A Test of the Efficiency of a Given Portfolio

TLDR

The relevant statistic has a tractable small‑sample distribution. The study analyzes a test for the ex ante efficiency of a given portfolio of assets. The authors derive the test’s power function to examine sensitivity to portfolio choice and asset count, and also develop an equivalent univariate test that offers diagnostic tools explaining null rejection. The study offers intuitive interpretations, such as a mean‑standard‑deviation geometric explanation, and empirical examples show that the multivariate approach yields more appropriate conclusions than traditional dependent‑univariate inference.

Abstract

A test for the ex ante efficiency of a given portfolio of assets is analyzed. The relevant statistic has a tractable small sample distribution. Its power function is derived and used to study the sensitivity of the test to the portfolio choice and to the number of assets used to determine the ex post mean-variance efficient frontier. Several intuitive interpretations of the test are provided, including a simple mean-standard deviation geometric explanation. A univariate test, equivalent to our multivariate-based method, is derived, and it suggests some useful diagnostic tools which may explain why the null hypothesis is rejected. Empirical examples suggest that the multivariate approach can lead to more appropriate conclusions than those based on traditional inference which relies on a set of dependent univariate statistics.