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

Which statement about principal components of yield curve changes is correct?

Principal components are orthogonal, meaning uncorrelated with one another, and the first few typically capture most of the variation in yield curve changes. Components are ordered by explained variance, adding more increases cumulative explained variance, and the full set equals the number of rates analyzed.

  1. APrincipal components are correlated with each other, which is why the level factor can be predicted from slope
  2. BPrincipal components are orthogonal (uncorrelated) with each other, and a few of them typically capture most of the variation in rate changesCorrect
  3. CAdding more principal components always lowers total explained variance
  4. DThe number of principal components extracted is always smaller than the number of rates analyzed

Explanation

PCA constructs components that are mutually uncorrelated, ordered by variance explained, and for yield curves the first few explain the great majority of variation. Extracting all components, equal in number to the rates, explains 100%, so the final option is wrong. Explained variance never falls as components are added.

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