Consider the following scenarios, determine how to hedge each scenario using bond futures, and comment on whether it would be appropriate to hedge the exposure.

a. A bond portfolio manager will be paid a large bonus if her $10 million portfolio earns 6 percent in the current fiscal year. She has done very well through the first nine months. However, she is concerned that interest rates might increase over the next few months.

b. The manager of a company is selling one of its warehouses. The deal will close in two months. The manager plans to buy six-month Treasury bills when the company receives payment for the warehouse space, but the manager is worried that interest rates might decline in the next two months.

c. Sam Blackwell plans to retire in a year. Upon retirement, he will be paid a lump sum based on the value of the securities in his defined-contribution retirement plan. Sam's portfolio consists largely of Treasury bonds, and he is worried that interest rates will be increasing in the coming year.