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Adding Risks: Samuelson's Fallacy of Large Numbers Revisited

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  • Ross, Stephen A.

Abstract

Samuelson called accepting a sequence of independent positive mean bets that are individually unacceptable a fallacy of large numbers, and subsequent researchers have extended Samuelson's condition on utility functions to assure that they would not allow this fallacy. By contrast, some behavioralists, arguing the merits of diversification, believe that it is simply wrong headed to refuse a long series of independent “good†bets out of a misguided faith in expected utility theory. Contrary to what one might infer from the literature, this paper shows that accepting sequences of good bets is both consistent with expected utility theory and quite usual.

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  • Ross, Stephen A., 1999. "Adding Risks: Samuelson's Fallacy of Large Numbers Revisited," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 34(3), pages 323-339, September.
    • Handle: RePEc:cup:jfinqa:v:34:y:1999:i:03:p:323-339_00
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    Cited by:

    1. Roelof Salomons, 2008. "A Theoretical And Practical Perspective On The Equity Risk Premium," Journal of Economic Surveys, Wiley Blackwell, vol. 22(2), pages 299-329, April.
    2. Iñigo Iturbe-Ormaetxe Kortajarene & Giovanni Ponti & Josefa Tomás Lucas, 2015. "Some (Mis)facts about Myopic Loss Aversion," Working Papers. Serie AD 2015-09, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
    3. Lin William Cong & Zhiguo He & Jiasun Li & Wei Jiang, 2021. "Decentralized Mining in Centralized Pools [Concentrating on the fall of the labor share]," The Review of Financial Studies, Society for Financial Studies, vol. 34(3), pages 1191-1235.
    4. Hammarlid, Ola, 2005. "When to accept a sequence of gambles," Journal of Mathematical Economics, Elsevier, vol. 41(8), pages 974-982, December.
    5. Sergio Sousa, 2010. "Small-scale changes in wealth and attitudes toward risk," Discussion Papers 2010-11, The Centre for Decision Research and Experimental Economics, School of Economics, University of Nottingham.
    6. Aloysius, John A., 2003. "Rational escalation of costs by playing a sequence of unfavorable gambles: the martingale," Journal of Economic Behavior & Organization, Elsevier, vol. 51(1), pages 111-129, May.
    7. Sergio Sousa, 2010. "Small-scale changes in wealth and attitudes toward risk," Discussion Papers 2010-11, The Centre for Decision Research and Experimental Economics, School of Economics, University of Nottingham.
    8. Dierkes, Maik & Erner, Carsten & Zeisberger, Stefan, 2010. "Investment horizon and the attractiveness of investment strategies: A behavioral approach," Journal of Banking & Finance, Elsevier, vol. 34(5), pages 1032-1046, May.
    9. Langer, Thomas & Weber, Martin, 2005. "Myopic prospect theory vs. myopic loss aversion: how general is the phenomenon?," Journal of Economic Behavior & Organization, Elsevier, vol. 56(1), pages 25-38, January.
    10. Zhengwei Sun & Ali E. Abbas, 2014. "On the sensitivity of the value of information to risk aversion in two-action decision problems," Environment Systems and Decisions, Springer, vol. 34(1), pages 24-37, March.
    11. Ilia Tsetlin & Robert L. Winkler, 2005. "Risky Choices and Correlated Background Risk," Management Science, INFORMS, vol. 51(9), pages 1336-1345, September.
    12. Gilles Boevi Koumou, 2020. "Diversification and portfolio theory: a review," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 34(3), pages 267-312, September.
    13. Xiaosheng Mu & Luciano Pomatto & Philipp Strack & Omer Tamuz, 2021. "From Blackwell Dominance in Large Samples to Rényi Divergences and Back Again," Econometrica, Econometric Society, vol. 89(1), pages 475-506, January.
    14. Mark Grinblatt & Juhani T. Linnainmaa, 2011. "Jensen's Inequality, Parameter Uncertainty, and Multi-period Investment," The Review of Asset Pricing Studies, Society for Financial Studies, vol. 1(1), pages 1-34.
    15. Aloysius, John A., 2005. "Ambiguity aversion and the equity premium puzzle: A re-examination of experimental data on repeated gambles," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 34(5), pages 635-655, October.
    16. Knispel, Thomas & Laeven, Roger J.A. & Svindland, Gregor, 2016. "Robust optimal risk sharing and risk premia in expanding pools," Insurance: Mathematics and Economics, Elsevier, vol. 70(C), pages 182-195.
    17. repec:cup:judgdm:v:1:y:2006:i::p:134-145 is not listed on IDEAS
    18. Michael L. DeKay & John C. Hershey & Mark D. Spranca, & Peter A. Ubel & David A. Asch, 2006. "Are medical treatments for individuals and groups like single-play and multiple-play gambles?," Judgment and Decision Making, Society for Judgment and Decision Making, vol. 1, pages 134-145, November.
    19. Dirk Tasche & Luisa Tibiletti, 2003. "A Shortcut to Sign Incremental Value at Risk for Risk Allocation," Journal of Risk Finance, Emerald Group Publishing Limited, vol. 4(2), pages 43-46, January.
    20. Robles-Zurita, José, 2018. "Alternation bias and sums of identically distributed monetary lotteries," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 72(C), pages 78-85.
    21. Andrei Semenov, 2003. "High-Order Consumption Moments and Asset Pricing," Working Papers 2003_4, York University, Department of Economics, revised Jan 2005.
    22. José Antonio Robles-Zurita, 2015. "Alternation Bias and Sums of Identically Distributed Monetary Lotteries," Working Papers 15.08, Universidad Pablo de Olavide, Department of Economics.
    23. Daniel Dimitrov, 2022. "Intergenerational Risk Sharing with Market Liquidity Risk," Tinbergen Institute Discussion Papers 22-028/VI, Tinbergen Institute.

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