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

A portfolio has key-rate 01s of $10,000 at the 5-year point and $20,000 at the 10-year point (gains per 1 bp fall in each rate). A hedger will short Instrument A, with key-rate 01s of $50 (5-year) and $10 (10-year) per contract, and Instrument B, with key-rate 01s of $0 (5-year) and $40 (10-year) per contract, to neutralize both key-rate exposures. How many contracts of each should be shorted?

Short 200 contracts of A and 450 of B. Instrument A is the only one with 5-year exposure, so 200 contracts cover that. Those 200 also hedge 2,000 of the 10-year exposure, leaving 18,000 for B at 40 each, which is 450 contracts.

  1. A200 of A and 450 of BCorrect
  2. B200 of A and 500 of B
  3. C450 of A and 200 of B
  4. D200 of A and 400 of B

Explanation

Only A has 5-year exposure, so 50a = 10,000 gives a = 200. The 10-year exposure then requires 10(200) + 40b = 20,000, so 40b = 18,000 and b = 450. The 500 figure comes from ignoring A's 10-year exposure (20,000/40).

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