A lower bound on the distribution function of the likelihood ratio test of portfolio efficiency is derived. An empirical application demonstrates that the bound may sometimes be used to infer rejection of the null hypothesis without appeal to asymptotic statistical approximations. A procedure for incorporating partial information about the zero‐beta intercept, in the multivariate framework, is also developed and applied.

This paper extends Kandel's [3] analysis of the testability of the mean‐variance efficiency of a market index when the return on some component of the index is not perfectly observable. In addition to information about the mean and variance of the missing asset, considered by Kandel, we explore the usefulness of information about the beta of the missing asset on the observed sub‐portfolio in an economy with a riskless asset. The results are somewhat more supportive of the notion that mean‐variance efficiency is testable on a subset of the assets.