Time Varying Market Time Varying Market EfficiencyEfficiency

Efficiency is dynamicEfficiency is dynamic We show this by looking at two We show this by looking at two

efficiency metricsefficiency metrics Short (intraday) horizonShort (intraday) horizon Longer-term (cross-section of monthly Longer-term (cross-section of monthly

stock returns)stock returns) We then draw implications from We then draw implications from

results on efficiency dynamicsresults on efficiency dynamics

Estimating short-horizon price Estimating short-horizon price efficiencyefficiency

We compute daily efficiency measures for We compute daily efficiency measures for individual stocks based on short-horizon return individual stocks based on short-horizon return predictabilitypredictability Chordia, Roll & Subrahmanyam (2005, Chordia, Roll & Subrahmanyam (2005,

2008)2008) In particular, with RET being return, and OIB In particular, with RET being return, and OIB

order imbalance, for each stock-day, we order imbalance, for each stock-day, we estimate efficiency as the Restimate efficiency as the R22 from the following from the following regression:regression:

Time-Variation in Short-Time-Variation in Short-Horizon Efficiency (RHorizon Efficiency (R22))

Funding Constraints and Funding Constraints and Market EfficiencyMarket Efficiency

Profitability from growth-value, Profitability from growth-value, momentum, accounting momentum, accounting profitability is time-varyingprofitability is time-varying

Varies with flows to mutual funds Varies with flows to mutual funds and hedge funds that most exploit and hedge funds that most exploit these anomaliesthese anomalies

Trends in Efficiency of the Cross-Section of

Monthly Stock Returns

Why is there cross-Why is there cross-sectional return sectional return predictability?predictability?

RiskRisk–Should be stableShould be stable

InefficiencyInefficiency–Should be unstableShould be unstable–arbitrageablearbitrageable

We investigate how cross-sectional We investigate how cross-sectional predictability has changed in recent predictability has changed in recent yearsyears

Separately for liquid and illiquid Separately for liquid and illiquid stocksstocks

Separately for NYSE and NasdaqSeparately for NYSE and Nasdaq

Why is the recent period Why is the recent period special?special?

Volume has increased to Volume has increased to astonishingly high levelsastonishingly high levels

Spreads have decreased considerablySpreads have decreased considerably What has been the effect of What has been the effect of

dramatically increased trading (about dramatically increased trading (about fourfold) and substantially reduced fourfold) and substantially reduced spreads (by about 90%) on cross-spreads (by about 90%) on cross-sectional return predictability?sectional return predictability?

Average turnover over time [Chordia, Roll, Average turnover over time [Chordia, Roll, Subrahmanyam (CRS) 2010]Subrahmanyam (CRS) 2010]

Bid-ask spreads over time, for small Bid-ask spreads over time, for small (<$10K) and large orders [CRS, (<$10K) and large orders [CRS, 2010]2010]

We investigate how predictability We investigate how predictability has changedhas changed

Find that it has virtually disappeared Find that it has virtually disappeared for liquid stocks, but not for illiquid for liquid stocks, but not for illiquid stocksstocks Liquid/Illiquid generally defined as Liquid/Illiquid generally defined as

stocks with below/above-median values stocks with below/above-median values of Amihud (2002) illiquidity measureof Amihud (2002) illiquidity measure

Findings hold across NYSE/AMEX Findings hold across NYSE/AMEX and Nasdaqand Nasdaq

Predictive variablesPredictive variables

Momentum (RET26, RET712)Momentum (RET26, RET712) TurnoverTurnover Book/MarketBook/Market IlliquidityIlliquidity Information-based Information-based characteristicscharacteristics

Dispersion of analyst forecasts (DISP)Dispersion of analyst forecasts (DISP) SUE (earnings drift)SUE (earnings drift) Accounting Accruals (ACC)Accounting Accruals (ACC)

NYSE/AMEX – Fama-MacBeth NYSE/AMEX – Fama-MacBeth predictive return regressionspredictive return regressions

Trend and turnover fits to Trend and turnover fits to Fama-MacBeth coefficientsFama-MacBeth coefficients

Trend and turnover fits to Fama-Trend and turnover fits to Fama-MacBeth coefficients, contd.MacBeth coefficients, contd.

Interpretation of trend Interpretation of trend coefficientscoefficients

Since RET26, RET712, and SUE Since RET26, RET712, and SUE positively predict returns, but DISP positively predict returns, but DISP and ACC negatively predict and ACC negatively predict returns, the trend coefficients returns, the trend coefficients indicate that all of these effects indicate that all of these effects have become less material over have become less material over timetime

Hedge Portfolio Returns- 5 Yr MA, Hedge Portfolio Returns- 5 Yr MA, NYSE/AMEXNYSE/AMEX

Hedge Portfolio Returns-5yr MA, Hedge Portfolio Returns-5yr MA, NasdaqNasdaq

Exponential decay modelExponential decay model

Let x be the MA of Fama-MacBeth Let x be the MA of Fama-MacBeth coefficient, a be its initial value and t be coefficient, a be its initial value and t be timetime

x=a exp(-bt) orx=a exp(-bt) or Ln(x/a)=-b tLn(x/a)=-b t We can estimate the above model via We can estimate the above model via

OLS without interceptOLS without intercept A positive b implies decay. We find that A positive b implies decay. We find that

all b estimates are positive and most all b estimates are positive and most are highly significantare highly significant

Estimates of decay model Estimates of decay model (positive b means decay)(positive b means decay)

A portfolio approach that A portfolio approach that uses the entire cross-uses the entire cross-sectionsection

Based on Lehmann (1990) and Based on Lehmann (1990) and Lewellen (2002)Lewellen (2002)

One dollar long (short) in stocks One dollar long (short) in stocks whose characteristics are above whose characteristics are above (below) cross-sectional mean:(below) cross-sectional mean:

Composite strategyComposite strategy

Rank stocks by characteristic and Rank stocks by characteristic and assign percentile ranksassign percentile ranks

Add percentile ranks to get Add percentile ranks to get composite characteristiccomposite characteristic

Use this rank as characteristic in Use this rank as characteristic in portfolio weight computationportfolio weight computation

Portfolio strategies over Portfolio strategies over time, individual time, individual componentscomponents

Composite portfolio Composite portfolio strategy over timestrategy over time

Composite portfolio Composite portfolio strategy over time, by strategy over time, by illiquidityilliquidity

Monthly reversals, Monthly reversals, portfolio strategyportfolio strategy

Portfolio strategy with and Portfolio strategy with and without 2008 and 2009without 2008 and 2009

Potential critiques and Potential critiques and defensesdefenses

Data mining? But out-of-sample Data mining? But out-of-sample evidence has confirmed the phenomena evidence has confirmed the phenomena in other countries and time periodsin other countries and time periods

Statistical power issue? But both Statistical power issue? But both subperiods have identical time-periods subperiods have identical time-periods and many anomalies are statistically and many anomalies are statistically significant in the first subperiodsignificant in the first subperiod

SummarySummary

Results are supportive of the Results are supportive of the notion that arbitrage due to lower notion that arbitrage due to lower trading costs has improved market trading costs has improved market efficiencyefficiency

Market phenomena based on Market phenomena based on market inefficiency are unstablemarket inefficiency are unstable

Perhaps new anomalies will arise Perhaps new anomalies will arise even as old ones disappeareven as old ones disappear

RemarksRemarks

The market seems to have become The market seems to have become more efficient by conventional metricsmore efficient by conventional metrics

But, unresolved issues:But, unresolved issues: Is it an issue of academic research Is it an issue of academic research

discovering anomalies or decreasing discovering anomalies or decreasing trading coststrading costs

Are there efficiency cycles (anomalies Are there efficiency cycles (anomalies arbitraged, disappear, arbitrage stops, arbitraged, disappear, arbitrage stops, they appear again)?they appear again)?

How should market How should market efficiency be efficiency be taught/presented?taught/presented?

It should be presented differently It should be presented differently from a static concept. I.e., from a static concept. I.e., Efficiency is indeed time-varying Efficiency is indeed time-varying It also is non-stationary, and likely It also is non-stationary, and likely

sensitive to time variation in liquiditysensitive to time variation in liquidity