Question

Given the following spot rates and assuming the bonds and the time periods are semi-annual:

Time Spot Rate 1 3.00% 2 3.30% 3 3.50% 4 3.90% 5 4.40% 6 4.75% 7 4.95% 8 5.05% 9 5.15% 10 5.25% 11 5.40% 12 5.50% 13 5.60% 14 5.65% 15 5.75% 16 5.80%

1.What is the price of a 4% coupon bond maturing in 5 years?

2. What is the YTM on the above bond?

3. What is the implied forward rate on a two-year bond issue in 18 months?

4. What is the implied forward rate on a 1-year bond issued in 5 years?

5. Suppose a 3-year, 0-coupon bond for delivery in 2 years traded in the futures market. What should its price be?

Answer 1

a. Have a look at the following table. Price = 94.818

b. Refer to the same table. YTM = 2.59%

c. Refer to the table. Implied forward rate = (1 + 0.0511/2) * (1 + 0.0642/2) * (1 + 0.0652/2) * (1 + 0.0616/2)

= 12.66% in 2 years i.e. forward rate 18 month hence for 2 years shall be 12.66%

d. Let the par value of ZCB be $100.

Implied forward rate for 3 years after 2 years = 19.96% (Refer to the table). Hence, price of bond 2 years hence = 100 / 1.1996 = 83.35948. This is the price at which the bond futures is expected to trade today.