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Chapter 9

Factor Models

An economist is someone who sees something in the real world and wonders if it would work in theory.

—Ronald Reagan

The CAPM can be interpreted as a single index factor model, and since we are already familiar with it, I will use the CAPM to introduce this important class of pricing models.

Factor models can be thought of as models of the conditional mean return to an asset (or portfolio of assets). We used unconditional mean return estimates as inputs to the optimal mean-variance efficient portfolios solved for in Chapters 6 and 7. To understand the difference, let r_it be the return on asset i at time t. Then the asset's unconditional mean return is simply the average return, that is, E(r_i) = . Now, think of the CAPM model:

For ease of exposition, drop the risk-free rate (that is, assume that cash earns no return) and take expectations (see the statistical review in the appendix to Chapter 5) noting that E(ε_i) = 0 by definition. Then,

Simply stated, this says that the expected return is now conditional on the market return. The market return is therefore the single factor and beta is the return (sometimes called the factor loading) to that factor.

There are ...