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FRM Part I · FRM Exam Part I · Commodity Forwards and Futures

An airline wants to hedge 2 million gallons of jet fuel purchases using heating oil futures. The standard deviation of monthly jet fuel price changes is 0.030, that of heating oil futures is 0.040, and their correlation is 0.80. What is the minimum-variance hedge ratio?

The minimum-variance hedge ratio is 0.60. It equals the correlation of 0.80 multiplied by the ratio of spot volatility to futures volatility, 0.030 divided by 0.040, which is 0.75. Inverting the ratio would wrongly give 1.07.

  1. A0.60Correct
  2. B1.07
  3. C0.80
  4. D0.75

Explanation

h* = rho x (sigma_S / sigma_F) = 0.80 x (0.030/0.040) = 0.80 x 0.75 = 0.60. The 1.07 option inverts the volatility ratio (0.80 x 1.333). The 0.80 option ignores the volatility ratio.

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