Response to the following problem:
A mutual fund plans to purchase $500,000 of 30-year Treasury bonds in four months. These bonds have a duration of 12 years and are priced at 96-08 (32nds). The mutual fund is concerned about interest rates changing over the next four months and is considering a hedge with T-bond futures contracts that mature in six months. The T-bond futures contracts are selling for 98-24 (32nds) and have a duration of 8.5 years.
a. If interest rate changes in the spot market exactly match those in the futures market, what type of futures position should the mutual fund create?
b. How many contracts should be used?
c. If the implied rate on the deliverable bond in the futures market moves 12 percent more than the change in the discounted spot rate, how many futures contracts should be used to hedge the portfolio?
d. What causes futures contracts to have a different price sensitivity than the assets in the spot markets?