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

A risk manager applies principal component analysis to daily changes in a set of par swap rates across maturities. The first three components explain 88%, 8% and 2% of total variance respectively. Which statement best describes how the first component is typically interpreted and used in hedging?

The first principal component of rate changes is typically a near-parallel level shift that explains most of the variance. Hedging exposure to it is therefore similar to matching DV01. Slope and curvature are captured by the second and third components.

  1. AIt represents a roughly parallel shift in rates, so hedging it is similar to matching DV01Correct
  2. BIt represents a change in curvature, so it is hedged with a butterfly only
  3. CIt represents idiosyncratic noise that can be ignored in hedging
  4. DIt represents a steepening of the curve, with short and long rates moving in opposite directions

Explanation

For interest rate curves, the first principal component is usually a level (near-parallel) shift and explains most variance. Neutralizing exposure to it is akin to matching DV01. The second component is slope and the third is curvature, so the other options mislabel the components.

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