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

A risk manager is hedging a 10-year bond position using a PCA-based approach with level and slope factors, and compares it with a single-variable regression hedge on the 10-year yield change. Which statement is most accurate?

A two-factor PCA hedge neutralizes exposure to both level and slope movements, whereas a single-variable regression hedge offsets only the average sensitivity and leaves slope risk unhedged. PCA factors are uncorrelated and do not explain all variance, so some residual risk remains.

  1. AThe two-factor PCA hedge neutralizes exposure to both parallel shifts and steepening, whereas a single-factor hedge neutralizes only the average sensitivity and leaves slope riskCorrect
  2. BThe single-factor regression hedge neutralizes slope risk because the regression residual is zero
  3. CThe PCA hedge removes all risk because three components explain 100% of variance
  4. DThe PCA hedge increases residual risk because the factors are correlated

Explanation

A two-factor PCA hedge matches the portfolio's exposures to level and slope, so those risks are neutralized. A single-variable regression hedge only offsets the average relationship, leaving slope and curvature residual risk. PCA factors are uncorrelated and the explained variance is less than 100%.

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