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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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  1. 29 September, 09:03
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    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.
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