A company wishes to hedge its exposure to a new fuel whose price changes have a $-0\mathrm{.}6$ correlation with gasoline futures price changes.

The company will lose $$1$ million for each one$-$dollar increase in the price per gallon of the new fuel over the next three months.

The standard deviation of price changes in new fuels is $50\%$ greater than that of gasoline futures prices.

If gasoline futures are used to hedge the exposure, how many gasoline futures contracts should be traded?

Each contract is on $42,000$ gallons.

Note that you cannot trade $-10\mathrm{.}6$ contracts. In this case, you should trade $-11$ contracts.

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