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Sufficient conditions for expected utility to imply drawdown-based performance rankings

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  • Schuhmacher, Frank
  • Eling, Martin

Abstract

The least restrictive sufficient condition for expected utility to imply Sharpe ratio rankings is the location and scale (LS) property (see [Sinn, 1983] and [Meyer, 1987]). The normal, the extreme value, and many other distributions commonly used in finance satisfy this property. We argue that the LS property is also sufficient for expected utility to imply drawdown-based performance measure rankings, because for investment funds satisfying the LS condition, the Sharpe ratio and drawdown-based performance measures result in identical rankings. Hence, the same conditions that provide an expected utility foundation for the Sharpe ratio also provide a foundation for drawdown-based performance measures. We conclude that from a decision-theoretic perspective, drawdown-based performance measures are as good as the Sharpe ratio.

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  • Schuhmacher, Frank & Eling, Martin, 2011. "Sufficient conditions for expected utility to imply drawdown-based performance rankings," Journal of Banking & Finance, Elsevier, vol. 35(9), pages 2311-2318, September.
  • Handle: RePEc:eee:jbfina:v:35:y:2011:i:9:p:2311-2318
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    References listed on IDEAS

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    Cited by:

    1. Auer, Benjamin R., 2015. "Does the choice of performance measure influence the evaluation of commodity investments?," International Review of Financial Analysis, Elsevier, vol. 38(C), pages 142-150.
    2. Schuhmacher, Frank & Auer, Benjamin R., 2014. "Sufficient conditions under which SSD- and MR-efficient sets are identical," European Journal of Operational Research, Elsevier, vol. 239(3), pages 756-763.
    3. Schuster, Martin & Auer, Benjamin R., 2012. "A note on empirical Sharpe ratio dynamics," Economics Letters, Elsevier, vol. 116(1), pages 124-128.
    4. Auer, Benjamin R., 2014. "Daily seasonality in crude oil returns and volatilities," Energy Economics, Elsevier, vol. 43(C), pages 82-88.
    5. Benjamin R. Auer, 2016. "Do Socially Responsible Investment Policies Add or Destroy European Stock Portfolio Value?," Journal of Business Ethics, Springer, vol. 135(2), pages 381-397, May.
    6. Landriault, David & Li, Bin & Li, Shu, 2015. "Analysis of a drawdown-based regime-switching Lévy insurance model," Insurance: Mathematics and Economics, Elsevier, vol. 60(C), pages 98-107.
    7. Tavakoli Baghdadabad, Mohammad Reza, 2014. "Average drawdown risk reduction and risk tolerances," Research in Economics, Elsevier, vol. 68(3), pages 264-276.
    8. Homm, Ulrich & Pigorsch, Christian, 2012. "Beyond the Sharpe ratio: An application of the Aumann–Serrano index to performance measurement," Journal of Banking & Finance, Elsevier, vol. 36(8), pages 2274-2284.
    9. Auer, Benjamin R. & Schuhmacher, Frank, 2016. "Do socially (ir)responsible investments pay? New evidence from international ESG data," The Quarterly Review of Economics and Finance, Elsevier, vol. 59(C), pages 51-62.
    10. David Landriault & Bin Li & Hongzhong Zhang, 2017. "A Unified Approach for Drawdown (Drawup) of Time-Homogeneous Markov Processes," Papers 1702.07786, arXiv.org.
    11. Schuhmacher, Frank & Eling, Martin, 2012. "A decision-theoretic foundation for reward-to-risk performance measures," Journal of Banking & Finance, Elsevier, vol. 36(7), pages 2077-2082.
    12. 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.
    13. 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.
    14. León, Angel & Moreno, Manuel, 2017. "One-sided performance measures under Gram-Charlier distributions," Journal of Banking & Finance, Elsevier, vol. 74(C), pages 38-50.
    15. Auer, Benjamin R. & Schuhmacher, Frank, 2013. "Diamonds — A precious new asset?," International Review of Financial Analysis, Elsevier, vol. 28(C), pages 182-189.
    16. 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.
    17. León, Ángel & Moreno, Manuel, 2015. "Lower Partial Moments under Gram Charlier Distribution: Performance Measures and Efficient Frontiers," QM&ET Working Papers 15-3, University of Alicante, D. Quantitative Methods and Economic Theory.
    18. Benjamin Auer, 2013. "The low return distortion of the Sharpe ratio," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 27(3), pages 299-306, September.

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