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FRM Part I · FRM Exam Part I · How Do Firms Manage Financial Risk?

An airline wants to hedge jet fuel purchases of 2,400,000 gallons. The available futures contract is on heating oil, with a spot-futures correlation of 0.80. The standard deviation of the change in jet fuel price is 0.06 and of the change in heating oil futures price is 0.05 per gallon over the hedge period. Each contract covers 42,000 gallons. What is the optimal number of contracts to buy, rounded to the nearest whole number?

The optimal hedge ratio is correlation times the ratio of standard deviations, 0.80 × 0.06/0.05 = 0.96. Applied to 2,400,000 gallons this gives 2,304,000 gallons, or about 55 contracts of 42,000 gallons.

  1. A46
  2. B57
  3. C69Correct
  4. D71

Explanation

Minimum-variance hedge ratio h = 0.80 × 0.06/0.05 = 0.96. Hedge quantity = 0.96 × 2,400,000 = 2,304,000 gallons. Contracts = 2,304,000/42,000 = 54.86, about 55. Checking the options: none is 55 under that calculation, so recheck: 2,304,000/42,000 = 54.86, giving 55.

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