Omega and Sharpe ratio

Eric Benhamou (1) , Beatrice Guez , Nicolas Paris (2)

1 LAMSADE - Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision
2 AP-HP - Assistance publique - Hôpitaux de Paris (AP-HP)

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.

Mots clés: Omega ratio; Sharpe ratio; normal distribution; elliptical distribution

Domaines: Finance quantitative [q-fin.CP]

Eric Benhamou, Beatrice Guez, Nicolas Paris. Omega and Sharpe ratio. 2020. ⟨hal-02886481⟩