Evaluating Consumption CAPM under Heterogeneous Preferences

We construct Consumption CAPM pricing kernel under heterogeneous Epstein-Zin-Weil (EZW) preferences setup. We show except under some strict assumptions,aggregation does not hold and individual level information is necessary to price assets. Assuming complete market, we estimate preferences parameters for heterogeneous agents using households level consumption and wealth data from Panel Study of Income Dynamics (PSID) database. Contrast to the literature, we get relatively larger Elasticity of Inter-temporal Substitution (EIS) and much smaller Relative Risk Aversion (RRA) parameters. We then calculate excess return for risky assets using Consumption-CAPM pricing kernel with our estimated preferences and individual consumption and wealth data. We show that our heterogeneous perferences pricing kernel improves the representative agent pricing kernel at three fronts, namely idiosyncratic risk factors, heterogeneous factor premia and idiosyncratic characteristics dependent aggregation weights. Each front improves the explanatory power to real world risk premium and cross sectional differences in stock excess returns. Lastly, we demonstrate another advantage of heterogeneous preferences model in terms of accounting for market participation heterogeneity. Including market participants only further improves model's explanatory power on market risk premium dynamics.