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An Economic Index of Riskiness

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  • Robert J. Aumann
  • Roberto Serrano

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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Paper provided by UCLA Department of Economics in its series Levine's Bibliography with number 321307000000000585.

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Date of creation: 09 Nov 2006
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Handle: RePEc:cla:levrem:321307000000000585

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  1. Rabin, Matthew, 2000. "Risk Aversion and Expected-Utility Theory: A Calibration Theorem," Department of Economics, Working Paper Series qt731230f8, Department of Economics, Institute for Business and Economic Research, UC Berkeley.
  2. Ignacio Palacios-Huerta & Roberto Serrano & Oscar Volij, 2003. "Rejecting Small Gambles Under Expected Utility," Economics Working Papers 0032, Institute for Advanced Study, School of Social Science.
  3. Aumann, Robert J & Kurz, Mordecai, 1977. "Power and Taxes," Econometrica, Econometric Society, vol. 45(5), pages 1137-61, July.
  4. Levy, Haim & Hanoch, Giora, 1970. "Relative Effectiveness of Efficiency Criteria for Portfolio Selection," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 5(01), pages 63-76, March.
  5. Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September.
  6. Hanoch, G & Levy, Haim, 1969. "The Efficiency Analysis of Choices Involving Risk," Review of Economic Studies, Wiley Blackwell, vol. 36(107), pages 335-46, July.
  7. Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228.
  8. Fishburn, Peter C, 1977. "Mean-Risk Analysis with Risk Associated with Below-Target Returns," American Economic Review, American Economic Association, vol. 67(2), pages 116-26, March.
  9. Peter C. Fishburn, 1984. "Foundations of Risk Measurement. I. Risk As Probable Loss," Management Science, INFORMS, vol. 30(4), pages 396-406, April.
  10. Hadar, Josef & Russell, William R, 1969. "Rules for Ordering Uncertain Prospects," American Economic Review, American Economic Association, vol. 59(1), pages 25-34, March.
  11. Tobin, James, 1969. "Comment on Borch and Feldstein," Review of Economic Studies, Wiley Blackwell, vol. 36(105), pages 13-14, January.
  12. 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.
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