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

A risk analyst applies principal component analysis to daily changes in a set of government par yields from 2 to 30 years. The first three components are extracted and interpreted. Which description of the first component is most consistent with typical empirical findings?

The first principal component is typically a level factor, a roughly parallel shift where all maturities move in the same direction by similar amounts. It explains most yield-curve variance. The slope (twist) and curvature (butterfly) factors are the second and third components.

  1. AA roughly parallel shift in which all maturities move in the same direction by similar amountsCorrect
  2. BA twist in which short rates rise while long rates fall
  3. CA butterfly movement in which the belly moves opposite to both the short and long ends
  4. DA movement that affects only maturities beyond 20 years

Explanation

For government yield curves the first principal component usually has loadings of the same sign across maturities, so it is the level (parallel shift) factor and explains most of the variance. The twist is the second component and the butterfly is the third.

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