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 103-08 per $100 of face value, its duration is nine years, and its yield to maturity is 7.68 percent.

(LG 24-4)

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. By how much does the value of the call position change if interest rates change +/–50 basis points?

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