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On the foundation of performance measures under asymmetric returns

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  • Christian Pedersen
  • Stephen Satchell
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    Abstract

    We examine two performance measures advocated for asymmetric return distributions: the Sortino ratio—originally introduced by Sortino and Price (Sortino F and Price L 1994 J. Investing 59-65)—and a measure based on power utility introduced in Leland (Leland H 1999 Financial Analysts J. 27-36). In particular, we investigate the role of the maximum principle in this context, and assess the conditions under which the measures satisfy it. Our results add further motivation for the use of a modified Sortino ratio, by placing it on a sound theoretical foundation. In this light, we discuss its relative merits compared with alternative approaches.

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    File URL: http://www.tandfonline.com/doi/abs/10.1088/1469-7688/2/3/304
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    Bibliographic Info

    Article provided by Taylor & Francis Journals in its journal Quantitative Finance.

    Volume (Year): 2 (2002)
    Issue (Month): 3 ()
    Pages: 217-223

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    Handle: RePEc:taf:quantf:v:2:y:2002:i:3:p:217-223

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    Cited by:
    1. Zieling, Daniel & Mahayni, Antje & Balder, Sven, 2014. "Performance evaluation of optimized portfolio insurance strategies," Journal of Banking & Finance, Elsevier, vol. 43(C), pages 212-225.
    2. Hwang, Soosung & Pedersen, Christian S., 2004. "Asymmetric risk measures when modelling emerging markets equities: evidence for regional and timing effects," Emerging Markets Review, Elsevier, vol. 5(1), pages 109-128, March.
    3. Mencía, Javier & Sentana, Enrique, 2009. "Multivariate location-scale mixtures of normals and mean-variance-skewness portfolio allocation," Journal of Econometrics, Elsevier, vol. 153(2), pages 105-121, December.
    4. Cumova, Denisa & Nawrocki, David, 2014. "Portfolio optimization in an upside potential and downside risk framework," Journal of Economics and Business, Elsevier, vol. 71(C), pages 68-89.
    5. Darolles, Serge & Gourieroux, Christian, 2010. "Conditionally fitted Sharpe performance with an application to hedge fund rating," Journal of Banking & Finance, Elsevier, vol. 34(3), pages 578-593, March.
    6. Neil Shephard & Silja Kinnebrock & Ole E. Barndorff-Neilsen, 2008. "Measuring downside risk - realised semivariance," Economics Series Working Papers 382, University of Oxford, Department of Economics.
    7. Beach, Steven L., 2011. "Semivariance decomposition of country-level returns," International Review of Economics & Finance, Elsevier, vol. 20(4), pages 607-623, October.
    8. Christian Bach, 2011. "Conservatism in Corporate Valuation," CREATES Research Papers 2011-32, School of Economics and Management, University of Aarhus.
    9. Bertrand, Philippe & Prigent, Jean-luc, 2011. "Omega performance measure and portfolio insurance," Journal of Banking & Finance, Elsevier, vol. 35(7), pages 1811-1823, July.
    10. Francisco Penaranda, 2007. "Portfolio choice beyond the traditional approach," LSE Research Online Documents on Economics 24481, London School of Economics and Political Science, LSE Library.

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