Incremental Variables and the Investment Opportunity Set

Abstract

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. (i) Adding an explanatory variable can attenuate the slopes in a regression. (ii) Adding a variable with marginal explanatory power always attenuates the values of other explanatory variables in the extremes of the regression’s fitted values. Without a restriction on portfolio weights, the maximum Sharpe ratios in the GRS statistic provide little information about an incremental variable’s impact on the portfolio opportunity set.

Keywords: Incremental variables, Investment opportunity set, Portfolio returns, Variable attenuation

JEL Classification: G11, G12