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 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 improvement 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 instrumental variables is equivalent to increasing the overall number of test assets and leads to substantial power gains