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Learning about Risk and Return: A Simple Model of Bubbles and Crashes

  • Wiliam Branch

    (University of Californis - Irvine)

  • George W. Evans


    (University of Oregon Economics Department)

This paper demonstrates that an asset pricing model with least-squares learning can lead to bubbles and crashes as endogenous responses to the fundamentals driving asset prices. When agents are risk-averse they generate forecasts of the conditional variance of a stock's return. Recursive updating of the conditional variance and expected return implies two mechanisms through which learning impacts stock prices: occasional shocks may lead agents to lower their risk estimate and increase their expected return, thereby triggering a bubble; along a bubble path recursive estimates of risk will increase and crash the bubble.

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Paper provided by University of Oregon Economics Department in its series University of Oregon Economics Department Working Papers with number 2008-1.

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Handle: RePEc:ore:uoecwp:2008-1
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  1. Evans, George W, 1991. "Pitfalls in Testing for Explosive Bubbles in Asset Prices," American Economic Review, American Economic Association, vol. 81(4), pages 922-30, September.
  2. Thomas Sargent & Noah Williams & Tao Zha, 2006. "The conquest of South American inflation," FRB Atlanta Working Paper No. 2006-20, Federal Reserve Bank of Atlanta.
  3. Marcet, A. & Nicolini, J.P., 1997. "Recurrent Hyperinflations and Learning," Papers 9721, Centro de Estudios Monetarios Y Financieros-.
  4. Jonathan Lewellen & Jay Shanken, 2002. "Learning, Asset-Pricing Tests, and Market Efficiency," Journal of Finance, American Finance Association, vol. 57(3), pages 1113-1145, 06.
  5. Eli Ofek & Matthew Richardson, 2003. "DotCom Mania: The Rise and Fall of Internet Stock Prices," Journal of Finance, American Finance Association, vol. 58(3), pages 1113-1138, 06.
  6. Wiliam Branch & George W. Evans, 2005. "A Simple Recursive Forecasting Model," University of Oregon Economics Department Working Papers 2005-3, University of Oregon Economics Department, revised 01 Feb 2005.
  7. Manuel S. Santos & Michael Woodford, 1997. "Rational Asset Pricing Bubbles," Econometrica, Econometric Society, vol. 65(1), pages 19-58, January.
  8. Eva Carceles-Poveda & Chryssi Giannitsarou, 2008. "Asset Pricing with Adaptive Learning," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 11(3), pages 629-651, July.
  9. Kenneth D. West, 1986. "A Specification Test for Speculative Bubbles," NBER Working Papers 2067, National Bureau of Economic Research, Inc.
  10. Grandmont, Jean-Michel, 1994. "Expectations formation and stability of large socioeconomic systems," CEPREMAP Working Papers (Couverture Orange) 9424, CEPREMAP.
  11. Volker Böhm & Carl Chiarella, 2005. "Mean Variance Preferences, Expectations Formation, And The Dynamics Of Random Asset Prices," Mathematical Finance, Wiley Blackwell, vol. 15(1), pages 61-97.
  12. De Long, J Bradford & Andrei Shleifer & Lawrence H. Summers & Robert J. Waldmann, 1990. "Noise Trader Risk in Financial Markets," Journal of Political Economy, University of Chicago Press, vol. 98(4), pages 703-38, August.
  13. Marcet, Albert & Sargent, Thomas J., 1989. "Convergence of least squares learning mechanisms in self-referential linear stochastic models," Journal of Economic Theory, Elsevier, vol. 48(2), pages 337-368, August.
  14. Kenneth A. Froot & Maurice Obstfeld, 1989. "Intrinsic Bubbles: The Case of Stock Prices," NBER Working Papers 3091, National Bureau of Economic Research, Inc.
  15. Geweke, John, 2001. "A note on some limitations of CRRA utility," Economics Letters, Elsevier, vol. 71(3), pages 341-345, June.
  16. Harrison Hong & Jose Scheinkman & Wei Xiong, 2005. "Asset Float and Speculative Bubbles," NBER Working Papers 11367, National Bureau of Economic Research, Inc.
  17. Bruce McGough, 2006. "Shocking Escapes," Economic Journal, Royal Economic Society, vol. 116(511), pages 507-528, 04.
  18. Allen F. & Morris S. & Postlewaite A., 1993. "Finite Bubbles with Short Sale Constraints and Asymmetric Information," Journal of Economic Theory, Elsevier, vol. 61(2), pages 206-229, December.
  19. Cho, In-Koo & Sargent, Thomas J., 2000. "Escaping Nash inflation," Working Paper Series 0023, European Central Bank.
  20. Cho, In-Koo & Kasa, Kenneth, 2008. "Learning Dynamics And Endogenous Currency Crises," Macroeconomic Dynamics, Cambridge University Press, vol. 12(02), pages 257-285, April.
  21. Harrison Hong & Jose A. Scheinkman & Wei Xiong, 2007. "Advisors and Asset Prices: A Model of the Origins of Bubbles," NBER Working Papers 13504, National Bureau of Economic Research, Inc.
  22. Blanchard, Olivier Jean, 1979. "Speculative bubbles, crashes and rational expectations," Economics Letters, Elsevier, vol. 3(4), pages 387-389.
  23. Evans, George W & Honkapohja, Seppo, 1998. "Economic Dynamics with Learning: New Stability Results," Review of Economic Studies, Wiley Blackwell, vol. 65(1), pages 23-44, January.
  24. Klaus Adam & Albert Marcet & Juan Pablo Nicolini, 2006. "Learning and Stock Market Volatility," Computing in Economics and Finance 2006 15, Society for Computational Economics.
  25. Timmermann, Allan, 1994. "Can Agents Learn to Form Rational Expectations? Some Results on Convergence and Stability of Learning in the UK Stock Market," Economic Journal, Royal Economic Society, vol. 104(425), pages 777-97, July.
  26. Robert C. Merton, 1980. "On Estimating the Expected Return on the Market: An Exploratory Investigation," NBER Working Papers 0444, National Bureau of Economic Research, Inc.
  27. Martin L. Weitzman, 2007. "Subjective Expectations and Asset-Return Puzzles," American Economic Review, American Economic Association, vol. 97(4), pages 1102-1130, September.
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