A mutual fund plans to purchase $10 million of 20-year T-bonds in two months. The bonds are yielding 7.68 percent. These bonds have a duration of 11 years. The mutual fund is concerned about interest rates changing over the next two months and is considering a hedge with a two-month option on a T-bond futures contract. Two-month calls with a strike price of 105 are priced at 1-25, and puts of the same maturity and exercise price are quoted at 2-09. The delta of the call is 0.5 and the delta of the put is -0.7. The current price of a deliverable T-bond is $103.2500 per $100 of face value, its duration is nine years, and its yield to maturity is 7.68 percent.
a. What type of option should the mutual fund purchase?
b. How many options should it purchase?
c. What is the cost of these options?
d. If rates change +/-50 basis points, what will be the impact on the price of the desired T-bonds?
e. What will be the effect on the value of the hedge if rates change +/- 50 basis points?
f. Diagram the effects of the hedge and the spot market value of the desired T-bonds.
g. What must be the change in interest rates to cause the change in value of the purchased T-bonds to exactly offset the cost of placing the hedge?