Sharpe Thinking with Asymmetrical Preferences

As we leave behind the assumption of normality in return distributions, the classical risk-reward Sharpe Ratio becomes,a questionable,tool for ranking,risky projects. In the spirit of Sharpe thinking, a more general risk-reward ratio © suit- able to compare skewed return distributions with respect to a benchmark, is in- troduced. This index captures,two types of asymmetry,information: (1) ”good” volatility (above the benchmark),and ”bad” volatility (below the benchmark),are di¤erently weighted, (2) asymmetrical preferences to ”small” and ”large” deviations from the benchmark,are modelled. The former goal is achieved,by using one-sided volatility measures, and the latter by choosing appropriate order for the one-sided moments,involved. The Omega,Index (see Cascon et al. (2002) and the Upside Potential Ratio (see Sortino (2000) follow as special cases of the index © .M ore- over, compatibility of the ranking rule based on ratio © with the expected utility framework,is proved. JEL Subject Classification: G0,G1,G2. Key words: Sharpe Index, One-Sided Risk Measures, First Order Risk Aver- sion. ,