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.
Frequently Asked Questions
What is a multifactor asset pricing model for stock returns?
A multifactor asset pricing model explains stock returns using several systematic drivers, such as market, size, value (book-to-market), momentum, profitability and investment factors. Factor returns are typically measured as either the excess return relative to the market or the spread between returns of two extreme portfolios formed from factor sorts. Barillas and Shanken compared models built from subsets of ten such factors using U.S. stock data for 1972 through 2013.
Which factor model best explains monthly U.S. stock returns?
A six-factor model was consistently best in Barillas and Shanken's 1972–2013 U.S. stock sample, regardless of initial assumptions. It includes market, size, investment, momentum, and monthly-updated versions of profitability and book-to-market (value). This model dominated recently introduced four-factor and five-factor models, though absolute performance testing cast doubt on the validity even of this model.
How do you compare asset pricing models using a Bayesian approach?
Barillas and Shanken applied a Bayesian procedure that compares all possible pricing models formed from subsets of ten candidate factors. Each model includes no more than one version of any factor that has two versions (size, value, profitability, investment). They also assessed the absolute performance of the top-ranked model against an unrestricted set of factors, using factor returns from U.S. common stocks during 1972 through 2013.
Is updating value and profitability factors monthly better than updating them annually?
In Barillas and Shanken's tests, factor models using value (book-to-market) and profitability factors updated monthly outperformed widely used models, including recently introduced four-factor and five-factor models. These results are based on gross factor returns for 1972–2013. Monthly-updated factors most likely have higher turnover than annually updated versions, so net-of-cost results may differ.
What are the limitations of factor model comparison studies like this one?
The findings use gross factor returns, so trading costs and shorting costs would reduce them, likely more for monthly-updated factors with higher turnover. Shorting may not always be feasible, and repeated reuse of U.S. stock data creates growing snooping bias, so new best models impound more luck. The methodology also assumes returns are independent and normally distributed over time, and adding other factors such as short-term reversal, long-term reversion, idiosyncratic volatility or liquidity could produce a new best model.