You are a portfolio manager running a fixed income portfolio all of one bond. The bond is XYZ

bond with a YTM of 5%, coupon 8%, term 6 years semiannual, BBB credit rating. The

reinvestment rate assumption is 3%.

You have a $500M pension liability with a duration of 8 years.

Two derivative instruments available are:

a.) Tbond futures, priced at 97 with a duration of 3 and

b.) Interest rate swaps with a duration of 3.

A.) Calculate the bond duration.

B.) Calculate the # of bonds needed to fund the liability.

C.) Explain the conditions to immunize the portfolio using a classical duration-match

immunization.

D.) Provide the number of Tbond contracts.

E.) If the reinvestment rate falls from 3% to 1%, provide the projected deficit.

F.) Provide the NP (notional principal of Interest Rate Swaps to hedge)

G.) Prove that the futures gain will > the loss attributed to the deficit.

H.) Prove that the IRS (interest rate swap) gain will > the loss attributed to the deficit.

I.) Indicate the type of swap needed.

The ZB US Treasury Bond Futures contract has a par of $100,000, an initial margin of $4,620, a

maintenance margin of $4,200. The duration is 5 years and it is priced at 99. As an investor you

open a futures trading account with $100,000.

A.) How many contracts can you open (long)?

B.) If the interest rates fall by 30 basis points, what is your ROI?

C.) If the interest rates fall by 30 basis points, what is your dollar profit?

D.) At what point will you get a margin call? Be specific.

E.) If the Federal Reserve started to raise the interest rates, would you

a. Stay long?

b. Reverse and go short?

c. Desire to increase or decrease your portfolio duration?