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Optimal Illusions and Decisions under Risk

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  • Gollier, Christian

Abstract

We examine a static one-risk-free-one-risky asset portfolio choice when the investor’s well-being is affected by the anticipatory feelings associated to potential capital gains and losses. These feelings can be manipulated by the choice of subjective beliefs on the distribution of returns. However, the bias of these endogenous subjective beliefs induces the choice of a portfolio that is suboptimal with respect to the objective expected utility of final wealth. We characterize the structure of these optimal beliefs. We first show that optimal subjective beliefs must be degenerated with only two possible returns. Moreover, under some weak conditions on the utility function, these two atoms are at the lower and upper bounds of the objectively feasible returns. When the intensity of anticipatory feelings is small, the formation of beliefs must be biased in favor of optimism, which implies an increase in the equilibrium demand for the risky asset. We also show that the optimal beliefs are approximately independent of the investor’s degree of risk aversion.

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Bibliographic Info

Paper provided by Institut d'Économie Industrielle (IDEI), Toulouse in its series IDEI Working Papers with number 340.

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Date of creation: Jan 2005
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Handle: RePEc:ide:wpaper:2376

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  1. Tversky, Amos & Kahneman, Daniel, 1992. " Advances in Prospect Theory: Cumulative Representation of Uncertainty," Journal of Risk and Uncertainty, Springer, vol. 5(4), pages 297-323, October.
  2. Rothschild, Michael & Stiglitz, Joseph E., 1971. "Increasing risk II: Its economic consequences," Journal of Economic Theory, Elsevier, vol. 3(1), pages 66-84, March.
  3. Susan Athey, 2002. "Monotone Comparative Statics Under Uncertainty," The Quarterly Journal of Economics, MIT Press, vol. 117(1), pages 187-223, February.
  4. Peter C. Fishburn & R. Burr Porter, 1976. "Optimal Portfolios with One Safe and One Risky Asset: Effects of Changes in Rate of Return and Risk," Management Science, INFORMS, vol. 22(10), pages 1064-1073, June.
  5. Gollier Christian, 1995. "The Comparative Statics of Changes in Risk Revisited," Journal of Economic Theory, Elsevier, vol. 66(2), pages 522-535, August.
  6. Edward L. Glaeser, 2004. "Psychology and the Market," American Economic Review, American Economic Association, vol. 94(2), pages 408-413, May.
  7. Guiso, Luigi & Jappelli, Tullio & Terlizzese, Daniele, 1996. "Income Risk, Borrowing Constraints, and Portfolio Choice," American Economic Review, American Economic Association, vol. 86(1), pages 158-72, March.
  8. Andrew B. Abel, 2001. "An exploration of the effects of pessimism and doubt on asset returns," Working Papers 01-1, Federal Reserve Bank of Philadelphia.
  9. Gollier, C. & Kimball, M.S., 1996. "New Methods in the Classical Economics of Uncertainty: Comparing Risks," Papers 96.412, Toulouse - GREMAQ.
  10. Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323-343, December.
  11. Athey, Susan, 2002. "Monotone Comparative Statics Under Uncertainty," Scholarly Articles 3372263, Harvard University Department of Economics.
  12. Tversky, Amos & Wakker, Peter, 1995. "Risk Attitudes and Decision Weights," Econometrica, Econometric Society, vol. 63(6), pages 1255-80, November.
  13. Andrew Caplin & John Leahy, 2001. "Psychological Expected Utility Theory And Anticipatory Feelings," The Quarterly Journal of Economics, MIT Press, vol. 116(1), pages 55-79, February.
  14. Eeckhoudt, Louis & Gollier, Christian, 1995. "Demand for Risky Assets and the Monotone Probability Ratio Order," Journal of Risk and Uncertainty, Springer, vol. 11(2), pages 113-22, September.
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Cited by:
  1. Brunnermeier, Markus K & Gollier, Christian & Parker, Jonathan A, 2007. "Optimal Beliefs, Asset Prices and the Preference for Skewed Returns," CEPR Discussion Papers 6181, C.E.P.R. Discussion Papers.
  2. Iwaki, Hideki & Osaki, Yusuke, 2010. "Some properties of subjective probabilities induced by optimal expectations," Finance Research Letters, Elsevier, vol. 7(2), pages 98-102, June.
  3. Alem, Yonas & Colmer, Jonathan, 2013. "Optimal Expectations and the Welfare Cost of Climate Variability," Working Papers in Economics 578, University of Gothenburg, Department of Economics.
  4. GOLLIER Christian & MUERMANN Alexander, 2006. "Optimal choice and beliefs with ex ante savoring ex post disappointment," LERNA Working Papers 06.18.211, LERNA, University of Toulouse.
  5. Patrick Roger & Marie-Hélène Broihanne & Maxime Merli, 2012. "In search of positive skewness: the case of individual investors," Working Papers of LaRGE Research Center 2012-04, Laboratoire de Recherche en Gestion et Economie (LaRGE), Université de Strasbourg (France).

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