Principal Component Analysis and Factor Models
Most financial portfolios consist of multiple assets, and their returns depend concurrently and dynamically on many economic and financial variables. Therefore, it is important to use proper multivariate statistical analyses to study the behavior and properties of portfolio returns. However, as demonstrated in the previous chapter, analysis of multiple asset returns often requires high-dimensional statistical models that are complicated and hard to apply. To simplify the task of modeling multiple returns, we discuss in this chapter some dimension reduction methods to search for the underlying structure of the assets. Principal component analysis (PCA) is perhaps the most commonly used statistical method in dimension reduction, and we start our discussion with the method. In practice, observed return series often exhibit similar characteristics leading to the belief that they might be driven by some common sources, often referred to as common factors. To study the common pattern in asset returns and to simplify portfolio analysis, various factor models have been proposed in the literature to analyze multiple asset returns. The second goal of this chapter is to introduce some useful factor models and demonstrate their applications in finance.
Three types of factor models are available for studying asset returns; see Connor (1995) and Campbell, Lo, and MacKinlay (1997). The first type is the macroeconomic factor models that ...