A five-factor model directed at capturing the size, value, profitability, and investment patterns in average stock returns performs better than the three-factor model of Fama and French (FF, 1993). The five-factor model׳s main problem is its failure to capture the low average returns on small stocks whose returns behave like those of firms that invest a lot despite low profitability. The model׳s performance is not sensitive to the way its factors are defined. With the addition of profitability and investment factors, the value factor of the FF three-factor model becomes redundant for describing average returns in the sample we examine.

Variables with strong marginal explanatory power in cross-section asset pricing regressions typically show less power to produce increments to average portfolio returns, for two reasons. (1) Adding an explanatory variable can attenuate the slopes in a regression. (2) Adding a variable with marginal explanatory power always attenuates the values of other explanatory variables in the extremes of a regression’s fitted values. Without a restriction on portfolio weights, the maximum Sharpe ratios in the GRS statistic of Gibbons, Ross, and Shanken (1989) provide little information about an incremental variable’s impact on the portfolio opportunity set.