William Gross is a fixed income fund manager. He managers fixed income portfolios on behalf of several clients. The current yield on all bonds is 8% p.a. with coupons paid annually A client comes to William and asks him to manage a bond portfolio to immunize their exposure to an existing liability. The liability requires the client to pay $3000,000 per year at the end of the next five years (i.e. one, two, three, four and five years from today respectively).

Calculate the dollar duration of your clients obligation. (3 marks)

To immunise the portfolio, your client has two assets a zero coupon bond with a 2 year duration and a face value of $160,000 and a perpetuity of 3,500 per annum. What combination of face value zero-coupon bond and perpetuity would immunize your clients obligation? (8 marks)

Finally, assume William Gross also has been asked to advise on an Australian investment fund which has a bond portfolio of $50 million. The duration of the portfolio is 6.20. William has decided to reduce the duration of its entire bond portfolio to 5. The futures contract it would use is priced at $100,000 and has a duration of 4.50. Assume that the conversion factor for the futures contract is 1.06. (3 marks)

Would the fund need to buy futures contracts or sell? Approximately, how many futures contracts would be needed to change the duration of the bond portfolio? What is expected to happen to interest rates?