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.