Answer-first summary for fast verification
Answer: 31.0
For a cross-hedge, the **minimum variance hedge ratio** is \[ h^* = \rho \times \frac{\sigma_S}{\sigma_F} \] Substitute the values: \[ h^* = 0.880 \times \frac{0.0210}{0.0280} = 0.880 \times 0.75 = 0.66 \] The optimal number of futures contracts is \[ N^* = h^* \times \frac{Q_A}{Q_F} \] where: - \(Q_A = 2{,}000{,}000\) gallons - \(Q_F = 42{,}000\) gallons per contract \[ N^* = 0.66 \times \frac{2{,}000{,}000}{42{,}000} \approx 0.66 \times 47.62 \approx 31.4 \] The nearest answer is **31 contracts**.
Author: Manit Arora
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Question 711.1. Viaflex Airlines expects to purchase 2.0 million gallons of jet fuel in two months and decides to use heating oil futures for hedging (each heating oil contract traded by the CME Group is on 42,000 gallons of heating oil). Their corporate treasury department decides to base the hedge on the last 15 months of price changes. The standard deviation of the change, , in jet fuel prices per gallon was \`0.0210$, and the standard deviation of the change, $\Delta F$, in the futures price for the contract on heating oil was $\. As this will be a cross-hedge, the correlation between the price changes is 0.880. Below are displayed the price changes and the resulting OLS regression line; for example, the coefficient of determination equals 0.7747, which is the square of the correlation coefficient.
Please note that although heating oil futures contracts will be used for this cross-hedge, Viaflex will NOT be "tailings the hedge;" i.e., the hedge will be based on the intended quantity of gallons purchased. Which of the following is nearest to the optimal number of contracts that should be used to hedge?
A
14.0
B
22.0
C
31.0
D
40.0
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