Omega and Sharpe Ratio

10 Pages Posted: 30 Oct 2019

See all articles by Eric Benhamou

Eric Benhamou

Université Paris Dauphine; EB AI Advisory; AI For Alpha

Beatrice Guez

AI For Alpha

Nicolas Paris

A.I. Square Connect

Date Written: October 14, 2019

Abstract

Omega ratio, defined as the probability-weighted ratio of gains over losses at a given level of expected return, has been advocated as a better performance indicator compared to Sharpe and Sortino ratio as it depends on the full return distribution and hence encapsulates all information about risk and return. We compute Omega ratio for the normal distribution and show that under some distribution symmetry assumptions, the Omega ratio is oversold as it does not provide any additional information compared to Sharpe ratio. Indeed, for returns that have elliptic distributions, we prove that the optimal portfolio according to Omega ratio is the same as the optimal portfolio according to Sharpe ratio. As elliptic distributions are a weak form of symmetric distributions that generalized Gaussian distributions and encompass many fat tail distributions, this reduces tremendously the potential interest for the Omega ratio.

Keywords: Omega ratio, Sharpe ratio, normal distribution, elliptical distribution

Suggested Citation

Benhamou, Eric and Guez, Beatrice and Paris, Nicolas, Omega and Sharpe Ratio (October 14, 2019). Available at SSRN: https://ssrn.com/abstract=3469888 or http://dx.doi.org/10.2139/ssrn.3469888

Eric Benhamou (Contact Author)

Université Paris Dauphine ( email )

Place du Maréchal de Tassigny
Paris, Cedex 16 75775
France

EB AI Advisory ( email )

35 Boulevard d'Inkermann
Neuilly sur Seine, 92200
France

AI For Alpha ( email )

35 boulevard d'Inkermann
Neuilly sur Seine, 92200
France

Beatrice Guez

AI For Alpha ( email )

35 boulevard d'Inkermann
Neuilly sur Seine, 92200
France

Nicolas Paris

A.I. Square Connect ( email )

35 Boulevard d'Inkermann
Neuilly sur Seine, 92200
France

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