Portfolio Correlation and the Power of Portfolio Efficiency Tests

Abstract

We propose a parametric family of tests of the mean-variance efficiency of a portfolio in a market with a risk-free asset. All tests in the family compare the mean-variance ratio of the tested portfolio (the benchmark portfolio) with the same ratio for a different portfolio, called the reference portfolio. The Gibbons-Ross-Shanken test belongs to this family, and the reference in this case is the ex-post tangency portfolio of the market. We show that the power of a test in our proposed family depends on the correlation between the benchmark and the reference portfolio. This correlation, and thus, the power of the test, can be manipulated by changing the value of the parameter that spans the family. In particular, for a given sample, a power maximizing test can be easily found in the family we propose. This power-maximizing test will generically not be the Gibbons-Ross-Shanken test.