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

An analyst notes that the third principal component of yield curve changes has loadings that are positive at short and long maturities and negative at intermediate maturities. How should this factor be interpreted, and what portfolio is most exposed?

This is the curvature (butterfly) factor, because the belly moves opposite to the short and long ends. Butterfly positions, such as a bullet versus a barbell, are the most exposed. A slope factor would change sign only once across maturities.

  1. AA level factor; a barbell-neutral duration portfolio is most exposed
  2. BA slope factor; a flattener position is most exposed
  3. CA curvature factor; a butterfly position (barbell versus bullet) is most exposedCorrect
  4. DA volatility factor; a portfolio of swaptions only is exposed

Explanation

Loadings that change sign twice, with the belly moving opposite to the wings, describe curvature (butterfly). Such a factor mainly affects butterfly trades combining a bullet and a barbell. A slope factor changes sign only once across maturities.

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