Testing Factor Models on Characteristic and Covariance Pure Plays

We test the recent Fama-French five-factor model and Hou-Xue-Zhang four-factor model using test assets from Fama-MacBeth regressions, which are pure plays on particular characteristics or covariances. Our tests resolve the errors-in-variable bias in Fama-MacBeth regressions with estimated betas. Monte Carlo evidence shows that the tests are unbiased even with time-varying stock betas and characteristics. For both factor models, characteristic pure plays generally have positive alphas, and covariance pure plays have negative alphas. The models fail especially in explaining returns to investment and when pure plays are momentum-neutral. The rejections are economically significant