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Reward-Risk Ratios

Journal of Investment Strategies, Forthcoming

16 Pages Posted: 10 Sep 2012 Last revised: 25 Nov 2013

Patrick Cheridito

ETH Zurich; Swiss Finance Institute

Eduard Kromer

University of California, Berkeley

Date Written: October 2013


We introduce three new families of reward-risk ratios, study their properties and compare them to existing examples. All ratios in the three families are monotonic and quasi-concave, which means that they prefer more to less and encourage diversification. Members of the second family are also scale invariant. The third family is a subset of the second one, and all its members only depend on the distribution of a return. In the second part of the paper we provide an overview of existing reward-risk ratios and discuss their properties. For instance, we show that, like the Sharpe ratio, every reward-deviation ratio violates the monotonicity property.

Keywords: Reward measures, risk measures, monotonicity, quasi-concavity, scale invariance, distribution based

JEL Classification: D81

Suggested Citation

Cheridito, Patrick and Kromer, Eduard, Reward-Risk Ratios (October 2013). Journal of Investment Strategies, Forthcoming. Available at SSRN: or

Patrick Cheridito

ETH Zurich ( email )

Department of Mathematics
8092 Zurich

Swiss Finance Institute ( email )

c/o University of Geneva
40, Bd du Pont-d'Arve
CH-1211 Geneva 4

Eduard Kromer (Contact Author)

University of California, Berkeley ( email )

Evans Hall
Berkeley, CA 3860 94720
United States

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