FRM Part I · FRM Exam Part I · How Do Firms Manage Financial Risk?
A firm holds 200,000 barrels of crude oil priced at USD 80 per barrel and hedges with futures contracts of 1,000 barrels each. The correlation between spot and futures price changes is 0.90, the standard deviation of spot changes is 3.0% and of futures changes is 2.5%. What is the minimum-variance number of contracts to short?
The firm should short 216 contracts. The minimum-variance hedge ratio is correlation times the ratio of spot to futures volatility, 0.90 x 3.0/2.5 = 1.08. Multiplying by 200,000 barrels and dividing by 1,000 barrels per contract gives 216.
- A180
- B216Correct
- C240
- D167
Explanation
Hedge ratio h = rho x sigma_S / sigma_F = 0.90 x 3.0/2.5 = 1.08. Contracts = 1.08 x 200,000 / 1,000 = 216. Using 0.90 without the volatility ratio gives 180; 1.2 x 200 = 240 ignores correlation.
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