Introduction

In the CAPM, beta is the measure of the sensitivity of a security's return to the market return. The equation of the security market line (19.5) shows that the relation between the risk premium and beta is linear.

The CAPM relies on restrictive assumptions about agents' preferences or security returns, and certainly its empirical implications have not been confirmed by data. In this chapter we consider models of security markets – all with a pricing relation similar to that of the CAPM – but with a factor (or factors) replacing the market return. These factors are typically taken to be proxies for such macroeconomic variables as gross domestic product, the rate of inflation, and so on. The relation between expected return and the measure of the sensitivity of a security's return to factor risk, like the corresponding relation in the case of the CAPM, is linear.

Exact Factor Pricing

There are K contingent claims f1, …, fK called factors. Each factor is normalized so as to have zero expectation. The number K of factors is small relative to the number of securities, and the factors may or may not lie in the asset span. The span of the factors and the risk-free claim e is the factor span, which is denoted by F ≡ span{e, f1, …, fK}. It is assumed that all K factors and the risk-free claim are linearly independent.