FRM Part I · FRM Exam Part I · Using Futures for Hedging
An airline hedges jet fuel using crude oil futures. The standard deviation of the change in jet fuel price is 0.30 and that of the futures price is 0.20 over the hedge period, with correlation 0.80. What is the minimum-variance hedge ratio?
The minimum-variance hedge ratio is 1.20, calculated as correlation times spot volatility divided by futures volatility: 0.80 times 0.30 divided by 0.20. Inverting the volatility ratio gives 0.53, which is wrong, and correlation alone ignores the relative volatility.
- A1.20Correct
- B0.53
- C0.80
- D1.50
Explanation
h* = rho x sigma_S / sigma_F = 0.80 x 0.30 / 0.20 = 1.20. Using sigma_F/sigma_S gives 0.53, which inverts the ratio. Using the correlation alone (0.80) ignores the volatility scaling.
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