A Test of the Efficiency of a Given Portfolio
分析了一种检验给定资产组合事前效率的方法，推导了检验统计量的小样本分布和功效函数，并提供了直观的几何解释和实证例子。
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.