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

In a principal components analysis (PCA) of historical changes in par or spot rates across the maturity spectrum, the first three components are typically interpreted as which of the following, in order of explanatory power?

The first three principal components of yield curve changes are conventionally interpreted as level, slope and curvature, in that order of explained variance. Level is a roughly parallel shift, slope is steepening or flattening, and curvature is a butterfly movement of the middle relative to the ends.

  1. ALevel, slope, curvatureCorrect
  2. BSlope, level, curvature
  3. CCurvature, level, slope
  4. DLevel, curvature, slope

Explanation

Empirical PCA of yield curve changes yields a first component that moves all rates in the same direction (level or parallel shift), a second that steepens or flattens the curve (slope), and a third that changes the curvature (butterfly). The other orderings do not match the usual ranking by explained variance.

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