Testing linear factor models on individual stocks using the average <italic>F</italic>-test

In this paper, we propose the average <italic>F</italic>-statistic for testing linear asset pricing models. The average pricing error, captured in the statistic, is of more interest than the <italic>ex post</italic> maximum pricing error of the multivariate <italic>F</italic>-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 <italic>F</italic>-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 the average <italic>F</italic>-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 in two sub-periods from 1967 to 1971 and from 1982 to 1986.