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Asset price bubbles from heterogeneous beliefs about mean reversion rates

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  • Xi Chen
  • Robert Kohn

Abstract

Harrison and Kreps showed in 1978 how the heterogeneity of investor beliefs can drive speculation, leading the price of an asset to exceed its intrinsic value. By focusing on an extremely simple market model—a finite-state Markov chain—the analysis of Harrison and Kreps achieved great clarity but limited realism. Here we achieve similar clarity with greater realism, by considering an asset whose dividend rate is a mean-reverting stochastic process. Our investors agree on the volatility, but have different beliefs about the mean reversion rate. We determine the minimum equilibrium price explicitly; in addition, we characterize it as the unique classical solution of a certain linear differential equation. Our example shows, in a simple and transparent manner, how heterogeneous beliefs about the mean reversion rate can lead to everlasting speculation and a permanent “price bubble.” Copyright Springer-Verlag 2011

Suggested Citation

  • Xi Chen & Robert Kohn, 2011. "Asset price bubbles from heterogeneous beliefs about mean reversion rates," Finance and Stochastics, Springer, vol. 15(2), pages 221-241, June.
    • Handle: RePEc:spr:finsto:v:15:y:2011:i:2:p:221-241
    DOI: 10.1007/s00780-010-0124-x
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    References listed on IDEAS

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    1. Jose A. Scheinkman & Wei Xiong, 2003. "Overconfidence and Speculative Bubbles," Journal of Political Economy, University of Chicago Press, vol. 111(6), pages 1183-1219, December.
    2. De Long, J Bradford & Shleifer, Andrei & Summers, Lawrence H & Waldmann, Robert J, 1991. "The Survival of Noise Traders in Financial Markets," The Journal of Business, University of Chicago Press, vol. 64(1), pages 1-19, January.
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    4. Hongjun Yan, 2008. "Natural Selection in Financial Markets: Does It Work?," Management Science, INFORMS, vol. 54(11), pages 1935-1950, November.
    5. Bernard Dumas & Alexander Kurshev & Raman Uppal, 2009. "Equilibrium Portfolio Strategies in the Presence of Sentiment Risk and Excess Volatility," Journal of Finance, American Finance Association, vol. 64(2), pages 579-629, April.
    6. Hongjun Yan, 2008. "Natural Selection in Financial Markets: Does It Work?," Management Science, INFORMS, vol. 54(11), pages 1935-1950, November.
    7. Radner, Roy, 1972. "Existence of Equilibrium of Plans, Prices, and Price Expectations in a Sequence of Markets," Econometrica, Econometric Society, vol. 40(2), pages 289-303, March.
    8. J. Michael Harrison & David M. Kreps, 1978. "Speculative Investor Behavior in a Stock Market with Heterogeneous Expectations," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 92(2), pages 323-336.
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    Cited by:

    1. Robert A. Jarrow, 2015. "Asset Price Bubbles," Annual Review of Financial Economics, Annual Reviews, vol. 7(1), pages 201-218, December.
    2. Carl Chen & Peter Lung & F. Wang, 2013. "Where are the sources of stock market mispricing and excess volatility?," Review of Quantitative Finance and Accounting, Springer, vol. 41(4), pages 631-650, November.
    3. Seunghyun Lee & Hyungbin Park, 2020. "Conditions for bubbles to arise under heterogeneous beliefs," Papers 2012.13753, arXiv.org, revised Oct 2021.

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    More about this item

    Keywords

    Asset price bubble; Heterogeneous beliefs; Minimal equilibrium price; 60H10; 91B50; G12; C73;
    All these keywords.

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

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