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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. George W. Evans & Seppo Honkapohja, . "Economic Dynamics with Learning: New Stability Results," Computing in Economics and Finance 1997 51, Society for Computational Economics.
  2. 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.
  3. 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.
  4. Volker Bohm & Carl Chiarella, 2000. "Mean Variance Preferences, Expectations Formation, and the Dynamics of Random Asset Prices," Research Paper Series 46, Quantitative Finance Research Centre, University of Technology, Sydney.
  5. Harrison Hong & Jose Scheinkman & Wei Xiong, 2005. "Asset Float and Speculative Bubbles," NBER Working Papers 11367, National Bureau of Economic Research, Inc.
  6. Albert Marcet & Juan P. Nicolini, 2003. "Recurrent Hyperinflations and Learning," American Economic Review, American Economic Association, vol. 93(5), pages 1476-1498, December.
  7. 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.
  8. Cho, In-Koo & Sargent, Thomas J., 2000. "Escaping Nash inflation," Working Paper Series 0023, European Central Bank.
  9. 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.
  10. Kenneth A. Froot & Maurice Obstfeld, 1989. "Intrinsic Bubbles: The Case of Stock Prices," NBER Working Papers 3091, National Bureau of Economic Research, Inc.
  11. 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.
  12. 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.
  13. Cho, In-Koo & Kasa, Kenneth, 2008. "Learning Dynamics And Endogenous Currency Crises," Macroeconomic Dynamics, Cambridge University Press, vol. 12(02), pages 257-285, April.
  14. Grandmont, Jean-Michel, 1994. "Expectations formation and stability of large socioeconomic systems," CEPREMAP Working Papers (Couverture Orange) 9424, CEPREMAP.
  15. Martin L. Weitzman, 2007. "Subjective Expectations and Asset-Return Puzzles," American Economic Review, American Economic Association, vol. 97(4), pages 1102-1130, September.
  16. Bruce McGough, 2003. "Shocking Escapes," Computing in Economics and Finance 2003 294, Society for Computational Economics.
  17. Thomas Sargent & Noah Williams & Tao Zha, 2006. "The Conquest of South American Inflation," NBER Working Papers 12606, National Bureau of Economic Research, Inc.
  18. West, Kenneth D, 1987. "A Specification Test for Speculative Bubbles," The Quarterly Journal of Economics, MIT Press, vol. 102(3), pages 553-80, August.
  19. 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.
  20. Manuel S. Santos & Michael Woodford, 1997. "Rational Asset Pricing Bubbles," Econometrica, Econometric Society, vol. 65(1), pages 19-58, January.
  21. Blanchard, Olivier Jean, 1979. "Speculative bubbles, crashes and rational expectations," Economics Letters, Elsevier, vol. 3(4), pages 387-389.
  22. Carceles-Poveda, Eva & Giannitsarou, Chryssi, 2007. "Asset Pricing with Adaptive Learning," CEPR Discussion Papers 6223, C.E.P.R. Discussion Papers.
  23. Geweke, John, 2001. "A note on some limitations of CRRA utility," Economics Letters, Elsevier, vol. 71(3), pages 341-345, June.
  24. 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.
  25. 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.
  26. 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.
  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.
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