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Moment characterization of higher-order risk preferences

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  • Ebert, Sebastian

Abstract

It is often said that prudence and temperance play key roles in aversion to negative skewness and kurtosis, respectively. This paper puts a new perspective on these relationships and presents a characterization of higher-order risk preferences in terms of statistical moments. An implication is, for example, that prudence implies preference for distributions with higher skewness as defined by all odd moments. Moreover, we show that this preference is robust towards variation in kurtosis as defined by all even moments. We thus speak of the kurtosis robustness feature of prudence. Further, we show that all higher-order risk preferences of odd order imply skewness preference, but for different distributions than prudence. Similar results are presented for temperance and higher-order risk preferences of even order that can be related to kurtosis aversion and have a skewness robustness feature.

Suggested Citation

  • Ebert, Sebastian, 2010. "Moment characterization of higher-order risk preferences," Bonn Econ Discussion Papers 17/2010, University of Bonn, Bonn Graduate School of Economics (BGSE).
    • Handle: RePEc:zbw:bonedp:172010
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    Cited by:

    1. Colasante, Annarita & Riccetti, Luca, 2020. "Risk aversion, prudence and temperance: It is a matter of gap between moments," Journal of Behavioral and Experimental Finance, Elsevier, vol. 25(C).
    2. Ebert, Sebastian, 2015. "On skewed risks in economic models and experiments," Journal of Economic Behavior & Organization, Elsevier, vol. 112(C), pages 85-97.
    3. Zaixing Li & Fei Chen & Lixing Zhu, 2017. "Estimating moments in ANOVA-type mixed models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 80(6), pages 697-715, November.
    4. Bottasso, Anna & Duchêne, Sébastien & Guerci, Eric & Hanaki, Nobuyuki & Noussair, Charles N., 2022. "Higher order risk attitudes of financial experts," Journal of Behavioral and Experimental Finance, Elsevier, vol. 34(C).
    5. Markus Dertwinkel-Kalt & Mats Köster, 2020. "Salience and Skewness Preferences [Risk-neutral Firms can Extract Unbounded Profits from Consumers with Prospect Theory Preferences]," Journal of the European Economic Association, European Economic Association, vol. 18(5), pages 2057-2107.
    6. Denuit, Michel & Rey, Béatrice, 2013. "Another look at risk apportionment," Journal of Mathematical Economics, Elsevier, vol. 49(4), pages 335-343.
    7. François Desmoulins-Lebeault & Luc Meunier, 2018. "Moment Risks: Investment for Self and for a Firm," Decision Analysis, INFORMS, vol. 15(4), pages 242-266, December.
    8. Ñíguez, Trino-Manuel & Paya, Ivan & Peel, David, 2016. "Pure higher-order effects in the portfolio choice model," Finance Research Letters, Elsevier, vol. 19(C), pages 255-260.
    9. Morten I. Lau & Hong Il Yoo, 2025. "Structural Estimation of Higher Order Risk Preferences," Econometrica, Econometric Society, vol. 93(5), pages 1855-1883, September.
    10. Ñíguez, Trino-Manuel & Perote, Javier, 2016. "Multivariate moments expansion density: Application of the dynamic equicorrelation model," Journal of Banking & Finance, Elsevier, vol. 72(S), pages 216-232.
    11. Michel Denuit & Liqun Liu, 2014. "Decreasing higher-order absolute risk aversion and higher-degree stochastic dominance," Theory and Decision, Springer, vol. 76(2), pages 287-295, February.
    12. Mirko S. Heinle & Kevin C. Smith, 2017. "A theory of risk disclosure," Review of Accounting Studies, Springer, vol. 22(4), pages 1459-1491, December.
    13. Chin Hon Tan & Chunling Luo, 2017. "Clear Preferences Under Partial Distribution Information," Decision Analysis, INFORMS, vol. 14(1), pages 65-73, March.
    14. Denuit, Michel & Rey, Beatrice, 2012. "Uni- And Multidimensional Risk Attitudes: Some Unifying Theorems," LIDAM Discussion Papers ISBA 2012014, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    15. Sebastian Ebert & Daniel Wiesen, 2011. "Testing for Prudence and Skewness Seeking," Management Science, INFORMS, vol. 57(7), pages 1334-1349, July.
    16. Christophe Courbage & Henri Loubergé & Béatrice Rey, 2018. "On the properties of high-order non-monetary measures for risks," The Geneva Papers on Risk and Insurance Theory, Springer;International Association for the Study of Insurance Economics (The Geneva Association), vol. 43(1), pages 77-94, May.
    17. Christophe Courbage & Béatrice Rey, 2016. "Decision Thresholds and Changes in Risk for Preventive Treatment," Health Economics, John Wiley & Sons, Ltd., vol. 25(1), pages 111-124, January.
    18. Brice Corgnet & Roberto Hernán González, 2023. "On The Appeal Of Complexity," Working Papers 2312, Groupe d'Analyse et de Théorie Economique Lyon St-Étienne (GATE Lyon St-Étienne), Université de Lyon.
    19. León, Angel & Moreno, Manuel, 2017. "One-sided performance measures under Gram-Charlier distributions," Journal of Banking & Finance, Elsevier, vol. 74(C), pages 38-50.
    20. Maria Debora Braga & Luigi Riso & Maria Grazia Zoia, 2025. "The Theoretical Properties of Novel Risk-Based Asset Allocation Strategies using Portfolio Volatility and Kurtosis," DISCE - Working Papers del Dipartimento di Politica Economica dipe0044, Università Cattolica del Sacro Cuore, Dipartimenti e Istituti di Scienze Economiche (DISCE).
    21. Thomas Åstebro & José Mata & Luís Santos-Pinto, 2015. "Skewness seeking: risk loving, optimism or overweighting of small probabilities?," Theory and Decision, Springer, vol. 78(2), pages 189-208, February.
    22. Michail Anthropelos & Paul Schneider, 2021. "Optimal Investment and Equilibrium Pricing under Ambiguity," Swiss Finance Institute Research Paper Series 21-78, Swiss Finance Institute.
    23. Trautmann, Stefan T. & Kuilen, Gijs van de, 2018. "Higher order risk attitudes: A review of experimental evidence," European Economic Review, Elsevier, vol. 103(C), pages 108-124.
    24. Denuit, Michel & Liu, Liqun, 2013. "Decreasing higher-order absolute risk aversion and higher-degree stochastic dominance," LIDAM Discussion Papers ISBA 2013007, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    25. Horvath, Ferenc, 2025. "Arbitrage-based recovery," Journal of Financial Economics, Elsevier, vol. 163(C).

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    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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