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Prospect Theory and the Law of Small Numbers in the Evaluation of Asset Prices

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  • B. Luppi

Abstract

We develop a model of one representative agent and one asset. The agent evaluates the earnings according to Prospect Theory and he does not know exactly the stochastic process generating earnings. While the earnings are generated by a random walk process, the agent considers a Markovian process, according to which firm’s earnings move between two regimes, represented by a mean-reverting process and a trend process, as in Barberis, Shleifer and Vishny (1998). We study how an agent who is loss averse evaluates the price of a stock when she takes into account the wrong stochastic process. This twofold departure from rationality determines permanent effects on stock prices, even in long run. First, the model shows that agent who evaluates the asset according to Prospect Theory consistently underestimates the asset, due to loss aversion bias. This is shown under two different assumption regarding the functional form of utility. A kinked linear utility function (as in Bernatzi and Thaler, 1985) and the o iginal and more general specification of Kahneman and Tversky (1979) are used.The model allows to explain observed phenomenon in the cross-section earnings return distribution. We solve this model and according to Barberis et all (1998), we evaluate the framework by using artificial data sets of earnings and prices simulated from the model. For plausible range of parameter values, it generates the empirical predictions of overreaction and underreaction observed in the data are explained.

Suggested Citation

  • B. Luppi, 2005. "Prospect Theory and the Law of Small Numbers in the Evaluation of Asset Prices," Working Papers 539, Dipartimento Scienze Economiche, Universita' di Bologna.
  • Handle: RePEc:bol:bodewp:539
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    References listed on IDEAS

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    1. Mehra, Rajnish & Prescott, Edward C., 1985. "The equity premium: A puzzle," Journal of Monetary Economics, Elsevier, vol. 15(2), pages 145-161, March.
    2. Kent D. Daniel, 2001. "Overconfidence, Arbitrage, and Equilibrium Asset Pricing," Journal of Finance, American Finance Association, vol. 56(3), pages 921-965, June.
    3. repec:hrv:faseco:30747159 is not listed on IDEAS
    4. Shlomo Benartzi & Richard H. Thaler, 1995. "Myopic Loss Aversion and the Equity Premium Puzzle," The Quarterly Journal of Economics, Oxford University Press, vol. 110(1), pages 73-92.
    5. Kahneman, Daniel & Tversky, Amos, 1979. "Prospect Theory: An Analysis of Decision under Risk," Econometrica, Econometric Society, vol. 47(2), pages 263-291, March.
    6. De Bondt, Werner F M & Thaler, Richard, 1985. " Does the Stock Market Overreact?," Journal of Finance, American Finance Association, vol. 40(3), pages 793-805, July.
    7. Nicholas Barberis, 2001. "Mental Accounting, Loss Aversion, and Individual Stock Returns," Journal of Finance, American Finance Association, vol. 56(4), pages 1247-1292, August.
    8. David M. Cutler & James M. Poterba & Lawrence H. Summers, 1991. "Speculative Dynamics," Review of Economic Studies, Oxford University Press, vol. 58(3), pages 529-546.
    9. Richard H. Thaler & Eric J. Johnson, 1990. "Gambling with the House Money and Trying to Break Even: The Effects of Prior Outcomes on Risky Choice," Management Science, INFORMS, vol. 36(6), pages 643-660, June.
    10. Kent Daniel & David Hirshleifer & Avanidhar Subrahmanyam, 1998. "Investor Psychology and Security Market Under- and Overreactions," Journal of Finance, American Finance Association, vol. 53(6), pages 1839-1885, December.
    11. Nicholas Barberis & Ming Huang, 2001. "Mental Accounting, Loss Aversion, and Individual Stock Returns," NBER Working Papers 8190, National Bureau of Economic Research, Inc.
    12. Nicholas Barberis & Ming Huang & Tano Santos, 2001. "Prospect Theory and Asset Prices," The Quarterly Journal of Economics, Oxford University Press, vol. 116(1), pages 1-53.
    13. Barberis, Nicholas & Shleifer, Andrei & Vishny, Robert, 1998. "A model of investor sentiment," Journal of Financial Economics, Elsevier, vol. 49(3), pages 307-343, September.
    14. Jegadeesh, Narasimhan & Titman, Sheridan, 1993. " Returns to Buying Winners and Selling Losers: Implications for Stock Market Efficiency," Journal of Finance, American Finance Association, vol. 48(1), pages 65-91, March.
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