Measuring the economic significance of mean-variance spanning

Abstract

This paper investigates the economic significance of mean-variance spanning tests using three classical statistical tests in a unified framework. I show how to compute confidence intervals about the Sharpe ratios of tangent portfolios, the variance of return of minimum variance portfolios, as well as the certainty equivalent utility gains. I apply this statistical framework to the question of whether US investors should diversify internationally. The analysis suggests that a strong statistical rejection of the hypothesis that there is no improvement in the minimum variance portfolio's standard deviation of return does not imply that there are no significant economic benefits to be made in terms of a substantial risk reduction. These results have important implications for empirical tests of mean-variance spanning as well as empirical assets pricing tests and minimum variance bounds on stochastic discount factors.