Answer-first summary for fast verification
Answer: 1.07
## Explanation The optimal hedge ratio is calculated using the formula: $$h = \rho \times \frac{\sigma_s}{\sigma_h}$$ Where: - $\rho$ = correlation coefficient = 0.8 - $\sigma_s$ = standard deviation of spot jet fuel prices - $\sigma_h$ = standard deviation of heating oil futures prices **Step 1: Calculate standard deviations** - $\sigma_s = \sqrt{0.0016} = 0.04$ - $\sigma_h = \sqrt{0.0009} = 0.03$ **Step 2: Apply the formula** $$h = 0.8 \times \frac{0.04}{0.03} = 0.8 \times 1.333 = 1.067 \approx 1.07$$ **Why other options are incorrect:** - **A (0.60)**: This results from reversing the standard deviations in the formula - **C (1.33)**: This is just the ratio of standard deviations without multiplying by the correlation - **D (1.42)**: This uses the variances directly instead of standard deviations
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An analyst at a logistics company is asked to recommend an appropriate hedging strategy using heating oil futures to hedge the volume of jet fuel required by its cargo planes. The analyst gathers the following relevant information about the spot price of jet fuel and the price of the appropriate heating oil futures contract:
What is the analyst's best estimate for the optimal hedge ratio?
A
0.60
B
1.07
C
1.33
D
1.42