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

A risk manager notes that PCA on a yield curve gives a first component explaining 85% of variance and the second explaining 10%. When deciding how many factors to use for hedging, which statement is most appropriate?

Use the first two or three factors. They jointly explain most of the variance, and the slope and curvature components capture risks a level-only hedge leaves open. PCA components are uncorrelated, so truncating them is practical and does not require keeping every factor.

  1. AUse only the first factor, since the others are always noise
  2. BUse the first two or three factors, since the cumulative variance explained is high and the later factors capture slope and curvature riskCorrect
  3. CUse all factors, since PCA components are correlated and none can be dropped
  4. DUse only the second factor, because the first is fully hedged by duration

Explanation

Typically a few components capture most variance, and including slope and curvature reduces residual risk left after a level-only hedge. PCA components are uncorrelated by construction, so dropping later ones does not create correlation issues. The later factors are not pure noise.

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