Approximate CAPM When Preferences Are CRRA

In general equilibrium models of financial markets, the cpital asset pricing formula does not hold when agents have von Neumann-Morgenstern utility with constant relative risk aversion. In this paper we examine under which conditions on endownments and dividens the pricing formula provides a good benchmark for equilibrium returns. While it is easy to construct examples where equilibrium returns are arbitrarily far from those predicted by CAPM, we show that there is a large class of economies where CAPM provides a very good approximation. Although the pricing formula does not hold exactly for the chosen specification, it turns out that pricing-errors are extremely small.