What combination of factors best predicts stock market returns at a monthly frequency? In the October 2015 draft of their paper entitled “Comparing Asset Pricing Models”, Francisco Barillas and Jay Shanken apply a Bayesian procedure to compare all possible pricing models based on subsets of a given set of pricing factors. They consider a total of ten factors: market, two versions of size, two versions of value (book-to-market), momentum, two versions of profitability, and two versions of investment. For each model tested, they include no more than one of any factor with two versions. In addition to comparing models (factor subsets), they also assess the absolute performance of the top-ranked model against an unrestricted set. As usually done, they employ factor returns that are either the excess return relative to the market or the spread between returns of two extreme portfolios formed from factor sorts. Using data for a broad sample of U.S. common stocks during 1972 through 2013, they find that:
- Five-factor and six-factor models that include a momentum factor, a value factor updated monthly and a profitability factor updated monthly dominate recently introduced four-factor and five-factor models of stock returns.
- The six-factor model including market, size, profitability calculated monthly, investment, book-to-market calculated monthly and momentum factors is consistently best, regardless of initial assumptions.
- However, absolute performance testing casts doubt on the validity even of this model.
In summary, evidence indicates that a six-factor model of stock returns with value and profitability factors updated monthly outperforms all widely used models.
Investors constructing stock screens may want to apply findings.
Cautions regarding findings include:
- As usual in factor model studies, factor returns are gross, not net. Including costs of factor portfolio reformation and shorting would reduce these returns, likely more for some factors than others. Specifically, the versions of factors that employ monthly updates most likely have higher turnover than versions with annual updates. Net findings may therefore differ from gross findings.
- Shorting of stocks in the short sides of factor portfolios may not always be feasible, limiting direct exploitation of findings.
- The body of work on U.S. stock return factor models largely re-uses data, with snooping bias growing over time such that new “best models” impound more and more luck.
- As noted in the paper, the methodology assumes returns are independent and normally distributed over time. They may not be so well behaved.
- Also as noted in the paper, adding other factors, such as short-term reversal, long-term reversion, idiosyncratic volatility and liquidity could result in a new best model.
