United Millers purchases corn to make cornflakes. When the price of corn increases, the cost of making cereal increases, resulting in lower profits. Historically, profits per quarter have been related to the price of corn according to the equation:

Profits = $8 million 1 million x price per bushel.

1. How many bushels of corn should United Millers purchase in the corn futures market to hedge its corn-price risk?
2. Suppose a multinational firm is harmed when the dollar depreciates. Specifically, suppose that its profits decrease by $200,000for every $.05 rise in the dollar/pound exchange rate. How many contracts should the firm enter? Should it take the long side or the short side of the contracts? (remember that one contract equivalent to $62,500).
3. The investment manager wishes to hedge interest rate uncertainty. Suppose that the portfolio manager has a $10 million bond portfolio with a modified duration of 9 years. If as feared, market interest rates increase and the bond portfolios yield also rises, say by 10 basis points (.1%), the fund will suffer a capital loss. Suppose the bond portfolio is twice as large, $20 million, but that its modified duration is only 4.5 years. Show that the proper hedge position in T-bond futures is the same as the value 100 contracts. (one T-bond contract is equivalent $100,000)