Risk management under Omega measure
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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.