Future Contracts Finance

Sec0101

1. The duration of a 20-year, 6 percent coupon Treasury bond selling at par is 10.292 years. The bond’s interest is paid semiannually, and the bond qualifies for delivery against the Treasury bond futures contract.

a. What is the modified duration of this bond?

MD= 10.292/1.03 = 9.99 years

b. What is the impact on the Treasury bond price if market interest rates increase 50 basis points?

Change in price= -9.992*.005*100000= $-4996

c. If you sold a Treasury bond futures contract at 96 and interest rates rose 50 basis points, what would be the change in the value of your futures position?

Change in price = -9.992*.005*96000= $-4796.16

d.      If you purchased the bond at par and sold the futures contract, what would be the net value of your hedge after the increase in interest rates?

 -4996+4796.16= $199.84

2.      Suppose a bank purchases a $1 million 90-day (360-day year) Eurodollar futures contract trading at 98.50.

a.      If the contract is reversed two days later by selling the contract at 98.55, what is the net profit?

(.9855-.9850)*(90/360)*1000000= $125

b.      What is the loss or gain if the price at reversal is 98.40?

 (.9840-.9850)*(90/360)*1000000= $-250

3.      Tree Row Bank has assets of $150 million, liabilities of $130 million, and equity of $20 million. The asset duration is six years, and the duration of the liabilities is four years. Market interest rates are 10 percent. Tree Row Bank wishes to hedge the balance sheet with Treasury bond futures contracts, which currently have a price quote of $95 per $100 face value for the benchmark 20-year, 6 percent coupon bond underlying the contract.

If you use a 6% coupon 20-year bond, and a price of $95, then the duration = 11.68385.

a. Should the bank go short or long on the futures contracts to establish the correct macrohedge?

The bank should sell futures contracts because a rise in interest rates would cause equity and futures contracts less valuable. The...