Liquidity and Market
Efficiency
Tarun Chordia (Emory)
Richard Roll (UCLA)
A. Subrahmanyam (UCLA)
Market Efficiency
Cannot be instantaneous
 CRS (2005) shows that order flows do
predict very short-term returns
 Efficiency is created in part by
arbitrageurs, who are subject to
transaction costs
 What is the empirical relation between
liquidity and market efficiency?

Liquidity
Has generally been related to broader
finance by way of a premium in asset
returns (Amihud and Mendelson, 1986)
 Also may play a role in moving prices to
efficient outcomes—this is what we
investigate

Efficiency over time
Secular decrease in bid-ask spreads
across the three tick regimes
 How did this affect efficiency?
 How does efficiency vary within the
day?

Interday efficiency measures
Open-close and close-open variance
ratios (viz. French and Roll, 1984)
 Daily return autocorrelations
 How have these varied across the three
tick size regimes corresponding to
increased liquidity?

Theoretical setting
A security is traded at dates 1 and 2
and pays off + at date 3 (variances v
and v).
 A demand of z2 arrives at period 2.
 In addition, a fraction kz1 arrives at
period 1 and (1-k)z1 at period 2 where
0<k<1.
 Variances of z1 and z2 both equal vz.

Equilibrium
Market makers with CARA utility and
risk aversion  absorb order flows
 The mass of market makers at dates 1
and 2 is M and N, with N>M
 Equilibrium is of the Walrasian type
 Let Pi and Qi be the price and order
imbalance at date i, respectively

Return Predictability
Central results
If the mass of market makers at date 2
is sufficiently large, lagged imbalances
positively predict future returns
 If markets are very liquid (market
makers’ risk bearing capacity is very
high), such predictability disappears.

Data
Comprehensive sample of NYSE stocks
that traded every day
 We construct five minute returns for
portfolio based on mid-quote returns
 If a stock did not trade in period t, it is
excluded from the t-1 portfolio
 Liquidity proxy is the effective spread,
averaged across the trading day

Decline in return predictability
R2 goes to more than 10% to virtually zero
 T-statistic also drops from around 12 to about
1-2
 The pattern in imbalance autocorrelations
(which are 0.28, 0.21, 0.21, respectively,
across the eighth, sixteenth, and decimal
regimes) is not sufficient to directly cause this
decrease.

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ESPR ($)
Figure 2. Value-Weighted Daily Average Effective Spread, NYSE, 1993-2002
0.200
0.175
0.150
0.125
0.100
0.075
0.050
0.025
Eighths Regime
Sixteenths Regime
Decimal Regime
0.000
Illiquid periods
Defined as days where the de-trended
effective spread is more than one
standard deviation above its mean
within each tick size regime
 We use an indicator variable, ILD, which
is one on illiquid days

Regressions using illiquidity indicator ILD (dependent
variable is mid-quote returns at time t)
Liquidity and predictability
The predictability of returns from
lagged order flows is greater on more
illiquid days
 The effect is present in every tick
regime

Market efficiency by time of
day
Since spreads vary by time of day
(McInish and Wood, 1992), there is
reason to expect a similar pattern in
return predictability
 We define two dummies, morn (9:3012), and eve (14:00-16:00)

Time-of-day effects
Intraday efficiency results
The market’s ability to accommodate
order flows was smaller during the
morning and, to a lesser extent, the
evening period within the eighth regime
 This effect has declined considerably
during the decimal period

Interday measures of
efficiency
We consider open-close and close-open variance
ratios, and return autocorrelations
 French and Roll (1984) show that these are
statistically greater than unity
 They show that this phenomenon is not due to
greater public information flows (by analyzing
business day closures) and argue that it may be due
to microstructure effects, mispricing, or private
information trading
 How do these quantities change across the three tick
regimes?

Daily variance ratios and
autocorrelations
Interpretation
The evidence is that variance ratios have increased
but autocorrelations appear to have declined
 We use mid-quote returns, so bid-ask bounce is not
an issue
 If mispricing were driving the increase in variance
ratios across time, autocorrelations should have
increased as the tick size decreased; but there is no
evidence of this.
 Consequently, the evidence is consistent with private
information being more effectively incorporated into
prices in the lower tick regimes, especially for smaller
firms.

Conclusions
The extent of return predictability from order
flows (an inverse measure of market
efficiency) has decreased over time and also
is higher on illiquid days.
 Variation in efficiency by time of day has
diminished following decimalization
 Variance ratios have increased whereas
autocorrelations have decreased in recent
years, suggesting an increase in private
information being incorporated into prices
following decimalization.
