Liquidity and Market Efficiency

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Liquidity and Market Efficiency

• Tarun Chordia (Emory)
• Richard Roll (UCLA)
• A. Subrahmanyam (UCLA)

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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?

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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 outcomesthis is what we investigate

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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?

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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?

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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 0ltklt1.
• Variances of z1 and z2 both equal vz.

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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 NgtM
• Equilibrium is of the Walrasian type
• Let Pi and Qi be the price and order imbalance at
  date i, respectively

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Return Predictability
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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.

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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

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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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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

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

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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 (930-12), and eve
  (1400-1600)

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Time-of-day effects
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Intraday efficiency results

• The markets 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

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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?

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Daily variance ratios and autocorrelations
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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.

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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.