Liquidity and Market Efficiency

Tarun Chordia (Emory)Tarun Chordia (Emory)

Richard Roll (UCLA)Richard Roll (UCLA)

A. Subrahmanyam A. Subrahmanyam (UCLA)(UCLA)

Market EfficiencyMarket Efficiency

Cannot be instantaneousCannot be instantaneous CRS (2005) shows that order flows CRS (2005) shows that order flows

do predict very short-term returnsdo predict very short-term returns Efficiency is created in part by Efficiency is created in part by

arbitrageurs, who are subject to arbitrageurs, who are subject to transaction coststransaction costs

What is the empirical relation What is the empirical relation between liquidity and market between liquidity and market efficiency?efficiency?

LiquidityLiquidity

Has generally been related to Has generally been related to broader finance by way of a broader finance by way of a premium in asset returns (Amihud premium in asset returns (Amihud and Mendelson, 1986)and Mendelson, 1986)

Also may play a role in moving Also may play a role in moving prices to efficient outcomes—this prices to efficient outcomes—this is what we investigateis what we investigate

Efficiency over timeEfficiency over time

Secular decrease in bid-ask Secular decrease in bid-ask spreads across the three tick spreads across the three tick regimesregimes

How did this affect efficiency?How did this affect efficiency? How does efficiency vary within How does efficiency vary within

the day?the day?

Interday efficiency Interday efficiency measuresmeasures

Open-close and close-open Open-close and close-open variance ratios (viz. French and variance ratios (viz. French and Roll, 1984)Roll, 1984)

Daily return autocorrelationsDaily return autocorrelations How have these varied across the How have these varied across the

three tick size regimes three tick size regimes corresponding to increased corresponding to increased liquidity?liquidity?

Theoretical settingTheoretical setting

A security is traded at dates 1 and 2 A security is traded at dates 1 and 2 and pays off and pays off ++ at date 3 at date 3 (variances v(variances v and v and v). ).

A demand of zA demand of z22 arrives at period 2. arrives at period 2. In addition, a fraction kzIn addition, a fraction kz11 arrives at arrives at

period 1 and (1-k)zperiod 1 and (1-k)z11 at period 2 at period 2 where 0<k<1.where 0<k<1.

Variances of zVariances of z11 and z and z22 both equal v both equal vzz. .

EquilibriumEquilibrium

Market makers with CARA utility and Market makers with CARA utility and risk aversion risk aversion absorb order flows absorb order flows

The mass of market makers at dates The mass of market makers at dates 1 and 2 is M and N, with N1 and 2 is M and N, with N>M>M

Equilibrium is of the Walrasian typeEquilibrium is of the Walrasian type Let PLet Pii and Q and Qii be the price and order be the price and order

imbalance at date i, respectivelyimbalance at date i, respectively

Return PredictabilityReturn Predictability

Central resultsCentral results

If the mass of market makers at If the mass of market makers at date 2 is sufficiently large, lagged date 2 is sufficiently large, lagged imbalances positively predict imbalances positively predict future returnsfuture returns

If markets are very liquid (market If markets are very liquid (market makers’ risk bearing capacity is makers’ risk bearing capacity is very high), such predictability very high), such predictability disappears.disappears.

DataData

Comprehensive sample of NYSE Comprehensive sample of NYSE stocks that traded every daystocks that traded every day

We construct five minute returns for We construct five minute returns for portfolio based on mid-quote returnsportfolio based on mid-quote returns

If a stock did not trade in period t, it is If a stock did not trade in period t, it is excluded from the t-1 portfolioexcluded from the t-1 portfolio

Liquidity proxy is the effective spread, Liquidity proxy is the effective spread, averaged across the trading dayaveraged across the trading day

Decline in return Decline in return predictabilitypredictability

RR22 goes to more than 10% to virtually zero goes to more than 10% to virtually zero T-statistic also drops from around 12 to T-statistic also drops from around 12 to

about 1-2about 1-2 The pattern in imbalance autocorrelations The pattern in imbalance autocorrelations

(which are 0.28, 0.21, 0.21, respectively, (which are 0.28, 0.21, 0.21, respectively, across the eighth, sixteenth, and decimal across the eighth, sixteenth, and decimal regimes) is not sufficient to directly cause regimes) is not sufficient to directly cause this decrease.this decrease.

Figure 2. Value-Weighted Daily Average Effective Spread, NYSE, 1993-2002

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Eighths Regime Sixteenths Regime Decimal Regime

Illiquid periodsIlliquid periods

Defined as days where the de-Defined as days where the de-trended effective spread is more trended effective spread is more than one standard deviation above than one standard deviation above its mean within each tick size its mean within each tick size regimeregime

We use an indicator variable, ILD, We use an indicator variable, ILD, which is one on illiquid dayswhich is one on illiquid days

Regressions using illiquidity indicator ILD Regressions using illiquidity indicator ILD (dependent variable is mid-quote returns at time (dependent variable is mid-quote returns at time t)t)

Liquidity and predictabilityLiquidity and predictability

The predictability of returns from The predictability of returns from lagged order flows is greater on lagged order flows is greater on more illiquid daysmore illiquid days

The effect is present in every tick The effect is present in every tick regimeregime

Market efficiency by time Market efficiency by time of dayof day

Since spreads vary by time of day Since spreads vary by time of day (McInish and Wood, 1992), there is (McInish and Wood, 1992), there is reason to expect a similar pattern reason to expect a similar pattern in return predictabilityin return predictability

We define two dummies, morn We define two dummies, morn (9:30-12), and eve (14:00-16:00)(9:30-12), and eve (14:00-16:00)

Time-of-day effectsTime-of-day effects

Intraday efficiency resultsIntraday efficiency results

The market’s ability to The market’s ability to accommodate order flows was accommodate order flows was smaller during the morning and, to smaller during the morning and, to a lesser extent, the evening a lesser extent, the evening period within the eighth regimeperiod within the eighth regime

This effect has declined This effect has declined considerably during the decimal considerably during the decimal periodperiod

Interday measures of Interday measures of efficiencyefficiency

We consider open-close and close-open We consider open-close and close-open variance ratios, and return autocorrelationsvariance ratios, and return autocorrelations

French and Roll (1984) show that these are French and Roll (1984) show that these are statistically greater than unitystatistically greater than unity

They show that this phenomenon is not due to They show that this phenomenon is not due to greater public information flows (by analyzing greater public information flows (by analyzing business day closures) and argue that it may business day closures) and argue that it may be due to microstructure effects, mispricing, or be due to microstructure effects, mispricing, or private information tradingprivate information trading

How do these quantities change across the How do these quantities change across the three tick regimes?three tick regimes?

Daily variance ratios and Daily variance ratios and autocorrelationsautocorrelations

InterpretationInterpretation The evidence is that variance ratios have increased The evidence is that variance ratios have increased

but autocorrelations appear to have declinedbut autocorrelations appear to have declined We use mid-quote returns, so bid-ask bounce is not We use mid-quote returns, so bid-ask bounce is not

an issuean issue If mispricing were driving the increase in variance If mispricing were driving the increase in variance

ratios across time, autocorrelations should have ratios across time, autocorrelations should have increased as the tick size decreased; but there is increased as the tick size decreased; but there is no evidence of this. no evidence of this.

Consequently, the evidence is consistent with Consequently, the evidence is consistent with private information being more effectively private information being more effectively incorporated into prices in the lower tick regimes, incorporated into prices in the lower tick regimes, especially for smaller firms. especially for smaller firms.

ConclusionsConclusions The extent of return predictability from The extent of return predictability from

order flows (an inverse measure of market order flows (an inverse measure of market efficiency) has decreased over time and efficiency) has decreased over time and also is higher on illiquid days.also is higher on illiquid days.

Variation in efficiency by time of day has Variation in efficiency by time of day has diminished following decimalizationdiminished following decimalization

Variance ratios have increased whereas Variance ratios have increased whereas autocorrelations have decreased in recent autocorrelations have decreased in recent years, suggesting an increase in private years, suggesting an increase in private information being incorporated into prices information being incorporated into prices following decimalization.following decimalization.