Omega and Sharpe ratio

Eric Benhamou (), Beatrice Guez and Nicolas Paris ()
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Nicolas Paris: AP-HP - Assistance publique - Hôpitaux de Paris (AP-HP)

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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 (search for similar items in EconPapers)
Date: 2020-07-01
New Economics Papers: this item is included in nep-fmk and nep-rmg
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Working Paper: Omega and Sharpe ratio (2019)
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