Case Study about Econometrics of Mean-Variance
Abstract: This paper provides a comprehensive survey of the econometrics of mean-variance efficiency tests. Starting with the classic F test of Gibbons, Ross and Shanken (1989) and its generalised 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 mean representing portfolios and Hansen-Jagannathan frontiers, and study the trade-offs between efficiency and robustness of using parametric and semiparametric likelihood procedures that assume either elliptical innovations or elliptical returns.
Introduction: Mean-variance analysis is widely regarded as the cornerstone of modern investment theory. Despite its simplicity, and the fact that more than five and a half decades have elapsed since Markowitz published his seminal work on the theory of portfolio allocation under uncertainty (Markowitz (1952)), it remains the most widely used asset allocation method. There are several reasons for its popularity. First, it provides a very intuitive assessment of the relative merits of alternative portfolios, as their risk and expected return characteristics can be compared in a two-dimensional graph.
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