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Towards a Purely Behavioral Definition of Loss Aversion

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  • Ghossoub, Mario

Abstract

This paper suggests a behavioral, preference-based definition of loss aversion for decision under risk. This definition is based on the initial intuition of Markowitz [30] and Kahneman and Tversky [19] that most individuals dislike symmetric bets, and that the aversion to such bets increases with the size of the stake. A natural interpretation of this intuition leads to defining loss aversion as a particular kind of risk aversion. The notions of weak loss aversion and strong loss aversion are introduced, by analogy to the notions of weak and strong risk aversion. I then show how the proposed definitions naturally extend those of Kahneman and Tversky [19], Schmidt and Zank [48], and Zank [54]. The implications of these definitions under Cumulative Prospect Theory (PT) and Expected-Utility Theory (EUT) are examined. In particular, I show that in EUT loss aversion is not equivalent to the utility function having an S shape: loss aversion in EUT holds for a class of utility functions that includes S-shaped functions, but is strictly larger than the collection of these functions. This class also includes utility functions that are of the Friedman-Savage [14] type over both gains and losses, and utility functions such as the one postulated by Markowitz [30]. Finally, I discuss possible ways in which one can define an index of loss aversion for preferences that satisfy certain conditions. These conditions are satisfied by preferences having a PT-representation or an EUT-representation. Under PT, the proposed index is shown to coincide with Kobberling and Wakker’s [22] index of loss aversion only when the probability weights for gains and losses are equal. In Appendix B, I consider some extensions of the study done in this paper, one of which is an extension to situations of decision under uncertainty with probabilistically sophisticated preferences, in the sense of Machina and Schmeidler [27].

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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 37628.

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Date of creation: 11 Aug 2011
Date of revision: 23 Mar 2012
Handle: RePEc:pra:mprapa:37628

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Keywords: Loss Aversion; Risk Aversion; Mean-Preserving Increase in Risk; Prospect Theory; Probability Weights; S-Shaped Utility;

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  1. Wakker, Peter & Tversky, Amos, 1993. " An Axiomatization of Cumulative Prospect Theory," Journal of Risk and Uncertainty, Springer, Springer, vol. 7(2), pages 147-75, October.
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  4. Kahneman, Daniel & Tversky, Amos, 1979. "Prospect Theory: An Analysis of Decision under Risk," Econometrica, Econometric Society, Econometric Society, vol. 47(2), pages 263-91, March.
  5. Benartzi, Shlomo & Thaler, Richard H, 1995. "Myopic Loss Aversion and the Equity Premium Puzzle," The Quarterly Journal of Economics, MIT Press, MIT Press, vol. 110(1), pages 73-92, February.
  6. Mehra, Rajnish & Prescott, Edward C., 1985. "The equity premium: A puzzle," Journal of Monetary Economics, Elsevier, Elsevier, vol. 15(2), pages 145-161, March.
  7. Koszegi, Botond & Rabin, Matthew, 2004. "A Model of Reference-Dependent Preferences," Department of Economics, Working Paper Series, Department of Economics, Institute for Business and Economic Research, UC Berkeley qt0w82b6nm, Department of Economics, Institute for Business and Economic Research, UC Berkeley.
  8. Botond Koszegi & Matthew Rabin, 2006. "Reference-Dependent Risk Attitudes," Levine's Bibliography 122247000000001267, UCLA Department of Economics.
  9. Kobberling, Veronika & Wakker, Peter P., 2005. "An index of loss aversion," Journal of Economic Theory, Elsevier, Elsevier, vol. 122(1), pages 119-131, May.
  10. Milton Friedman & L. J. Savage, 1948. "The Utility Analysis of Choices Involving Risk," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 56, pages 279.
  11. Machina Mark J. & Schmeidler David, 1995. "Bayes without Bernoulli: Simple Conditions for Probabilistically Sophisticated Choice," Journal of Economic Theory, Elsevier, Elsevier, vol. 67(1), pages 106-128, October.
  12. Dana, Rose-Anne & Carlier, Guillaume, 2011. "Optimal Demand for Contingent Claims when Agents have law Invariant Utilities," Economics Papers from University Paris Dauphine, Paris Dauphine University 123456789/2317, Paris Dauphine University.
  13. Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, Elsevier, vol. 2(3), pages 225-243, September.
  14. Xue Dong He & Xun Yu Zhou, 2011. "Portfolio Choice Under Cumulative Prospect Theory: An Analytical Treatment," Management Science, INFORMS, INFORMS, vol. 57(2), pages 315-331, February.
  15. Frederick Mosteller & Philip Nogee, 1951. "An Experimental Measurement of Utility," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 59, pages 371.
  16. Nicholas Barberis & Ming Huang & Tano Santos, 2001. "Prospect Theory And Asset Prices," The Quarterly Journal of Economics, MIT Press, MIT Press, vol. 116(1), pages 1-53, February.
  17. Neilson, William S, 2002. " Comparative Risk Sensitivity with Reference-Dependent Preferences," Journal of Risk and Uncertainty, Springer, Springer, vol. 24(2), pages 131-42, March.
  18. Machina,Mark & Schmeidler,David, 1991. "A more robust definition of subjective probability," Discussion Paper Serie A, University of Bonn, Germany 365, University of Bonn, Germany.
  19. Knetsch, Jack L & Sinden, J A, 1984. "Willingness to Pay and Compensation Demanded: Experimental Evidence of an Unexpected Disparity in Measures of Value," The Quarterly Journal of Economics, MIT Press, MIT Press, vol. 99(3), pages 507-21, August.
  20. Pavlo Blavatskyy, 2011. "Loss aversion," Economic Theory, Springer, Springer, vol. 46(1), pages 127-148, January.
  21. Bowman, David & Minehart, Deborah & Rabin, Matthew, 1999. "Loss aversion in a consumption-savings model," Journal of Economic Behavior & Organization, Elsevier, Elsevier, vol. 38(2), pages 155-178, February.
  22. Hadar, Josef & Russell, William R, 1969. "Rules for Ordering Uncertain Prospects," American Economic Review, American Economic Association, American Economic Association, vol. 59(1), pages 25-34, March.
  23. Botond Koszegi & Matthew Rabin, 2009. "Reference-Dependent Consumption Plans," American Economic Review, American Economic Association, American Economic Association, vol. 99(3), pages 909-36, June.
  24. Ortoleva, Pietro, 2008. "Status Quo Bias, Multiple Priors and Uncertainty Aversion," MPRA Paper 12243, University Library of Munich, Germany.
  25. Harry Markowitz, 1952. "The Utility of Wealth," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 60, pages 151.
  26. Ulrich Schmidt & Horst Zank, 2005. "What is Loss Aversion?," Journal of Risk and Uncertainty, Springer, Springer, vol. 30(2), pages 157-167, January.
  27. Bernard, Carole & Ghossoub, Mario, 2009. "Static Portfolio Choice under Cumulative Prospect Theory," MPRA Paper 15446, University Library of Munich, Germany.
  28. Samuelson, William & Zeckhauser, Richard, 1988. " Status Quo Bias in Decision Making," Journal of Risk and Uncertainty, Springer, Springer, vol. 1(1), pages 7-59, March.
  29. Tversky, Amos & Kahneman, Daniel, 1992. " Advances in Prospect Theory: Cumulative Representation of Uncertainty," Journal of Risk and Uncertainty, Springer, Springer, vol. 5(4), pages 297-323, October.
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