A0266
Title: A robust GRS statistic
Authors: William Pouliot - University of Birmingham (United Kingdom) [presenting]
Abstract: The GRS statistic is a cross-sectional test of the one-factor capital asset pricing model. That statistic is not appropriate for tests of the K-factor model. Using the same data as prior studies, it is shown that they did not use the specific GRS statistic. To provide clarity on which GRS statistic to use, the detailed mathematical derivation of the cross-sectional variance of the OLS estimators of the estimated intercepts of the K-factor model is provided. This variance is then used to construct the enhanced version of the GRS statistic implemented in the literature. Assumptions underlying that statistic assume invariance of cross-sectional variances and covariances of the idiosyncratic errors in these models. The robust version of the GRS statistic (for the K-factor model) is constructed, allowing for time variation of the variances and covariances of the cross-sectional errors. The consistency of that estimator is established, and then the corresponding asymptotic distribution is also established. When this statistic is calculated on the same data used in a prior study, it allows for a more nuanced comparison between three-, four-, and five-factor models. A comparison of the power functions of the GRS and the GRS developed for the K factor model is also undertaken.
