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FRM Part I · FRM Exam Part I · Applying Duration, Convexity, and DV01

A $200 million portfolio has key rate durations of 1.5 at the 5-year point and 3.0 at the 10-year point. A manager hedges both exposures by shorting two bonds. Bond A has a 5-year key rate duration of 3.0 and a 10-year key rate duration of 0. Bond B has a 5-year key rate duration of 0.4 and a 10-year key rate duration of 8.0. What short positions in market value neutralize both key rate exposures?

Short $90 million of Bond A and $75 million of Bond B. The 10-year exposure of 600 requires 600/8 = 75 of B. B also offsets 30 of the 5-year exposure, leaving 270 to be hedged by A at 3.0, which requires 90.

  1. AShort $100 million of A and $75 million of B
  2. BShort $90 million of A and $75 million of BCorrect
  3. CShort $110 million of A and $75 million of B
  4. DShort $75 million of A and $90 million of B

Explanation

Dollar exposures: 5-year = 200 x 1.5 = 300; 10-year = 200 x 3.0 = 600. Only B has 10-year exposure, so 8.0 x b = 600 gives b = 75. B contributes 0.4 x 75 = 30 at 5 years, so A must cover 300 - 30 = 270, giving a = 270/3.0 = 90. Ignoring B's 5-year exposure gives 100; adding it instead of subtracting gives 110; 75/90 swaps the positions.

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