Asset Pricing with Heterogeneous Preferences: An Analytical Approach

We analyze existence and properties of equilibrium in a class of models with heterogeneous risk aversion and habits based on past aggregate consumption. We solve a new model in closed form and derive necessary and sufficient conditions for equilibrium existence. Existence conditions constrain preference heterogeneity and, thus, the variability in the risk premium
generated by the model and the counter cyclical properties of the risk free rate. Our results suggest that the behavior of the risk free rate is an important indicator of potential issues with numerically solved models. Quantitative studies show the small-sample problems with the long-horizon predictive regressions and analyze how preference heterogeneity impacts variation in the risk free rate and price of risk and, therefore, price dividend ratio forecasts of future stock returns.