How do widely recognized stock return anomalies (return variations unexplained by asset pricing models) mesh with efficient portfolio selection theory? In their paper entitled “Investing in Stock Market Anomalies”, Turan Bali, Stephen Brown and Ozgur Demirtas examine five prominent stock market anomalies whose existence is robust through time and across markets (size, book-to-market, short-term reversal, intermediate-term momentum and long-term reversion) in contexts of efficient portfolio selection via mean-variance and stochastic dominance methods. In other words, they test whether portfolios that apply these anomalies exhibit exceptionally good combinations of return and volatility, or obviously outperform on a purely statistical basis. Both these portfolio selection methods have shortcomings related to their inclusion of extreme, impractical choices. The authors consider relaxed (“Almost”) versions of these methods that prohibit such choices as “pathological.” The authors form value-weighted size and book-to-market portfolios annually and value-weighted reversal, momentum and reversion portfolios monthly. Using monthly data for July 1926 through December 2008 (990 months) for a broad sample of U.S. stocks to construct diversified anomaly portfolios, they find that:
- Based on the traditional mean-variance efficient portfolio selection method, only momentum (ranking stocks on 12-month past return, with a skip month) clearly enhances efficiency. Over the entire sample period, momentum winners have both higher average gross return and lower volatility than momentum losers.
- Based on the traditional stochastic dominance portfolio selection method, none of the five anomalies clearly enhance efficiency.
- With relaxed mean-variance and stochastic dominance efficient portfolio selection methods:
- Small and high book-to-market stocks do not clearly beat big and low book-to-market stocks.
- Short-term (one-month) losers clearly beat short-term winners.
- Momentum winners clearly beat momentum losers at a six-month investment horizon.
- Long-term (return from five years ago to one year ago) losers beat long term winners at investment horizons of one year and longer.
- An equal-weighted portfolio that combines the high-return parts of all five anomalies clearly beats one that combines the low-return parts at investment horizons of six months to five years.
- A portfolio that weights equally each of the high-return parts of all five anomalies clearly beats the broad value-weighted U.S. stock market at investment horizons of one to five years.
- Head-to-head comparisons of pairs of the five anomalies provide some evidence for the superior performance of: (1) size, short-term reversal and momentum for investment horizons of one to 12 months; and, (2) book-to-market and long-term reversion for investment horizons of three to five years.
- The relative strengths of small, high book-to-market, short-term loser, momentum winner and long-term loser stocks increase when investors include consideration of economic variables (monthly inflation rate, monthly growth in industrial production, default spread, aggregate dividend yield and detrended short-term interest rate).
In summary, evidence from a range of tests employing full distributions of returns provides varying degrees of justification for use of five widely accepted stock return anomalies in the context of formal methods for constructing efficient portfolios. Short-term reversal and intermediate-term momentum appear to be the most valuable anomalies at a gross level.
Cautions regarding these findings include:
- The study apparently ignores trading frictions in assessing portfolio performance. Realistic trading frictions, especially for portfolios reformed monthly, may well alter return distributions to the point of changing conclusions. In other words, gross and net return distributions may be materially different.
- The study does not investigate whether the anomalies weaken over time.
- The mean-variance efficient portfolio selection method essentially assumes a normal distribution of stock returns, contrary to empirical evidence.
- Ignoring the extreme portfolio choices available via traditional mean-variance and stochastic dominance methods seems similar to exclusion of outliers (wild tail effects) in empirical data. It is not obvious whether the exclusions are merited or simply convenient. People sometimes make “pathological” choices.
