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Answer: 0.2599
## Explanation The optimal hedge ratio (h*) is calculated using the formula: \[ h^* = \rho \times \frac{\sigma_S}{\sigma_F} \] Where: - \(\rho\) = correlation between spot and futures price changes = 0.3876 - \(\sigma_S\) = standard deviation of spot price changes = 0.57 - \(\sigma_F\) = standard deviation of futures price changes = 0.85 \[ h^* = 0.3876 \times \frac{0.57}{0.85} \] \[ h^* = 0.3876 \times 0.6706 \] \[ h^* = 0.2599 \] Therefore, the optimal hedge ratio is 0.2599, which corresponds to option D. This hedge ratio represents the proportion of the spot position that should be hedged using futures contracts to minimize risk.
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The hedge ratio is the ratio of derivatives to a spot position (or vice versa that achieves an objective such as minimizing or eliminating risk. Suppose that the standard deviation of quarterly changes in the price of a commodity is 0.57, the standard deviation of quarterly changes in the price of a futures contract on the commodity is 0.85, and the correlation between the two changes is 0.3876. What is the optimal hedge ratio for a 3-month contract?
A
0.1893
B
0.2135
C
0.2381
D
0.2599