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An economic index of riskiness

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Author Info
Robert J. Aumann () (Hebrew University of Jerusalem)
Roberto Serrano () (Brown University and IMDEA Social Sciences)

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Abstract

Define the riskiness of a gamble as the reciprocal of the absolute risk aversion (ARA) of an individual with constant ARA who is indifferent between taking and not taking that gamble. We characterize this index by axioms, chief among them a \"duality\" axiom which, roughly speaking, asserts that less risk-averse individuals accept riskier gambles. The index is homogeneous of degree 1, monotonic with respect to first and second order stochastic dominance, and for gambles with normal distributions, is half of variance/mean. Examples are calculated, additional properties derived, and the index is compared with others in the literature.

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Publisher Info
Paper provided by Instituto Madrileño de Estudios Avanzados (IMDEA) Ciencias Sociales in its series Working Papers with number 2007-08.

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Date of creation: 28 Feb 2007
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Publication status: Published in Journal of Political Economy 116(5), October 2008: 810-836
Handle: RePEc:imd:wpaper:wp2007-08

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Related research
Keywords: riskiness; risk aversion; expected utility; decision making;

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Find related papers by JEL classification:
C00 - Mathematical and Quantitative Methods - - General - - - General
C43 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Index Numbers and Aggregation
D00 - Microeconomics - - General - - - General
D80 - Microeconomics - - Information, Knowledge, and Uncertainty - - - General
D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
E44 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Financial Markets and the Macroeconomy
G00 - Financial Economics - - General - - - General

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References listed on IDEAS
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  1. Hadar, Josef & Russell, William R, 1969. "Rules for Ordering Uncertain Prospects," American Economic Review, American Economic Association, vol. 59(1), pages 25-34, March. [Downloadable!] (restricted)
  2. Hanoch, G & Levy, Haim, 1969. "The Efficiency Analysis of Choices Involving Risk," Review of Economic Studies, Blackwell Publishing, vol. 36(107), pages 335-46, July. [Downloadable!] (restricted)
  3. Palacios-Huerta, Ignacio & Serrano, Roberto, 2006. "Rejecting small gambles under expected utility," Economics Letters, Elsevier, vol. 91(2), pages 250-259, May. [Downloadable!] (restricted)
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  4. Aumann, Robert J & Kurz, Mordecai, 1977. "Power and Taxes," Econometrica, Econometric Society, vol. 45(5), pages 1137-61, July. [Downloadable!] (restricted)
  5. Diamond, Peter A. & Stiglitz, Joseph E., 1974. "Increases in risk and in risk aversion," Journal of Economic Theory, Elsevier, vol. 8(3), pages 337-360, July. [Downloadable!] (restricted)
  6. Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September. [Downloadable!] (restricted)
  7. Tobin, James, 1969. "Comment on Borch and Feldstein," Review of Economic Studies, Blackwell Publishing, vol. 36(105), pages 13-14, January. [Downloadable!] (restricted)
  8. Matthew Rabin, 2000. "Risk Aversion and Expected-Utility Theory: A Calibration Theorem," Econometrica, Econometric Society, vol. 68(5), pages 1281-1292, September.
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