The Hansen ratio in mean--variance portfolio theory

TL;DR

The paper introduces the Hansen ratio, a new measure linking mean and variance in portfolio theory, providing a simplified description of the efficient frontier and dual pricing bounds, with extensions to preferences and Hilbert spaces.

Contribution

It proposes the Hansen ratio as a novel, parsimonious tool for mean-variance analysis, extending its application to monotone preferences and Hilbert space frameworks.

Findings

Hansen ratio effectively characterizes the efficient frontier.

Extension to monotone preferences broadens applicability.

Multiperiod IID returns example illustrates practical use.

Abstract

It is shown that the ratio between the mean and the $L^2$-norm leads to a particularly parsimonious description of the mean-variance efficient frontier and the dual pricing kernel restrictions known as the Hansen-Jagannathan (HJ) bounds. Because this ratio has not appeared in economic theory previously, it seems appropriate to name it the Hansen ratio. The initial treatment of the mean-variance theory via the Hansen ratio is extended in two directions, to monotone mean-variance preferences and to arbitrary Hilbert space setting. A multiperiod example with IID returns is also discussed.