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Answer: 0.42 (MV hedge) and 49.0% (R^2)
The minimum variance hedge ratio is \[ h^* = \rho\frac{\sigma_S}{\sigma_F} = 0.70\times\frac{0.12}{0.20} = 0.42 \] For a simple regression of spot changes on futures changes, the coefficient of determination is \[ R^2 = \rho^2 = 0.70^2 = 0.49 = 49\% \] So the correct answer is **0.42 and 49.0%**.
Author: Manit Arora
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Question 153.4. Assume the volatility (standard deviation) of the change in prices for the spot price of wheat and the futures price, respectively, are 12% and 20%. The (coefficient of) correlation between changes in the two prices is 0.70. What is, respectively, the minimum variance hedge ratio and the R^2 (coefficient of determination) from the regression of the change in spot price against change in futures prices?
A
1.167 (MV hedge) and 7.0% (R^2)
B
0.42 (MV hedge) and 7.0% (R^2)
C
0.42 (MV hedge) and 49.0% (R^2)
D
0.42 (MV hedge) and 42.0% (R^2)
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