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

A risk manager hedges a bond portfolio against the first two principal components of yield curve changes, which are interpreted as a level shift and a slope (steepening/flattening) change. Which exposure is most likely to remain as the main source of residual term structure risk?

Curvature, or butterfly, movements are the main residual risk. Principal component analysis usually finds level, slope and curvature as the first three factors. Hedging the first two neutralizes parallel and steepening exposure, leaving the third factor, which changes the middle of the curve relative to the ends.

  1. ACurvature (butterfly) movements captured by the third factorCorrect
  2. BParallel shifts of the whole curve
  3. CSteepening and flattening of the curve
  4. DChanges in the overall level of rates

Explanation

The first PC is typically the level, the second the slope and the third the curvature. Hedging the first two removes most level and slope risk, so the remaining systematic term structure risk lies mainly in the third, curvature factor.

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