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The computational property of the Aumann–Serrano performance index under risk-averse and risk-loving preference

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  • Hodoshima, Jiro

Abstract

We consider computational aspects of the Aumann–Serrano (AS) performance index proposed by Kadan and Liu (2014). When investors are not only risk averse but also risk loving, the original implicit equation of the AS performance index has in general two solutions of the true index and a pseudo index of zero. This makes it difficult to search for the true index by programs of solving nonlinear equations. On the other hand, an implicit equation of another equivalent performance index based on utility indifference pricing is a continuous and strictly decreasing function, which makes it always easy to find the true index by programs.

Suggested Citation

  • Hodoshima, Jiro, 2021. "The computational property of the Aumann–Serrano performance index under risk-averse and risk-loving preference," Finance Research Letters, Elsevier, vol. 39(C).
    • Handle: RePEc:eee:finlet:v:39:y:2021:i:c:s1544612319312905
    DOI: 10.1016/j.frl.2020.101588
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    References listed on IDEAS

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    1. Robert J. Aumann & Roberto Serrano, 2008. "An Economic Index of Riskiness," Journal of Political Economy, University of Chicago Press, vol. 116(5), pages 810-836, October.
    2. Dean P. Foster & Sergiu Hart, 2009. "An Operational Measure of Riskiness," Journal of Political Economy, University of Chicago Press, vol. 117(5), pages 785-814.
    3. Sergiu Hart, 2011. "Comparing Risks by Acceptance and Rejection," Journal of Political Economy, University of Chicago Press, vol. 119(4), pages 617-638.
    4. 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.
    5. Hodoshima, Jiro & Miyahara, Yoshio, 2020. "Utility indifference pricing and the Aumann–Serrano performance index," Journal of Mathematical Economics, Elsevier, vol. 86(C), pages 83-89.
    6. Kadan, Ohad & Liu, Fang, 2014. "Performance evaluation with high moments and disaster risk," Journal of Financial Economics, Elsevier, vol. 113(1), pages 131-155.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Aumann–Serrano performance index; Utility indifference pricing; Inner rate of risk aversion; Risk loving; Risk averse;
    All these keywords.

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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