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

Which statement about the principal components extracted from a covariance matrix of yield curve changes is correct?

Principal components are uncorrelated with one another, ordered by the variance they explain. This orthogonality lets a risk manager measure and hedge exposure to each factor, such as level and slope, separately, and often just the first few components are enough to capture most curve movement.

  1. AThe components are mutually correlated, so the level factor predicts the slope factor
  2. BThe components are uncorrelated (orthogonal) with each other, which simplifies hedging against each factor separatelyCorrect
  3. CThe number of components exceeds the number of rates, so the data are compressed
  4. DComponent variances must all be equal after rotation

Explanation

PCA produces orthogonal, uncorrelated components ordered by variance, so exposures to each can be hedged separately. The number of components equals the number of original variables, and eigenvalues differ, with the first the largest.

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