Principal Component Analysis: A First Look

This closing note of the unit takes the SVD from the previous note and applies it to the single most common real-world use case in quantitative finance: extracting a small number of dominant, uncorrelated statistical risk factors from a large panel of asset returns. This is principal component analysis (PCA), and — as this note shows — it is not a separate technique to learn, but the SVD applied to one specific kind of matrix: a mean-centred data matrix. This is a first look only; the full eigenportfolio derivation, choosing $K\ll N$ factors, and the connection to the existing PCA pillar-support stub (staged in topics-queue.md, needed by the APT statistical-factors topic) are developed at greater depth in learn/library/mathematics/linear-algebra-ii/ and the portfolio-management unit.

Learning objectives. By the end of this note you should be able to: