The econometrics of mean-variance efficiency tests: a survey

This paper provides a comprehensive survey of the econometrics of mean-variance efficiency tests. Starting with the classic F-test of Gibbons et al. (1989) and its generalized method of moments version, I analyse the effects of the number of assets and portfolio composition on test power. I then discuss asymptotically equivalent tests based on portfolio weights, and study the trade-offs between efficiency and robustness of using parametric and semi-parametric likelihood procedures that assume either elliptical innovations or elliptical returns. After reviewing finite sample tests, I conclude with a discussion of mean-variance-skewness efficiency and spanning tests, and other interesting extensions. Copyright The Author(s). Journal compilation Royal Economic Society 2009