A direct test for the mean variance efficiency of a portfolio

We develop a direct test for examining the mean-variance efficiency of a given bench-mark asset return. Unlike traditional tests for mean-variance efficiency, this test allows for the possibility that short positions in the primitive assets may not be possible. Using this test, we can not reject the hypothesis that the value weighted return on exchange traded stocks is mean-variance efficient with reference to the mean-variance frontier generated by the 25 stock portfolios constructed by Fama and French (1993), when short selling is not allowed.