Suppose that the standard deviation of quarterly changes in the prices of a commodity is $0.65, the standard deviation of quarterly changes in a futures price on the commodity is $0.81, and the coeﬃcient of correlation between the two changes is 0.8. What is the optimal hedge ratio for a three-month contract? What does it mean?

Question

Business

Payton Cooper

29 September, 08:10

Suppose that the standard deviation of quarterly changes in the prices of a commodity is $0.65, the standard deviation of quarterly changes in a futures price on the commodity is $0.81, and the coeﬃcient of correlation between the two changes is 0.8. What is the optimal hedge ratio for a three-month contract? What does it mean?

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Answers (1)

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Zaid Cordova · Answer 1

The optimal hedge is 0.642 and it means that the size of the future positions should be 64.2% of the exposure of the company in a 3 month-hedge.

Explanation:

optimal hedge ratio

= coeﬃcient of correlation * (standard deviation of quarterly changes in the prices of a commodity/standard deviation of quarterly changes in a futures price on the commodity)

= 0 ... 8 * (0.65/0.81)

= 0.642

Therefore, The optimal hedge is 0.642 and it means that the size of the future positions should be 64.2% of the exposure of the company in a 3 month-hedge.