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FRM Part I · FRM Exam Part I · Interest Rates

A pension fund has a liability with a present value of USD 50 million and a modified duration of 10. It will invest USD 50 million in two bonds: Bond X with modified duration 4 and Bond Y with modified duration 12, so that asset and liability values and durations are both matched. How much should it invest in Bond Y?

The fund should put USD 37.5 million in Bond Y. Setting the weighted average duration equal to 10 gives 12w + 4(1 - w) = 10, so w is 0.75 of USD 50 million. The dollar duration of the assets then equals the liability's 500.

  1. AUSD 37.5 millionCorrect
  2. BUSD 12.5 million
  3. CUSD 30.0 million
  4. DUSD 25.0 million

Explanation

Let w be the weight in Bond Y: 12w + 4(1 - w) = 10, so 8w = 6 and w = 0.75. The investment in Y is 0.75 × 50 = USD 37.5 million. Check: 37.5 × 12 + 12.5 × 4 = 450 + 50 = 500, which equals 50 × 10. USD 12.5 million is the amount in Bond X, not Y, and USD 25.0 million would give a duration of only 8.

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