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FRM Part II · FRM Exam Part II · Regression Hedging and Principal Component Analysis

A risk manager is deciding how many principal components to retain when hedging a bond portfolio against yield curve moves. Which approach is most consistent with PCA practice?

Retain the small number of leading components that jointly explain most of the total variance, typically level, slope and curvature for yield curves. The remaining low-eigenvalue components contribute little variance, so ignoring them simplifies the hedge with minimal loss of accuracy.

  1. AKeep the few components that together explain most of the variance, since the remainder is largely noiseCorrect
  2. BKeep all components because dropping any one makes the hedge invalid
  3. CKeep only the components with the smallest eigenvalues because they capture idiosyncratic risk
  4. DKeep exactly one component per maturity so each rate has its own hedge

Explanation

Yield curve changes are highly correlated, so two or three components typically explain over 95% of variance. Retaining these reduces dimensionality while capturing the main risk. Keeping all components defeats the purpose of PCA.

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