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Heterogeneous Expectations and Speculative Behaviour in a Dynamic Multi-Asset Framework

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Abstract

Following the framework of a one risky - one riskless asset model developed by Brock and Hommes (1998), this paper considers a discrete-time model of a financial market where heterogeneous groups of agents allocate their wealth amongst multiple risky assets and a riskless asset. Agents follow different expectation formation schemes for both first and second moments of the distribution of returns. Instead of using a Walrasian auctioneer scenario as the market clearing mechanism, a market maker scenario is used. In particular, the paper focuses on the case of two risky assets and two agent types, fundamentalists and trend chasers. Conditions for the stability of the “fundamental” equilibrium are established in terms of the key parameters, in particular the extrapolation rate of the trend chasers and the weight of the two groups in the market. Numerical explorations are performed in order to analyze the combined effect of the interaction between heterogeneous traders and the diversification among multiple risky assets. Particular attention is paid to the effect of the correlation between the risky assets. It turns out that investors’ anticipated correlation and portfolio diversification do not always have a stabilizing role, but rather may act as a further source of complexity in the financial market.

Suggested Citation

  • 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.
  • Handle: RePEc:uts:rpaper:166
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    File URL: https://www.uts.edu.au/sites/default/files/qfr-archive-02/QFR-rp166.pdf
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    References listed on IDEAS

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    1. C. H. Hommes, 2001. "Financial markets as nonlinear adaptive evolutionary systems," Quantitative Finance, Taylor & Francis Journals, vol. 1(1), pages 149-167.
    2. Bohm, Volker & Wenzelburger, Jan, 2005. "On the performance of efficient portfolios," Journal of Economic Dynamics and Control, Elsevier, vol. 29(4), pages 721-740, April.
    3. 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.
    4. Jianping Mei & Hsien-Hsing Liao (ed.), 2003. "Asset Pricing," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 4647.
    5. William A. Brock & Cars H. Hommes, 1997. "A Rational Route to Randomness," Econometrica, Econometric Society, vol. 65(5), pages 1059-1096, September.
    6. Chiarella, Carl & Dieci, Roberto & Gardini, Laura, 2002. "Speculative behaviour and complex asset price dynamics: a global analysis," Journal of Economic Behavior & Organization, Elsevier, vol. 49(2), pages 173-197, October.
    7. Beja, Avraham & Goldman, M Barry, 1980. " On the Dynamic Behavior of Prices in Disequilibrium," Journal of Finance, American Finance Association, vol. 35(2), pages 235-248, May.
    8. Xue-Zhong He, 2003. "Asset Pricing, Volatility and Market Behaviour: A Market Fraction Approach," Research Paper Series 95, Quantitative Finance Research Centre, University of Technology, Sydney.
    9. 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.
    10. 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.
    11. Day, Richard H. & Huang, Weihong, 1990. "Bulls, bears and market sheep," Journal of Economic Behavior & Organization, Elsevier, vol. 14(3), pages 299-329, December.
    12. Westerhoff, Frank H., 2004. "Multiasset Market Dynamics," Macroeconomic Dynamics, Cambridge University Press, vol. 8(05), pages 596-616, November.
    13. Chiarella, Carl & He, Xue-Zhong, 2003. "Heterogeneous Beliefs, Risk, And Learning In A Simple Asset-Pricing Model With A Market Maker," Macroeconomic Dynamics, Cambridge University Press, vol. 7(04), pages 503-536, September.
    14. Fernando Fernandez-Rodriguez & Maria-Dolores Garcia-Artiles & Juan Manuel Martin-Gonzalez, 2002. "A model of speculative behaviour with a strange attractor," Applied Mathematical Finance, Taylor & Francis Journals, vol. 9(3), pages 143-161.
    15. Lux, Thomas, 1998. "The socio-economic dynamics of speculative markets: interacting agents, chaos, and the fat tails of return distributions," Journal of Economic Behavior & Organization, Elsevier, vol. 33(2), pages 143-165, January.
    16. 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.
    17. Gaunersdorfer, Andrea, 2000. "Endogenous fluctuations in a simple asset pricing model with heterogeneous agents," Journal of Economic Dynamics and Control, Elsevier, vol. 24(5-7), pages 799-831, June.
    18. Wenzelburger, Jan, 2004. "Learning to predict rationally when beliefs are heterogeneous," Journal of Economic Dynamics and Control, Elsevier, vol. 28(10), pages 2075-2104, September.
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    More about this item

    Keywords

    heterogeneous beliefs; asset pricing; portfolio choice; bifurcation analysis; comovements in stock prices;

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • D84 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Expectations; Speculations
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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