however, close to the 10% boundary). The

market beta is negative in all periods and significant in four out of five periods (2008 is an

exception).

In regression (1), the coefficient on change in order imbalance, 1:2OIB∆ , is positive in

all the periods and statistically significant in all the periods but 2007 and 2008. In regression

(2) that includes FF3 and momentum variables, we find that while the coefficient on 1:2OIB∆

remains positive in all periods, it is statistically insignificant in 1998, 2007 and 2008.21 The

reduction in significance of 1:2OIB∆ in the multivariate specifications may reflect the

association between 1:2OIB∆ and the added control variables.

21 The specifications in (1) and (2) were also estimated excluding 1:2OIB∆ variable. The estimates of the rest of

variables remain qualitatively and quantitatively similar. These results are available upon request.

20

Similar to the univariate results in Panel A, the effects of the other control variables

vary across individual periods. We find evidence that the larger stocks performed relatively

well during the crashes of 1998 and 2008. Further, the negative and significant relation of

B/M to returns in 2001 and 2007 indicates that growth stocks performed relatively well

during the crashes of 2001 and 2007.

Hence, the empirical evidence indicates that stocks with greater volatility, greater

trading intensity and higher sensitivity to market risk experience consistently greater loses in

times of market downturns. We also document further cross-sectional effects related to

market size and B/M stock characteristics, but these effects are specific to the individual

crashes. Finally, we find a positive association between returns and change in order

imbalance, expected to reflect the price impact of changes in supply and demand for stocks in

the crash periods.

The relation between stock characteristics and returns in times of strong market

downturns associated with an increase in selling activity may have different potential sources.

One source is that the level of the characteristic under consideration exposes stocks to the

market trend without a change in relative preferences for holding stocks with this

characteristic. Another source is a change in preferences for holding these stocks.

In the first case, to the extent that the characteristic under consideration is associated

with common factors in stock returns, cross-sectional variation in its level may imply more or

less exposure to the overall downward trend in times of crashes. The negative effect of a

stock’s beta on its crash-period return is an obvious example – stocks with greater exposure

to market fluctuations are subject to greater losses when the market drops. Similarly, it is

possible that in the periods of high volatility associated with a market crash, stocks with

greater volatility are subject to greater excess downside volatility, and this effect is in excess

of the exposure to systematic risk as measured by the market beta (Ang et al. (2006)). Further,

21

the fact that high turnover stocks earn consistently lower returns in times of market

downturns may simply be attributed to the fact that, in times of market crashes associated

with a higher selling activity (Table II), high trading volume implies massive selling, ceteris

paribus. The prices of heavily sold stocks are pushed down, especially under conditions of

increased illiquidity typical to crash periods. It is important to note that following the same

argumentation above, in times of market recoveries, associated with high market activity

driven by the flow of positive news and an increase in buyer-initiated trades, we expect a

reversal in the described relation between stock characteristics and returns from negative to

positive.

In the second case, changes in investor preferences for holding stocks with specific

characteristics in times of crashes and the existence of related trading pressures may underlie

the documented relations between stock characteristics and returns. For instance, if supply

pressures in times of crises are particularly strong for volatile stocks, then evidence of

negative association between returns and volatility might be linked to flight to quality in these

periods. Similarly, the negative relation between returns and turnover (market beta) might be

due to a flight away from stocks with high turnover (high market risk). 22 The next section

provides direct evidence on existence of flights in the stock market by studying the cross-

section of changes in order imbalance of individual stocks in the crash periods.

22 As discussed in Beber et al. (2011), order flow may contain less information than price changes “if a substantial portion of the price formation process is due to unambiguous public information resulting in instantaneous price adjustments (absent contemporaneous or subsequent trade)”. It is therefore not to be ruled out that changes in stocks’ supply and demand do not completely reflect investors’ re-evaluation of the merits of stocks with specific characteristics.

22

B. Order Imbalance

INSERT TABLE IV HERE

Table IV presents cross-sectional analysis of the change in order imbalance from the

pre-crash benchmark period to the crash period, 1:2OIB∆ . The univariate evidence is reported

in Panel A. We identify three cross-sectional variables with consistent patterns across all five

crash periods. First, a stock’s benchmark volatility is negatively associated with 1:2OIB∆ ,

implying an increase in market supply of volatile stocks (the negative coefficient is however

insignificant at the conventional levels in 1998 and 2001). This finding is consistent with the

phenomenon of flight to quality in times of crashes. It also supports the negative association

between crash period returns and benchmark volatility shown in Table III, consistent with the

idea that supply pressures lead to a particularly strong drop in prices of the volatile stocks.

The second systematic pattern is a highly significant positive association between firm size

and 1:2OIB∆ in all periods. This relation indicates flight to size in times of crashes.

Furthermore, in all periods we find a negative effect of the B/M ratio of a stock on 1:2OIB∆ ,

implying a relative increase in supply of value stocks in these periods.

For the rest of the variables, the evidence is not uniform across the analyzed periods.

There is a highly significant and positive relation between 1:2OIB∆ and benchmark turnover in

the 1998, 2001 and 2002 periods. To the extent that turnover measures a dimension of asset

liquidity, this evidence is consistent with the phenomenon of flight to liquidity during market

downturns. However, the coefficient on turnover is negative in 2007 and 2008. This negative

relation is statistically significant in 2007 and marginally significant in 2008 (the t-statistic in

2008 is close to 10% boundary). The evidence for 2007 and 2008 requires an interpretation.

In 2007 and 2008 the nature of the crash was related to a dry-up of liquidity in credit markets,

an episode known as the credit crunch. As investors needed liquidity and the demand for

23

illiquid assets was particularly low (i.e. these assets were difficult to sell), they might have

satisfied their liquidity needs by overselling liquid assets, thereby reversing the direction of

the order flow.23 Finally, we find a negative significant relation between the pre-crash returns

RET1 and 1:2OIB∆ during the 2001 and 2002 market crashes, implying that stocks with recent

gains were subject to more sales in these periods.

We now estimate multivariate regressions to explain the cross-sectional variation of

1:2OIB∆ . We present two sets of estimates based on the following specifications:

1:2, 0 1 1, 2 1,log( )i i i iOIB VOLA TURNβ β β ε∆ = + + + (3)

1:2, 0 1 1, 2 1, 3 4 5 6 1,log( ) log( ) /i i i i i i i iOIB VOLA TURN BETA SIZE B M Retγ γ γ γ γ γ γ ε∆ = + + + + + + + (4)

Panel B of Table IV summarizes our multivariate evidence. The estimates for

volatility and turnover in specification (3) are qualitatively similar to those in the univariate

regressions in Panel A. The only difference is that the effect of volatility becomes statistically

insignificant in 2007. However, once we include the FF3 and the pre-crash return as control

variables for 1:2OIB∆ (specification (4)), the coefficient on volatility turns insignificant in all

periods but 2008.24 The analysis of the estimates of the added control variables suggests that

firm size plays an important role in explaining the changes in order imbalance and might be

capturing part of the effect associated with volatility. Specifically, there is a positive and

highly significant relation between firm size and 1:2OIB∆ for all five crashes, suggesting that

flight to size is a prevailing characteristic of market behavior in times of crashes. The positive

effect of turnover on 1:2OIB∆ in 1998, 2001 and 2002 periods remains statistically significant

23 See Brunnermeier (2009) who quotes a Wall Street saying “If you can’t sell what you want to sell, sell what you can sell.” 24 For the crash of 2008, the return and order imbalance specifications were additionally estimated excluding the financial company stocks (SIC codes: 6000-6999) from the sample. The cross-sectional evidence remained qualitatively similar to that presented in the paper. These additional estimates are available upon request. The four-digit 12 industry classification codes were obtained from Kenneth French's website: http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html

24

in this specification. The negative effect of turnover on 1:2OIB∆ in 2007 is not affected by the

inclusion of control variables too. In regard of past returns, the negative sign of the estimates

in 1998, 2001 and 2002 is consistent with the findings from the univariate regressions. For

the market beta and B/M, the results are typically insignificant, and do not show a consistent

sign pattern. The drop in significance of the effect of B/M on 1:2OIB∆ in the multivariate

specification may indicate that the univariate effect of B/M on 1:2OIB∆ (see Table IV, Panel

A) is driven by the effect of size (which is in the denominator of the book-to-market ratio).

Reviewing the evidence in this section, our central finding is that flight to size is a

characteristic of the trading behavior in times of market crashes (regardless of their special

features and economic background). Since it is reasonable to argue that a common feature of

the periods of strong market declines is an increase in the level of uncertainty in the market,

we may conjecture that flight to size is a reflection of an increase in aversion to uncertainty in

these periods. Indeed, Zhang (2006) presents evidence consistent with size being inversely

related to information uncertainty of a firm’ value (i.e. the ambiguity with respect to the value

implications of new information). Furthermore, recent literature demonstrates that smaller

firms have higher sensitivity to aggregate cash flow news (Campbell and Vuolteenaho (2004),

Da and Warachka (2009), Campbell, Polk and Vuolteenaho (2010)) and higher exposure to

consumption risk (Parker and Julliard (2005), Jagannathan and Wang (2007)). In times of

crises associated with uncertainty, an increase in risk aversion, and bad current or expected

economic states, the smaller stocks may be avoided since they may be perceived as

particularly exposed to negative cash flow shocks and realizations of negative consumption

growth.

25

IV. Market Recoveries – Cross-sectional Evidence

In this section, we present empirical analyses of the cross-sectional determinants of returns

and changes in order imbalance during periods of recoveries following market crashes.

A. Returns

INSERT TABLE V HERE

Table V reports the results of the analysis of stock returns. The cross-sectional variables

employed in the analysis include the crash period volatility and turnover, the FF3 stock

characteristics, and the crash period return.

The univariate evidence presented in Panel A shows significant differences to the

findings from regressions for the crash period in Table III. The evidence for stock volatility

indicates a reversal in the return - volatility relation from significant negative to significant

positive from crash to recovery periods in three out of four analyzed recoveries (1998, 2001

and 2002). The volatility coefficient is insignificant in 2007. An even stronger reversal

pattern is observed in the case of the return - turnover relation, where the negative and

significant effect found in univariate regressions for crash periods turns to a positive and

highly significant effect in all analyzed recoveries. Turning to the results for the stock beta,

we observe a pattern very similar to the one described for volatility and turnover ― the effect

of stock beta on returns reverses from negative to highly significant positive when moving

from market crashes to recoveries in all periods.

Regarding the firm size, we find a consistent positive and significant effect of this

variable on returns in all periods. This contrasts with the findings in crash periods, where the

evidence related to the size – return relation was mixed. In the univariate regressions related

to the recovery periods there is no ambiguity about the fact that larger stocks earn higher

returns. In terms of the B/M characteristic, we find a significant negative relation to returns in

26

1998, 2001, and 2007. In 2002 the effect is positive but significant only at the 10% level.

Finally, the recovery returns are negatively related to the crash returns in 1998, 2001, and

2002, implying greater recovery gains for stocks with greater losses during market crashes.

The change in order imbalance from crash to recovery periods, 2:3OIB∆ , shows a consistent

positive effect across all periods. This effect is significant at the conventional levels in 2001,

2002 and 2007.

We now turn to the multivariate analysis of the recovery returns. Similar to the crash

periods, we estimate two specifications. The first one in (5) does not control for FF3 and past

return variables, and the second one in (6) controls for these variables.

3, 0 1 2, 2 2, 3 3,log( )i i i i iRet VOLA TURN OIBβ β β β ε= + + + ∆ + (5)

3, 0 1 2, 2 2, 3 4 5 6 2, 7 3,log( ) log( ) /i i i i i i i i iRet VOLA TURN BETA SIZE B M Ret OIB uγ γ γ γ γ γ γ γ= + + + + + + + ∆ +

(6)

The estimation results are reported in Panel B of Table V. The estimates of (5) are

qualitatively similar to those from univariate regressions; specifically, we find positive effects

of crash-period volatility and turnover on recovery returns in all periods and also, a positive

and significant impact of 2:3OIB∆ on returns in all periods. The only noticeable difference is

that the significance of the positive volatility coefficient is reduced in some years.

The results for the augmented specification in (6) are presented in Panel B of Table V.

The estimates indicate that the results described above are in general robust to the controls we

added. There are only mild changes in terms of statistical significance for a few cases, but the

overall picture is maintained. With regard to the control variables, we observe that the beta –

return relation is positive and significant in the recoveries associated with the 2001, 2002 and

2007 periods, as in the univariate regressions, but turns insignificant in the recovery of 1998.

In the case of firm size, while the univariate regressions indicate a consistent highly

significant positive relation of firm size to recovery returns in all periods, the multivariate

27

evidence shows some variation across the periods. The positive significant relation of size to

returns is maintained in 2002 only; in 1998 and 2001, this effect turns insignificant and, in

2007, it switches to negative and significant. This atypical pattern may be due to a

misspecification of the recovery period of the 2007 crash. In fact, the market volatility and

illiquidity indicators remained at high levels during this recovery (see Figure 2) perhaps due

to the uncertainty about the economic conditions in the United States. In the case of B/M, the

results are consistent with the univariate evidence, with the growth stocks tending to perform

better during recoveries. Finally, the effect of crash returns on recovery returns is negative in

three cases, which coincides with the univariate findings. This confirms that stocks with

greater loses during crashes perform better in the periods of recovery. This reversal feature is

consistent with the idea of deviations from fundamentals or overreaction during periods of

financial distress. Finally we find a highly significant positive association between recovery

returns and changes in order imbalance in all the periods, indicating that changes in trading

patterns from crash to recovery play an important role as determinants of the recovery returns.

Summarizing the evidence in this section, one of our central findings is the reversal

effect in the relation of volatility, turnover and the market beta of a stock to its return from

negative in times of market crashes to positive in times of recoveries. This reversal effect

supports the discussion in section III.A., in the sense that volatility, turnover and the market

beta are characteristics, which capture stocks’ sensitivity to a market trend. There is further

evidence of highly significant positive relation of the recovery returns to the

contemporaneous changes in order imbalance, 2:3OIB∆ . It is noteworthy that this positive

relation is typically stronger in the periods of recovery compared to the periods of market

crashes (Table III, Panel B). This finding makes the analysis of the determinants of 2:3OIB∆

in the next section particularly interesting.

28

B. Order Imbalance

INSERT TABLE VI HERE

Table VI presents cross-sectional analysis of changes in the order imbalance from

crash to recovery periods, 2:3OIB∆ . Starting from the univariate evidence in Panel A, we find

a consistent negative relation between crash period volatility and 2:3OIB∆ (this relation is

insignificant at the conventional levels in 2002 and 2007). This evidence suggests that the

flight to quality phenomenon might persist during some recovery periods, which is consistent

with the idea of persistence in risk aversion and the fact that volatility mean reverts slowly to

the lower long-term level (as can be seen in Figure 1 for all periods); this is also consistent

with persistence in margins (with margins being particularly high for volatile stocks) when

the underlying volatility process follows an ARCH process as in Brunnemeier and Pedersen

(2009). With respect to turnover, we find a consistent negative sign for all periods too (this

effect is insignificant in 2007). In other words, in recovery periods there is more demand for

stocks that showed lower levels of trading activity during the preceding market crash. We do

not find significant effects for the market beta - 2:3OIB∆ relation. Regarding firm size effect,

we find a negative and highly significant relation of size to 2:3OIB∆ in 1998, 2001 and 2002.

This suggests an increase in the demand for the smaller stocks in these recovery periods. In

the same three periods, we find a positive and significant relation between B/M ratio and

2:3OIB∆ in 1998, 2001 and 2002, implying higher demand for value stocks. Finally, the

coefficient on the crash-period return is negative in three out of four periods. This negative

effect is significant in 1998 and 2001, implying a higher demand in recoveries for stocks that

showed greater losses in the preceding crash periods.

We next turn to the multivariate analysis of 2:3OIB∆ . We estimate the following two

regressions:

29

2:3, 0 1 2, 2 2,log( )i i i iOIB VOLA TURNβ β β ε∆ = + + + (7)

2:3, 0 1 2, 2 2, 3 4 5 6 2,log( ) log( ) /i i i i i i i iOIB VOLA TURN BETA SIZE B M Retγ γ γ γ γ γ γ ε∆ = + + + + + + + (8)

The estimates of the coefficients of volatility and turnover in specification (7) are

qualitatively similar to the univariate results. It is remarkable that once we control for the FF3

stock characteristics and the crash returns as in (8), we find that the effects of volatility and

turnover are negative in all periods, and are also statistically significant in all periods, with

exception of 2007 for both variables. As a result, these findings provide an evidence of

trading patterns consistent with flight to quality (low-volatility stocks) and flight to low-

turnover stocks in the periods of recovery. Moreover, multivariate evidence indicates a

consistent negative association between crash returns and 2:3OIB∆ in all periods, implying an

increase in demand for stocks with greater crash period losses. The size – return relation is

negative and significant in 1998, 2001 and 2002, implying a flight back to smaller stocks in

the recovery periods. Regarding the beta, we find a positive sign across all the periods, but it

is significant only in 2002. In the case of B/M ratio, in the multivariate specification we do

not document any significant effects.

Summarizing the evidence in this section, we find that recoveries following market

crashes are typically characterized by flights to stocks with low crash-period turnover and

volatility and flight to crash-period losers. There is further evidence of an increase in demand

for smaller stocks in these periods.

V. Summary and Conclusions

In this paper, we study the cross-sectional determinants of stock returns and trading activity

around five recent episodes of market crashes in the United States during the period 1998-

30

2008. Following an event study approach, we identify a number of systematic patterns

consistent across the analyzed periods.

With respect to returns, we find that a stock’s turnover, volatility, and market beta are

important determinants of its return in both the periods of crashes and subsequent recoveries.

There is strong evidence that stocks characterized by high turnover, high volatility and high

market beta experience consistently greater losses during market crashes. During market

recoveries, the negative relation of turnover, volatility and beta to returns reverts to positive.

In other words, the stocks with higher levels of these variables gain more during recoveries.

We suggest two alternative interpretations of the documented effects. First, characteristics

like volatility, turnover and market beta may expose a stock to the market trend, ceteris

paribus. This would explain the reversal of the cross-sectional relation of returns to these

variables from the crash period (when market drops and there is an increase in selling activity)

to the recovery period (when market rises and there is an increase in buying activity). Second,

the analyzed periods may be characterized by changes in investor preferences for holding

stocks with these characteristics, which will be reflected in changes of the premium

demanded for holding these stocks and adjustments in their supply and demand, i.e. flights. In

the latter case, supply and demand pressures associated with these flights might explain the

documented cross-sectional effects in returns. In fact, as expected, our evidence indicates that

crash and recovery returns are positively related to the contemporaneous changes in order

imbalance.

We provide a direct analysis of flights in periods of market crashes and recoveries by

studying cross-sectional determinants of changes in order imbalance in these periods. To the

best of our knowledge, our study is the first to present direct evidence on flights in the stock

market around recent crisis events. We uncover a compelling evidence of flight to size in

times of crashes – there is a positive and significant relation between stock size and crash-

31

period change in order imbalance for all analyzed events. This effect is distinct from the

phenomena of flight to liquidity and flight to quality discussed in the literature. In addition to

flight to size, during the 2008 crash we find evidence of flight to quality. Moreover, during

the market crashes in 1998, 2001 and 2002, there is a highly significant and positive relation

between stock turnover and the crash-period change in order imbalance, which can be

interpreted as flight to liquidity in these periods. The recoveries following market crashes are

characterized by a rise in demand for the crash-period losers, stocks with low crash-period

volatility (consistent with flight to quality) and low crash-period turnover. There is a further

evidence of an increase in demand for the smaller stocks during recoveries.

Overall, the results in this paper suggest that cross-sectional patterns of returns in times of

crises are determined by (i) a stock’s market “sensitivity” characteristics – we conjecture that

volatility and turnover, in addition to systematic risk as measured by the market beta, are

such stock characteristics – and (ii) supply and demand pressures (flights) specific to the

periods of crashes and recoveries.

The paper presents a number of new empirical regularities that have not been considered

in the existing literature such as the role of turnover as a cross-sectional determinant of

returns in times of crashes and recoveries, and the compelling evidence of flight to size

characterizing market crashes. A priority for future research is disentangling the primitive

sources that drive these effects, which will allow us to evaluate alternative theoretical

explanations.

32

REFERENCES Amihud, Y., H. Mendelson, and L. H. Pedersen, 2006, Liquidity and Asset Prices, Foundations and Trends in Finance 1, 269-364. Amihud, Y., H. Mendelson, and R.A. Wood, 1990, Liquidity and the 1987 Stock Market Crash, Journal of Portfolio Management 16, 65–69. Ang, A., R. J. Hodrick, Y. Xing, and X. Zhang, 2006, The Cross-section of Volatility and Expected Returns, Journal of Finance 61, 259-299. Baxter, M. and R.G. King, 1999, Measuring Business Cycles: Approximate Band-pass Filters, The Review of Economics and Statistics 81, 575-593.

Beber, A., M. W. Brandt, and K. A. Kavajecz, 2011, What Does Equity Sector Orderflow Tell Us about the Economy?, Review of Financial Studies, forthcoming.

Berk, J., R. Green, and V. Naik, 1999, Optimal Investment, Growth Options, and Security Returns, Journal of Finance 54, 1553–1607. Bernardo, A.E., and I. Welch, 2004, Liquidity and Financial Market Runs, Quarterly Journal of Economics, 119, 135-158. Blume, M., A. MacKinlay, and B. Terker, 1989, Order Imbalances and Stock Price Movements on October 19 and 20, 1987, Journal of Finance 44, 827–848. Brunnermeier, M., and L. Pedersen, 2009, Market Liquidity and Funding Liquidity, Review of Financial Studies, 22, 2201-2238. Brunnermeier, M., 2009, Deciphering the 2007-08 Liquidity and Credit Crunch, Journal of Economic Perspectives, 23, 77-100. Caballero, R. and A. Krishnamurthy, 2008, Collective Risk Management in a Flight to Quality Episode, Journal of Finance 63, 2195-2236. Campbell, J. and A. Kyle, 1993, Smart Money, Noise Trading and Stock Price Behavior, Review of Economic Studies 60, 1–34. Campbell, J., C. Polk, and T. Vuolteenaho, 2010, Growth or Glamour? Fundamentals and Systematic Risk in Stock Returns, Review of Financial Studies 23, 305–344. Campbell, J., and T. Vuolteenaho, 2004, Bad Beta, Good Beta, American Economic Review 94, 1249-1275. Carlson, M., A. Fisher, and R. Giammarino, 2004, Corporate Investment and Asset Price Dynamics: Implications for the Cross-section of Returns, Journal of Finance 59, 2577–2603. Carlson, M., A. Fisher, and R. Giammarino, 2006, Corporate Investment and Asset Price Dynamics: Implications for SEO Event Studies and Long-run Performance, Journal of Finance 61, 1009–1034.

33

Chordia, T., R. Roll, and A. Subrahmanyam, 2000, Commonality in Liquidity, Journal of Financial Economics 56, 3-28. Chordia, T., R. Roll, and A. Subrahmanyam, 2002, Order imbalance, liquidity, and market returns, Journal of Financial Economics 65, 111-130. Chordia, T., and A. Subrahmanyam, 2004, Order Imbalance and Individual Stock Returns: Theory and Evidence, Journal of Financial Economics 72, 485-518. Da, Z., and M. Warachka, 2009, Cashflow Risk, Systematic Earnings Revisions, and the Cross-section of Stock Returns, Journal of Financial Economics 44, 448–468. Dornbusch, R., Y.C. Park, and S. Claessens, 2000, Contagion: Understanding How It Spreads, The World Bank Research Observer 15, 177-977. Easley, D. and M. O'Hara, 2010, Liquidity and Valuation in an Uncertain World, Journal of Financial Economics 97, 1-11. Edelen, R. M. and J. B. Warner, 2001, Aggregate Price Effects of Institutional Trading: A Study of Mutual Fund Flow Data and Market Returns, Journal of Financial Economics 59, 195-220.

Engle, R., 1982, Autoregressive Conditional Heteroskedasticity with Estimates of the Variance of UK Inflation, Econometrica 50, 987-1008.

Evans, M., und R. Lyons, 2002, Order Flow and. Exchange Rate Dynamics, Journal of Political Economy 110, 170-180. Fama, E. F. and K. R. French, 1992, The Cross-section of Expected Stock Returns, Journal of Finance 47, 427-465. Garleanu, N., and L. H. Pedersen, 2007, Liquidity and Risk Management, NBER Working Paper 12887. Gomes, J., L. Kogan, and L. Zhang, 2003, Equilibrium Cross Section of Returns, Journal of Political Economy 111, 693–732. Greenspan, A, 2004, Risk and Uncertainty in Monetary Policy, Remarks for the AEA Meetings. Gromb, D., and Vayanos, D., 2002, Equilibrium and Welfare in Markets with Financially Constrained Arbitrageurs, Journal of Financial Economics 66, 361-407. Hameed, A., W. Kang, and S. Viswanathan, Market Declines and Liquidity, 2009, Journal of Finance 65, 257-294. Harrigan, J., 2000, The impact of the Asia Crisis on US industry: An almost free lunch?, Federal Reserve Bank of New York Economic Policy Review. 6, 71-78.

34

Hasbrouck, J., 1988, The Quotes, Inventories and Information, Journal of Financial Economics, 22, 229-252. Hasbrouck, J., 1991a, Measuring the Information Content of Stock Trades, Journal of Finance 46, 179-207. Hasbrouck, J., 1991b, The Summary Informativeness of Stock Trades: An Econometric Analysis, Review of Financial Studies 4, 571-595. Hasbrouck, J., and D. Seppi, 2001, Common Factors in Prices, Order Flows and Liquidity, Journal of Financial Economics 59, 383-411. Hodrick, R. and E.C. Prescott, 1997, Postwar U.S. Business Cycles: An Empirical Investigation, Journal of Money, Credit and Banking 29, 1–16. Jagannathan, R. and Y. Wang, 2007, Lazy Investors, Discretionary Consumption, and the Cross-Section of Stock Returns, Journal of Finance 62, 1623 – 1661. Jegadeesh, N. and S. Titman, 1993, Returns to Buying Winners and Selling Losers: Implications for Stock Market Efficiency, Journal of Finance 48, 65-91. King, M., and S. Wadhwani, 1990, Transmission of Volatility between Stock Markets, Review of Financial Studies 3, 5-33. Kiyotaki, N. and J. Moore, 2002, Evil is the Root of All Money, American Economic Review Papers and Proceedings 92, 62–66. Knight, F. H., 1921, Risk, Uncertainty and Profit Boston: Houghton Mifflin. Krishnamurthy, A., 2009, Amplification Mechanisms in Liquidity Crises, American Economic Association Journals - Macroeconomics. Kurov, A. and D. Lasser, 2002, Price Dynamics in the Regular and E-mini Futures Markets, Journal of Financial and Quantitative Analysis 39, 365-384. Kyle, A.S., and W. Xiong, 2001, Contagion as a Wealth Effect, Journal of Finance 56, 1401-1440. Lauterbach, B. and U. Ben-Zion, 1993, Stock Market Crashes and the Performance of Circuit Breakers: Empirical Evidence, Journal of Finance 48, 1909–1925. Morris, S. E. and H. S. Shin, 2004, Liquidity Black Holes. Cowles Foundation Discussion Paper. Novy-Marx, R., 2010, Operating Leverage, forthcoming in Review of Finance. Parker, J. and C. Julliard, 2005, Consumption Risk and the Cross-Section of Expected Returns, Journal of Political Economy, 113, 185-222.

35

Sarkar A., and J. Schrader, 2010, Financial Amplification Mechanisms and the Federal Reserve’s Supply of Liquidity during the Crisis, Federal Reserve Bank of New York Staff Reports, no. 431. Shleifer, A. and R. Vishny, 1997, The Limits of Arbitrage, Journal of Finance 52, 35-55. Vayanos, D., 2004, Flight to Quality, Flight to Liquidity and the Pricing of Risk, NBER Working Paper. Xiong, W., 2001, Convergence Trading with Wealth Effects: An Amplification Mechanism in Financial Markets, Journal of Financial Economics 62, 2001, 247-292. Zhang, L., 2005, The Value Premium, Journal of Finance 60, 67–103. Zhang, X. F., 2006, Information Uncertainty and Stock Returns, Journal of Finance 61, 105-135.

Table I. Definition of the Benchmark, Crash and Recovery Intervals

First Last # First Last # First Last # First Last # First Last # day day days day day days day day days day day days day day days

1Benchmark

2Crash

3Recovery - - -9/13/2007 10/10/2007 2010/10/2002 11/6/2002 209/24/2001 10/26/2001 2510/9/1998 11/19/1998 30

9/3/2008 11/20/2008 57

100

7/21/1998 10/8/1998 57 9/17/2001 9/21/2001 5 5/20/2002

1/28/1998 6/19/1998 100 3/21/2001 8/10/2001 100

1998 2001 2002 2007 2008

7/17/2007 9/12/2007 4110/9/2002 100

100 3/14/2008 8/5/2008100 1/24/2007 6/17/200711/26/2002 4/19/2002

Intervals

Table II. Summary Statistics

This table reports cross-sectional averages of cumulative crash and recovery returns, RET2 and RET3; crash and recovery changes in order imbalance, ∆OIB1:2 and ∆OIB2:3; volatility in benchmark, crash and recovery periods, VOLA1, VOLA2 and VOLA3, measured as a standard deviation of daily returns in the respective period; natural logarithm of average turnover in benchmark, crash and recovery periods, log(TURN1), log(TURN2) and log(TURN3); CAPM beta, BETA, measured in the period of the 36 months prior to a crash; natural logarithm of market size measured on the last day of the benchmark interval, log(SIZE); book-to-market ratio, measured as a ratio of book value of a firm at the end of the fiscal year preceding the crash and average market size in the last month of that fiscal year, B/M; and cumulative return in the period of six months preceding a crash, RET1. For each variable we report its cross-sectional mean and standard deviation. Additionally, for returns and changes in order imbalance, we report t-statistics for equality of means of these variables to zero.

1998 2001 2002 2007 2008

RET2 mean -0.248 -0.087 -0.284 -0.100 -0.502

std.dev. 0.201 0.089 0.233 0.134 0.223t-stat -46.983 *** -36.473 *** -39.075 *** -23.081 *** -68.198 ***

RET3 mean 0.192 0.086 0.138 0.055

std.dev. 0.213 0.208 0.201 0.091 -t-stat 33.386 *** 15.271 *** 21.854 *** 18.603 ***

∆∆∆∆OIB1:2 mean -0.039 -0.091 -0.057 -0.069 -0.017

std.dev. 0.132 0.244 0.111 0.085 0.050t-stat -11.246 *** -13.891 *** -16.446 *** -25.080 *** -10.256 ***

∆∆∆∆OIB2:3 mean 0.037 0.126 0.063 0.011

std.dev. 0.151 0.239 0.140 0.078 -t-stat 9.299 *** 19.594 *** 14.431 *** 4.280 ***

VOLA1 mean 0.022 0.028 0.024 0.017 0.030

std.dev. 0.012 0.023 0.014 0.007 0.014

VOLA2 mean 0.032 0.042 0.032 0.028 0.066

std.dev. 0.018 0.036 0.018 0.014 0.033

VOLA3 mean 0.032 0.035 0.034 0.020 -std.dev. 0.019 0.026 0.020 0.011

log(TURN1) mean 0.862 0.870 1.101 2.097 2.373

std.dev. 0.924 1.161 0.978 0.655 0.702

log(TURN2) mean 0.872 1.233 1.168 2.367 2.602

std.dev. 0.961 1.245 1.023 0.631 0.743

log(TURN3) mean 0.868 0.907 1.158 2.048 -

std.dev. 1.001 1.227 1.170 0.676

BETA mean 0.819 0.660 0.558 1.237 1.126std.dev. 0.616 0.849 0.733 0.773 0.536

log(SIZE) mean 13.444 13.286 13.694 14.844 14.602std.dev. 1.976 2.236 2.155 1.516 1.606

B/M mean 0.526 0.783 0.648 0.440 0.737std.dev. 0.421 0.920 0.667 0.278 0.864

RET1 mean 0.004 0.043 0.200 0.034 0.022

std.dev. 0.250 0.312 0.388 0.126 0.249t-stat 0.794 5.152 *** 16.522 *** 8.420 *** 2.669 ***

Table III. Cross-section of Crash-period Returns

This table reports cross-sectional regressions of crash returns, RET2, on (i) benchmark volatility, VOLA1, (ii) benchmark turnover, log(TURN1), (iii) the CAPM beta, BETA, (iv) market size, log(SIZE), (v) book-to-market ratio, B/M (vi) the cumulative return in the period of six months preceding a crash, RET1, and (vii) the change in order imbalance from benchmark to crash period, ∆OIB1:2. For further details of definition of the variables see Table II. Robust Newey-West (1987) t-statistics are reported below coefficient estimates. *, **, *** indicate significance at the 10%, 5%, 1% levels. Panel A presents the estimates of univariate regressions and Panel B the estimates of multivariate regressions.

Panel A. Univariate regressions (dependent variable: RET2)

Intercept Variable Intercept Variable Intercept Variable Intercept Variable Intercept Variable

VOLA1 -0.170 *** -3.517 *** -0.067 *** -0.699 *** -0.200 *** -3.405 *** -0.039 *** -3.629 *** -0.309 *** -6.381 ***

-11.653 -5.489 -12.575 -3.314 -16.206 -6.120 -2.651 -3.732 -16.504 -9.562

R24.32% 2.37% 4.21% 4.09% 16.47%

log(TURN1) -0.208 *** -0.047 *** -0.076 *** -0.013 *** -0.205 *** -0.072 *** -0.021 -0.037 *** -0.280 *** -0.094 ***

-29.274 -8.162 -21.993 -5.605 -16.759 -8.976 -1.416 -5.039 -9.860 -8.400R2 4.75% 2.89% 9.23% 3.34% 8.64%

BETA -0.199 *** -0.058 *** -0.077 *** -0.015 *** -0.230 *** -0.095 *** -0.060 *** -0.032 *** -0.334 *** -0.149 ***-19.483 -6.229 -26.184 -4.634 -25.417 -8.770 -8.242 -5.241 -18.390 -9.977

R2 3.35% 1.93% 8.87% 3.36% 12.75%

log(SIZE) -0.340 *** 0.007 ** -0.085 *** 0.000 -0.157 *** -0.009 ** -0.320 *** 0.015 *** -0.845 *** 0.023 ***-9.186 2.472 -5.025 -0.069 -2.967 -2.553 -6.693 4.836 -11.787 4.947

R2 0.51% 0.00% 0.74% 2.84% 2.85%

B/M -0.253 *** 0.012 -0.078 *** -0.011 *** -0.273 *** -0.015 -0.054 *** -0.103 *** -0.464 *** -0.051 ***-23.335 0.678 -23.411 -2.647 -26.172 -1.059 -5.806 -5.002 -40.085 -3.402

R2 0.07% 1.28% 0.18% 4.60% 3.83%

RET1 -0.246 *** -0.002 -0.086 *** -0.015 -0.285 *** 0.008 -0.100 *** 0.022 -0.505 *** 0.166 ***

-41.534 -0.068 -34.454 -1.390 -32.339 0.405 -19.714 0.480 -64.050 4.304R2 0.00% 0.29% 0.02% 0.04% 3.42%

∆∆∆∆OIB1:2 -0.246 *** 0.056 -0.083 *** 0.046 *** -0.282 *** 0.048 -0.092 *** 0.113 ** -0.495 *** 0.375 **

-36.790 1.288 -29.476 3.915 -28.412 0.587 -16.434 2.001 -61.136 2.181

R2 0.13% 1.62% 0.05% 0.52% 0.70%

1998 2001 2002 2007 2008

39

Panel B. Multivariate regressions (dependent variable: RET2)

Intercept -0.152 *** -0.387 *** -0.051 *** -0.035 -0.116 *** -0.015 0.002 -0.025 -0.233 *** -0.434 ***-10.757 -6.466 -9.247 -1.598 -6.844 -0.202 0.141 -0.407 -9.170 -6.263

VOLA1 -2.594 *** -1.326 ** -0.673 *** -0.354 -3.239 *** -2.171 *** -2.751 *** -1.023 -5.350 *** -4.481 ***

-4.194 -2.105 -3.055 -1.563 -6.081 -3.154 -2.567 -0.925 -7.053 -4.388

log(TURN1) -0.042 *** -0.046 *** -0.014 *** -0.016 *** -0.073 *** -0.059 *** -0.024 *** -0.029 *** -0.044 *** -0.043 ***

-6.746 -6.865 -5.691 -5.479 -7.463 -5.448 -2.980 -3.566 -3.826 -3.470

BETA -0.047 *** -0.009 *** -0.056 *** -0.018 *** -0.035-4.941 -3.272 -4.936 -2.692 -1.310

log(SIZE) 0.017 *** 0.000 -0.007 0.005 0.013 ***4.555 -0.272 -1.560 1.393 3.063

B/M 0.036 * -0.015 *** -0.025 -0.092 *** 0.029 *1.650 -3.160 -1.577 -4.636 1.780

RET1 -0.006 -0.012 0.026 0.018 0.102 ***

-0.221 -1.164 1.471 0.397 3.075

∆OIB1:2 0.105 ** 0.051 0.059 *** 0.059 *** 0.162 * 0.196 ** 0.078 0.046 0.079 0.056

2.429 1.148 4.962 5.001 1.872 2.169 1.375 0.822 0.498 0.366

R2 7.65% 10.80% 7.44% 9.83% 13.61% 16.81% 5.63% 10.92% 18.05% 20.05%Adj R2 7.46% 10.37% 7.24% 9.37% 13.36% 16.24% 5.34% 10.26% 17.78% 19.44%F 39.72 24.81 37.05 21.46 53.74 29.41 18.98 16.64 67.46 32.78N 1442 1442 1386 1386 1027 1027 958 958 923 923

20071998 20082001 2002

40

Table IV. Cross-section of Crash-period Changes in Order Imbalance

This table reports cross-sectional regressions of the changes in order imbalance from benchmark to crash period, ∆OIB1:2, on (i) benchmark volatility, VOLA1, (ii) benchmark turnover, log(TURN1), (iii) the CAPM beta, BETA, (iv) market size, log(SIZE), (v) book-to-market ratio, B/M (vi) the cumulative return in the period of six months preceding a crash, RET1 . For further details of definition of the variables see Table II. Robust Newey-West (1987) t-statistics are reported below coefficient estimates. *, **, *** indicate significance at the 10%, 5%, 1% levels. Panel A presents the estimates of univariate regressions and Panel B the estimates of multivariate regressions.

Panel A. Univariate regressions (dependent variable: ∆OIB1:2)

Intercept Variable Intercept Variable Intercept Variable Intercept Variable Intercept Variable

VOLA1 -0.026 *** -0.580 -0.078 *** -0.463 -0.038 *** -0.781 ** -0.056 *** -0.749 *** 0.0004 -0.571 ***

-2.717 -1.417 -5.503 -1.001 -4.765 -2.280 -9.220 -2.272 0.120 -5.176

R20.28% 0.13% 0.98% 0.43% 2.65%

log(TURN1) -0.057 *** 0.023 *** -0.130 *** 0.045 *** -0.087 *** 0.027 *** -0.041 ** -0.013 *** -0.004 -0.005

-8.464 4.244 -10.630 5.339 -9.905 5.025 -3.380 -2.430 -0.434 -1.641

R22.65% 4.61% 5.70% 1.02% 0.59%

BETA -0.040 *** 0.002 -0.103 *** 0.019 ** -0.060 *** 0.005 -0.061 *** -0.006 * -0.005 -0.010 ***

-5.666 0.263 -11.566 2.175 -11.616 1.064 -10.341 -1.566 -1.282 -3.390

R20.01% 0.43% 0.11% 0.33% 1.20%

log(SIZE) -0.314 *** 0.021 *** -0.408 *** 0.024 *** -0.284 *** 0.017 *** -0.162 *** 0.006 *** -0.073 *** 0.004 ***

-10.233 9.688 -7.174 6.083 -8.084 7.046 -5.439 3.255 -3.576 2.887

R29.81% 4.81% 10.38% 1.25% 1.51%

B/M -0.025 *** -0.026 *** -0.076 *** -0.019 * -0.045 *** -0.019 * -0.060 *** -0.019 ** -0.013 *** -0.005 *-4.238 -2.799 -9.326 -1.956 -7.621 -1.848 -12.931 -1.965 -5.423 -1.813

R2 0.73% 0.51% 1.30% 0.40% 0.86%

RET1 -0.039 *** -0.017 -0.088 *** -0.070 *** -0.050 *** -0.033 ** -0.070 *** 0.019 -0.017 *** 0.008

-10.435 -1.179 -13.956 -2.858 -12.220 -2.522 -23.445 0.827 -10.029 1.050R2 0.11% 0.80% 1.33% 0.08% 0.16%

20081998 2001 2002 2007

41

Panel B. Multivariate regressions (dependent variable: ∆OIB1:2)

Intercept -0.032 *** -0.320 *** -0.113 *** -0.336 *** -0.066 *** -0.275 *** -0.039 *** -0.130 ** 0.001 -0.037 *-3.444 -7.691 -6.965 -4.783 -6.263 -6.824 -3.34074 -3.222 0.125 -1.683

VOLA1 -1.298 *** 0.286 -0.615 -0.002 -0.879 ** 0.103 -0.360 0.352 -0.564 *** -0.524 **

-3.135 0.543 -1.439 -0.004 -2.506 0.223 -0.89528 0.775 -3.675 -2.010

log(TURN1) 0.027 *** 0.011 * 0.046 *** 0.027 *** 0.028 *** 0.012 ** -0.012 * -0.015 ** 0.000 -0.002

4.636 1.801 5.398 3.101 5.072 2.400 -1.86006 -2.383 -0.084 -0.593

BETA -0.012 * 0.008 -0.001 -0.001 0.002-1.829 1.077 -0.155 -0.321 0.369

log(SIZE) 0.020 *** 0.016 *** 0.015 *** 0.006 *** 0.003 **8.007 3.658 6.036 2.851 2.235

B/M 0.007 0.005 0.008 -0.009 0.0020.944 0.511 0.773 -0.821 0.368

RET1 -0.023 * -0.054 ** -0.021 ** 0.017 0.001

-1.667 -2.287 -2.207 0.724 0.099

R2 4.00% 10.41% 4.84% 6.66% 6.94% 11.98% 1.11% 2.57% 2.65% 3.27%Adj R2 3.86% 10.04% 4.71% 6.25% 6.76% 11.46% 0.90% 1.95% 2.44% 2.63%F 30.18 28.01 35.4054 16.48 38.25 23.16 5.34 4.18 12.52 5.16N 1442 1442 1386 1386 1027 1027 958 958 923 923

1998 2001 2002 20082007

42

Table V. Cross-section of Recovery-period Returns

This table reports cross-sectional regressions of crash returns, RET3, on (i) crash volatility, VOLA2, (ii) crash turnover, log(TURN2), (iii) the CAPM beta, BETA, (iv) market size, log(SIZE), (v) book-to-market ratio, B/M (vi) the crash return, RET2, and (vii) the change in order imbalance from benchmark to crash period, ∆OIB2:3. For further details of definition of the variables see Table II. Robust Newey-West (1987) t-statistics are reported below coefficient estimates. *, **, *** indicate significance at the 10%, 5%, 1% levels. Panel A presents the estimates of univariate regressions and Panel B the estimates of multivariate regressions.

Panel A. Univariate regressions (dependent variable: RET3)

Intercept Variable Intercept Variable Intercept Variable Intercept VariableVOLA2 0.099 *** 2.750 *** 0.068 *** 0.412 * 0.004 4.181 *** 0.046 *** 0.077

5.818 4.703 8.475 1.920 0.220 6.091 4.739 0.210R2 4.91% 0.37% 11.16% 0.01%

log(TURN2) 0.142 *** 0.057 *** 0.056 *** 0.024 *** 0.084 *** 0.046 *** 0.015 ** 0.016 ***

21.895 10.223 7.891 5.912 11.826 7.462 2.471 6.139R2 7.34% 2.19% 5.55% 2.88%

BETA 0.145 *** 0.049 *** 0.071 *** 0.021 *** 0.080 *** 0.102 *** 0.030 *** 0.015 ***14.163 4.532 11.327 2.557 11.139 8.406 6.408 4.639

R2 2.21% 0.74% 13.87% 2.13%

log(SIZE) 0.028 0.012 *** -0.040 0.009 *** 0.012 0.009 *** -0.012 0.004 ***0.746 4.240 -1.235 4.102 0.342 3.674 -0.513 2.729

R2 1.26% 1.05% 0.97% 0.76%

B/M 0.219 *** -0.064 *** 0.110 *** -0.031 *** 0.125 *** 0.019 * 0.066 *** -0.039 ***20.270 -3.417 16.193 -4.306 14.766 1.651 9.747 -2.797

R2 1.28% 2.00% 0.38% 1.64%***RET2 0.076 *** -0.444 *** 0.068 *** -0.192 0.038 * -0.349 *** 0.049 *** 0.011

9.745 -14.191 8.467 -2.619 1.675 -4.540 12.853 0.364R2 17.22% 0.66% 16.47% 0.02%

∆OIB2:3 0.185 *** 0.058 0.078 *** 0.057 ** 0.131 *** 0.103 ** 0.053 *** 0.213 ***

28.092 1.311 13.764 2.541 19.513 2.299 18.108 5.348

R2 0.17% 0.43% 0.51% 3.35%

20021998 2001 2007

43

Panel B. Multivariate regressions (dependent variable: RET3)

Intercept 0.082 *** -0.014 0.025 ** 0.030 -0.062 *** -0.224 *** 0.017 0.113 **4.924 -0.250 2.527 0.763 -3.167 -4.553 1.230 2.365

VOLA2 1.621 *** 0.559 0.308 0.392 * 3.704 *** 2.002 *** 0.513 0.398

2.695 0.985 1.504 1.824 5.675 3.211 1.313 1.060

log(TURN2) 0.059 *** 0.041 *** 0.029 *** 0.020 *** 0.054 *** 0.023 *** 0.009 * 0.005

8.518 5.792 6.036 3.289 8.235 3.677 1.793 0.889

BETA 0.003 0.013 * 0.058 *** 0.013 ***0.247 1.678 5.199 2.919

log(SIZE) 0.005 0.001 0.011 *** -0.005 **1.399 0.211 3.718 -2.080

B/M -0.028 -0.029 *** 0.013 -0.052 **-1.418 -3.448 0.984 -2.400

RET2 -0.379 *** -0.109 -0.213 *** 0.014

-12.301 -1.511 -3.076 0.530

∆OIB2:3 0.193 *** 0.117 ** 0.100 0.097 *** 0.285 *** 0.235 *** 0.217 *** 0.222 ***

4.021 2.417 4.105 *** 3.879 5.486 4.620 5.499 5.651

R2 10.31% 21.86% 3.68% 5.47% 18.00% 28.77% 4.36% 7.96%Adj R2 10.12% 21.46% 3.47% 4.99% 17.76% 28.28% 4.05% 7.28%F 52.35 54.44 17.51 11.32 73.77 57.94 14.3387 11.62N 1370 1370 1377 1377 1012 1012 948 948

20071998 2001 2002

44

Table VI. Cross-section of Recovery-period Changes in Order Imbalance

This table reports cross-sectional regressions of the changes in order imbalance from crash to recovery period, ∆OIB2:3, on (i) crash volatility, VOLA2, (ii) crash turnover, log(TURN2), (iii) the CAPM beta, BETA, (iv) market size, log(SIZE), (v) book-to-market ratio, B/M (vi) crash return, RET2 . For further details of definition of the variables see Table II. Robust Newey-West (1987) t-statistics are reported below coefficient estimates. *, **, *** indicate significance at the 10%, 5%, 1% levels. Panel A presents the estimates of univariate regressions and Panel B the estimates of multivariate regressions.

Panel A. Univariate regressions (dependent variable: ∆OIB2:3)

Intercept Variable Intercept Variable Intercept Variable Intercept VariableVOLA2 0.076 *** -1.241 *** 0.161 *** -0.858 *** 0.071 *** -0.247 0.017 * -0.225

7.262 -4.446 13.062 -3.339 5.858 -0.692 1.759 -0.674R2 2.00% 1.20% 0.08% 0.11%

log(TURN2) 0.077 *** -0.048 *** 0.186 *** -0.049 *** 0.133 *** -0.059 *** 0.016 -0.002

9.651 -7.996 13.254 -6.233 11.675 -8.498 1.011 -0.351R2 10.08% 6.40% 18.63% 0.03%

BETA 0.046 *** -0.011 0.132 *** -0.009 0.062 *** 0.003 0.009 * 0.0015.719 -1.466 16.343 -1.264 11.008 0.573 1.863 0.410

R2 0.22% 0.11% 0.03% 0.02%

log(SIZE) 0.327 *** -0.022 *** 0.481 *** -0.027 *** 0.381 *** -0.023 *** -0.011 0.0019.216 -8.888 8.937 -7.198 9.152 -8.272 -0.373 0.773

R2 8.15% 6.20% 12.42% 0.08%

B/M 0.023 *** 0.028 ** 0.106 *** 0.026 *** 0.033 *** 0.048 *** 0.008 0.0083.425 2.402 13.713 2.981 3.402 2.967 1.241 0.525

R2 0.58% 0.97% 4.66% 0.07%

RET2 0.021 *** -0.068 *** 0.095 *** -0.355 *** 0.068 *** 0.015 0.008 ** -0.030

3.100 -3.776 9.571 -4.760 7.506 0.593 2.283 -1.349R2 0.82% 1.72% 0.06% 0.24%

20071998 2001 2002

45

Panel B. Multivariate regressions (dependent variable: ∆OIB2:3)

Intercept 0.084 *** 0.308 *** 0.205 *** 0.466 *** 0.121 *** 0.231 *** 0.020 -0.00757.525 6.944 13.444 6.968 8.511 5.013 1.230 -0.1647

VOLA2 -0.253 -1.358 *** -0.541 ** -1.137 *** 0.421 -0.577 * -0.22828 -0.3606

-0.778 -4.055 -2.049 -3.764 1.245 -1.621 -0.65646 -0.8424

log(TURN2) -0.046 *** -0.030 *** -0.046 *** -0.026 *** -0.060 *** -0.050 *** -0.00132 -0.0042

-7.069 -4.563 -5.722 -2.768 -8.545 -7.199 -0.20577 -0.6255

BETA 0.011 0.002 0.016 *** 0.00331.565 0.322 2.951 0.8271

log(SIZE) -0.017 *** -0.022 *** -0.009 *** 0.0017-6.310 -5.000 -3.081 0.7669

B/M -0.007 -0.009 0.010 0.0108-0.810 -0.928 0.478 0.7292

RET2 -0.105 *** -0.466 *** -0.046 -0.0406 *

-4.993 -6.294 -1.566 -1.705

R2 10.01% 16.14% 6.86% 12.13% 18.86% 21.45% 0.14% 0.82%Adj R2 9.88% 15.77% 6.72% 11.75% 18.69% 20.98% -0.07% 0.19%F 76.80 44.17 50.61 31.55 117.23 45.74 0.66251 1.30N 1370 1370 1377 1377 1012 1012 948 948

20071998 2001 2002

Figure 1. Stock Market Crashes and Recoveries

This figure illustrates the development of the S&P 500 index, the market volatility index VIX, and the average absolute quoted spread of the NYSE common stocks, denoted Illiquidity, during the years in which the analyzed crises events took place. At the beginning of each year the Illiquidity is normalized to be equal to the corresponding level of the VIX. The defined crash and recovery intervals are indicated using vertical lines.

1998

900

1000

1100

1200

1300

J F M M A M J J A S O N D

S&

P 5

00

0

10

20

30

40

50

VIX

S&P500

VIX

Illiquidity

2001

900

1000

1100

1200

1300

1400

J F M A M J J A S O N D

S&

P 5

00

0

10

20

30

40

50

VIX

S&P500

VIX

Illiquidity

2002

700

800

900

1000

1100

1200

J F M A M J J A S O N D

S&

P 5

00

0

10

20

30

40

50

VIX

S&P500VIX

Illiquidity

2007

900

1000

1100

1200

1300

1400

1500

1600

J F M A M J J A S O N D

S&

P 5

00

0

10

20

30

40

50

VIX

S&P500

VIX

Illiquidity

2008

700

800

900

1000

1100

1200

1300

1400

1500

J F M A M J J A S O N D

S&

P 5

00

0

20

40

60

80

100

VIX

S&P500

VIX

Illiquidity