Multifactor Models and their Applications

Abstract

Multifactor models are popular models in portfolio analysis (see Chapter 4) and they are applied in various manners. A typical application is to create an index (tracking) portfolio, which will be discussed in Chapter 11,or a tilted portfolio,a portfolio which is responsive or nonresponsive to a specific factor such as interest rate. Multifactor models are also often associated with finance theory.In this chapter, we first review the CAPM (capital asset pricing model) in finance theory. Although the CAPM itself is derived under very strong conditions, the market model associated with the CAPM has been popular, especially in an academic world, and no doubt it has been playing an important role as a kernel (core) model leading us to alternative (modified) models. In fact, various CAPM-like models have been proposed to improve the poor empirical performance of the original CAPM market model. Some of such models are introduced in Section 2 and Rosenberg’s models in Chapter 8 are also regarded as such.However,though these empirical models are modifications of the market model, they are not consistent with the CAPM theory as they stand. Those modified models are mostly multifactor models of the form $${X_{it}} = {\alpha _{io}} + {f_{1t}} + \cdots + {\alpha _{iq}}{f_{qt}} + {\varepsilon _{it}}$$ (1.1) (see Chapters 4 and 5 on some statistical specifications of this model).