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

A portfolio has key rate 01s (gain per 1 bp fall) of $600 at 2 years and $400 at 10 years, so its DV01 is $1,000. It is hedged with a short position in a 5-year bond whose entire DV01 of $1,000 sits at the 5-year point. The 2-year rate rises 20 bp, the 5-year rate rises 10 bp and the 10-year rate is unchanged. What is the net P&L of the hedged position?

The net P&L is a loss of $2,000. The portfolio loses $12,000 from the 2-year rate rise, while the short 5-year bond gains $10,000 from the 10-year-equivalent 10 bp rise at the 5-year point. The DV01 hedge is imperfect because the shift is not parallel.

  1. A-$2,000Correct
  2. B+$2,000
  3. C-$12,000
  4. D$0

Explanation

Portfolio: 2-year rate up 20 bp gives -600 x 20 = -12,000; the 10-year is unchanged. Short 5-year bond: rate up 10 bp gives +1,000 x 10 = +10,000. Net = -$2,000. The unhedged loss is $12,000, and $0 would only result from a parallel shift assumption.

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