Another Test of the Efficiency of a Given Portfolio

Abstract

I propose a new finite sample mean-variance efficiency test based on the risk reduction of the global minimum variance (GMV) portfolio. The GMV test statistic has a straightforward geometric and portfolio interpretation and complements nicely the celebrated GRS test in Gibbons, Ross and Shanken (1989). In practical applications, the GMV test leads to a rejection of the null hypothesis of mean-variance efficiency much more often than the GRS test. This imposes a higher bar on testing the efficiency of a given portfolio. The power of the GMV test increases in the improvement of the global minimum variance portfolio. Using test asset returns scaled by pre-determined instrumental variables is equivalent to increasing the overall number of test assets and leads to power gains. I also present the asymptotic versions of both tests as well as joint test leading to a test of mean-variance spanning.