IDEAS home Printed from https://ideas.repec.org/a/eee/finlet/v39y2021ics1544612319312905.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S1544612319312905
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.frl.2020.101588?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    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. 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)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Jiro Hodoshima & Toshiyuki Yamawake, 2022. "Comparing Dynamic and Static Performance Indexes in the Stock Market: Evidence From Japan," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 29(2), pages 171-193, June.
    2. Hodoshima, Jiro & Yamawake, Toshiyuki, 2022. "Temporal aggregation of the Aumann–Serrano and Foster–Hart performance indexes," International Review of Financial Analysis, Elsevier, vol. 83(C).
    3. Jiro Hodoshima & Tetsuya Misawa & Yoshio Miyahara, 2020. "Stock Performance Evaluation Incorporating High Moments and Disaster Risk: Evidence from Japan," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 27(2), pages 155-174, June.
    4. Lu, Richard & Horng, Tzyy-Leng & Horng, Min-Sun & Wang, Amy Z.-H., 2023. "A performance evaluation of portfolio insurance under the Black and Scholes framework: An application of the economic index of riskiness," The Quarterly Review of Economics and Finance, Elsevier, vol. 89(C), pages 269-276.
    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. Bi, Hongwei & Huang, Rachel J. & Tzeng, Larry Y. & Zhu, Wei, 2019. "Higher-order Omega: A performance index with a decision-theoretic foundation," Journal of Banking & Finance, Elsevier, vol. 100(C), pages 43-57.
    7. Niu, Cuizhen & Guo, Xu & McAleer, Michael & Wong, Wing-Keung, 2018. "Theory and application of an economic performance measure of risk," International Review of Economics & Finance, Elsevier, vol. 56(C), pages 383-396.
    8. Hellman, Ziv & Schreiber, Amnon, 2018. "Indexing gamble desirability by extending proportional stochastic dominance," Games and Economic Behavior, Elsevier, vol. 109(C), pages 523-543.
    9. Heller, Yuval & Schreiber, Amnon, 2020. "Short-term investments and indices of risk," Theoretical Economics, Econometric Society, vol. 15(3), July.
    10. Ehsani, Sina & Lien, Donald, 2015. "A note on minimum riskiness hedge ratio," Finance Research Letters, Elsevier, vol. 15(C), pages 11-17.
    11. Jiro Hodoshima & Toshiyuki Yamawake, 2020. "The Aumann–Serrano Performance Index for Multi-Period Gambles in Stock Data," JRFM, MDPI, vol. 13(11), pages 1-18, November.
    12. Yuval Heller & Amnon Schreiber, 2020. "Short-Term Investments and Indices of Risk," Papers 2005.06576, arXiv.org.
    13. Yang, Jen-Wei & Chiu, Shih-Yung & Yen, Kuang-Chieh, 2023. "Does the realized distribution-based measure dominate particular moments? Evidence from cryptocurrency markets," Finance Research Letters, Elsevier, vol. 51(C).
    14. Leiss, Matthias & Nax, Heinrich H., 2018. "Option-implied objective measures of market risk," Journal of Banking & Finance, Elsevier, vol. 88(C), pages 241-249.
    15. Jiro Hodoshima & Toshiyuki Yamawake, 2021. "Sensitivity of Performance Indexes to Disaster Risk," Risks, MDPI, vol. 9(2), pages 1-22, February.
    16. Klaas Schulze, 2015. "General dual measures of riskiness," Theory and Decision, Springer, vol. 78(2), pages 289-304, February.
    17. Soo Hong Chew & Jacob S. Sagi, 2022. "A critical look at the Aumann-Serrano and Foster-Hart measures of riskiness," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 74(2), pages 397-422, September.
    18. Kuang-Liang Chang & Charles Ka Yui Leung, 2022. "How did the asset markets change after the Global Financial Crisis?," Chapters, in: Charles K.Y. Leung (ed.), Handbook of Real Estate and Macroeconomics, chapter 12, pages 312-336, Edward Elgar Publishing.
    19. Antonio Cabrales & Olivier Gossner & Roberto Serrano, 2013. "Entropy and the Value of Information for Investors," American Economic Review, American Economic Association, vol. 103(1), pages 360-377, February.
    20. Moti Michaeli, 2021. "On Measuring Welfare ‘Behind a Veil of Ignorance’," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 56(1), pages 57-66, January.

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:finlet:v:39:y:2021:i:c:s1544612319312905. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/frl .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.