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

A risk manager runs principal component analysis on daily changes in the 2-, 5-, 10- and 30-year par swap rates. The first three components explain 88%, 8% and 3% of total variance. Which statement best describes how the first component is typically interpreted and used in hedging?

The first principal component is typically a parallel level shift of the curve, with all rates moving together. Hedging it therefore means offsetting the portfolio's overall DV01 exposure. Slope and curvature are the second and third components and need separate long-short or butterfly hedges.

  1. AIt represents a parallel shift of the curve, so hedging it means matching the portfolio's overall DV01 exposureCorrect
  2. BIt represents a change in curvature, so hedging it requires offsetting butterfly positions
  3. CIt represents a steepening or flattening, so hedging it requires a long-short position across maturities
  4. DIt represents idiosyncratic noise that cannot be hedged with swaps

Explanation

For interest rate term structures, the first principal component is usually a roughly parallel level shift in which all rates move in the same direction. Neutralizing it means offsetting the portfolio's net DV01. Slope is the second component and curvature the third.

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