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

A trader holds a portfolio whose exposure to the slope factor from a PCA of the yield curve is zero, but whose exposure to the level factor is large and positive. Which statement best describes the portfolio's risk to a sudden 2-year/10-year curve steepening that is a pure slope move with no level change?

The portfolio is largely unaffected by a pure slope move because its slope factor exposure is zero and principal components are orthogonal. Its large level exposure matters only if the curve shifts in parallel. The idea that PCA factors are correlated is incorrect.

  1. AIt is largely unaffected by the pure slope move, though it remains exposed to level shiftsCorrect
  2. BIt loses value because the level exposure is also sensitive to slope changes
  3. CIt gains value because level exposure is positive
  4. DIt is unaffected by any curve move because PCA factors are correlated

Explanation

Principal components are orthogonal (uncorrelated), so a pure slope move does not move the level factor. With zero slope exposure, the portfolio's P&L from a pure slope move is approximately zero. The level exposure matters only for level shifts. The claim that factors are correlated is wrong, as PCA factors are uncorrelated by construction.

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