Time Varying Market Efficiency Efficiency is dynamic Efficiency is dynamic We show this by looking at two efficiency metrics We show this by looking at two efficiency metrics Short (intraday) horizon Short (intraday) horizon Longer-term (cross-section of monthly stock returns) Longer-term (cross-section of monthly stock returns) We then draw implications from results on efficiency dynamics We then draw implications from results on efficiency dynamics

Estimating short-horizon price efficiency We compute daily efficiency measures for individual stocks based on short-horizon return predictability We compute daily efficiency measures for individual stocks based on short-horizon return predictability Chordia, Roll & Subrahmanyam (2005, 2008) Chordia, Roll & Subrahmanyam (2005, 2008) In particular, with RET being return, and OIB order imbalance, for each stock-day, we estimate efficiency as the R 2 from the following regression: In particular, with RET being return, and OIB order imbalance, for each stock-day, we estimate efficiency as the R 2 from the following regression:

Time-Variation in Short- Horizon Efficiency (R 2 )

Funding Constraints and Market Efficiency Profitability from growth-value, momentum, accounting profitability is time-varying Profitability from growth-value, momentum, accounting profitability is time-varying Varies with flows to mutual funds and hedge funds that most exploit these anomalies Varies with flows to mutual funds and hedge funds that most exploit these anomalies

Trends in Efficiency of the Cross-Section of Monthly Stock Returns

Why is there cross-sectional return predictability? Risk Risk –Should be stable Inefficiency Inefficiency –Should be unstable –arbitrageable

We investigate how cross-sectional predictability has changed in recent years Separately for liquid and illiquid stocks Separately for liquid and illiquid stocks Separately for NYSE and Nasdaq Separately for NYSE and Nasdaq

Why is the recent period special? Volume has increased to astonishingly high levels Volume has increased to astonishingly high levels Spreads have decreased considerably Spreads have decreased considerably What has been the effect of dramatically increased trading (about fourfold) and substantially reduced spreads (by about 90%) on cross- sectional return predictability? What has been the effect of dramatically increased trading (about fourfold) and substantially reduced spreads (by about 90%) on cross- sectional return predictability?

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

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

We investigate how predictability has changed Find that it has virtually disappeared for liquid stocks, but not for illiquid stocks Find that it has virtually disappeared for liquid stocks, but not for illiquid stocks Liquid/Illiquid generally defined as stocks with below/above-median values of Amihud (2002) illiquidity measure Liquid/Illiquid generally defined as stocks with below/above-median values of Amihud (2002) illiquidity measure Findings hold across NYSE/AMEX and Nasdaq Findings hold across NYSE/AMEX and Nasdaq

Predictive variables Momentum (RET26, RET712) Momentum (RET26, RET712) Turnover Turnover Book/Market Book/Market Illiquidity Illiquidity Information-based characteristics Information-based characteristics 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 predictive return regressions

Trend and turnover fits to Fama-MacBeth coefficients

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

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

Hedge Portfolio Returns- 5 Yr MA, NYSE/AMEX

Hedge Portfolio Returns-5yr MA, Nasdaq

Exponential decay model Let x be the MA of Fama-MacBeth coefficient, a be its initial value and t be time Let x be the MA of Fama-MacBeth coefficient, a be its initial value and t be time x=a exp(-bt) or x=a exp(-bt) or Ln(x/a)=-b t Ln(x/a)=-b t We can estimate the above model via OLS without intercept We can estimate the above model via OLS without intercept A positive b implies decay. We find that all b estimates are positive and most are highly significant A positive b implies decay. We find that all b estimates are positive and most are highly significant

Estimates of decay model (positive b means decay)

A portfolio approach that uses the entire cross-section Based on Lehmann (1990) and Lewellen (2002) Based on Lehmann (1990) and Lewellen (2002) One dollar long (short) in stocks whose characteristics are above (below) cross- sectional mean: One dollar long (short) in stocks whose characteristics are above (below) cross- sectional mean:

Composite strategy Rank stocks by characteristic and assign percentile ranks Rank stocks by characteristic and assign percentile ranks Add percentile ranks to get composite characteristic Add percentile ranks to get composite characteristic Use this rank as characteristic in portfolio weight computation Use this rank as characteristic in portfolio weight computation

Portfolio strategies over time, individual components

Composite portfolio strategy over time

Composite portfolio strategy over time, by illiquidity

Monthly reversals, portfolio strategy

Portfolio strategy with and without 2008 and 2009

Potential critiques and defenses Data mining? But out-of-sample evidence has confirmed the phenomena in other countries and time periods Data mining? But out-of-sample evidence has confirmed the phenomena in other countries and time periods Statistical power issue? But both subperiods have identical time-periods and many anomalies are statistically significant in the first subperiod Statistical power issue? But both subperiods have identical time-periods and many anomalies are statistically significant in the first subperiod

Summary Results are supportive of the notion that arbitrage due to lower trading costs has improved market efficiency Results are supportive of the notion that arbitrage due to lower trading costs has improved market efficiency Market phenomena based on market inefficiency are unstable Market phenomena based on market inefficiency are unstable Perhaps new anomalies will arise even as old ones disappear Perhaps new anomalies will arise even as old ones disappear

Remarks Remarks The market seems to have become more efficient by conventional metrics The market seems to have become more efficient by conventional metrics But, unresolved issues: But, unresolved issues: Is it an issue of academic research discovering anomalies or decreasing trading costs Is it an issue of academic research discovering anomalies or decreasing trading costs Are there efficiency cycles (anomalies arbitraged, disappear, arbitrage stops, they appear again)? Are there efficiency cycles (anomalies arbitraged, disappear, arbitrage stops, they appear again)?

How should market efficiency be taught/presented? It should be presented differently from a static concept. I.e., It should be presented differently from a static concept. I.e., Efficiency is indeed time-varying Efficiency is indeed time-varying It also is non-stationary, and likely sensitive to time variation in liquidity It also is non-stationary, and likely sensitive to time variation in liquidity