Intertemporal Asset Pricing with Heterogeneous Consumers and Without Demand Aggregation

Abstract

Consumer heterogeneity raises two problems in the derivation of the intertemporal asset-pricing model. First, it is implausible to assume that all assets' returns are multivariate normal (or exhibit separability). Second, the stocliastically varying distribution of wealth among consumers is a vector of state variables which may add a large number of parameters to the two-parameter asset-pricing model. Consider the first problem. The SharpeLintner asset-pricing model (CAPM) is derived under the assumption that all assets' returns are multivariate normal (or, more generally, that they exhibit separability).' Whereas it may be plausible to assume that stocks' returns are multivariate normal, it is implausible to assume that all financial assets' returns are multivariate normal. (Financial assets are defined to be the assets in zero net supply.) For example, over a finite time interval a call option's return has a truncated (possibly normal or lognormal) distribution Consumer heterogeneity raises two problems in the derivation of the intertemporal asset-pricing model. First, it is implausible to assume that all assets' returns are multivariate normal (or exhibit separability). Second, the stochastically varying distribution of wealth among consumers is a vector of state variables which may add a large number of parameters to the twoparameter asset-pricing model. Both problems are resolved in a complete market. Optimality of the competitive equilibrium implies that prices, production, and aggregate consumption are the same as in the equilibrium of a central planner or composite consumer. In the composite consumer's observationally equivalent equilibrium no distributional assumptions are necessary about zero net supply assets. Also the wealth distribution among heterogeneous consumers becomes an irrelevant state variable. *1 thank Philip H. Dybvig, Jonathan E. Ingersoll, and Edward C. Prescott for helpful criticism on earlier drafts. I remain responsible for errors. 1. Related work includes Mossin (1966), Fama (1970, 1971), Black (1972), and Ross (1976, 1978). The CAPM may be derived under the assumption of quadratic utility without any distributional assumptions. The assumption of quadratic utility resolves the first but not the second of the two problems outlined below.