PCA (Principal Component Analysis)
Quantitative Finance glossary · Probability, Statistics & Linear Algebra
Definition
Linear dimensionality reduction via the eigendecomposition of the covariance matrix; in yield-curve analysis the top 3 factors typically explain ≥ 95% of variance (level, slope, curvature).
PCA (Principal Component Analysis) in plain English
PCA is a way to squeeze a complicated dataset with many overlapping measurements down to a few numbers that capture most of what's actually going on. It hunts for the directions in which the data varies the most and keeps just those, throwing away the redundant detail. For example, the interest rates on bonds of many different lengths tend to move together, and PCA reveals that almost all their wiggling boils down to just three simple stories: the whole curve shifting up or down (level), tilting steeper or flatter (slope), and bowing in the middle (curvature) — together explaining over 95% of the movement. It's like describing a person's whole outfit with 'mostly blue, a bit formal' instead of listing every thread.
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