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Beyond the Sharpe ratio: An application of the Aumann–Serrano index to performance measurement

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  • Homm, Ulrich
  • Pigorsch, Christian
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    Abstract

    We propose a performance measure that generalizes the Sharpe ratio. The new performance measure is monotone with respect to stochastic dominance and consistently accounts for mean, variance and higher moments of the return distribution. It is equivalent to the Sharpe ratio if returns are normally distributed. Moreover, the two performance measures are asymptotically equivalent as the underlying distributions converge to the normal distribution. We suggest a parametric and a non-parametric estimator for the new performance measure and provide an empirical illustration using mutual funds and hedge funds data.

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    Bibliographic Info

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

    Volume (Year): 36 (2012)
    Issue (Month): 8 ()
    Pages: 2274-2284

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    Handle: RePEc:eee:jbfina:v:36:y:2012:i:8:p:2274-2284

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

    Related research

    Keywords: Performance measurement; Sharpe ratio; Aumann–Serrano index of riskiness; Skewness; Kurtosis; Non-normality;

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    References

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    Cited by:
    1. 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.
    2. 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.
    3. Schulze, Klaas, 2014. "Existence and computation of the Aumann–Serrano index of riskiness and its extension," Journal of Mathematical Economics, Elsevier, vol. 50(C), pages 219-224.
    4. Chen, Yi-Ting & Ho, Keng-Yu & Tzeng, Larry Y., 2014. "Riskiness-minimizing spot-futures hedge ratio," Journal of Banking & Finance, Elsevier, vol. 40(C), pages 154-164.
    5. 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.

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