On Aggregate Measures of Alpha

with Raymond Kan, 2022, working paper. [pdf coming soon].

In this paper, we explore the statistical properties of several goodness-of-fit measures that have been recently proposed by Fama and French (2015), (2018). In particular, building on Kan and Robotti (2017), we show how to carry out valid asymptotic inference on averages of absolute values of pricing errors produced by beta-pricing models with traded factors. In this context, we show that the popular test of Gibbons, Ross, and Shanken (1989) is not uniformly most powerful. We also tackle the challenging task of formally comparing averages of absolute values of pricing errors across models that can be nested or non-nested, correctly specified or misspecified. Finally, we investigate the sampling distributions of other newly proposed R-squared-type measures of asset mispricing. We demonstrate the relevance of our findings by means of Monte Carlo simulations and several empirical illustrations.