You are in charge of the risk management division at Hacks, Inc. Hacks assets consist of investments worth $30 million today in 3-year zero-coupon bonds (i.e. the present value of the 3-year zero is $30 million). Hacks liabilities consist of a single payment of $43 million due in 10 years. The term structure of interest rates is flat at 5%. Assume that all shifts in the term structure are parallel.

a. What is the Macaulay and Modified duration of Hacks assets?

b. Hacks think that interest rates may rise to 5.5%. Compute the exact change in the value of Hacks assets and compare this with the approximate change using duration.

c. Consider the net worth of Hacks. What is the modified duration of net worth? What is the duration-based approximate change in net worth from an increase in rates from 5% to 5.5%?

d. Suppose you have access to a 3-month futures contract on a 20-year zero-coupon bond with face value of $1 million. Describe the position you need to take in these futures to duration hedge your net worth. (You need to explain how many contracts and whether you are short or long.)