18-MultiFactorModels Page 529 Wednesday, February 4, 2004 1:10 PM

I

CHAPTER

18

Multifactor Models and

Common Trends for

Common Stocks

n this chapter we discuss how multifactor models are used in the man-

agement of equity portfolios; in Chapter 20 we will discuss how they

are applied to bond portfolio management. Multifactor models are a

broad family of econometric models. Essentially, a multivariate process

admits a multifactor representation if it can be approximately (or

exactly) expressed as a function of another multivariate process of a

smaller dimensionality. The general multifactor formulation of a model

has to be clearly distinguished from the economic theory that might be

behind it. In fact, multifactor models might be the expression of an eco-

nomic theory as well as the result of an explicit econometric dimension-

ality reduction process.

For example, the Capital Asset Pricing Model (CAPM) is a general

equilibrium theory which is embodied in a single-factor linear model. In

this case, the factorization is the expression of a theoretical formulation.

The same considerations apply to the Arbitrage Pricing Theory (APT): a

multifactor model embodies a pricing theory based on the absence of

arbitrage. However, given a multivariate process, econometric factor

analysis techniques yield a dimensionality reduction which is also

embodied in a multifactor model. In the latter case the process is purely

statistic, not supported by theory. In this sense, the statement, often

found in the literature, that CAPM and APT are factor models might be

slightly misleading. It should be clear that both are economic theories,

general equilibrium and arbitrage pricing respectively, which happen to

be expressed as multifactor models.

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