A decision-theoretic foundation for reward-to-risk performance measures

► We analyze commonly used two-parameter performance measures. ► These include partial-moments-, value-at-risk-based and many other performance ratios. ► We prove that all these measures are a strictly increasing function in the Sharpe ratio. ► We base our result on the locations-scale- and two other plausible and mild conditions. ► This result provides a decision-theoretic foundation for all these popular measures.