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A coffee producer holds (owns) a current inventory of coffee worth $6 million (or 1,500,000 pounds)...

A coffee producer holds (owns) a current inventory of coffee worth $6 million (or 1,500,000 pounds) at current spot prices of $4.00 per pound. He plans to sell this inventory in 12 months, or on December 23, 2020. He fears that the price of coffee could fall in 12 months. He is considering a minimum variance (risk) hedge of his inventory using the coffee futures contract. The current price of Dec 2020 coffee futures is $4.10 per pound and the size of one coffee futures contract is 37,500 pounds. The standard deviation of the coffee spot and futures prices are 0.85 and 0.93, respectively. The correlation between futures and spot prices is 0.92. Assume that the coffee spot and futures prices on Dec. 23, 2020 (contract maturity date) are both at $3.80 per pound. What are the optimal number (N*) of coffee futures contracts he should trade today to hedge the value of his coffee inventory ?

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