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Fractional-moment CAPM with loss aversion

Author

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  • Wu, Yahao
  • Wang, Xiao-Tian
  • Wu, Min

Abstract

In this paper, we present a new fractional-order value function which generalizes the value function of Kahneman and Tversky [Kahneman D, Tversky A. Prospect theory: an analysis of decision under risk. Econometrica 1979;47:263–91; Tversky A, Kahneman D. Advances in prospect theory: cumulative representation of uncertainty. J. Risk Uncertainty 1992;4:297–323], and give the corresponding fractional-moment versions of CAPM in the cases of both the prospect theory [Kahneman D, Tversky A. Prospect theory: an analysis of decision under risk. Econometrica 1979;47:263–91; Tversky A, Kahneman D. Advances in prospect theory: cumulative representation of uncertainty. J. Risk Uncertainty 1992;4:297–323] and the expected utility model. The models that we obtain can be used to price assets when asset return distributions are likely to be asymmetric stable Levy distribution during panics and stampedes in worldwide security markets in 2008. In particular, from the prospect theory we get the following fractional-moment CAPM with loss aversion:E(Ri-R0)=E[(W-W0)+-0.12(Ri-R0)]+2.25E[(W0-W)+-0.12(Ri-R0)]E[(W-W0)+-0.12(W-R0)]+2.25E[(W0-W)+-0.12(W-R0)]·E(W-R0),

Suggested Citation

  • Wu, Yahao & Wang, Xiao-Tian & Wu, Min, 2009. "Fractional-moment CAPM with loss aversion," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1406-1414.
    • Handle: RePEc:eee:chsofr:v:42:y:2009:i:3:p:1406-1414
    DOI: 10.1016/j.chaos.2009.03.060
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    References listed on IDEAS

    as
    1. El Naschie, M.S., 2007. "The Fibonacci code behind super strings and P-Branes. An answer to M. Kaku’s fundamental question," Chaos, Solitons & Fractals, Elsevier, vol. 31(3), pages 537-547.
    2. 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.
    3. Arjan B. Berkelaar & Roy Kouwenberg & Thierry Post, 2004. "Optimal Portfolio Choice under Loss Aversion," The Review of Economics and Statistics, MIT Press, vol. 86(4), pages 973-987, November.
    4. El Naschie, M. Saladin, 2006. "Intermediate prerequisites for E-infinity theory (Further recommended reading in nonlinear dynamics and mathematical physics)," Chaos, Solitons & Fractals, Elsevier, vol. 30(3), pages 622-628.
    5. El Naschie, M.S., 2006. "Elementary prerequisites for E-infinity," Chaos, Solitons & Fractals, Elsevier, vol. 30(3), pages 579-605.
    6. Haim Levy, 2006. "Capital Asset Prices with Heterogeneous Beliefs," The Journal of Business, University of Chicago Press, vol. 79(3), pages 1317-1354, May.
    7. Daniel Kahneman & Amos Tversky, 2013. "Prospect Theory: An Analysis of Decision Under Risk," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 6, pages 99-127, World Scientific Publishing Co. Pte. Ltd..
    8. Grüne, Lars & Semmler, Willi, 2008. "Asset pricing with loss aversion," Journal of Economic Dynamics and Control, Elsevier, vol. 32(10), pages 3253-3274, October.
    9. Levy, Moshe & Solomon, Sorin, 1997. "New evidence for the power-law distribution of wealth," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 242(1), pages 90-94.
    10. Jumarie, Guy, 2009. "From Lagrangian mechanics fractal in space to space fractal Schrödinger’s equation via fractional Taylor’s series," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 1590-1604.
    11. Benoit Mandelbrot, 1963. "New Methods in Statistical Economics," Journal of Political Economy, University of Chicago Press, vol. 71, pages 421-421.
    12. William F. Sharpe, 1964. "Capital Asset Prices: A Theory Of Market Equilibrium Under Conditions Of Risk," Journal of Finance, American Finance Association, vol. 19(3), pages 425-442, September.
    13. Francisco J. Gomes, 2005. "Portfolio Choice and Trading Volume with Loss-Averse Investors," The Journal of Business, University of Chicago Press, vol. 78(2), pages 675-706, March.
    14. El Naschie, M.S., 2005. "On Penrose view of transfinite sets and computability and the fractal character of E-infinity spacetime," Chaos, Solitons & Fractals, Elsevier, vol. 25(3), pages 531-533.
    15. Cass, David & Stiglitz, Joseph E., 1970. "The structure of investor preferences and asset returns, and separability in portfolio allocation: A contribution to the pure theory of mutual funds," Journal of Economic Theory, Elsevier, vol. 2(2), pages 122-160, June.
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