Principal Component Analysis

Principal component analysis (PCA) is a statistical technique that identifies the dominant independent factors driving yield curve movements. Applied to Treasury yields, it consistently produces three factors that explain over 99% of yield variation:

• PC1 (Level): a roughly parallel shift affecting all maturities equally. Explains ~85-90% of yield variation.
• PC2 (Slope): a tilt that moves short and long rates in opposite directions. Explains ~8-12% of yield variation.
• PC3 (Curvature/Twist): a bowing that moves the belly relative to the wings. Explains ~1-3% of yield variation.

This decomposition, first documented by Litterman and Scheinkman (1991), is foundational to yield curve analysis. It means that the vast majority of yield curve movements can be described by just three numbers: how much the curve shifted, tilted, and bowed.

The blog post "Ten Treasury Curve Snapshots That Tell the Story of a Generation" uses this level/slope/twist framework to characterize each major market event's yield curve impact:

• Level-dominant: parallel shifts driven by broad rate expectations (e.g., ZIRP → all rates near zero)
• Slope-dominant: tightening or easing cycles that affect the front end more than the long end (e.g., 2022 bear flattener)
• Curvature-dominant: relative value shifts in the belly (rarer, often driven by supply or hedging flows)

PCA is also used in the ACM term premium model to extract pricing factors from the yield curve, and in risk management systems to decompose portfolio exposure into level, slope, and curvature risk.