In this paper, we present a survey on the various approaches that can be used to test whether the mean-variance frontier of a set of assets spans or intersects the frontier of a larger set of assets. We analyze the restrictions on the return distribution that are needed to have mean-variance spanning or intersection. The paper explores the duality between mean-variance frontiers and volatility bounds, analyzes regression-based test procedures for spanning and intersection, and shows how these regression-based tests are related to tests for mean-variance efficiency, performance measurement, optimal portfolio choice and specification error bounds. © 2001 Elsevier Science B.V.
DeRoon, F. A., & Nijman, T. E. (2001). Testing for mean-variance spanning: A survey. Journal of Empirical Finance, 8(2), 111–155. https://doi.org/10.1016/S0927-5398(01)00022-6