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Sensitivity of Performance Indexes to Disaster Risk

Author

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  • Jiro Hodoshima

    (Faculty of Economics, Nagoya University of Commerce and Business, 4-4 Sagamine, Komenoki-cho, Nisshin-shi, Aichi 470-0193, Japan)

  • Toshiyuki Yamawake

    (Faculty of Economics, Nagoya University of Commerce and Business, 4-4 Sagamine, Komenoki-cho, Nisshin-shi, Aichi 470-0193, Japan)

Abstract

We examine how sensitive the new performance indexes incorporating high moments and disaster risk are to disaster risk. The new performance indexes incorporating high moments and disaster risk are the Aumann-Serrano performance index and Foster-Hart performance index proposed by Kadan and Liu. These performance indexes provide evaluations sensitive to the underlying risk. We show, by numerical examples and empirical examples, how sensitive these indexes are to disaster risk. Although these indexes are known to be either quite sensitive or excessively sensitive to disaster risk or maximum loss in the literature, we show by the regression analysis of the index and summary statistics these indexes are in fact not excessively sensitive to maximum loss in representative stock data, which contain disastrous observations. The numerical estimate of the Foster-Hart performance index is found to be effective in showing the performance index. Our analysis suggests these indexes can handle various empirical data containing quite disastrous observations.

Suggested Citation

  • Jiro Hodoshima & Toshiyuki Yamawake, 2021. "Sensitivity of Performance Indexes to Disaster Risk," Risks, MDPI, vol. 9(2), pages 1-22, February.
    • Handle: RePEc:gam:jrisks:v:9:y:2021:i:2:p:40-:d:498644
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    References listed on IDEAS

    as
    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. , & ,, 2015. "The Foster-Hart measure of riskiness for general gambles," Theoretical Economics, Econometric Society, vol. 10(1), January.
    3. 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.
    4. Farinelli, Simone & Ferreira, Manuel & Rossello, Damiano & Thoeny, Markus & Tibiletti, Luisa, 2008. "Beyond Sharpe ratio: Optimal asset allocation using different performance ratios," Journal of Banking & Finance, Elsevier, vol. 32(10), pages 2057-2063, October.
    5. Sergiu Hart, 2011. "Comparing Risks by Acceptance and Rejection," Journal of Political Economy, University of Chicago Press, vol. 119(4), pages 617-638.
    6. Jiro Hodoshima, 2019. "Stock performance by utility indifference pricing and the Sharpe ratio," Quantitative Finance, Taylor & Francis Journals, vol. 19(2), pages 327-338, February.
    7. Eling, Martin & Schuhmacher, Frank, 2007. "Does the choice of performance measure influence the evaluation of hedge funds?," Journal of Banking & Finance, Elsevier, vol. 31(9), pages 2632-2647, September.
    8. Kadan, Ohad & Liu, Fang, 2014. "Performance evaluation with high moments and disaster risk," Journal of Financial Economics, Elsevier, vol. 113(1), pages 131-155.
    9. Abhinav Anand & Tiantian Li & Tetsuo Kurosaki & Young Shin Kim, 2017. "The equity risk posed by the too-big-to-fail banks: a Foster–Hart estimation," Annals of Operations Research, Springer, vol. 253(1), pages 21-41, June.
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