The Basics of Financial Econometrics: Tools, Concepts, and Asset Management Applications

CHAPTER 12

Factor Analysis and Principal Components Analysis

After reading this chapter you will understand:

• What factor analysis is.
• What a factor model is.
• How a factor model might or might not be the result of factor analysis.
• The difference between a factor model and a multiple regression.
• How to estimate the parameters of a factor model.
• How to estimate factor scores.
• What principal components analysis is.
• How to construct principal components.
• The difference between a factor model and principal components analysis.

In this chapter we describe factor models and principal components analysis (PCA). Both techniques are used to “simplify” complex data sets composed of multiple time series as a function of a smaller number of time series. Factor models and PCA find many applications in portfolio management, risk management, performance measurement, corporate finance, and many other areas of financial analytics.

In Chapter 3 we described multiple regression analysis, a statistical model that assumes a simple linear relationship between an observed dependent variable and one or more explanatory variables. Although factor models and PCA share many similarities with linear regression analysis, there are also significant differences. In this chapter, we will distinguish between linear regressions, factor models, factor analysis, and PCA. We begin with a review of the fundamental properties and assumptions about linear regressions.

ASSUMPTIONS OF LINEAR REGRESSION

First recall from ...