On Dec 15, 2009, a bond portfolio manager holds $1 million of T-bonds that pay a coupon rate of 7% semiannually and mature in 23 years. The bond is currently priced at 102 and has a modified duration of 7. The manager would like to sell the bonds on Jan 31st. The current March T-bond futures is at 98. The characteristics of the deliverable bond imply a modified duration of 9.
a. How many futures contracts do you buy or sell to hedge your position?
b. If the bonds are sold on Jan 31st at a price of 95 and the futures price is on the day is 93, how well did the hedge work?