An Extension of the Consumption-Based CAPM Model

We extend the Consumption-based CAPM (C-CAPM) model to representative agents with different risk attitudes. We first use the concept of expectation dependence and show that for a risk averse representative agent, it is the first-degree expectation dependence (FED) rather than the covariance that determines C-CAPM’s riskiness. We extend the assumption of risk aversion to prudence and propose the measure of second-degree expectation dependence (SED) to obtain the values of asset price and equity premium. These theoretical results are linked to the equity premium puzzle. Using the same dataset as in Campbell (2003), the estimated measures of relative risk aversion from FED and SED approximations are much lower than those obtained in the original study and correspond to the theoretical values often discussed in the literature. The theoretical model is then generalized to higher-degree risk changes and higher-order risk averse representative agents.