Asset Price and Wealth Dynamics under Heterogeneous Expectations

In order to characterize asset price and wealth dynamics arising from the interaction of heterogeneous agents with CRRA utility, a discrete time stationary model in terms of return and wealth proportions (among different types of agents) is established. When fundamentalists and chartists are the main heterogeneous agents in the model, it is found that in the presence of heterogeneous agents the stationary model can have multiple steady-states. The steady-state is unstable when the chartists extrapolate strongly and (locally) stable when they extrapolate weakly. The convergence to the steady-state follows an optimal selection principle — the return and wealth proportions tend to the steady-state which has relatively higher return. More importantly, heterogeneity can generate instability which, under the stochastic processes of the dividend yield and extrapolation rates, results in switching of the return among different states, such as steady-state, periodic and aperiodic cycles from time to time. The model that is finally developed displays the essential characteristics of the standard asset price dynamics model assumed in continuous time finance, in that the asset price is fluctuating around a geometrically growing trend. The model also displays the volatility clustering that is an essential feature of empirically observed asset returns. Acknowledgments. An early version of this paper was presented at the 7th Asia Pacific Finance Association Annual Conference, Shanghai, July 24-26, 2000, the 2nd CeNDEF Workshop on Economic Dynamics, University of Amsterdam, January 4-6, 2001, the 19th Economic Theory Workshop, University of Technology, Sydney, February 1-2, 2001 and seminars at the University of Melbourne, the University of New South Wales, and the University of Bielefeld. In particular, we would like to thank Chris Adam, Volker Bohm, Cars Hommes, Willi Semmler and Jan Wenzelburger for stimulating comments and discussion. The authors are responsible for any remaining errors in this paper. 1 2 CARL CHIARELLA AND XUE-ZHONG HE