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

Listed author(s):
  • 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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File URL: http://www.aeaweb.org/aej/mac/data/2008-0128_data.zip
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File URL: http://www.aeaweb.org/aej/mac/app/2008-0128_app.pdf
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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: 159-191

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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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References listed on IDEAS
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  1. Thomas Sargent & Noah Williams & Tao Zha, 2006. "The Conquest of South American Inflation," NBER Working Papers 12606, National Bureau of Economic Research, Inc.
  2. Branch, William A. & Evans, George W., 2006. "A simple recursive forecasting model," Economics Letters, Elsevier, vol. 91(2), pages 158-166, May.
  3. 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.
  4. GRANDMONT, Jean-Michel, 1997. "Expectations formation and stability of large socioeconomic systems," CORE Discussion Papers 1997088, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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  7. Bruce McGough, 2006. "Shocking Escapes," Economic Journal, Royal Economic Society, vol. 116(511), pages 507-528, 04.
  8. 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.
  9. Carceles-Poveda, Eva & Giannitsarou, Chryssi, 2007. "Asset Pricing with Adaptive Learning," CEPR Discussion Papers 6223, C.E.P.R. Discussion Papers.
  10. 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 777-797, July.
  11. Woodford, Michael & Santos, Manuel S., 1995. "Rational asset pricing bubbles," UC3M Working papers. Economics 3913, Universidad Carlos III de Madrid. Departamento de Economía.
  12. In-Koo Cho & Kenneth Kasa, 2003. "Learning Dynamics and Endogenous Currency Crises," Computing in Economics and Finance 2003 132, Society for Computational Economics.
  13. 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.
  14. Martin L. Weitzman, 2007. "Subjective Expectations and Asset-Return Puzzles," American Economic Review, American Economic Association, vol. 97(4), pages 1102-1130, September.
  15. Froot, Kenneth A & Obstfeld, Maurice, 1991. "Intrinsic Bubbles: The Case of Stock Prices," American Economic Review, American Economic Association, vol. 81(5), pages 1189-1214, December.
  16. J. Bradford De Long & Andrei Shleifer & Lawrence H. Summers & Robert J. Waldmann, "undated". "Noise Trader Risk in Financial Markets," J. Bradford De Long's Working Papers _124, University of California at Berkeley, Economics Department.
  17. 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.
  18. 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.
  19. Harrison Hong & José Scheinkman & Wei Xiong, 2006. "Asset Float and Speculative Bubbles," Journal of Finance, American Finance Association, vol. 61(3), pages 1073-1117, 06.
  20. George W. Evans & Seppo Honkapohja, "undated". "Economic Dynamics with Learning: New Stability Results," Computing in Economics and Finance 1997 51, Society for Computational Economics.
  21. Evans, George W, 1991. "Pitfalls in Testing for Explosive Bubbles in Asset Prices," American Economic Review, American Economic Association, vol. 81(4), pages 922-930, September.
  22. 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.
  23. Geweke, John, 2001. "A note on some limitations of CRRA utility," Economics Letters, Elsevier, vol. 71(3), pages 341-345, June.
  24. Cho, In-Koo & Sargent, Thomas J., 2000. "Escaping Nash inflation," Working Paper Series 0023, European Central Bank.
  25. Klaus Adam & Albert Marcet & Juan Pablo Nicolini, 2006. "Learning and Stock Market Volatility," Computing in Economics and Finance 2006 15, Society for Computational Economics.
  26. 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.
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  28. Blanchard, Olivier Jean, 1979. "Speculative bubbles, crashes and rational expectations," Economics Letters, Elsevier, vol. 3(4), pages 387-389.
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