IDEAS home Printed from https://ideas.repec.org/p/uts/rpaper/254.html
   My bibliography  Save this paper

A Framework for CAPM with Heterogenous Beliefs

Author

Abstract

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.

Suggested Citation

  • Carl Chiarella & Roberto Dieci & Xue-Zhong He, 2009. "A Framework for CAPM with Heterogenous Beliefs," Research Paper Series 254, Quantitative Finance Research Centre, University of Technology, Sydney.
  • Handle: RePEc:uts:rpaper:254
    as

    Download full text from publisher

    File URL: https://www.uts.edu.au/sites/default/files/qfr-archive-03/QFR-rp254.pdf
    Download Restriction: no

    References listed on IDEAS

    as
    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. Westerhoff, Frank H., 2004. "Multiasset Market Dynamics," Macroeconomic Dynamics, Cambridge University Press, vol. 8(05), pages 596-616, November.
    3. C. Chiarella & X-Z. He, 2001. "Asset price and wealth dynamics under heterogeneous expectations," Quantitative Finance, Taylor & Francis Journals, vol. 1(5), pages 509-526.
    4. J. Doyne Farmer & Laszlo Gillemot & Fabrizio Lillo & Szabolcs Mike & Anindya Sen, 2004. "What really causes large price changes?," Quantitative Finance, Taylor & Francis Journals, vol. 4(4), pages 383-397.
    5. 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.
    6. Chiarella, Carl & He, Xue-Zhong & Hommes, Cars, 2006. "A dynamic analysis of moving average rules," Journal of Economic Dynamics and Control, Elsevier, vol. 30(9-10), pages 1729-1753.
    7. Chiarella, Carl & Dieci, Roberto & He, Xue-Zhong, 2007. "Heterogeneous expectations and speculative behavior in a dynamic multi-asset framework," Journal of Economic Behavior & Organization, Elsevier, vol. 62(3), pages 408-427, March.
    8. 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.
    9. 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.
    10. Detemple Jerome & Murthy Shashidhar, 1994. "Intertemporal Asset Pricing with Heterogeneous Beliefs," Journal of Economic Theory, Elsevier, vol. 62(2), pages 294-320, April.
    11. Westerhoff, Frank H. & Dieci, Roberto, 2006. "The effectiveness of Keynes-Tobin transaction taxes when heterogeneous agents can trade in different markets: A behavioral finance approach," Journal of Economic Dynamics and Control, Elsevier, vol. 30(2), pages 293-322, February.
    12. Chiarella, Carl & He, Xue-Zhong, 2002. "Heterogeneous Beliefs, Risk and Learning in a Simple Asset Pricing Model," Computational Economics, Springer;Society for Computational Economics, vol. 19(1), pages 95-132, February.
    13. Laurent Calvet & Jean-Michel Grandmont & Isabelle Lemaire, 2001. "Aggregation of Heterogenous Beliefs and Asset Pricing in Complete Financial Markets," Working Papers 2001-01, Center for Research in Economics and Statistics.
    14. 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.
    15. 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.
    16. 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.
    17. William A. Brock & Cars H. Hommes, 1997. "A Rational Route to Randomness," Econometrica, Econometric Society, vol. 65(5), pages 1059-1096, September.
    18. 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.
    19. Simone Alfarano & Thomas Lux & Friedrich Wagner, 2005. "Estimation of Agent-Based Models: The Case of an Asymmetric Herding Model," Computational Economics, Springer;Society for Computational Economics, vol. 26(1), pages 19-49, August.
    20. 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.
    21. Miller, Edward M, 1977. "Risk, Uncertainty, and Divergence of Opinion," Journal of Finance, American Finance Association, vol. 32(4), pages 1151-1168, September.
    22. Abel, Andrew B., 2002. "An exploration of the effects of pessimism and doubt on asset returns," Journal of Economic Dynamics and Control, Elsevier, vol. 26(7-8), pages 1075-1092, July.
    23. Xue-Zhong He & Youwei Li, 2008. "Heterogeneity, convergence, and autocorrelations," Quantitative Finance, Taylor & Francis Journals, vol. 8(1), pages 59-79.
    24. 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.
    25. 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.
    26. 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 937-974.
    27. Williams, Joseph T., 1977. "Capital asset prices with heterogeneous beliefs," Journal of Financial Economics, Elsevier, vol. 5(2), pages 219-239, November.
    28. 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.
    29. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Qi Nan Zhai, 2015. "Asset Pricing Under Ambiguity and Heterogeneity," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 16, June.
    2. Matthias Raddant & Friedrich Wagner, 2016. "Phase transition in the S&P stock market," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 11(2), pages 229-246, October.
    3. Xue-Zhong He & Lei Shi, 2012. "Disagreement in a Multi-Asset Market," International Review of Finance, International Review of Finance Ltd., vol. 12(3), pages 357-373, September.
    4. Lei Shi, 2010. "Portfolio Analysis and Equilibrium Asset Pricing with Heterogeneous Beliefs," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 9, June.
    5. Xue-Zhong He, 2012. "Recent Developments on Heterogeneous Beliefs and Adaptive Behaviour of Financial Markets," Research Paper Series 316, Quantitative Finance Research Centre, University of Technology, Sydney.
    6. Xue‐Zhong He & Lei Shi, 2012. "Boundedly rational equilibrium and risk premium," Accounting and Finance, Accounting and Finance Association of Australia and New Zealand, vol. 52(1), pages 71-93, March.
    7. Carl Chiarella & Roberto Dieci & Xue-Zhong He & Kai Li, 2013. "An evolutionary CAPM under heterogeneous beliefs," Annals of Finance, Springer, vol. 9(2), pages 185-215, May.
    8. Carl Chiarella & Roberto Dieci & Xue-Zhong He, 2013. "Time-varying beta: a boundedly rational equilibrium approach," Journal of Evolutionary Economics, Springer, vol. 23(3), pages 609-639, July.
    9. Xue-Zhong He & Lei Shi, 2010. "Differences in Opinion and Risk Premium," Research Paper Series 271, Quantitative Finance Research Centre, University of Technology, Sydney.
    10. Carl Chiarella & Roberto Dieci & Xue-Zhong He, 2011. "The dynamic behaviour of asset prices in disequilibrium: a survey," International Journal of Behavioural Accounting and Finance, Inderscience Enterprises Ltd, vol. 2(2), pages 101-139.
    11. Kai Li, 2014. "Asset Price Dynamics with Heterogeneous Beliefs and Time Delays," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 13, June.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:uts:rpaper:254. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Duncan Ford). General contact details of provider: http://edirc.repec.org/data/qfutsau.html .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.