Cross-hedging jet fuel with heating oil futures

Question

An airline will buy 3{,}000{,}000 gallons of jet fuel in three months. There is no liquid jet-fuel future, so it cross-hedges with heating oil futures (1 contract = 42{,}000 gallons). From a regression of monthly changes in the jet-fuel price on monthly changes in the futures price, the standard deviations are \sigmaS = \0.03/gal and \sigmaF = \0.05/gal with correlation \rho = 0.75. How many futures contracts should the airline buy to minimize the variance of its fuel cost?

Accepted Answer

The variance-minimizing hedge ratio (regression beta of spot changes on futures changes) is h^ = ho\,\frac{\sigmaS}{\sigmaF} = 0.75 \cdot \frac{0.03}{0.05} = 0.75 \cdot 0.6 = 0.45. This says each gallon of fuel exposure should be hedged with 0.45 gallons of futures, because jet fuel is less volatile than the heating-oil future and only 75\% correlated. The hedged quantity is h^ 	imes 	ext{exposure} = 0.45 	imes 3{,}000{,}000 = 1{,}350{,}000 	ext{ gallons.} Dividing by the contract size gives the number of contracts: N^ = \frac{h^ 	imes QS}{QF} = \frac{1{,}350{,}000}{42{,}000} \approx 3…

Cross-hedging jet fuel with heating oil futures

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