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An Economic Index Of Riskiness

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Author Info
Roberto Serrano ()
Robert J. Aumann () (CEMFI, Centro de Estudios Monetarios y Financieros)

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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 positively homogeneous, continuous, and subadditive, respects first and second order stochastic dominance, and for normally distributed gambles, is half of variance/mean. Examples are calculated, additional properties derived, and the index is compared with others.

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Publisher Info
Paper provided by CEMFI in its series Working Papers with number wp2007_0706.

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Date of creation: Jun 2007
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Handle: RePEc:cmf:wpaper:wp2007_0706

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Related research
Keywords: Riskiness risk aversion expected utility decision making under uncertainty portfolio choice Sharpe ratio value at risk coherent measures of risk.

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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

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. Aumann, Robert J & Kurz, Mordecai, 1977. "Power and Taxes," Econometrica, Econometric Society, vol. 45(5), pages 1137-61, July. [Downloadable!] (restricted)
  3. 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)
  4. 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)
  5. 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)
  6. Tobin, James, 1969. "Comment on Borch and Feldstein," Review of Economic Studies, Blackwell Publishing, vol. 36(105), pages 13-14, January. [Downloadable!] (restricted)
  7. 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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  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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