An Exact Test of the Improvement of the Minimum Variance Portfolio

I propose an exact finite sample test of the risk reduction of the global minimum variance (GMV) portfolio. The GMV test statistic is proportional to the reduction in the variance of the GMV portfolio and has a straightforward geometric and portfolio interpretation and complements 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 no improvement in the GMV portfolio more often than the GRS test rejects the null hypothesis of no im- provement in the risk-return profile of the tangent portfolio. The power of the GMV test increases with the variance reduction of the global minimum variance portfolio. Using test asset returns scaled by pre-determined predictive variables is equivalent to increasing the overall number of test assets and leads to substantial power gains