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FRM Part I · FRM Exam Part I · Modeling Non-Parallel Term Structure Shifts and Hedging

A PCA of yield curve changes yields a first component with loadings of 0.45, 0.50, 0.52, 0.51 across the 2-, 5-, 10- and 30-year key rates, and a second component with loadings of -0.60, -0.25, 0.30, 0.70. Which statement is correct?

The second component is a slope factor. Its loadings move from negative at short maturities to positive at long maturities, so short and long rates move in opposite directions, a steepening or flattening. The first component, with similar positive loadings, is the level factor.

  1. AThe first component is a steepening/flattening factor because its loadings are all positive
  2. BThe second component is a slope factor because its loadings change sign across maturitiesCorrect
  3. CThe second component is a level factor because it has the largest loading on the 30-year rate
  4. DThe first component is a curvature factor because loadings are nearly equal

Explanation

A component whose loadings go from negative at short maturities to positive at long maturities moves short and long rates in opposite directions, which is a slope (twist) factor. The first component has same-signed, similar loadings, so it is level. Curvature would show a sign pattern like negative-positive-negative.

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