Suppose that there's a callable bond with an effective duration of 3 years and an effective convexity of -2. Use effective duration and convexity as substitutes for modified versions. All bonds sell at par.

a. What is the second-order percent price sensitivity to a rate change for the callable bond?

b. Suppose you're a dealer in the bond, what would you do to offset this sensitivity? Assume the only other bonds available are a callable bond with 5 yrs of duration and convexity of -1.5 and straight bonds with durations of 1, 2 and 5 years. Further, assume that these straight bonds have zero convexity for simplicity. Last, assume that all of these bonds came in any FV and sell at par. How many of each bond would you choose to eliminate the original callable bond's price sensitivity to rates?