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FRM Part II · FRM Exam Part II · Risk Management for Changing Interest Rates: Asset-Liability Management and Duration Techniques

A portfolio manager holds bonds worth $200 million with modified duration 6.0. She hedges to a target modified duration of 2.0 by selling futures. The cheapest-to-deliver-based futures contract has a price of $125,000 per contract and a modified duration of 8.0 (assume yield beta of 1). Approximately how many contracts should she sell?

She should sell about 800 contracts. The required change in dollar duration is the duration reduction of 4 times $200 million, which is $800 million per unit yield change. Each contract provides 8 times $125,000, or $1 million, so 800 contracts are needed.

  1. A800Correct
  2. B1,600
  3. C1,200
  4. D400

Explanation

Contracts = (D_target - D_portfolio) x V / (D_futures x futures price) = (2-6) x 200,000,000 / (8 x 125,000) = -800,000,000/1,000,000 = -800. So sell 800. Using the full duration of 6 instead of the change gives 1,200. Omitting the target-duration offset... using 2 instead of 4 gives 400.

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