Question

The following table gives government bond prices (all have par value = $1000 and annual coupon payment):

Bond		Maturity (Years)		Coupon (%)		Yield to Maturity
A		1		0.0		0.02
B		2		0.0		0.04
C		3		7.0		0.05
D		4		9.0		0.055
E		5		9.0		0.07
F		3		0.0		0.0512
G		4		0.0		0.0568
H		5		0.0		0.0624

     

a.     Which coupon-paying bond (bonds) is (are) mispriced by more than $1? Why?  

b. Consider Bond C and Bond F, both with 3 years to maturity but with different coupon rates. Why are the yields to maturity different? Would the difference in yields imply that one is better “buy” than the other? Why or why not?

Answer 1

Assuming zero coupon bonds to reflect correct yields

One year zero rate (bond A)= 0.02 or 2%

Two year zero rate (bond B) = 0.04 or 4%

Three year zero rate (bond F) = 0.0512 or 5.12%

Four year zero rate (bond G) = 0.0568 or 5.68%

One year zero rate (bond H) = 0.0624 or 6.24%

Now, price of Bond C = 70/0.05*(1-1/1.05^3)+1000/1.05^3 = $1054.46

Price as per zero rates in market

= 70/1.02+70/1.04^2+1070/1.0512^3 = $1054.49

So, the bond is almost correctly priced

price of Bond D = 90/0.055*(1-1/1.055^4)+1000/1.055^4 = $1122.68

Price as per zero rates in market

= 90/1.02+90/1.04^2+90/1.0512^3+1090/1.0568^4 = $1122.81

So, the bond is almost correctly priced

price of Bond E = 90/0.07*(1-1/1.07^5)+1000/1.07^5 = $1082.00

Price as per zero rates in market

= 90/1.02+90/1.04^2+90/1.0512^3+90/1.0568^4 + 1090/1.0624^5 = $1126.43

So, the bond is incorrectly priced

BOND E is mispriced by more than $1

b) Bond C and bond F's yields are different because of the coupon rates. Both bonds have different cashflows occuring at different points of time for which appropriate interest rates are different.

The difference in yields do not make one bond better than the other as the cashflows are occuring at different points of time. However, one should note that zero coupon bonds do not have reinvestment risk and the YTM is the same as realised yield. The higher the coupon rate, higher is the reinvestment risk