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Adding Risks: Samuelson's Fallacy of Large Numbers Revisited

Published online by Cambridge University Press:  06 April 2009

Stephen A. Ross
Affiliation:
Sloan School of Management, Massachusetts Institute of Technology, 50 Memorial Drive, Cambridge, MA 02142.

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.

Type
Research Article
Copyright
Copyright © School of Business Administration, University of Washington 1999

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References

Benartzi, S., and Thaler, R. H.. “Risk Aversion or Myopia? The Fallacy of Small Numbers and its Implications for Retirement Savings”. Unpubl. Manuscript, Univ. of Chicago (1996).Google Scholar
Diamond, D. W.Financial Intermediation and Delegated Monitoring”. Review of Economic Studies, 51 (1984), 393414.CrossRefGoogle Scholar
Durrett, R.Probability: Theory and Examples, 2nd ed.Belmont, CA: Wadsworth Publishing (1996).Google Scholar
Hellwig, M. F.The Assessment of Large Compounds of Independent Gambles”. Journal of Economic Theory, 67 (1995), 299326.CrossRefGoogle Scholar
Huberman, G., and Ross, S. A.. “Portfolio Turnpike Theorems, Risk Aversion, and Regularly Varying Utility Functions”. Econometrica, 51 (1983), 13451361.CrossRefGoogle Scholar
Kahneman, D., and Tversky, A.. “Prospect Theory: An Analysis of Decision under Risk”. Econometrica, 47 (1979), 263291.CrossRefGoogle Scholar
Kimball, M. S.Standard Risk Aversion”. Econometrica, 61 (1993), 589611.CrossRefGoogle Scholar
Lippman, S. A., and Mamer, J. W.. “When Many Wrongs Make a Right”. Probability in the Engineering and Informational Sciences, 2 (1988), 115127.CrossRefGoogle Scholar
Nielsen, L. T.Attractive Compounds of Unattractive Investments and Gambles”. Scandinavian Journal of Economics, 87 (1985), 463473.CrossRefGoogle Scholar
Pratt, J. W., and Zeckhauser, R. J.. “Proper Risk Aversion”. Econometrica, 55 (1987), 143154.CrossRefGoogle Scholar
Ross, S. A.Portfolio Turnpike Theorems for Constant Policies”. Journal of Financial Economics, 1 (1974a), 171198.CrossRefGoogle Scholar
Ross, S. A. Comment on “Consumption and Portfolio Choices with Transaction Costs,” by Multherjee, R. and Zabel, E., in Essays on Economic Behavior under Uncertainty. Amsterdam: North-Holland Publishing Co. (1974b).Google Scholar
Ross, S. A.How Proper are ‘Proper’ Utility Functions?” Unpubl. Manuscript, Sloan School, MIT (1998).Google Scholar
Samuelson, P.Risk and Uncertainty: A Fallacy of Large Numbers”. Scientia, 98 (1963), 108113.Google Scholar
Samuelson, P.The ‘Fallacy’ of Maximizing the Geometric Mean in Long Sequences of Investing or Gambling”. Proceedings of the National Academy of Sciences, 68 (1971), 24932496.CrossRefGoogle ScholarPubMed
Samuelson, P.Additive Insurance Via the √N Law: Domar-Musgrave to the Rescue of the Brownian Motive”. Unpubl. Manuscript, MIT (1984).Google Scholar