Is the Fama-French five-factor (market, size, book-to-market, profitability, investment) model of stock returns optimal? In the September 2015 draft of their paper entitled “Choosing Factors”, Eugene Fama and Kenneth French investigate potential improvements to the overall predictive power of their five-factor model. Specifically, they examine:

- Using a profitability factor based on cash rather than operating profit, or substituting a quality-minus-junk factor for the profitability factor.
- Calculating the value, investment and profitability factors from small stocks only (where they are stronger) rather than as the average for small stocks and big stocks.

They frame model optimality in terms of: (1) parsimony (simplicity, meaning few explanatory factors); (2) the ability of chosen factors to explain performance of portfolios sorted on other factors; (3) accordance with the dividend discount valuation model. Using factor-related data for a broad sample of U.S. stocks during July 1963 through December 2014 (618 months), *they find that:*

- Constructing the profitability factor with cash instead of operating profit improves the ability of the model to predict performance of many portfolios sorted on other factors.
- Constructing the value, profitability and investment factor returns using only small stocks improves the ability of the model to predict performance of many portfolios sorted on other factors, especially when the sorts include microcaps.

In summary, *evidence indicates that the **five-factor model substituting cash profitability for operating profitability and employing only small stocks to calculate value, investment and profitability factor returns may be close to optimal.*

The authors conclude: “Based on the evidence here, we would choose this model (or one augmented with a momentum factor) in applications.”

Cautions regarding findings include:

- Factor return calculations are gross, not net. Incorporating costs of portfolio reformations and shorting costs would reduce factor strength. Moreover, factor models may not translate to practical stock screening because:
- To the extent that shorting stocks in the “minus” sides of factor portfolios is not feasible due to stock borrowing constraints, factor returns are not realistic.
- Since different factors/factor constructions may drive different portfolio turnovers, net findings may differ from gross findings.

- As acknowledged by the authors, testing many factor combinations and factor constructions on the same data introduces data snooping bias, such that the predictive power of the best model likely overstates its expected performance with new data.