The Generalized Treynor Ratio: A Note

Abstract

This paper presents a generalization of the Treynor ratio in a multi-index setup. The solution proposed in this paper is the simplest measure that keeps Treynor's original interpretation of the ratio of abnormal excess return (Jensen's alpha) to systematic risk exposure (the beta) and preserves the same key geometric and analytical properties as the original single index measure. The Generalized Treynor ratio is defined as the abnormal return of a portfolio per unit of weighted-average systematic risk, the weight of each risk loading being the value of the corresponding risk premium. Each risk premium is normalized to ensure the unit corresponding beta of the benchmark portfolio.

Keywords: Asset pricing, portfolio management, funds performance, Jensen's alpha, Treynor ratio

JEL Classification: G11, G12