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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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    Citations

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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. Ole E. Barndorff-Nielsen & Silja Kinnebrock & Neil Shephard, 2008. "Measuring downside risk - realised semivariance," OFRC Working Papers Series 2008fe01, Oxford Financial Research Centre.
    6. Valeri Zakamouline, 2014. "Portfolio performance evaluation with loss aversion," Quantitative Finance, Taylor & Francis Journals, vol. 14(4), pages 699-710, April.
    7. 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.
    8. 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.
    9. 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.
    10. repec:bla:ausecp:v:56:y:2017:i:2:p:134-162 is not listed on IDEAS
    11. Bertrand, Philippe & Prigent, Jean-luc, 2011. "Omega performance measure and portfolio insurance," Journal of Banking & Finance, Elsevier, vol. 35(7), pages 1811-1823, July.
    12. Christian Bach, 2011. "Conservatism in Corporate Valuation," CREATES Research Papers 2011-32, Department of Economics and Business Economics, Aarhus University.
    13. 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.
    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. 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.
    16. Beach, Steven L., 2011. "Semivariance decomposition of country-level returns," International Review of Economics & Finance, Elsevier, vol. 20(4), pages 607-623, October.
    17. repec:gam:jrisks:v:6:y:2018:i:1:p:12-:d:132609 is not listed on IDEAS
    18. 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.
    19. 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.
    20. 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.
    21. repec:ipg:wpaper:2014-510 is not listed on IDEAS

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