
Omega and Sharpe ratio
Benhamou, Éric; Guez, Beatrice; Paris, Nicolas (2019), Omega and Sharpe ratio. https://basepub.dauphine.fr/handle/123456789/21204
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Type
Document de travail / Working paperExternal document link
https://hal.archives-ouvertes.fr/hal-02886481Date
2019Series title
Preprint LamsadePublished in
Paris
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Show full item recordAuthor(s)
Benhamou, ÉricLaboratoire d'analyse et modélisation de systèmes pour l'aide à la décision [LAMSADE]
Guez, Beatrice
Paris, Nicolas

Abstract (EN)
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.Subjects / Keywords
Omega ratio; Sharpe ratio; normal distribution; elliptical distributionRelated items
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Benhamou, Éric; Guez, Beatrice (2018) Article accepté pour publication ou publié
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Benhamou, Eric; Guez, Beatrice; Paris, Nicolas (2018) Article accepté pour publication ou publié