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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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  2. Albert Marcet & Juan P. Nicolini, 1995. "Recurrent hyperinflations and learning," Economics Working Papers 244, Department of Economics and Business, Universitat Pompeu Fabra, revised Nov 2001.
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  4. Kenneth D. West, 1986. "A Specification Test for Speculative Bubbles," NBER Working Papers 2067, National Bureau of Economic Research, Inc.
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  7. 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.
  8. George W. Evans & Seppo Honkapohja, . "Economic Dynamics with Learning: New Stability Results," Computing in Economics and Finance 1997 51, Society for Computational Economics.
  9. Branch, William A. & Evans, George W., 2006. "A simple recursive forecasting model," Economics Letters, Elsevier, vol. 91(2), pages 158-166, May.
  10. Jean-Michel Grandmont, 1997. "Expectations Formation and Stability of Large Socioeconomic Systems," Working Papers 97-27, Centre de Recherche en Economie et Statistique.
  11. 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.
  12. 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.
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  17. Cho, In-Koo & Kasa, Kenneth, 2008. "Learning Dynamics And Endogenous Currency Crises," Macroeconomic Dynamics, Cambridge University Press, vol. 12(02), pages 257-285, April.
  18. Geweke, John, 2001. "A note on some limitations of CRRA utility," Economics Letters, Elsevier, vol. 71(3), pages 341-345, June.
  19. 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.
  20. Thomas Sargent & Noah Williams & Tao Zha, 2009. "The Conquest of South American Inflation," Journal of Political Economy, University of Chicago Press, vol. 117(2), pages 211-256, 04.
  21. Bruce McGough, 2006. "Shocking Escapes," Economic Journal, Royal Economic Society, vol. 116(511), pages 507-528, 04.
  22. 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.
  23. 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.
  24. Martin L. Weitzman, 2007. "Subjective Expectations and Asset-Return Puzzles," American Economic Review, American Economic Association, vol. 97(4), pages 1102-1130, September.
  25. Allan Timmermann, 1996. "Excess Volatility and Predictability of Stock Prices in Autoregressive Dividend Models with Learning," Review of Economic Studies, Oxford University Press, vol. 63(4), pages 523-557.
  26. 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.
  27. Klaus Adam & Albert Marcet & Juan Pablo Nicolini, 2006. "Learning and Stock Market Volatility," Computing in Economics and Finance 2006 15, Society for Computational Economics.
  28. 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.
  29. Blanchard, Olivier Jean, 1979. "Speculative bubbles, crashes and rational expectations," Economics Letters, Elsevier, vol. 3(4), pages 387-389.
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