# Using Bootstrap to Test Mean-Variance Efficiency of a Given Portfolio

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## Abstract

This paper proposes tests of unconditional mean-variance efficiency using bootstrap method that does not depend on specific distributional assumptions. We reject the mean-variance efficiency of the CRSP value- weighted stock index for five of the seven consecutive ten-year subperiods from 1926 to 1993, whereas the F-test of Gibbons, Ross, and Shanken (GRS, 1989) only rejects two of the seven subperiods. A further examination of the size of the tests reveals that, under various alternative distributional specifications for the error terms, the GRS test tends to over-reject the null hypothesis, while the bootstrap test has sizes close to the nominal levels. However, the GRS test has a slightly higher power than the bootstrap test.

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