Incremental variables and the investment opportunity set

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