Answer-first summary for fast verification
Answer: 0.2599
The optimal hedge ratio is calculated using the formula: $$h^* = \rho_{S,F} \frac{\sigma_S}{\sigma_F}$$ Where: - $\rho_{S,F}$ = correlation between spot and futures = 0.3876 - $\sigma_S$ = standard deviation of spot price changes = 0.57 - $\sigma_F$ = standard deviation of futures price changes = 0.85 Substituting the values: $$h^* = 0.3876 \times \frac{0.57}{0.85} = 0.3876 \times 0.6706 = 0.2599$$ Therefore, the optimal hedge ratio is 0.2599, which corresponds to option D.
Author: LeetQuiz Editorial Team
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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
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