“On the (Ab)use of Omega ?”

Abstract

Several recent finance articles use the Omega measure (Keating and Shadwick, 2002), defined as a ratio of potential gains out of possible losses, for gauging the performance of funds or active strategies, in substitution of the traditional Sharpe ratio, with the arguments that return distributions are not Gaussian and volatility is not always the relevant risk metric. Other authors also use Omega for optimizing (non-linear) portfolios with important downside risk. However, we question in this article the relevance of such approaches. First, we show through a basic illustration that the Omega ratio is inconsistent with the Second-order Stochastic Dominance criterion. Furthermore, we observe that the trade-off between return and risk corresponding to the Omega measure, may be essentially influenced by the mean return. Next, we illustrate in static and dynamic frameworks that Omega-based optimal portfolios can be closely associated with classical optimization paradigms depending on the chosen threshold used in Omega. Finally, we present robustness checks on long-only asset and hedge fund databases, that confirm our results.

An omega portfolio model with dynamic return thresholds

“…(2019) and Caporin et al. (2018) have documented, portfolios that only maximize the Omega ratio can lead to excessive risky asset allocation.…”

“…As pointed out by Caporin et al. (2018), the research related to the Omega ratio can be classified under two approaches. The first is to use the Omega ratio in the evaluation of investing strategies in contrast to the Sharpe ratio (SR) (Keating and Shadwick, 2002; Georgantas et al., 2021).…”

“…Caporin et al. (2018) indicate that the return threshold can be specified exogenously, as it may vary in relation to investment objectives and individual preferences. However, a misspecification of the τ value in the Omega ratio can mislead the asset allocation when ranking available investments.…”

“…To determine the typical behavior of the optimal portfolios, Caporin et al. (2018) perform the maximum Omega ratio for various thresholds (−2.00%, 0%, 5.00%, 7.00%, and 10.00%) in their iso‐Omega analysis.…”

“…The first is to use the Omega ratio in the evaluation of investing strategies in contrast to the Sharpe ratio (SR) (Keating and Shadwick, 2002;Georgantas et al, 2021). As a ranking criterion, Caporin et al (2018) show that the Omega ratio is far more severe than just inconsistent with the second-order stochastic dominance criterion. The second approach involves considering the Omega ratio as an objective function for portfolio optimization in order to introduce DSR into the estimation of optimal portfolio weights (Kapsos et al, 2014a(Kapsos et al, , 2014bSharma et al, 2017;Caçador et al, 2021;Sehgal and Mehra, 2021).…”