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

A desk wants a PCA-based hedge of a swap book using the first three components (explaining 98% of variance) rather than a bucketed key-rate hedge on ten maturities. Which is the most accurate statement about this approach?

A three-factor PCA hedge needs only three instruments, simplifying the hedge, but it leaves residual risk from the omitted components and from changes in the factor structure over time. Orthogonality does not eliminate risk, and no guarantee of superiority over key-rate hedging exists.

  1. AIt reduces the number of hedging instruments needed but leaves residual risk from omitted components and from instability of the factors over timeCorrect
  2. BIt eliminates all interest-rate risk because the components are orthogonal
  3. CIt requires ten hedging instruments because each component needs one per maturity
  4. DIt guarantees a hedge that is better than the key-rate approach in every scenario

Explanation

PCA hedging with three factors needs only three instruments, yet the omitted 2% of variance and any change in the estimated eigenvectors leave residual risk. Orthogonality does not remove risk, and the method is not dominant in every scenario.

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