the same risk aversion parameter aj=a, so that agents who follow the same forecasting rule have the same demand. Hence, in the end, in the heterogeneous agents model of Brock and Hommes (1998), the agents are only heterogeneous in the beliefs they can choose from.

6.3  A modified heterogeneous agents
asset pricing model

6.3.1  Utility-maximizing beliefs

As in the BH model we consider a market with N agents who can select independently from each other a strategy h from a finite set of H different beliefs or forecasting rules to base trading decisions upon. Agents have to make a capital allocation decision between a risky asset P and a risk free asset F. Agent j can choose to invest at time t a fraction yj,t of his wealth Wj,t in the risky asset P and a fraction 1-yj,t in the risk free asset F. If Pt is the price of the risky asset at time t and Dt is the dividend paid at time t, then the net return of the risky asset at time t+1 is defined as rt+1P=(Pt+1+Dt+1-Pt)/Pt and the net risk free return is denoted by rF and is assumed to be constant. The net return of the agent's j complete portfolio C at time t+1 is then equal to
rj,t+1c=(1-yj,t) rF+yj,t rt+1P=rF+yj,t (rt+1P-rF),
where rt+1P-rF is the excess return on the risky asset. In this section we derive the demand function for the risky asset if the agent has constant relative risk aversion and determines his optimal demand for the risky asset by maximizing his mean-variance utility curve on his capital allocation line. The demand function is derived under the assumption that the agent makes price predictions. In subsection 6.3.2 we present the demand function for the risky asset if the agent does not make price predictions, but only chooses to buy or sell short the asset on the basis of a technical trading strategy.

We make the following assumptions regarding the trading process. All agents are price takers. That is, an agent cannot influence the market's equilibrium price by his individual investment decision. Further, the model follows a Walrasian equilibrium price scenario. Each agent j chooses a strategy h and makes an optimal investment decision yj,th in the time interval (t-1, t), before the setting of the equilibrium price at time t. Expectations about future prices and dividends are made on the basis of the information set of past equilibrium prices and dividends {Pt-i, Dt-i: i ≥ 1 } (note that Pt and Dt

244