Risk management under Omega measure

TL;DR

This paper demonstrates the equivalence of the Omega measure and Sharpe ratio under elliptic distributions, explores portfolio optimization methods, and highlights differences when asymmetric returns are involved.

Contribution

It establishes the equivalence of Omega and Sharpe under certain distributions and develops an active-set algorithm for portfolio optimization without short sales.

Findings

Omega and Sharpe are equivalent under elliptic distributions.

Active-set algorithm effectively optimizes portfolios without short sales.

Omega and Sharpe differ with asymmetric return distributions.

Abstract

We prove that the Omega measure, which considers all moments when assessing portfolio performance, is equivalent to the widely used Sharpe ratio under jointly elliptic distributions of returns. Portfolio optimization of the Sharpe ratio is then explored, with an active-set algorithm presented for markets prohibiting short sales. When asymmetric returns are considered we show that the Omega measure and Sharpe ratio lead to different optimal portfolios.