A Note on the GRS Test

37 Pages Posted: 18 Feb 2021

See all articles by Mark J. Kamstra

Mark J. Kamstra

York University - Schulich School of Business

Ruoyao Shi

UC Riverside

Date Written: December 24, 2020


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

Suggested Citation

Kamstra, Mark J. and Shi, Ruoyao, A Note on the GRS Test (December 24, 2020). Available at SSRN: https://ssrn.com/abstract=3775089 or http://dx.doi.org/10.2139/ssrn.3775089

Mark J. Kamstra (Contact Author)

York University - Schulich School of Business ( email )

4700 Keele Street
Toronto, Ontario M3J 1P3

Ruoyao Shi

UC Riverside ( email )

900 University Avenue
Riverside, CA 92521
United States
9518271494 (Phone)

HOME PAGE: http://ruoyaoshi.github.io

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