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A Framework for CAPM with Heterogenous Beliefs

We introduce heterogeneous beliefs in to the mean-variance framework of the standard CAPM, in contrast to the standard approach which assumes homogeneous beliefs. By assuming that agents form optimal portfolios based upon their heterogeneous beliefs about conditional means and covariances of the risky asset returns, we set up a framework for the CAPM that incorporates the heterogeneous beliefs when the market is in equilibrium. In this framework we first construct a consensus belief (with respect to the means and covariances of the risky asset returns) to represent the aggregate market belief when the market is in equilibrium. We then extend the analysis to a repeated one-period set-up and establish a framework for a dynamic CAPM using a market fraction model in which agents are grouped according to their beliefs. The exact relation between heterogeneous beliefs, the market equilibrium returns and the ex-ante beta-coeffcients is obtained. CAPM and Heterogeneous beliefs.

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File URL: http://www.business.uts.edu.au/qfrc/research/research_papers/rp254.pdf
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Paper provided by Quantitative Finance Research Centre, University of Technology, Sydney in its series Research Paper Series with number 254.

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Length: 17
Date of creation: 01 Aug 2009
Date of revision:
Handle: RePEc:uts:rpaper:254
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  1. Carl Chiarella & Roberto Dieci & Xue-Zhong He, 2008. "Heterogeneity, Market Mechanisms, and Asset Price Dynamics," Research Paper Series 231, Quantitative Finance Research Centre, University of Technology, Sydney.
  2. Louis K.C. Chan & Jason Karceski & Josef Lakonishok, 1999. "On Portfolio Optimization: Forecasting Covariances and Choosing the Risk Model," NBER Working Papers 7039, National Bureau of Economic Research, Inc.
  3. William A. Brock & Cars H. Hommes, 1997. "A Rational Route to Randomness," Econometrica, Econometric Society, vol. 65(5), pages 1059-1096, September.
  4. Andrew B. Abel, 2001. "An Exploration of the Effects of Pessimism and Doubt on Asset Returns," NBER Working Papers 8132, National Bureau of Economic Research, Inc.
  5. Gaunersdorfer, A. & Hommes, C.H., 2000. "A Nonlinear Structural Model for Volatility Clustering," CeNDEF Working Papers 00-02, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
  6. Cars Hommes & Carl Chiarella & Xue-Zhong He, 2004. "A Dynamical Analysis of Moving Average Rules," Computing in Economics and Finance 2004 238, Society for Computational Economics.
  7. Miller, Edward M, 1977. "Risk, Uncertainty, and Divergence of Opinion," Journal of Finance, American Finance Association, vol. 32(4), pages 1151-68, September.
  8. Pok-sang Lam & Stephen G. Cecchetti & Nelson C. Mark, 2000. "Asset Pricing with Distorted Beliefs: Are Equity Returns Too Good to Be True?," American Economic Review, American Economic Association, vol. 90(4), pages 787-805, September.
  9. Frank Westerhoff, 2003. "Multi-Asset Market Dynamics," Computing in Economics and Finance 2003 88, Society for Computational Economics.
  10. Timothy C. Johnson, 2004. "Forecast Dispersion and the Cross Section of Expected Returns," Journal of Finance, American Finance Association, vol. 59(5), pages 1957-1978, October.
  11. Carl Chiarella & Roberto Dieci & Laura Gardini, 2005. "The Dynamic Interaction of Speculation and Diversification," Applied Mathematical Finance, Taylor & Francis Journals, vol. 12(1), pages 17-52.
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  13. LeBaron, Blake, 2006. "Agent-based Computational Finance," Handbook of Computational Economics, in: Leigh Tesfatsion & Kenneth L. Judd (ed.), Handbook of Computational Economics, edition 1, volume 2, chapter 24, pages 1187-1233 Elsevier.
  14. Frank Westerhoff, 2004. "The effectiveness of Keynes-Tobin transaction taxes when heterogeneous agents can trade in different markets: A behavioral finance approach," Computing in Economics and Finance 2004 14, Society for Computational Economics.
  15. Zapatero, Fernando, 1998. "Effects of financial innovations on market volatility when beliefs are heterogeneous," Journal of Economic Dynamics and Control, Elsevier, vol. 22(4), pages 597-626, April.
  16. Williams, Joseph T., 1977. "Capital asset prices with heterogeneous beliefs," Journal of Financial Economics, Elsevier, vol. 5(2), pages 219-239, November.
  17. Carl Chiarella & Roberto Dieci & Xue-Zhong He, 2005. "Heterogeneous Expectations and Speculative Behaviour in a Dynamic Multi-Asset Framework," Research Paper Series 166, Quantitative Finance Research Centre, University of Technology, Sydney.
  18. Carl Chiarella & Xue-Zhong He, 2001. "Asset Price and Wealth Dynamics Under Heterogeneous Expectations," Research Paper Series 56, Quantitative Finance Research Centre, University of Technology, Sydney.
  19. Laurent Calvet & Jean-Michel Grandmont & Isabelle Lemaire, 2001. "Aggregation of Heterogenous Beliefs and Asset Pricing in Complete Financial Markets," Working Papers 2001-01, Centre de Recherche en Economie et Statistique.
  20. He, Xue-Zhong & Li, Youwei, 2007. "Power-law behaviour, heterogeneity, and trend chasing," Journal of Economic Dynamics and Control, Elsevier, vol. 31(10), pages 3396-3426, October.
  21. Chiarella, Carl & He, Xue-Zhong, 2002. "Heterogeneous Beliefs, Risk and Learning in a Simple Asset Pricing Model," Computational Economics, Society for Computational Economics, vol. 19(1), pages 95-132, February.
  22. Hommes, Cars H., 2006. "Heterogeneous Agent Models in Economics and Finance," Handbook of Computational Economics, in: Leigh Tesfatsion & Kenneth L. Judd (ed.), Handbook of Computational Economics, edition 1, volume 2, chapter 23, pages 1109-1186 Elsevier.
  23. Carl Chiarella & Roberto Dieci & Xue-Zhong He, 2006. "Aggregation of Heterogeneous Beliefs and Asset Pricing Theory: A Mean-Variance Analysis," Research Paper Series 186, Quantitative Finance Research Centre, University of Technology, Sydney.
  24. Brock, William A. & Hommes, Cars H., 1998. "Heterogeneous beliefs and routes to chaos in a simple asset pricing model," Journal of Economic Dynamics and Control, Elsevier, vol. 22(8-9), pages 1235-1274, August.
  25. J. Doyne Farmer & Laszlo Gillemot & Fabrizio Lillo & Szabolcs Mike & Anindya Sen, 2003. "What really causes large price changes?," Papers cond-mat/0312703, arXiv.org, revised Apr 2004.
  26. Xue-Zhong He & Lei Shi, 2009. "Portfolio Analysis and Zero-Beta CAPM with Heterogeneous Beliefs," Research Paper Series 244, Quantitative Finance Research Centre, University of Technology, Sydney.
  27. Xue-Zhong He & Youwei Li, 2008. "Heterogeneity, convergence, and autocorrelations," Quantitative Finance, Taylor & Francis Journals, vol. 8(1), pages 59-79.
  28. Chan, Louis K C & Karceski, Jason & Lakonishok, Josef, 1999. "On Portfolio Optimization: Forecasting Covariances and Choosing the Risk Model," Review of Financial Studies, Society for Financial Studies, vol. 12(5), pages 937-74.
  29. Simone Alfarano & Thomas Lux & Friedrich Wagner, 2005. "Estimation of Agent-Based Models: The Case of an Asymmetric Herding Model," Computational Economics, Society for Computational Economics, vol. 26(1), pages 19-49, August.
  30. Detemple Jerome & Murthy Shashidhar, 1994. "Intertemporal Asset Pricing with Heterogeneous Beliefs," Journal of Economic Theory, Elsevier, vol. 62(2), pages 294-320, April.
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