The Consumption-Based Capital Asset Pricing Model

Abstract

The paper provides conditions on the primitives of a continuous-time economy under which there exist equilibria obeying the Consumption-Based Capital Asset Pricing Model (CCAPM). The paper also extends the equilibrium characterization of interest rates of Cox, Ingersoll, and Ross (1985) to multi-agent economies. We do not use a Markovian state assumption. THIS WORK PROVIDES sufficient conditions on agents' primitives for the validity of the Consumption-Based Capital Asset Pricing Model (CCAPM) of Breeden (1979). As a necessary condition, Breeden showed that in a continuous-time equilibrium satisfying certain regularity conditions, one can characterize returns on securities as follows. The expected rate of return on any security in excess of the riskless interest rate (the security's expected excess rate of return) is a multiple common to all securities of the instantaneous covariance of this excess return with aggregate consumption increments. This common multiple is the Arrow-Pratt measure of risk aversion of a representative agent. (Rubinstein (1976) published a discrete-time precursor of this result.) The exis- tence of equilibria satisfying Breeden's regularity conditions had been an open issue. We also show that the validity of the CCAPM does not depend on Breeden's assumption of Markov state information, and present a general asset pricing model extending the results of Cox, Ingersoll, and Ross (1985) as well as the discrete-time results of Rubinstein (1976) and Lucas (1978) to a multi-agent environment. Since the CCAPM was first proposed, much effort has been directed at finding sufficient conditions on the model primitives: the given assets, the agents' preferences, the agents' consumption endowments, and (in a production econ- omy) the feasible production sets. Conditions sufficient for the existence of continuous-time equilibria were shown in Duffie (1986), but the equilibria demonstrated were not shown to satisfy the additional regularity required for the CCAPM. In particular, Breeden assumed that all agents choose pointwise interior consumption rates, in order to characterize asset prices via the first order conditions of the Bellman equation. Interiority was also assumed by Huang (1987) in demonstrating a representative agent characterization of equilibrium, an approach exploited here. The use of dynamic programming and the Bellman equation, aside from the difficulty it imposes in verifying the existence of interior 1 Financial support from the National Science Foundation is gratefully acknowledged. We thank