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Continuous Cumulative Prospect Theory and Individual Asset Allocation

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  • Davies, G.B.
  • Satchell, S.E.
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    Abstract

    We implement the Cumulative Prospect Theory (CPT) framework (Tversky and Kahneman 1992) into a model of individual asset allocation, building on earlier work by Hwang and Satchell (2003) where they derive explicit formulae for the asset allocation decision using a loss aversion utility function. We apply Prelec’s probability weighting function (1998) to continuous distributions and derive the formulae for the optimal asset allocation between risky and safe assets. US equity returns data are used to examine the feasible parameter space. The earlier results of Hwang and Satchell are confirmed and the more complex model is compatible with observed equity proportions. The parameters are highly interconnected, but feasible combinations indicate that more inverse-S shaped deviations from linear probability weightings are associated with lower risk taking behaviour.

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    File URL: http://www.econ.cam.ac.uk/research/repec/cam/pdf/cwpe0467.pdf
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    Bibliographic Info

    Paper provided by Faculty of Economics, University of Cambridge in its series Cambridge Working Papers in Economics with number 0467.

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    Length: 54
    Date of creation: Nov 2004
    Date of revision:
    Handle: RePEc:cam:camdae:0467

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    Web page: http://www.econ.cam.ac.uk/index.htm

    Related research

    Keywords: Cumulative Prospect Theory; asset allocation; non-linear decisions weights;

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    References

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    1. J. L. Knight & S. E. Satchell & K. C. Tran, 1995. "Statistical modelling of asymmetric risk in asset returns," Applied Mathematical Finance, Taylor & Francis Journals, vol. 2(3), pages 155-172.
    2. Friend, Irwin & Blume, Marshall E, 1975. "The Demand for Risky Assets," American Economic Review, American Economic Association, vol. 65(5), pages 900-922, December.
    3. Chip Heath & Steven Huddart & Mark Lang, 1999. "Psychological Factors And Stock Option Exercise," The Quarterly Journal of Economics, MIT Press, vol. 114(2), pages 601-627, May.
    4. 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.
    5. Tversky, Amos & Kahneman, Daniel, 1991. "Loss Aversion in Riskless Choice: A Reference-Dependent Model," The Quarterly Journal of Economics, MIT Press, vol. 106(4), pages 1039-61, November.
    6. Daniel Kahneman & Jack L. Knetsch & Richard H. Thaler, 1991. "Anomalies: The Endowment Effect, Loss Aversion, and Status Quo Bias," Journal of Economic Perspectives, American Economic Association, vol. 5(1), pages 193-206, Winter.
    7. Nicholas Barberis & Ming Huang & Tano Santos, 2001. "Prospect Theory And Asset Prices," The Quarterly Journal of Economics, MIT Press, vol. 116(1), pages 1-53, February.
    8. Richard H. Thaler & Shlomo Benartzi, 2001. "Naive Diversification Strategies in Defined Contribution Saving Plans," American Economic Review, American Economic Association, vol. 91(1), pages 79-98, March.
    9. Y. Malevergne & D. Sornette, 2001. "General framework for a portfolio theory with non-Gaussian risks and non-linear correlations," Papers cond-mat/0103020, arXiv.org.
    10. Han Bleichrodt & Jose Luis Pinto, 2000. "A Parameter-Free Elicitation of the Probability Weighting Function in Medical Decision Analysis," Management Science, INFORMS, vol. 46(11), pages 1485-1496, November.
    11. Amos Tversky & Daniel Kahneman, 1979. "Prospect Theory: An Analysis of Decision under Risk," Levine's Working Paper Archive 7656, David K. Levine.
    12. Drazen Prelec, 1998. "The Probability Weighting Function," Econometrica, Econometric Society, vol. 66(3), pages 497-528, May.
    13. Tversky, Amos & Wakker, Peter, 1995. "Risk Attitudes and Decision Weights," Econometrica, Econometric Society, vol. 63(6), pages 1255-80, November.
    14. Benartzi, Shlomo & Thaler, Richard H, 1995. "Myopic Loss Aversion and the Equity Premium Puzzle," The Quarterly Journal of Economics, MIT Press, vol. 110(1), pages 73-92, February.
    15. Fennema, Hein & van Assen, Marcel, 1998. "Measuring the Utility of Losses by Means of the Tradeoff Method," Journal of Risk and Uncertainty, Springer, vol. 17(3), pages 277-95, December.
    16. Charles A. Holt & Susan K. Laury, 2002. "Risk Aversion and Incentive Effects," American Economic Review, American Economic Association, vol. 92(5), pages 1644-1655, December.
    17. Camerer, Colin F & Ho, Teck-Hua, 1994. "Violations of the Betweenness Axiom and Nonlinearity in Probability," Journal of Risk and Uncertainty, Springer, vol. 8(2), pages 167-96, March.
    18. Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323-343, December.
    19. Craig R. Fox & Amos Tversky, 1998. "A Belief-Based Account of Decision Under Uncertainty," Management Science, INFORMS, vol. 44(7), pages 879-895, July.
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    Cited by:
    1. Connors, Richard D. & Sumalee, Agachai, 2009. "A network equilibrium model with travellers' perception of stochastic travel times," Transportation Research Part B: Methodological, Elsevier, vol. 43(6), pages 614-624, July.
    2. Ulrich Schmidt & Chris Starmer & Robert Sugden, 2008. "Third-generation prospect theory," Journal of Risk and Uncertainty, Springer, vol. 36(3), pages 203-223, June.

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