We prove that the Omega measure, which considers all moments when assessing portfolio performance, is equivalent to the widely used Sharpe ratio under a jointly normal distribution . Portfolio optimization of the Sharpe ratio is  explored, with a novel active-set algorithm presented for markets prohibiting short sales. Experimental results show an improvement in average solution time of over an order of magnitude when compared to standard optimization techniques .
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 .
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a jointly normal distribution
jointly elliptic distributions of returns
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then
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a novel
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Experimental results show an improvement in average solution time of over an order of magnitude when compared to standard optimization techniques
When asymmetric returns are considered we show that the Omega measure and Sharpe ratio lead to different optimal portfolios