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Optimal Illusions and Decisions under Risk

  • Christian Gollier

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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Paper provided by CESifo Group Munich in its series CESifo Working Paper Series with number 1382.

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Date of creation: 2005
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Handle: RePEc:ces:ceswps:_1382
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  1. Rothschild, Michael & Stiglitz, Joseph E., 1971. "Increasing risk II: Its economic consequences," Journal of Economic Theory, Elsevier, vol. 3(1), pages 66-84, March.
  2. Andrew B. Abel, 2001. "An Exploration of the Effects of Pessimism and Doubt on Asset Returns," NBER Working Papers 8132, National Bureau of Economic Research, Inc.
  3. 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.
  4. Susan Athey, 2002. "Monotone Comparative Statics Under Uncertainty," The Quarterly Journal of Economics, MIT Press, vol. 117(1), pages 187-223, February.
  5. Athey, Susan, 2002. "Monotone Comparative Statics Under Uncertainty," Scholarly Articles 3372263, Harvard University Department of Economics.
  6. 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.
  7. 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.
  8. 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.
  9. 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.
  10. Gollier Christian, 1995. "The Comparative Statics of Changes in Risk Revisited," Journal of Economic Theory, Elsevier, vol. 66(2), pages 522-535, August.
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