A Note on the GRS Test

Abstract

The Gibbons, Ross, and Shanken (1989) F-test of mean-variance efficiency of asset returns is stated incorrectly for the multi-factor case. We first derive the correct formula for the test statistic for the general case of K factors and N test assets, then highlight the impact of the error in common applications. The ranking of competing models can be scrambled if the original (incorrect) formula is used, and tests of factor models over-reject. While the impact is material only for horizons of less than 20 or so years of monthly data, given the theoretical interpretation of the (correctly) calculated GRS statistic, we recommend that researchers use the correct formula regardless of sample size.

Keywords: GRS test, degrees of freedom adjustment

JEL Classification: G12, G14