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The standard deviation of monthly changes in the spot price of live cattle is (in cents per pound) 1.2. The standard deviation of monthly changes in the futures price of live cattle for the closest contract is 1.4. The correlation between the futures price changes and the spot price changes is 0.7. It is now October 15. A beef producer is committed to purchasing 200,000 pounds of live cattle on November 15. The producer wants to use the December live cattle futures contracts to hedge its risk. Each contract is for the delivery of 40,000 pounds of cattle. What strategy should the beef producer follow?

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Answer:

The answer is below

Explanation:

The optimal hedge ratio shows the degree of correlation between an asset or liability and the final product.

The optimal hedge ratio = correlation * (standard deviation of monthly changes in the spot price) /  (standard deviation of monthly changes in the futures price)

The optimal hedge ratio = 0.7 * (1.2/1.4) = 0.6

The beef producer requires a long position = 0.6 * 200000 lbs  = 120000 lbs of cattle.

The beef producer should take a long position in 3 December contracts closing out the position on November 15.

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