Uniqueness of Equilibria in the CAPM

Abstract

Nowadays the classical two-period Capital Asset Pricing Model is one of the cornerstones of modern finance. Developed by Sharpe [1964], Lintner [1965], and Mossin [1966], it is widely used both by practitioners and theorists, since it gives us a manageable and attractive way of thinking about risk and required return on a risky investment. Given this successful theory one is forced to ask why the question of uniqueness of equilibria was not intensively investigated for a long time. It should be clear that without uniqueness the CAPM looses much of its relevance: if there are many equilibria, on which can investors base their investment decisions? And what is the “correct” risk premium for risky assets? In this chapter we give a condition for uniqueness of CAPM-equilibria which is based on the risk aversion and the endowments of the investors. Our condition is compatible with non-increasing absolute risk aversion.