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Chapter

12

Factor Analysis and Principal Components Analysis

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fter 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 fac-
tor 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.