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

Frank Schuhmacher and Martin Eling

Journal of Banking & Finance, 2012, vol. 36, issue 7, 2077-2082

Abstract: In this paper we prove that partial-moments-based performance measures (e.g., Omega, Kappa, upside-potential ratio, Sortino–Satchell ratio, Farinelli–Tibiletti ratio), value-at-risk-based performance measures (e.g., VaR ratio, CVaR ratio, Rachev ratio, generalized Rachev ratio), and other admissible performance measures are a strictly increasing function in the Sharpe ratio. The theoretical basis of this result is the location and scale property and two other plausible and mild conditions. Our result provides a decision-theoretic foundation for all these frequently used performance measures. Moreover, it might explain the empirical finding that all these measures typically lead to very similar rankings.

Keywords: Asset management; Performance measurement; Sharpe ratio; Location and scale condition; Risk and reward measurement (search for similar items in EconPapers)
JEL-codes: D81 G10 G11 G23 G29 (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (29)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:jbfina:v:36:y:2012:i:7:p:2077-2082

DOI: 10.1016/j.jbankfin.2012.03.013

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