Power enhancement for testing multi-factor asset pricing models via Fisher’s method

Testing multi-factor asset pricing models is instrumental for asset pricing theory and practice. However, due to the accumulation of errors in estimating high-dimensional parameters, traditional quadratic-form tests such as the Wald test perform poorly against the sparse alternative hypothesis, i.e., a few mispriced assets. Fan et al. (2015b) introduced a powerful testing procedure by adding a power enhancement component to the Wald test statistic and proved power enhancement properties. To provide an alternative to their methodology, we first instantiate the power enhancement component by introducing a new maximum-form test statistic and then study the asymptotic joint distribution of the Wald test statistic and the maximum test statistic. We prove that these two test statistics are asymptotically independent. Given their asymptotic independence, we propose a new power-enhanced testing procedure to combine their respective power based on Fisher’s method (Fisher, 1925). Theoretically, we prove that the new power-enhanced test retains the desired nominal significance level and achieves asymptotically consistent power against more general alternatives. Furthermore, we demonstrate the finite-sample performance of our proposed power-enhanced test in both simulation studies and an empirical study of testing market efficiency using asset returns of the Russel-2000 portfolio.