A portfolio manager, who has a bond portfolio with a value of $10 million and duration of 6 years, is interested in immunizing the portfolio against changes in interest rates over the next 2 months. Suppose that the closest-to-maturity Treasury bond futures contract traded on the Chicago Board of Trade has a size of $100,000 face value, a quoted futures price of 98-15, and a delivery month in 3 months. Assume that the following three bonds are eligible for delivery.

a) Which of the above three bonds is cheapest to deliver (CTD)?

b) How should the portfolio manager immunize the bond portfolio against changes in interest rates over the next 2 months? In your answer clearly specify his position in the Treasury bond futures contract (buy/sell) and the number of contracts.

Forecast of quoted spot price of bond on first elivery date 115-03 125-15 130-09 Duration on first delivery date in years Bond Conversion factor 10 15 16 1.1687 1.1813 1.2083 3