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A Reexamination of the Relationship Between Preferences and Moment Orderings by Rational Risk-Averse Investors

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  • Patrick L. Brockett

    (Graduate School of Business, Department of Management Science and Information Systems, University of Texas, Austin, TX 78712.)

  • James R. Garven

    (Department of Finance, E.J. Ourso College of Business Administration, Louisiana State University, Baton Rouge, LA 70803.)

Abstract

This article examines the relationship between risk, return, skewness, and utility-based preferences. Examples are constructed showing that, for any commonly used utility function, it is possible to have two continuous unimodal random variables X and Y with positive and equal means, X having a larger variance and lower positive skewness than Y, and yet X has larger expected utility than Y, contrary to persistent folklore concerning U‴ > 0 implying skewness preference for risk averters. In additon, it is shown that ceteris paribus analysis of preferences and moments, as occasionally used in the literature, is impossible since equality of higher-order central moments implies the total equality of the distributions involved. The Geneva Papers on Risk and Insurance Theory (1998) 23, 127–137. doi:10.1023/A:1008674127340

Suggested Citation

  • Patrick L. Brockett & James R. Garven, 1998. "A Reexamination of the Relationship Between Preferences and Moment Orderings by Rational Risk-Averse Investors," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 23(2), pages 127-137, December.
    • Handle: RePEc:pal:genrir:v:23:y:1998:i:2:p:127-137
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    Cited by:

    1. Eric Jondeau & Michael Rockinger, 2006. "Optimal Portfolio Allocation under Higher Moments," European Financial Management, European Financial Management Association, vol. 12(1), pages 29-55, January.
    2. D. A. Peel, 2008. "Introduction: economics of betting markets," Applied Economics, Taylor & Francis Journals, vol. 40(1), pages 1-3.
    3. David Peel & David Law, 2009. "A More General Non‐expected Utility Model as an Explanation of Gambling Outcomes for Individuals and Markets," Economica, London School of Economics and Political Science, vol. 76(302), pages 251-263, April.
    4. Juliane Proelss & Denis Schweizer, 2014. "Polynomial goal programming and the implicit higher moment preferences of US institutional investors in hedge funds," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 28(1), pages 1-28, February.
    5. Nalpas, Nicolas & Simar, Leopold & Vanhems, Anne, 2016. "Portfolio Selection in a Multi-Input Multi-Output Setting:a Simple Monte-Carlo-FDH Algorithm," LIDAM Discussion Papers ISBA 2016022, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    6. Kaas, Rob & Dhaene, Jan & Goovaerts, Marc J., 2000. "Upper and lower bounds for sums of random variables," Insurance: Mathematics and Economics, Elsevier, vol. 27(2), pages 151-168, October.
    7. Matteo Benuzzi & Matteo Ploner, 2024. "Skewness-seeking behavior and financial investments," Annals of Finance, Springer, vol. 20(1), pages 129-165, March.
    8. Niu, Cuizhen & Wong, Wing-Keung & Xu, Qunfang, 2017. "Higher-Order Risk Measure and (Higher-Order) Stochastic Dominance," MPRA Paper 75948, University Library of Munich, Germany.
    9. Mateane, Lebogang, 2020. "Risk preferences, global market conditions and foreign debt: Is there any role for the currency composition of FX reserves?," EconStor Preprints 227484, ZBW - Leibniz Information Centre for Economics.
    10. Ebert, Sebastian & Wiesen, Daniel, 2009. "An experimental methodology testing for prudence and third-order preferences," Bonn Econ Discussion Papers 21/2009, University of Bonn, Bonn Graduate School of Economics (BGSE).
    11. Christodoulakis, George & Peel, David, 2006. "The relationship between expected utility and higher moments for distributions captured by the Gram-Charlier class," Finance Research Letters, Elsevier, vol. 3(4), pages 273-276, December.
    12. Fahrenwaldt, Matthias A. & Sun, Chaofan, 2020. "Expected utility approximation and portfolio optimisation," Insurance: Mathematics and Economics, Elsevier, vol. 93(C), pages 301-314.
    13. Cuizhen Niu & Wing-Keung Wong & Qunfang Xu, 2017. "Kappa ratios and (higher-order) stochastic dominance," Risk Management, Palgrave Macmillan, vol. 19(3), pages 245-253, August.
    14. Wang, Chou-Wen & Liu, Kai & Li, Bin & Tan, Ken Seng, 2022. "Portfolio optimization under multivariate affine generalized hyperbolic distributions," International Review of Economics & Finance, Elsevier, vol. 80(C), pages 49-66.
    15. Thierry Chauveau & Sylvain Friederich & Jérôme Héricourt & Emmanuel Jurczenko & Catherine Lubochinsky & Bertrand Maillet & Christophe Moussu & Bogdan Négréa & Hélène Raymond-Feingold, 2004. "La volatilité des marchés augmente-t-elle ?," Revue d'Économie Financière, Programme National Persée, vol. 74(1), pages 17-44.
    16. Chin Hon Tan & Chunling Luo, 2017. "Clear Preferences Under Partial Distribution Information," Decision Analysis, INFORMS, vol. 14(1), pages 65-73, March.
    17. Chan, Raymond H. & Chow, Sheung-Chi & Guo, Xu & Wong, Wing-Keung, 2022. "Central moments, stochastic dominance, moment rule, and diversification with an application," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    18. repec:ebl:ecbull:v:7:y:2007:i:2:p:1-9 is not listed on IDEAS
    19. Gaudry, Marc, 2018. "The utility of journeys, from Dupuit's constant-time bridge crossing hops to commutes of chosen duration and reliability in the Paris region," Transport Policy, Elsevier, vol. 70(C), pages 53-68.
    20. D. A. Peel, 2012. "Further examples of the impact of skewness on the expected utility of a risk-averse agent," Applied Economics Letters, Taylor & Francis Journals, vol. 19(12), pages 1117-1121, August.
    21. Eichner, Thomas & Wagener, Andreas, 2012. "Tempering effects of (dependent) background risks: A mean-variance analysis of portfolio selection," Journal of Mathematical Economics, Elsevier, vol. 48(6), pages 422-430.
    22. Ulrich Blum & Marc Gaudry, 2000. "SNUS-2.5, a Multimoment Analysis of Road Demand, Accidents and their Severity in Germany, 1968 – 1989," Working Papers of BETA 2000-11, Bureau d'Economie Théorique et Appliquée, UDS, Strasbourg.
    23. Andreas Oehler & Julian Schneider, 2022. "Gambling with lottery stocks?," Journal of Asset Management, Palgrave Macmillan, vol. 23(6), pages 477-503, October.
    24. Emmanuel Jurczenko & Bertrand Maillet & Paul Merlin, 2008. "Efficient Frontier for Robust Higher-order Moment Portfolio Selection," Post-Print halshs-00336475, HAL.
    25. David A. Peel & Davind Law, 2009. "An Explanation of Optimal Each-Way Bets based on Non-Expected Utility Theory," Journal of Gambling Business and Economics, University of Buckingham Press, vol. 3(2), pages 15-35, September.

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