The duration of a 20-year, 8 percent coupon Treasury bond selling at par is 10.292 years. The bond’s interest is paid semiannually, and the bond qualifies for delivery against the Treasury bond futures contract.

a. What is the modified duration of this bond?

b. What is the impact on the Treasury bond price if market interest rates increase 50 basis points?

c. If you sold a Treasury bond futures contract at 95 and interest rates rose 50 basis points, what would be the change in the value of your futures position?

d. If you purchased the bond at par and sold the futures contract, what would be the net value of your hedge after the increase in interest rates?