A continuous heterogeneous agent model for multi-asset pricing and portfolio construction under market matching friction

We propose a novel continuous Heterogeneous Agent Model (HAM) that applies to the general n>1 risky assets. In this model, every heterogeneous investor is identified with the continuous variables reflecting their personal characteristics. The heterogeneity of the market is captured by the distribution of these variables. By introducing market friction via a matching-based pricing mechanism, we derive a pricing equation from market clearing. The equation extends the classical CAPM and specifies how the bounded rationality and heterogeneity of investors can drive the actual price of risky assets away from their CAPM price. A system of ordinary (stochastic) differential equations are derived to govern the evolution of the total wealth and market value of risky assets held by the entire market (individual investors). From the equation system, a rolling-window-based maximum likelihood algorithm is developed to calibrate the model, which turn our HAM to a forecast tool for stock returns and an adaptive adjustment strategy for portfolio construction. This bridges the theoretical study on HAMs with the empirical studies of asset pricing and portfolio theory. We apply this tool to the Chinese A-share market and make a comparative analysis on its performance. The results demonstrate that compared to the classical forecast approaches in literature, our HAM has the advantage in identifying the tail risk in real market, which results in a more profitable portfolio in a variety of different investment horizons.