Tests of Mean-Variance Spanning

Abstract

In this paper, we conduct a comprehensive study of tests for mean-variance spanning. Under the popular regression framework of Huberman and Kandel (1987), we provide geometric interpretations of three asymptotic tests (likelihood ratio, Wald, and Lagrange multiplier) of mean-variance spanning. Under normality assumption, we present their exact distributions and analyze their power comprehensively. Under general distributional assumptions, we review spanning tests based on the generalized method of moments (GMM), provide new GMM spanning test, and evaluate their performance. In addition, we compare the performance of various spanning tests in the regression framework with those cast in the stochastic discount factor framework. Our results suggest that the two set-ups have similar properties when returns are normally distributed, but the regression framework performs better when returns follow a multivariate Student-t distribution.