Sharpe Thinking with Asymmetrical Preferences

15 Pages Posted: 13 Nov 2002

See all articles by Luisa Tibiletti

Luisa Tibiletti

University of Turin - Department of Management

Simone Farinelli

Core Dynamics GmbH

Date Written: October, 9, 2002


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 Phi suitable to compare skewed return distributions with respect to a benchmark, is introduced. This index captures two types of asymmetry information: (1) "good" volatility (above the benchmark) and "bad" volatility (below the benchmark) are differently 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 Phi. Moreover, compatibility of the ranking rule based on ratio Phi with the expected utility framework is proved.

Keywords: Sharpe Index, One-Sided Risk Measures, First Order Risk Aversion

JEL Classification: G0, G1, G2

Suggested Citation

Tibiletti, Luisa and Farinelli, Simone, Sharpe Thinking with Asymmetrical Preferences (October, 9, 2002). Available at SSRN: or

Luisa Tibiletti (Contact Author)

University of Turin - Department of Management ( email ) Unione Sovietica, 218 bis
Turin, Turin 10100
39-11-670-6229 (Phone)
39-11-670-6238 (Fax)


Simone Farinelli

Core Dynamics GmbH ( email )

Scheuzerstrasse 43
Zurich, 8006

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