A note on heterogeneous beliefs with CRRA utilities

TL;DR

This paper extends previous models of agents with diverse beliefs about asset dividends by incorporating CRRA utilities, deriving key financial quantities and analyzing the impact of risk aversion on equilibrium outcomes.

Contribution

It generalizes Brown & Rogers (2009) by including CRRA utility functions, providing new analytical expressions for equilibrium prices and risk measures.

Findings

Derived expressions for state price density and riskless rate

Analyzed effects of risk aversion on equilibrium asset prices

Extended understanding of heterogeneous beliefs in financial models

Abstract

This note will extend the research presented in Brown & Rogers (2009) to the case of CRRA agents. We consider the model outlined in that paper in which agents had diverse beliefs about the dividends produced by a risky asset. We now assume that the agents all have CRRA utility, with some integer coefficient of relative risk aversion. This is a generalisation of Brown & Rogers which considered logarithmic agents. We derive expressions for the state price density, riskless rate, stock price and wealths of the agents. This sheds light on the effects of risk aversion in an equilibrium with diverse beliefs.