Principal Components Analysis and Factor Analysis
Abstract: In investment management, multifactor risk modeling is the most common application of financial modeling. Multifactor risk models, or simply factor models, are linear regressions over a number of variables called factors. Factors can be exogenous variables or abstract variables formed by portfolios. Exogenous factors (or known factors) can be identified from traditional fundamental analysis or economic theory from macroeconomic factors. Abstract factors, also called unidentified or latent factors, can be determined with factor analysis or principal component analysis. Principal component analysis identifies the largest eigenvalues of the variance-covariance matrix or the correlation matrix. The largest eigenvalues correspond to eigenvectors that identify the entire market and sectors that correspond to industry classification. Factor analysis can be used to identify the structure of the latent factors.
Principal component analysis (PCA) and factor analysis are statistical tools that allow a modeler to (1) reduce the number of variables in a model (i.e., to reduce the dimensionality), and (2) identify if there is structure in the relationships between variables (i.e., to classify variables). In this entry, we explain PCA and factor analysis. We illustrate and compare both techniques using a ...
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