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

A portfolio has key-rate exposures of $20,000 per bp at the 2-year point and $40,000 per bp at the 10-year point (it loses that amount per 1 bp rise in the relevant rate). A manager hedges only the total DV01 of $60,000 using payer (pay-fixed) 10-year swaps, each with a DV01 of $800 that gains when rates rise and has no 2-year exposure, so 75 contracts are used. The curve then twists so that the 2-year rate falls 10 bp and the 10-year rate rises 20 bp. What is the net profit or loss of the hedged portfolio?

The hedged portfolio gains $600,000. The portfolio makes $200,000 on the 2-year fall but loses $800,000 on the 10-year rise, a net loss of $600,000. The 75 payer swaps gain $1,200,000 on the 20 bp 10-year rise. The net is +$600,000, showing that DV01 matching does not protect against twists.

  1. AGain of $600,000Correct
  2. BLoss of $600,000
  3. CZero, because total DV01 was matched
  4. DGain of $1,200,000

Explanation

Portfolio: 2-year gain of 20,000 x 10 = +200,000; 10-year loss of 40,000 x 20 = -800,000; net -600,000. Swaps: 75 x 800 x 20 = +1,200,000. Net = -600,000 + 1,200,000 = +600,000. The zero answer wrongly assumes a parallel shift, and -600,000 is the unhedged result.

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