to choose from a finite set of fundamental and trend following trading techniques. How many traders are using a particular technique in predicting prices depends on the past performances of these techniques, as measured by past profits or forecasting accuracy. Emphasis is placed on the change in dynamical behavior when the intensity of choice parameter, measuring how quickly agents switch between forecasting techniques, is varied. It is found that increasing this intensity of choice can lead to market instability and the emergence of complicated dynamics for asset prices and returns, with irregular switching between phases where prices are near to the fundamental value and phases of optimism where traders extrapolate trends. An extremely rich asset price dynamics emerges, with bifurcation routes to strange attractors, especially if switching to more successful strategies becomes more rapid. It is also found that even when costs of information gathering and trading are zero, then fundamentalists are in general not able to drive other trader types out of the market. Thus it is concluded that simple technical trading rules may survive evolutionary competition in a heterogeneous world where prices and beliefs coevolve over time and that therefore the Friedman argument should be considered with care. See e.g. Hommes (2001) for a survey and an extensive discussion of these points.
One of the goals of heterogeneous agents modeling is to develop simple financial asset pricing models that mimic the well-known characteristics of real financial return distributions, such as little autocorrelation in the returns, volatility clustering and fat tails. Gaunersdorfer and Hommes (2000) develop a model in which volatility clustering becomes an endogenous phenomenon by the interaction of heterogeneous agents. Volatility clustering is caused by the coexistence of attractors, a stable fundamental steady state and a stable (quasi) periodic cycle. The time series properties of the model are compared with the daily closing prices of the S&P 500 in the period August 1961 through May 2000 and furthermore a GARCH model is estimated. It is concluded that the model approximates reality fairly well.
This chapter is an extension of the Brock and Hommes (1998) model in that it adds a real moving-average technical trading strategy to the set of beliefs the traders can choose from. Moving averages are well known and frequently used prediction rules in financial practice. They are intended to smooth out an otherwise volatile time series and to show its underlying directional trend. Furthermore, the model proposed in this chapter assumes that traders have constant relative risk aversion. That is, every trader in a given belief group invests the same proportion of his individual wealth in the risky asset. Hence, traders take the same amount of risk relative to their wealth. In the Brock and Hommes (1998) model, in contrast, it is assumed that the traders have constant absolute risk aversion. Irrespective of their individual wealth every trader in a certain belief group will