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

A portfolio manager holds a liability with a DV01 of USD 42,000 and hedges with two bonds: Bond A has DV01 of USD 600 per USD 1 million face and Bond B has DV01 of USD 900 per USD 1 million face. The manager wants to hold equal face amounts of A and B (long) so that total DV01 matches the liability. What face amount of each bond is needed?

The manager needs USD 28 million face of each bond. Each USD 1 million pair contributes DV01 of 600 + 900 = 1,500, and 42,000 divided by 1,500 equals 28 million.

  1. AUSD 28 millionCorrect
  2. BUSD 70 million
  3. CUSD 46.7 million
  4. DUSD 35 million

Explanation

Per USD 1 million of each, combined DV01 = 600 + 900 = 1,500. Required = 42,000 / 1,500 = 28 million of each. 70 million uses only Bond A's DV01; 46.7 million uses only Bond B's; 35 million averages the DV01s wrongly (42,000/1,200).

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