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On the foundation of performance measures under asymmetric returns

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  • Christian Pedersen
  • Stephen Satchell

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.

Suggested Citation

  • Christian Pedersen & Stephen Satchell, 2002. "On the foundation of performance measures under asymmetric returns," Quantitative Finance, Taylor & Francis Journals, vol. 2(3), pages 217-223.
    • Handle: RePEc:taf:quantf:v:2:y:2002:i:3:p:217-223
    DOI: 10.1088/1469-7688/2/3/304
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    Cited by:

    1. Christian Bach & Peter O. Christensen, 2016. "Consumption-based equity valuation," Review of Accounting Studies, Springer, vol. 21(4), pages 1149-1202, December.
    2. 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.
    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. Sager, Michael & Taylor, Mark P., 2014. "Generating currency trading rules from the term structure of forward foreign exchange premia," Journal of International Money and Finance, Elsevier, vol. 44(C), pages 230-250.
    5. Bernard, Carole & Vanduffel, Steven & Ye, Jiang, 2019. "Optimal strategies under Omega ratio," European Journal of Operational Research, Elsevier, vol. 275(2), pages 755-767.
    6. Ole E. Barndorff-Nielsen & Silja Kinnebrock & Neil Shephard, 2008. "Measuring downside risk - realised semivariance," OFRC Working Papers Series 2008fe01, Oxford Financial Research Centre.
    7. Valeri Zakamouline, 2014. "Portfolio performance evaluation with loss aversion," Quantitative Finance, Taylor & Francis Journals, vol. 14(4), pages 699-710, April.
    8. 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.
    9. Massimiliano Caporin & Luca Corazzini & Michele Costola, 2014. "Measuring the Behavioral Component of Financial Fluctuations: An Analysis Based on the S&P 500," CREATES Research Papers 2014-33, Department of Economics and Business Economics, Aarhus University.
    10. Michele Costola & Massimiliano Caporin, 2016. "Rational Learning For Risk-Averse Investors By Conditioning On Behavioral Choices," Annals of Financial Economics (AFE), World Scientific Publishing Co. Pte. Ltd., vol. 11(01), pages 1-26, March.
    11. Penaranda, Francisco, 2007. "Portfolio choice beyond the traditional approach," LSE Research Online Documents on Economics 24481, London School of Economics and Political Science, LSE Library.
    12. Dragicevic, Arnaud Z., 2019. "Rethinking the forestry in the Aquitaine massif through portfolio management," Forest Policy and Economics, Elsevier, vol. 109(C).
    13. Rakesh Gupta & Junhao Yang & Thadavillil Jithendranathan, 2017. "Diversification into Emerging Markets – An Australian and the US Perspective Using a Time-varying Approach," Australian Economic Papers, Wiley Blackwell, vol. 56(2), pages 134-162, June.
    14. Bertrand, Philippe & Prigent, Jean-luc, 2011. "Omega performance measure and portfolio insurance," Journal of Banking & Finance, Elsevier, vol. 35(7), pages 1811-1823, July.
    15. Christian Bach, 2011. "Conservatism in Corporate Valuation," CREATES Research Papers 2011-32, Department of Economics and Business Economics, Aarhus University.
    16. 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.
    17. León, Angel & Moreno, Manuel, 2017. "One-sided performance measures under Gram-Charlier distributions," Journal of Banking & Finance, Elsevier, vol. 74(C), pages 38-50.
    18. 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.
    19. Beach, Steven L., 2011. "Semivariance decomposition of country-level returns," International Review of Economics & Finance, Elsevier, vol. 20(4), pages 607-623, October.
    20. David F. Babbel & Miguel A. Herce, 2018. "Stable Value Funds Performance," Risks, MDPI, Open Access Journal, vol. 6(1), pages 1-40, February.
    21. Sharma, Prateek & Vipul,, 2015. "Performance of risk-based portfolios under different market conditions: Evidence from India," Research in International Business and Finance, Elsevier, vol. 34(C), pages 397-411.
    22. 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.
    23. Miles Gietzmann & Adam Ostaszewski, 2014. "Why managers with low forecast precision select high disclosure intensity: an equilibrium analysis," Review of Quantitative Finance and Accounting, Springer, vol. 43(1), pages 121-153, July.
    24. repec:ipg:wpaper:2014-510 is not listed on IDEAS

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