An endowment economy with heterogeneous agents and incomplete asset markets is specified, parameterized and solved using a numerical solution algorithm. The model features two types of infinitely lived agents who are endowed with different sources for non-tradable income. Despite not being able to insure against endowment risk, individuals are able to partially diversify away idiosyncratic risk by trading in a limited set of competitive asset markets. Numerical results indicate that the model can account for substantially more of the variability in intertemporal marginal rates of substitution documented by Hensen and Jagannathan (1990) than can models based on a representative agent. In addition, the model can generate a mean risk-free rate of interest smaller than the rate of time preference and potentially account for the so called 'risk-free rate puzzle'.

The representative agent theory of asset pricing is modified to incorporate heterogeneous agents and incomplete markets. The model features two types of agents who differ up to a nontradable, idiosyncratic component in their endowment processes. Numerical solutions indicate that individuals are able to diversify a substantial portion of their idiosyncratic income risk through riskless borrowing and lending alone. Restrictions on the variability of intertemporal marginal rates of substitution ( Hansen and Jagannathan (1991) ) are used to argue that incomplete markets, as modeled here, cannot account for the properties of asset returns that are anomalous from the perspective of representative agent theory.

One of the most puzzling features of currency prices is the forward premium anomaly : the tendency for high interest rate currencies to appreciate. We characterize the anomaly in the context of affine models of the term structure of interest rates. In affine models, the anomaly requires either that state variables have asymmetric effects on state prices in different currencies or that nominal interest rates take on negative values with positive probability. We find the quantitative properties of either alternative to have important shortcomings.

Forward and spot exchange rates between major currencies imply large standard deviations of both predictable returns from currency speculation and of the equilibrium price measure (the intertemporal marginal rate of substitution). Representative agent theory with time‐additive preferences cannot account for either of these properties. We show that the theory does considerably better along these dimensions when the representative agent's preferences exhibit habit persistence, but that the theory fails to reproduce some of the other properties of the data—in particular, the strong autocorrelation of forward premiums.