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

Key rates are set at 2, 5 and 10 years. A key rate shift is applied in which the 5-year rate rises by 10 bp, the 2-year and 10-year rates are unchanged, and shifts between key rates are linearly interpolated. What is the implied shift at the 7-year maturity?

The shift at 7 years is 6 bp. The triangular shift declines linearly from 10 bp at the 5-year key rate to zero at the 10-year key rate, so at 7 years it retains 3/5 of the full 10 bp move.

  1. A4 bp
  2. B6 bpCorrect
  3. C7 bp
  4. D5 bp

Explanation

The shift falls linearly from 10 bp at 5 years to 0 at 10 years. At 7 years the weight is (10 - 7)/(10 - 5) = 3/5, giving 10 x 0.6 = 6 bp. Using 2/5 gives 4 bp, which measures the distance from the wrong end.

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