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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 ten par swap rates. The first three components explain 88%, 8% and 2% of total variance. Which statement best describes the typical interpretation of these components for a swap curve?

The first component is the level or parallel shift, the second is slope, and the third is curvature. Level explains most variance because rates tend to move together across maturities, and the later components capture progressively smaller twisting and bending movements.

  1. AThe first is a level (parallel shift), the second a slope (steepening/flattening), the third a curvature factorCorrect
  2. BThe first is a curvature factor, the second a level factor, the third a slope factor
  3. CAll three components represent parallel shifts of different magnitudes
  4. DThe first captures idiosyncratic noise, while the third captures the common parallel shift

Explanation

For yield curves, PCA typically yields level, slope and curvature as the first three components, ordered by explained variance. Level dominates because rates mostly move together. Other options misorder or misdescribe the factors.

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