How special is the Fama-French three-factor model (market, size, book-to-market ratio) compared to other possible three-factor models? In their November 2012 paper entitled “Firm Characteristics and Empirical Factor Models: a Data-Mining Experiment”, Leonid Kogan and Mary Tian systematically compare explanatory breadth for all 351 three-factor and 2,925 four-factor (linear) models for predicting stock returns that can be formed from 27 firm characteristics other than size and book-to-market ratio. They measure explanatory breadth of a model by how well it captures the average future return differences across value-weighted deciles from annual sorts on the characteristics not used in the model. Using monthly returns and annual/quarterly firm characteristics for a broad sample of non-financial U.S. stocks during 1971 through 2011, they find that:
- About two thirds of alternative three-factor models outperform the Fama-French model in terms of breadth of explanatory power. Specifically:
- The Fama-French three-factor model explains decile returns for eight of 27 characteristics.
- The best-performing three-factor model over the entire sample period uses market, standardized unexplained earnings and cash flow-to-price ratio, explaining decile returns for 15 of 25 other characteristics.
- Each of the top-twenty three-factor models explains decile returns for at least 12 of 25 other characteristics.
- Return momentum is the most challenging characteristic to explain. None of the three-factor models that do not include momentum explain its decile returns over the entire sample period.
- The best-performing four-factor model over the entire sample period uses market, momentum, Ohlson score (financial distress) and asset growth, explaining decile returns for 16 of 24 other characteristics. Many of the best four-factor models add momentum, standardized unexpected earnings, investment-to-assets ratio or asset growth to a top-performing three-factor model.
- Three-factor model performance rankings are sensitive to both sample period and factor construction methodology, suggesting that data snooping bias dominates the ranking process. In particular, there is no correlation between model performance ranks for:
- The first and second halves of the sample period.
- The largest and smallest halves of the sample by market capitalization.
In summary, evidence suggests that size and book-to-market factors may not be among the best choices for explaining future returns of stocks, but it is difficult to tell which combination of factors is best.
Cautions regarding findings include:
- This study focuses on breadth, not depth, of model explanatory power. In other words, tests do not measure exploitability of the factor models.
- Returns used in the study are gross, not net. Consideration of realistic trading frictions and portfolio turnover (which may differ across firm characteristic sorts and factor combinations) may affect findings.
