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

  • Schuhmacher, Frank
  • Eling, Martin

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.

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Article provided by Elsevier in its journal Journal of Banking & Finance.

Volume (Year): 36 (2012)
Issue (Month): 7 ()
Pages: 2077-2082

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Handle: RePEc:eee:jbfina:v:36:y:2012:i:7:p:2077-2082
Contact details of provider: Web page: http://www.elsevier.com/locate/jbf

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