A Test for Mean-Variance Efficiency of a given Portfolio under Restrictions

This study proposes a test for mean-variance efficiency of a given portfolio under general linear investment restrictions. We introduce a new definition of pricing error or “alpha” and as an efficiency measure we propose to use the largest positive alpha for any vertex of the portfolio possibilities set. To allow for statistical inference, we derive the asymptotic least favorable sampling distribution of this test statistic. Using the new test, we cannot reject market portfolio efficiency relative to beta decile stock portfolios if short-selling is not allowed.