Question

Interest Rate Risk [LO2] 

Bond J is a 4 percent coupon bond. Bond K is a 12 percent coupon bond. Both bonds have nine years to maturity, make semiannual payments, and have a YTM of 8 percent. If interest rates suddenly rise by 2 percent, what is the percentage price change of these bonds? What if rates suddenly fall by 2 percent instead? What does this problem tell you about the interest rate risk of lower-coupon bonds?

Answer 1

We use pv formuale in excel to find the price of bond. Price and interest rates are inversely proportional to the each other.
=pv(rate,nper,pmt,fv,type)
Bond J:
rate=8%/2
nper=9*2=18
pmt=1000*(4%/2)=20
fv=1000
type=0
=pv(8%/2,18,-20,-1000,0)=746.81
Now the YTM rises by 2% then new price of bond
=pv(10%/2,18,-20,-1000,0)=649.31
% change in price=(final/initial)-1
=(649.31/746.81)-1=-13.06%
Now the YTM falls by 2% then new price of bond
=pv(6%/2,18,-20,-1000,0)=862.46
% change in price=(final/initial)-1
=(862.46/746.81)-1=15.49%

Bond K:
rate=8%/2
nper=9*2=18
pmt=1000*(12%/2)=60
fv=1000
type=0
=pv(8%/2,18,-60,-1000,0)=1253.19
Now the YTM rises by 2% then new price of bond
=pv(10%/2,18,-60,-1000,0)=1116.90
% change in price=(final/initial)-1
=(1116.90/1253.19)-1=-10.88%
Now the YTM falls by 2% then new price of bond
=pv(6%/2,18,-60,-1000,0)=1412.61
% change in price=(final/initial)-1
=(1412.61/1116.90)-1=12.72%
Lower coupon bond has higher percentage change and means higher interest rate risk than higher copupon bond