A Continuous Heterogeneous Agent Model for Multi-Asset Pricing and Portfolio Construction Under Market Matching Friction

The heterogeneous agent model (HAM) is a powerful tool to study the stock price dynamics and stylized anomalies in financial markets. However, existing HAMs often focus on the one-asset scenario which makes them hard to apply for the empirical studies of asset pricing and portfolio selection. In addition, the mainstream HAMs assume no matching friction in the market, which cannot reflect the complexity in real finance market. To fill the gap, we propose a novel continuous HAM that applies to the general n > 1 risky assets with market matching friction. In our HAM, every heterogeneous investor is identified with continuous variables that represent their personal characteristics. The heterogeneity of the market is then captured by the distribution of these continuous variables. By introducing market friction via a matchingbased pricing mechanism, we derive a pricing equation from market clearing condition. The pricing 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. With the pricing equation, 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 HAM. Based on the calibration, our HAM provides a forecast tool for the future return of stocks and an adaptive adjustment strategy for portfolio construction, which, therefore, bridges the HAMs with the empirical studies of asset pricing and portfolio theory. As an application, we take the tool into the Chinese A-share market and make a comparative analysis on the performance of our HAM against the classical approaches in literature. The results demonstrate that our HAM has the advantage in identifying the tail risk in real market, which results in a more profitable portfolio after risk discount. The outperformance of our HAM is robust with respect to different investment horizons, which validates the effectiveness of our HAM in real-world applications