14 - Representative Investors in a Heterogeneous CRRA Model

Abstract

This chapter presents the fundamental aggregation theorem for CRRA utility when investors might exhibit heterogeneous beliefs, heterogeneous risk tolerance parameters, and heterogeneous time discount factors. The theorem characterizes a representative investor who sets prices. The representative investor has features that are similar, but may not be equivalent, to CRRA utility. It establishes a general theorem concerning the existence and nonuniqueness of a representative investor. The theorem applies to the case when investors hold heterogeneous beliefs, heterogeneous rates of time preference, and heterogeneous coefficients of relative risk aversion (CRRA utility). It is very important to understand that there are several notions of what constitutes a representative investor. The notion used in the present approach is different from the notion of a representative investor used in the traditional approach to asset pricing. The chapter discusses why the traditional notion is inappropriate for studying the impact of behavioral heterogeneity on asset prices. The highlights of literature are reviewed and described the manner in which the approach adopted here follows the literature and the manner in which it departs from the literature. The chapter concludes with the fact that efficiency plays a key role in the derivation of the general aggregation result to follow.