3. On December 15^th, 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 in currently priced at 102 and has a modified duration of 7. The manager would like to sell the bonds on January 31^st. The current March T-Bond futures is at 98. The characteristics of the deliverable bond imply a modified duration of 9.

How many futures contracts do you buy or sell to hedge your position?

If the bonds are sold on Jan 31^st at a price of 95 and the futures price is on that day is 93, how well did the hedge work?

Need to show all my work and steps detailed