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Answer: 0.75
The farmer sold 10 contracts, each for 5,000 bushels, so she hedged: \[ 10 \times 5{,}000 = 50{,}000 \text{ bushels} \] Her exposure was 100,000 bushels, so the hedge ratio implied by her position is: \[ h^* = \frac{50{,}000}{100{,}000} = 0.5 \] For an optimal hedge: \[ h^* = \rho \frac{\sigma_S}{\sigma_F} \] Substitute the volatilities: \[ 0.5 = \rho \times \frac{0.60}{0.90} = \rho \times \frac{2}{3} \] Solve for \(\rho\): \[ \rho = 0.5 \times \frac{3}{2} = 0.75 \] **Correct answer: B) 0.75**.
Author: Manit Arora
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Q-154.3. A wheat farmer hedged her future sale of 100,000 bushels of wheat by selling forward 10 contracts (each for 5,000 bushels). The standard deviation of monthly changes in the spot and futures price of wheat is, respectively, $0.60 and $0.90. What was her correlation assumption?
A
0.67
B
0.75
C
0.80
D
0.90
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