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

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  • Schuhmacher, Frank
  • Eling, Martin

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.

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Bibliographic Info

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

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Web page: http://www.elsevier.com/locate/jbf

Related research

Keywords: Asset management; Performance measurement; Sharpe ratio; Location and scale condition; Risk and reward measurement;

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References

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Citations

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Cited by:
  1. Bosch-Badia, Maria Teresa & Montllor-Serrats, Joan & Tarrazon-Rodon, Maria-Antonia, 2014. "Unveiling the embedded coherence in divergent performance rankings," Journal of Banking & Finance, Elsevier, vol. 42(C), pages 154-165.
  2. Auer, Benjamin R. & Schuhmacher, Frank, 2013. "Robust evidence on the similarity of Sharpe ratio and drawdown-based hedge fund performance rankings," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 24(C), pages 153-165.
  3. Auer, Benjamin R. & Schuhmacher, Frank, 2013. "Performance hypothesis testing with the Sharpe ratio: The case of hedge funds," Finance Research Letters, Elsevier, vol. 10(4), pages 196-208.
  4. Auer, Benjamin R., 2014. "Should hedge funds be cautious reporting high returns?," Research in International Business and Finance, Elsevier, vol. 30(C), pages 195-201.
  5. Benjamin Auer, 2013. "The low return distortion of the Sharpe ratio," Financial Markets and Portfolio Management, Springer, vol. 27(3), pages 299-306, September.

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