Question

A two-year corporate bond has a coupon rate of 4 percent. The one-year spot rate is 3 percent and the forward rate is 5 percent. The bond’s credit spread is 1 percent for both the one-year and the two-year maturities

a. What is the price of the bond expressed as a percentage of its face value?

b. What is the bond’s yield to maturity?

c. What is the bond price calculated with the bond’s yield to maturity?

d. Calculate the bond duration first with the duration formula and then with duration as the weighted average maturity of the bond cash flow.

e. What would be the maturity of a zero-coupon bond with the same interest-rate risk as the two-year corporate bond assuming that the two bonds have the same credit risk

f. Calculate the percentage change in the bond price if the yield rises by 20 basis points.

g. Calculate the percentage change in the bond price if the yield rises by 20 basis points using the bond duration and compare your answer to the one in the previous question.

Answer 1

a) 2 year spot rate = (1.03*1.05)^0.5-1 = 0.039952 or 4.00%

So, the bond's discount rate will be 3+1 = 4% for one year and 4+1=5% for two years

So, for a bond with $100 face value, price P = 4/1.04+104/1.05^2 = 98.18586 or $98.19

So, the bond will trade at 98.19% of the face value.

b) The bond's yield to maturity (y) is given by

4/(1+y) + 104/(1+y)^2 = 98.19

Solving , we get y =0.049753 or 4.98%

So, the YTM of the bond is 4.98%

c) Price of the bond P = 4/1.0498+ 104/1.0498^2 =$98.19

d) The Duration formula is D =

= 1*4/(98.19*1.0498^1+ 2*104/98.19*1.0498^2)

= 1.96 years

Bond cashflows are

for 1st year = 4/1.0498 = $3.81025

For 2nd year = 104/1.0498^2 =$94.36701

So, weighted average maturity = 3.81025/98.19 *1 + 94.36701/98.19* 2

=1.96 years