Heterogeneous Expectations with Multiple Risky Assets

We extend the heterogeneous agent model of Brock and Hommes (1997, 1998) to a setting with two risky assets. Agents choose between a trend-following rule and a fundamentalist rule using evolutionary switching based on past performance. The expectation rules operate on both assets simultaneously: the forecast for each asset depends on the lagged price deviation of the other, introducing cross-asset expectations as a new channel for endogenous comovement. In the deterministic skeleton we derive the threshold intensity of choice at which the fundamental steady state loses stability and show that cross-asset expectations lower it: the fundamental steady state destabilizes sooner, and the interval of stable non-fundamental dynamics that follows shrinks. In the stochastic system, they amplify the realized correlation far beyond the exogenous baseline: as the intensity of switching approaches the pitchfork threshold the realized correlation approaches one, however weakly the two fundamentals are correlated. This amplification is non-monotonic in the intensity of choice and it operates through the structure of expectations alone.