FRM Part I · FRM Exam Part I · Using Futures for Hedging
A firm will sell 50,000 barrels of crude oil in one year and hedges with one-year futures. Each contract covers 1,000 barrels. The minimum-variance hedge ratio is 1.0 and the annual risk-free rate is 5% with annual compounding. Ignoring rounding, using a tailing factor of 1/(1+r)^T, approximately how many contracts should the firm short?
The firm should short about 47.6 contracts. The untailed hedge is 50 contracts (50,000 barrels divided by 1,000, times a hedge ratio of 1), and the tailing factor of 1/1.05 reduces this to about 47.6 because of daily settlement.
- A47.6Correct
- B50.0
- C52.5
- D45.2
Explanation
Untailed hedge is 50,000/1,000 x 1.0 = 50 contracts. Tail factor = 1/1.05 = 0.95238. Tailed hedge = 50 x 0.95238 = 47.62 contracts. Option C wrongly multiplies by 1.05; option B ignores tailing.
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