Question 10. Minimum Variance Commodity Hedge (13 marks) Choc Full of Good Inc., a producer of powdered hot chocolate, has just received a large order that will require the purchase of 800 metric tons of cocoa in 3 months. The current spot price of cocoa is US $3,055 per metric ton. The standard deviation of the change in spot cocoa price is 0.2. Mr. Dulce, the CFO of Choc Full, is considering a minimum-variance hedge of this future cocoa purchase using the three-month cocoa futures contract. The contract size is 10 metric tons. The standard deviation of the change in cocoa futures price is 0.25. The covariance between the change in the spot and futures cocoa price is 0.035. The annually compounded interest rate faced by the company is 5%, the three-month storage cost is $2.5 per metric ton, and the convenience yield is $0.5 per metric ton. a. What is the futures price per metric ton of cocoa? (2 marks) b. Should the company long or short cocoa futures? (1 mark) c. Compute the minimum-variance hedge ratio. (1 mark) d. How many contracts should be traded? (1 mark) e. What is the estimated effectiveness of this minimum variance hedge? (1 mark) f. What is the correlation of the change in the spot and futures cocoa price? (1 mark) g. What is the profit from this hedged position if the spot cocoa price in three months turns out to be $3,100? (3 marks) h. Calculate the gain/loss on spot position, the gain/loss on futures position, and the profits from this hedged position by hypothesizing that the spot cocoa price in three months will range from $2,900 to $3,200, with increments of $25. Plot these numbers on a graph. Explain what you see from the graph in terms of the relationship between the gain/loss on spot position, gain/loss on futures position, and hedged profits/losses. (Hint: Use an Excel spreadsheet to do this one.) (3 marks)