Testing Linear Factor Models on Individual Stocks Using the Average F Test

Abstract

We propose the average F statistic for testing linear asset pricing models. The average pricing error, captured in the the statistic, is of more interest than the ex post maximum pricing error of the multivariate F statistic that is associated with extreme long and short positions and excessively sensitive to small perturbations in the estimates of asset means and covariances. The average F test can be applied to thousands of individual stocks and thus is free from the information loss or the data snooping biases from grouping. This test is robust to ellipticity, and more importantly, our simulation and bootstrapping results show that the power of average F test continues to increase as the number of stocks increases. Empirical tests using individual stocks from 1967 to 2006 demonstrate that the popular four factor model (i.e. Fama-French three factors and momentum) is rejected two sub-periods from from 1967 to 1971 and from 1982 to 1986.