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

  • William A. Branch
  • George W. Evans

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 need to make forecasts of the conditional variance of a stock's return. Recursive updating of both the conditional variance and the expected return implies several mechanisms through which learning impacts stock prices. Extended periods of excess volatility, bubbles, and crashes arise with a frequency that depends on the extent to which past data is discounted. A central role is played by changes over time in agents' estimates of risk. (JEL D81, D83, E32, G01, G12)

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File URL: http://www.aeaweb.org/articles.php?doi=10.1257/mac.3.3.159
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Article provided by American Economic Association in its journal American Economic Journal: Macroeconomics.

Volume (Year): 3 (2011)
Issue (Month): 3 (July)
Pages: 159-91

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Handle: RePEc:aea:aejmac:v:3:y:2011:i:3:p:159-91
Note: DOI: 10.1257/mac.3.3.159
Contact details of provider: Web page: https://www.aeaweb.org/aej-macro
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  1. In-Koo Cho & Noah Williams & Thomas J. Sargent, 2002. "Escaping Nash Inflation," Review of Economic Studies, Oxford University Press, vol. 69(1), pages 1-40.
  2. Grandmont, Jean-Michel, 1994. "Expectations formation and stability of large socioeconomic systems," CEPREMAP Working Papers (Couverture Orange) 9424, CEPREMAP.
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  8. 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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  11. 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.
  12. Eva Carceles Poveda & Chryssi Giannitsarou, 2006. "Asset pricing with adaptive learning," Computing in Economics and Finance 2006 25, Society for Computational Economics.
  13. J. Bradford De Long & Andrei Shleifer & Lawrence H. Summers & Robert J. Waldmann, . "Noise Trader Risk in Financial Markets," J. Bradford De Long's Working Papers _124, University of California at Berkeley, Economics Department.
  14. Manuel S. Santos & Michael Woodford, 1993. "Rational Asset Pricing Bubbles," Working Papers 9304, Centro de Investigacion Economica, ITAM.
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  17. 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.
  18. 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.
  19. 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.
  20. 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.
  21. 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.
  22. Geweke, John, 2001. "A note on some limitations of CRRA utility," Economics Letters, Elsevier, vol. 71(3), pages 341-345, June.
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  24. 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.
  25. 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.
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