In February 2018 a U.S. grain trader who supplies corn gluten feed has growing concerns that the price of the commodity will fall before her current inventory of 10,000 tons is sold in August to be shipped overseas. However, there is no futures contract on corn gluten feed, so she decides to hedge the price risk using the September soybean meal futures. Each soybean meal futures contract is for 100 tons. At the time she puts the hedge in place, the spot price of corn gluten feed is $490 per ton. The standard deviation of the change in this price over the life of the hedge is estimated to be $7.525. The September futures price of soybean meal at that time is $336 per ton and the standard deviation of the change in this over the life of the hedge is $4.98. The coefficient of correlation between the spot price change and futures price change is 0.87.
a. What is the minimum variance hedge ratio?
b. Should the hedger take a long or short futures position?
c. What is the optimal number of futures contracts when issues associated with daily settlement were not considered?
d. What is the optimal number of futures contracts required if the daily settlement of futures contracts were taken into account?
e. Suppose that the grain trader sells her entire inventory to an overseas client on August 7 and closes out her futures position at that time. On that date, the spot price of corn gluten feed is $412 per ton, while the September futures price of soybean meal is $316 per ton. What is the effective (net) hedged price per ton which the trader will receive if the hedge from part c above were the one which was used?