Question: On March 31, a firm learns that it will have additional funds available July 31. It will use the funds to purchase $6,000,000 par value of the USTA 8.5% bonds maturing in 20 years. Interest is paid semiannually on June 1 and December 1. The bonds are rated A2 and are selling for 65.875 per 100 and yielding 10.2%. The modified duration is 6.4. The firm is considering hedging the anticipated purchase with November T-bond futures. The futures price is 61.25. The futures contract has a coupon of 10.75% and matures in 25 years. It has determined that the implied yield on the futures contact is 9.40% and the modified duration of the contract is 7.1. On July 31, the bonds are priced at 69.375. The November futures price is 66.50. The firm believes that the USTA bond yield will change 1 point for every 1 point change in the yield on the bond underlying the futures contract. Face value underlying the T-bond contract is $100,000.
a. Will they be exposed to an increase or decrease in the price of the bonds?
b. On March 31, how much are the spot bonds worth?
c. On July 31, how much are the spot bonds worth?
d. How much did the bond position increase or decrease (must state if increase or decrease and the amount)?
e. On March 31, how much is one futures contract worth? How many futures contracts are needed (round up)? Do you buy or sell the futures contracts?
f. On July 31, does the firm buy or sell the futures contracts? How much is one futures contract worth?
g. Is there is a gain or loss on the futures contract? If so, how much is the gain or loss on all the contracts combined?
h. On July 31, what is the net gain or loss on the combined bond position and the futures contracts (must state if gain or loss and the amount)?