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Answer: Short 1,122 contracts
Use the optimal hedge ratio with tailing. - Hedge ratio: \(h^* = \rho \times \frac{\sigma_S}{\sigma_F} = 0.9 \times \frac{20\%}{20\%} = 0.9\) - Exposure: 1,200,000 barrels - Crude oil futures contract size: 1,000 barrels - Tailing adjustment: multiply by \(\frac{S_0}{F_0} = \frac{106}{102}\) So the number of short contracts is: \[ N = 0.9 \times \frac{1{,}200{,}000}{1{,}000} \times \frac{106}{102} \approx 1{,}122 \] Therefore, the correct initial trade is **short 1,122 contracts**.
Author: Manit Arora
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Q-156.1 Rolling the hedge forward
An oil producer wants to employ a stack-and-roll hedge by rolling over one-month contracts in order to minimize (hedge) the price risk of 1.2 million barrels of oil that will be sold (by the oil producer) in 12 months. The spot price of oil is $106, the one-month futures price is $102, and the 12-month futures price is $98. The correlation between changes in the spot and futures price is 0.9, and both the spot and futures prices have the same 20% volatility. If the oil producer wants to tail the hedge, what is the initial trade?
A
Short 90 contracts
B
Short 94 contracts
C
Short 1,080 contracts
D
Short 1,122 contracts
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