Are portfolios of U.S. stocks that are double-sorted to capture benefits of two complementary return anomalies attractive? In their July 2020 paper entitled “Interacting Anomalies”, Karsten Müller and Simon Schmickler test all possible double-sorted portfolios across 102 stock return anomalies (10,302 double-sorts). They employ 5×5 double-sorts, first ranking stocks into fifths (quintiles) for one anomaly and then re-sorting each of these quintiles into fifths for the second anomaly. They focus on the four “corner” portfolios involving the extreme high and low quintiles for both anomalies. They evaluate average returns, Sharpe ratios and factor model alphas of both equal-weighted (EW) and value-weighted (VW) versions of these portfolios, emphasizing performance gains from anomaly interactions. They correct for multiple hypothesis testing (data snooping bias) using the Bonferroni correction. Using trading and accounting data for a broad sample of U.S. common stocks with annual (quarterly) accounting data lagged by six (four) months during 1970 through 2017, they find that:
- Among all EW (VW) double-sorted portfolios, 797 (351) exhibit statistically significant gross interaction gains over the full sample period after correcting for data snooping bias.
- Anomalies related to past returns (particularly short-term reversal) and costs of trading (particularly size) are most likely to generate statistically significant interaction gains. For example:
- The best strategy combines short-term reversal and illiquidity.
- The top 10 EW portfolios almost all involve short-term reversal.
- Other important past return anomalies are momentum, change in momentum and maximum return.
- Other important costs-of-trading anomalies are bid-ask spread, turnover and idiosyncratic volatility.
- The top EW (VW) portfolios generate gross average monthly returns above 4% (3%) and Sharpe ratios above 2.0 (1.5).
- However, these portfolios have high turnover and high trading frictions, and their gross performance is best during bear markets when trading frictions are elevated.
- Gross profitability of top portfolios declines over time as trading frictions fall.
- Gross average monthly return of the top 1% of portfolios drops from 2.5% to 1.5% since the early 2000s.
- Strategies based on short-term reversal dominate during 1970-2000, but earnings-based anomalies interacting with costs-of-trading anomalies displace them after 2000.
- Statistical significance of interaction gains fades starting in the 1990s.
- Out-of-sample trading strategies using double-sorted portfolios selected based solely on best past performance generate EW (VW) gross average monthly returns up to 4% (2.7%) and annualized gross Sharpe ratios up to 2.7 (1.4).
- Results are comparable to those for state-of-the-art machine learning strategies, suggesting that machine learning actually exploits relatively simple combinations of anomalies.
- Assuming trading frictions of about 0.1% for large capitalization stocks and 0.2% for small capitalization stocks and 100% monthly turnover has only modest effects on strategy performance. Shorting costs may have a material effect since profitability concentrates in short sides of portfolios.
- A long-only, post-publication VW strategy excluding microcaps delivers 0.7% multi-factor gross monthly alpha.
In summary, evidence indicates that double-sorting of U.S. stocks on certain anomalies may generate attractive gross performance, but: (1) the effect fades over time; and, (2) the best double-sorts tend to involve high trading frictions.
The authors provide at Interacting Anomalies tools and data to compare performances of trading strategies for over 10,000 anomaly combinations.
Cautions regarding findings include:
- Reported performance data are gross, not net.
- Some double-sort portfolios may be more costly to maintain (higher turnover) than others, confounding comparison on a net basis.
- The benchmark levels of trading frictions used in the study appear reasonable for modern trading but much too low for much of the sample period (see “Trading Frictions over the Long Run”), thereby underestimating full-sample impacts.
- The methodology is beyond the reach of most investors, who would bear fees for delegating to a fund manager.
