An asset pricing model with accuracy-driven evolution of heterogeneous expectations

Starting from the work of Hommes et al. (2005a), we propose an alternative version of their asset pricing model with heterogeneous agents and asynchronous updating of beliefs. In particular, we assume that the predictors are selected based on their accuracy in predicting the market price of the risky asset, measured as an absolute prediction error, and not on the net profits made by fundamentalists and trend followers. From a mathematical point of view, the deterministic skeleton of the present model is a two-dimensional piecewise-smooth map. We present an analytical study of the fundamental equilibrium and the coexisting non-fundamental equilibria and propose a comparison with the results in Hommes et al. (2005a). A robustness check is also conducted by considering an accuracy measured by squared prediction errors, a fitness measure often adopted in theoretical and experimental studies because of its smoothness and for being equivalent to risk-adjusted profits. The comparisons reveal that these different fitness measures do not modify the stability of the fundamental equilibrium. However, non-fundamental equilibria, their stability and the out-of-equilibrium dynamics are affected.