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

Why do practitioners often prefer a PCA-based approach over a model with many correlated key-rate shifts when hedging term structure risk?

PCA converts correlated rate changes into uncorrelated components, and a few of them explain most of the variance. Hedgers can therefore neutralize exposure to just a few factors with fewer instruments, though some residual risk remains and the components must be re-estimated from historical data.

  1. APCA components are uncorrelated, so a few factors capture most variance and reduce the number of hedging instruments neededCorrect
  2. BPCA guarantees that the hedge is exact against any non-parallel shift
  3. CPCA components are fixed over time and never need re-estimation
  4. DPCA eliminates the need for historical yield data

Explanation

PCA transforms correlated rate changes into uncorrelated components, with the first few explaining most variance, so hedging can target a small number of factors. It does not give an exact hedge for all shifts, since residual variance remains. Components are estimated from historical data and can change over time.

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