Before revision: 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.
After revision: 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 explored, with a novel active-set algorithm presented for markets prohibiting short sales.