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

A refiner wants to hedge its exposure to jet fuel prices using heating oil futures. The standard deviation of monthly jet fuel price changes is 0.040, the standard deviation of monthly heating oil futures price changes is 0.050, and the correlation between the two is 0.75. What is the minimum variance hedge ratio?

The minimum variance hedge ratio is 0.60. It equals the correlation times the ratio of spot volatility to futures volatility: 0.75 multiplied by 0.040/0.050, which is 0.75 times 0.80. Inverting the volatility ratio would wrongly give 0.94.

  1. A0.60Correct
  2. B0.94
  3. C0.75
  4. D1.00

Explanation

h* = rho x (sigma_S / sigma_F) = 0.75 x (0.040 / 0.050) = 0.75 x 0.80 = 0.60. The option 0.94 comes from inverting the volatility ratio (0.75 x 1.25). The option 0.75 ignores the volatility ratio.

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