Substitution, Risk Aversion, and the Temporal Behavior of Consumption and Asset Returns: A Theoretical Framework

TLDR

These recursive preferences allow risk attitudes to be disentangled from intertemporal substitutability and, in an infinite‑horizon representative‑agent setting, embed both the atemporal CAPM and the intertemporal consumption‑CAPM as special cases despite homothetic preferences and separable consumption‑portfolio decisions. The paper develops a class of recursive, non‑expected‑utility preferences over intertemporal consumption lotteries. The authors prove existence of recursive intertemporal utility functions and optimal solutions by extending Kreps and Porteus’s temporal‑lottery space to an infinite horizon, thereby establishing a suitable domain for utility functions. The resulting model shows asset systematic risk depends on covariance with both market return and consumption growth, integrates atemporal non‑expected‑utility theories into a temporal framework, and derives intertemporal asset‑pricing formulas for homogeneous members of that class.

Abstract

This paper develops a class of recursive, but not necessarily expected utility, preferences over intertemporal consumption lotteries. An important feature of these general preferences is that they permit risk attitudes to be disentangled from the degree of intertemporal substitutability. Moreover, in an infinite horizon, representative agent context these preference specifications lead to a model of asset returns in which appropriate versions of both the atemporal CAPM and the intertemporal consumption-CAPM are nested as special cases. In our general model, systematic risk of an asset is determined by covariance with both the return to the market portfolio and consumption growth, while in each of the existing models only one of these factors plays a role. This result is achieved despite the homotheticity of preferences and the separability of consumption and portfolio decisions. Two other auxiliary analytical contributions which are of independent interest are the proofs of (i) the existence of recursive intertemporal utility functions, and (ii) the existence of optima to corresponding optimization problems. In proving (i), it is necessary to define a suitable domain for utility functions. This is achieved by extending the formulation of the space of temporal lotteries in Kreps and Porteus (1978) to an infinite horizon framework. A final contribution is the integration into a temporal setting of a broad class of atemporal non-expected utility theories. For homogeneous members of the class due to Chew (1985) and Dekel (1986), the corresponding intertemporal asset pricing model is derived.