A Framework for CAPM with Heterogeneous Beliefs

Abstract

The Sharpe–Lintner–Mossin (Sharpe 1964; Lintner 1965; Mossin 1966) Capital Asset Pricing Model (CAPM) plays a central role in modern finance theory. It is founded on the paradigm of homogeneous beliefs and a rational representative agent. However, froma theoretical perspective this paradigmhas been criticized on a number of grounds, in particular concerning its extreme assumptions about homogeneous beliefs, information about the economic environment, and the computational ability on the part of the rational representative economic agent.

The impact of heterogeneous beliefs among investors on the market equilibrium price has been an important focus in the CAPM literature. A number of models with investorswho have heterogeneous beliefs have been previously studied.¹ A common finding in this strand of research is that heterogeneous beliefs can affect aggregate market returns. However, the question remains as to how exactly does heterogeneity affect themarket risk of risky assets? In much of this earlier work, the heterogeneous beliefs reflect either differences of opinion among the investors² or differences in information upon which investors are trying to learn by using some Bayesian updating rule.³ Heterogeneity has been investigated in the context of either CAPM–like mean–variancemodels (for instance, Lintner 1969; Miller 1977;Williams 1977; and Mayshar 1982) or Arrow–Debreu contingent claims models (as in Varian 1985;Abel 1989; 2002; and Calvet et al. 2004).