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Optimal Illusions and Decisions under Risk

Author

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  • Christian Gollier
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.

Suggested Citation

  • Christian Gollier, 2005. "Optimal Illusions and Decisions under Risk," CESifo Working Paper Series 1382, CESifo.
    • Handle: RePEc:ces:ceswps:_1382
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    References listed on IDEAS

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    Cited by:

    1. Raphaël Giraud & Jean-Marc Tallon, 2011. "Are beliefs a matter of taste? A case for objective imprecise information," Theory and Decision, Springer, vol. 71(1), pages 23-31, July.
    2. Markus K. Brunnermeier & Jonathan A. Parker & Christian Gollier, 2007. "Optimal Beliefs, Asset Prices, and the Preference for Skewed Returns," American Economic Review, American Economic Association, vol. 97(2), pages 159-165, May.
    3. repec:hal:journl:halshs-00442869 is not listed on IDEAS
    4. Marie-Hélène Broihanne & Maxime Merli & Patrick Roger, 2016. "Diversification, gambling and market forces," Review of Quantitative Finance and Accounting, Springer, vol. 47(1), pages 129-157, July.
    5. Markus K. Brunnermeier & Jonathan A. Parker, 2005. "Optimal Expectations," American Economic Review, American Economic Association, vol. 95(4), pages 1092-1118, September.
    6. 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.
    7. Christian Gollier & Alexander Muermann, 2010. "Optimal Choice and Beliefs with Ex Ante Savoring and Ex Post Disappointment," Management Science, INFORMS, vol. 56(8), pages 1272-1284, August.
    8. 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.
    9. 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.
    10. D’Hondt, Catherine & McGowan, Richard & Roger, Patrick, 2021. "Trading leveraged Exchange-Traded products is hazardous to your wealth," The Quarterly Review of Economics and Finance, Elsevier, vol. 80(C), pages 287-302.
    11. Ajay Singh Behl, 2010. "Children and labour supply," Applied Economics Letters, Taylor & Francis Journals, vol. 17(3), pages 251-255, February.
    12. M. Trojanowska & P. M. Kort, 2010. "The Worst Case for Real Options," Journal of Optimization Theory and Applications, Springer, vol. 146(3), pages 709-734, September.
    13. 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.

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    Keywords

    anticipatory feelings; portfolio choice; overconfidence; positive thinking; endogenous beliefs;
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