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FRM Part I · FRM Exam Part I · Using Futures for Hedging

An airline needs to hedge 3,000,000 gallons of jet fuel with heating oil futures. Each contract covers 42,000 gallons. The correlation between changes in jet fuel and heating oil prices is 0.90, the standard deviation of jet fuel price changes is 0.040 and of heating oil futures price changes is 0.030 per period. Ignoring tailing, what number of contracts (nearest whole) is the minimum-variance hedge?

The minimum-variance hedge is about 86 contracts. The hedge ratio is 0.90 times 0.040 over 0.030, or 1.20, and multiplying by 3,000,000 gallons divided by 42,000 gallons per contract (71.43) gives 85.7, rounded to 86.

  1. A71
  2. B86Correct
  3. C95
  4. D54

Explanation

h* = 0.90 x 0.040/0.030 = 1.20. Contracts = 1.20 x 3,000,000/42,000 = 1.20 x 71.43 = 85.7, so 86. Option A omits the hedge ratio; option D uses 0.90 x 0.03/0.04 = 0.675, giving 48, not 54, and is also inverted.

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