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

A firm wants to hedge a spot exposure of 2,000,000 barrels of crude oil for one year using futures with a minimum-variance hedge ratio of 0.90. Each futures contract covers 1,000 barrels. Ignoring tailing, how many contracts should be sold, and what is the approximate tailed number if the annual discount factor is 1/1.05 (round to the nearest whole contract)?

The untailed hedge is 0.90 times 2,000 contracts' worth of exposure, or 1,800 contracts. Tailing divides by 1.05 to reflect daily settlement over one year, giving about 1,714 contracts. Multiplying by 1.05 would wrongly increase the position.

  1. A1,800 untailed; 1,714 tailedCorrect
  2. B2,000 untailed; 1,905 tailed
  3. C1,800 untailed; 1,890 tailed
  4. D1,714 untailed; 1,800 tailed

Explanation

Untailed number = 0.90 × 2,000,000 / 1,000 = 1,800. Tailing multiplies by 1/1.05: 1,800/1.05 = 1,714.3, about 1,714. Option 2 omits the hedge ratio; option 3 multiplies by 1.05 instead of dividing.

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