You are a portfolio manager running a fixed income portfolio all of one bond.The bond is an XYZ bond with a YTM of 5%, coupon of 8%, term of 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.)T-bond 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 T-bond 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.