Residential Energy LLC would like to use crude oil futures contracts to hedge its inventory of heating oil. The size of its inventory is 475,555 gallons of heating oil. An analyst at Residential Energy has calculated a beta equal to 0.12 and an R-squared equal to 0.875. To calculate these numbers, the analyst used a linear regression of heating oil price changes per gallon against crude oil futures price changes per barrel. The size of 1 crude oil futures is 1,000 barrels, which is equivalent to 42,000 gallons.

If the target beta is zero, what is the optimal number of futures contracts that should be used for hedging?

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