Annals of Finance

, Volume 9, Issue 2, pp 185–215 | Cite as

An evolutionary CAPM under heterogeneous beliefs

  • Carl Chiarella
  • Roberto Dieci
  • Xue-Zhong He
  • Kai Li
Symposium

Abstract

Heterogeneity and evolutionary behaviour of investors are two of the most important characteristics of financial markets. This paper incorporates the adaptive behaviour of agents with heterogeneous beliefs and establishes an evolutionary capital asset pricing model (ECAPM) within the mean-variance framework. We show that the rational behaviour of agents switching to better-performing trading strategies can cause large deviations of the market price from the fundamental value of one asset to spill over to other assets. Also, this spill-over effect is associated with high trading volumes and persistent volatility characterized by significantly decaying autocorrelations of, and positive correlation between, price volatility and trading volume.

Keywords

Evolutionary CAPM Heterogeneous beliefs Market stability Spill-over effects Volatility Trading volume 

JEL Classification

D84 G12 

Notes

Acknowledgments

We would like to thank Cars Hommes for a stimulating discussion in the early stages of this project. We are grateful to valuable comments from two anonymous referees. Dieci gratefully acknowledges a Visiting Professor Appointment at the Quantitative Finance Research Centre, UTS Business School, during which this work was finalised. Dieci also acknowledges support from MIUR under project PRIN 2009 “Local interactions and global dynamics in economics and finance: models and tools” and from EU COST within Action IS1104 “The EU in the new complex geography of economic systems: models, tools and policy evaluation”. Financial support for Chiarella and He from the Australian Research Council (ARC) under Discovery Grant (DP110104487) is gratefully acknowledged.

References

  1. Ang, A., Chen, J.: CAPM over the long run: 1926 to 2001. J Empir Finance 14, 1–40 (2007)CrossRefGoogle Scholar
  2. Banerjee, S., Kremer, I.: Disagreement and learning: dynamic patterns of trade. J Finance 65, 1269–1302 (2010)CrossRefGoogle Scholar
  3. Bollerslev, T.: Generalized autoregressive conditional heteroskedasticity. J Econ 31, 307–327 (1986)Google Scholar
  4. Bollerslev, T., Engle, R., Wooldridge, J.: A capital asset pricing model with time varying covariances. J Polit Econ 96, 116–131 (1988)CrossRefGoogle Scholar
  5. Braun, P., Nelson, D., Sunier, A.: Good news, bad news, volatility and betas. J Finance 50, 1575–1603 (1990)CrossRefGoogle Scholar
  6. Brock, W., Hommes, C.: A rational route to randomness. Econometrica 65, 1059–1095 (1997)CrossRefGoogle Scholar
  7. Brock, W., Hommes, C.: Heterogeneous beliefs and routes to chaos in a simple asset pricing model. J Econ Dyn Control 22, 1235–1274 (1998)CrossRefGoogle Scholar
  8. Campbell, J., Vuolteenaho, T.: Bad beta, good beta. Am Econ Rev 94, 1249–1275 (2004)CrossRefGoogle Scholar
  9. Chen, S.-H., Huang, Y.: Risk preference, forecasting accuracy and survival dynamics: simulations based on a multi-asset agent-based artifical stock market. J Econ Behav Organ 67, 702–717 (2008)CrossRefGoogle Scholar
  10. Chiarella, C., Dieci, R., Gardini, L.: The dynamic interaction of speculation and diversification. Appl Math Finance 12(1), 17–52 (2005)CrossRefGoogle Scholar
  11. Chiarella, C., Dieci, R., He, X.: Heterogeneity, market mechanisms and asset price dynamics. In: Hens, T., Schenk-Hoppé, K.R. (eds.) Handbook of Financial Markets: Dynamics and Evolution, pp. 277–344. Elsevier, Amsterdam (2009)Google Scholar
  12. Chiarella, C., Dieci, R., He, X.: A framework for CAPM with heterogeneous beliefs. In: Bischi, G.-I., Chiarella, C., Gardini, L. (eds.) Nonlinear Dynamics in Economics, Finance and Social Sciences: Essays in Honour of John Barkley Rosser Jr, pp. 353–369. Springer, Berlin (2010)Google Scholar
  13. Chiarella, C., Dieci, R., He, X.: Do heterogeneous beliefs diversify market risk? Eur J Finance 17(3), 241–258 (2011)CrossRefGoogle Scholar
  14. Chiarella, C., Dieci, R., He, X.: Time-varying beta: a boundedly rational equilibrium approach. J Evol Econ (2012) doi: 10.1007/s00191-011-0233-5
  15. Chiarella, C., He, X., Zheng, M.: An analysis of the effect of noise in a heterogeneous agent financial market model. J Econ Dyn Control 35, 148–162 (2011)CrossRefGoogle Scholar
  16. Dieci, R., Westerhoff, F.: Heterogeneous speculators, endogenous fluctuations and interacting markets: a model of stock prices and exchange rates. J Econ Dyn Control 34, 743–764 (2010a)CrossRefGoogle Scholar
  17. Dieci, R., Westerhoff, F.: On the inherent instability of international financial markets: natural nonlinear interactions between stock and foreign exchange markets, BERG (Bamberg Economic Research Group) on Government and Growth Working Paper Series, no. 79, University of Bamberg (2010b)Google Scholar
  18. Dybvig, P., Ross, S.: Differential information and performance measurement using a security market line. J Finance 40, 383–400 (1985)CrossRefGoogle Scholar
  19. Engle, R.: Autoregressive conditional heteroscedasticity with estimates of the variance of UK inflation. Econometrica 50, 987–1008 (1982)CrossRefGoogle Scholar
  20. Evstigneev, I., Hens, T., Schenk-Hoppé, K.R.: Evolutionary finance. In: Hens, T., Schenk-Hoppé, K.R. (eds.) Handbook of Financial Markets: Dynamics and Evolution, pp. 507–566. Elsevier, Amsterdam (2009)Google Scholar
  21. Fama, E., French, K.: The value premium and the CAPM. J Finance 61(5), 2163–2185 (2006)CrossRefGoogle Scholar
  22. Hamilton, J.: A new approach to the economic analysis of nonstationary time series and the business cycle. Econometrica 57(2), 357–384 (1989)CrossRefGoogle Scholar
  23. Hamilton, J.: Analysis of time series subject to changes in regime. J Econ 45, 39–70 (1990)Google Scholar
  24. Hansen, L., Richard, S.: The role of conditioning information in deducing testable restrictions implied by dynamic asset pricing models. Econometrica 55, 587–613 (1987)CrossRefGoogle Scholar
  25. He, X., Li, Y.: Power law behaviour, heterogeneity, and trend chasing. J Econ Dyn Control 31, 3396–3426 (2007)CrossRefGoogle Scholar
  26. Hens, T., Schenk-Hoppé, K.R.: Handbook of Financial Markets: Dynamics and Evolution. Handbooks in Finance. Elsevier, Amsterdam (2009)Google Scholar
  27. Hommes, C.: Financial markets as nonlinear adaptive evolutionary systems. Quant Finance 1, 149–167 (2001)CrossRefGoogle Scholar
  28. Hommes, C.: Heterogeneous agent models in economics and finance. In: Tesfatsion, L., Judd, K.L. (eds.) Agent-based Computational Economics, Vol. 2 of Handbook of Computational Economics, pp. 1109–1186. Elsevier, North-Holland (2006)Google Scholar
  29. Hommes, C., Wagener, F.: Complex evolutionary systems in behavioral finance. In: Hens, T., Schenk-Hoppé, K.R. (eds.) Handbook of Financial Markets: Dynamics and Evolution, pp. 217–276. Elsevier, Amsterdam (2009)Google Scholar
  30. Jagannathan, R., Wang, Z.: The conditional CAPM and cross-section of expected returns’. J Finance 51, 3–53 (1996)CrossRefGoogle Scholar
  31. LeBaron, B.: Agent-based computational finance. In: Tesfatsion, L., Judd, K.L. (eds.) Agent-based Computational Economics, vol. 2 of Handbook of Computational Economics, pp. 1187–1233. Elsevier, North-Holland (2006)Google Scholar
  32. Lewellen, J., Nagel, S.: The conditional CAPM does not explain asset-pricing anomalies. J Financial Econ 82(3), 289–314 (2006)CrossRefGoogle Scholar
  33. Lintner, J.: The valuation of risk assets and the selection of risky investments in stock portfolios and capital budgets. Rev Econ Stud 47, 13–37 (1965)Google Scholar
  34. Lux, T. Stochastic behavioural asset pricing and stylized facts. In: Hens, T., Schenk-Hoppé, K.R. (eds.) Handbook of Financial Markets: Dynamics and Evolution: pp. 161–215. Elsevier, Amsterdam (2009)Google Scholar
  35. Marsili, M., Raffaelli, G., Ponsot, B.: Dynamic instability in generic model of multi-assets markets. J Econ Dyn Control 33, 1170–1181 (2009)CrossRefGoogle Scholar
  36. Mossin, J.: Equilibrium in a capital asset market. Econometrica 35, 768–783 (1966)CrossRefGoogle Scholar
  37. Sharpe, W.: Capital asset prices: a theory of market equilibrium under conditions of risk’. J Finance 19, 425–442 (1964)Google Scholar
  38. Westerhoff, F.: Multiasset market dynamics. Macroecon Dyn 8, 591–616 (2004)Google Scholar
  39. Westerhoff, F., Dieci, R.: The effectiveness of Keynes-Tobin transaction taxes when heterogeneous agents can trade in different markets: a behavioral finance approach. J Econ Dyn Control 30, 293–322 (2006)CrossRefGoogle Scholar
  40. Zhu, M., Wang, D., Guo, M.: Stochastic equilibria of an asset pricing model with heterogeneous beliefs and random dividends. J Econ Dyn Control 35, 131–147 (2011)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Carl Chiarella
    • 1
  • Roberto Dieci
    • 2
  • Xue-Zhong He
    • 1
  • Kai Li
    • 1
  1. 1.Finance Discipline Group, UTS Business SchoolUniversity of Technology, SydneyBroadwayAustralia
  2. 2.Department of MathematicsUniversity of BolognaBolognaItaly

Personalised recommendations