The Hansen Ratio in Mean-Variance Portfolio Theory

Abstract

It is shown that the ratio between the mean and the L2-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 multi-period example with IID returns is also discussed.

Keywords: Hansen Ratio, Hansen-Jagannathan Inequality, Efficient Frontier, Monotone Mean-Variance Preference

JEL Classification: G11, G12, C02