The Dynamic Interaction of Speculation and Diversification
AbstractA discrete time model of a financial market is developed, in which heterogeneous interacting groups of agents allocate their wealth between two risky assets and a riskless asset. In each period each group formulates its demand for the risky assets and the risk-free asset according to myopic mean-variance maximizazion. The market consists of two types of agents: fundamentalists, who hold an estimate of the fundamental values of the risky assets and whose demand for each asset is a function of the deviation of the current price from the fundamental, and chartists, a group basing their trading decisions on an analysis of past returns. The time evolution of the prices is modelled by assuming the existence of a market maker, who sets excess demand of each asset to zero at the end of each trading period by taking an offsetting long or short position, and who announces the next period prices as functions of the excess demand for each asset and with a view to long-run market stability. The model is reduced to a seven-dimensional nonlinear discrete-time dynamical system, that describes the time evolution of prices and agents' beliefs about expected returns, variances and correlation. The unique steady state of the model is determined and the local asymptotic stability of the equilibrium is analysed, as a function of the key parameters that characterize agents' behaviour. In particular it is shown that when chartists update their expectations sufficiently fast, then the stability of the equilibrium is lost through a supercritical Neimark-Hopf bifurcation, and self-sustained price fluctuations along an attracting limit cycle appear in one or both markets. Global analysis is also performed, by using numerical techniques, in order to understand the role played by the chartists' behaviour in the transition to a regime characterized by irregular oscillatory motion and coexistence of attractors. It is also shown how changes occurring in one market may affect the price dynamics of the alternative risky asset, as a consequence of the dynamic updating of agents' portfolios.
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Bibliographic InfoArticle provided by Taylor and Francis Journals in its journal Applied Mathematical Finance.
Volume (Year): 12 (2005)
Issue (Month): 1 ()
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- Volker Böhm & Carl Chiarella, 2005.
"Mean Variance Preferences, Expectations Formation, And The Dynamics Of Random Asset Prices,"
Wiley Blackwell, vol. 15(1), pages 61-97.
- Volker Bohm & Carl Chiarella, 2000. "Mean Variance Preferences, Expectations Formation, and the Dynamics of Random Asset Prices," Research Paper Series 46, Quantitative Finance Research Centre, University of Technology, Sydney.
- C. Chiarella & X-Z. He, 2001.
"Asset price and wealth dynamics under heterogeneous expectations,"
Taylor and Francis Journals, vol. 1(5), pages 509-526.
- 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.
- Xue-Zhong (Tony) He & Carl Chiarella, 2001. "Asset Price and Wealth Dynamics under Heterogeneous Expectations," CeNDEF Workshop Papers, January 2001 5A.2, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
- Day, Richard H. & Huang, Weihong, 1990.
"Bulls, bears and market sheep,"
Journal of Economic Behavior & Organization,
Elsevier, vol. 14(3), pages 299-329, December.
- Carl Chiarella, 1992. "The Dynamics of Speculative Behaviour," Working Paper Series 13, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
- Frank Westerhoff, 2003.
"Multi-Asset Market Dynamics,"
Computing in Economics and Finance 2003
88, Society for Computational Economics.
- 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.
- Taylor, Mark P. & Allen, Helen, 1992. "The use of technical analysis in the foreign exchange market," Journal of International Money and Finance, Elsevier, vol. 11(3), pages 304-314, June.
- Carl Chiarella & Giulia Iori, 2002. "A simulation analysis of the microstructure of double auction markets," Quantitative Finance, Taylor and Francis Journals, vol. 2(5), pages 346-353.
- Carl Chiarella & Xue-Zhong He, 1999.
"Heterogeneous Beliefs, Risks and Learning in a Simple Asset Pricing Model,"
Research Paper Series
18, Quantitative Finance Research Centre, University of Technology, Sydney.
- 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.
- Xue-Zhong He & Carl Chiarella, 1999. "Heterogeneous Beliefs, Risk and Learning in a Simple Asset-Pricing Model," Computing in Economics and Finance 1999 223, Society for Computational Economics.
- 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.
- repec:att:wimass:9530 is not listed on IDEAS
- Chiarella, Carl & He, Xue-Zhong, 2003.
"Heterogeneous Beliefs, Risk, And Learning In A Simple Asset-Pricing Model With A Market Maker,"
Cambridge University Press, vol. 7(04), pages 503-536, September.
- Carl Chiarella & Xue-Zhong He, 2000. "Heterogeneous Beliefs, Risk and Learning in a Simple Asset Pricing Model with a Market Maker," Research Paper Series 35, Quantitative Finance Research Centre, University of Technology, Sydney.
- William A. Brock & Cars H. Hommes, 1997.
"A Rational Route to Randomness,"
Econometric Society, vol. 65(5), pages 1059-1096, September.
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