Introduction

Beta pricing (see Section 18.5) implies that the risk premium on any security or portfolio is proportional to the covariance of its return with a frontier return. However, beta pricing by itself gives no guidance as to which returns are frontier returns. We will use the term Capital Asset Pricing Model (CAPM) if the market return is a frontier return. Note that the CAPM is here identified with a property of equilibrium security prices, not with a class of models of security markets. Therefore, it will be necessary to determine what restrictions on preferences or payoffs give rise to equilibria that conform to the CAPM definition.

Under the CAPM the market return, being a frontier return, can be taken as the reference portfolio in the beta pricing equation, resulting in the security market line, which relates the risk premium on any security to the covariance between the return on that security and the market return.

In Chapter 14 we derived the equation of the security market line by applying consumption-based security pricing under the assumption that agents have quadratic utilities. The derivation was generalized in Chapter 16. In this chapter we derive the CAPM in an equilibrium under the assumption that agents take variance as a measure of consumption risk (mean-variance preferences). This condition is satisfied when agents' preferences have an expected utility representation with quadratic utilities and also when security payoffs are multivariate normally distributed.