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

In a PCA of a yield curve's rate changes, the first three components are typically interpreted as level, slope and curvature. A portfolio manager observes that the loadings of the second component are negative for short maturities and positive for long maturities. A one-standard-deviation positive shock to this component most nearly represents:

The shock represents a steepening: short rates fall and long rates rise. Loadings that change sign from negative at short maturities to positive at long maturities define the slope factor, and a positive shock moves the two ends in opposite directions.

  1. AA parallel upward shift of the curve
  2. BA steepening of the curve, with short rates falling and long rates risingCorrect
  3. CA flattening of the curve, with short rates rising and long rates falling
  4. DAn increase in curvature, with the middle rates moving opposite to both ends

Explanation

Loadings negative at the short end and positive at the long end mean a positive shock lowers short rates and raises long rates, which steepens the curve. A parallel shift would have same-signed loadings; curvature would show a sign change twice.

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