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Downside risk aversion vs decreasing absolute risk aversion: an intuitive exposition

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  • James K. Hammitt

    (Harvard University (Center for Risk Analysis)
    Toulouse School of Economics (University of Toulouse Capitole))

Abstract

Downside risk aversion (downside RA) and decreasing absolute risk aversion (DARA) are different concepts that describe preferences for which the harm from bearing risk is lessened by an increase in wealth. This note presents some intuitive explanations of the difference between the two concepts using simple lotteries and graphical analysis. All risk-averse utility functions exhibit downside risk aversion, except those that exhibit sufficiently strong increasing absolute risk aversion. In a sense, downside RA is to be expected: adding downside risk to a baseline lottery is analogous to increasing risk while adding upside risk is analogous to decreasing risk. The difference between the two concepts can be attributed to the use of different measures of the harm from risk bearing: downside RA measures harm using the utility premium and DARA measures harm using the risk premium. The two premia can change at different rates and even in different directions as wealth increases.

Suggested Citation

  • James K. Hammitt, 2023. "Downside risk aversion vs decreasing absolute risk aversion: an intuitive exposition," Theory and Decision, Springer, vol. 95(1), pages 1-10, July.
    • Handle: RePEc:kap:theord:v:95:y:2023:i:1:d:10.1007_s11238-022-09911-x
    DOI: 10.1007/s11238-022-09911-x
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    References listed on IDEAS

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    1. Louis Eeckhoudt & Harris Schlesinger, 2006. "Putting Risk in Its Proper Place," American Economic Review, American Economic Association, vol. 96(1), pages 280-289, March.
    2. Menegatti, Mario, 2001. "On the Conditions for Precautionary Saving," Journal of Economic Theory, Elsevier, vol. 98(1), pages 189-193, May.
    3. Menezes, C & Geiss, C & Tressler, J, 1980. "Increasing Downside Risk," American Economic Review, American Economic Association, vol. 70(5), pages 921-932, December.
    4. Kimball, Miles S, 1990. "Precautionary Saving in the Small and in the Large," Econometrica, Econometric Society, vol. 58(1), pages 53-73, January.
    5. Gollier, Christian, 2021. "A general theory of risk apportionment," Journal of Economic Theory, Elsevier, vol. 192(C).
    6. Paan Jindapon & Liqun Liu & William S. Neilson, 2021. "Comparative risk apportionment," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 9(1), pages 91-112, April.
    7. Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September.
    8. Milton Friedman & L. J. Savage, 1948. "The Utility Analysis of Choices Involving Risk," Journal of Political Economy, University of Chicago Press, vol. 56, pages 279-279.
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