Question

8. a) Consider Bond C – a 4% coupon bond that has 10 years to maturity. It makes semi-annual payments and has a YTM of 7%. If interest rates suddenly drop by 2%, what is the percentage change of the bond? What does this problem tell you about the relationship between interest rate and bond price?

b) Consider another bond – Bond D, which is a 10% coupon bond. Similar to Bond C, it has 10 years to maturity. It also makes semi-annual payments and have a YTM of 7%. If interest rates suddenly drop by 2%, what is the percentage change of the bonds? Comparing the percentage change of bond C and bond D, what does this tell you about the interest rate risk of bonds with higher coupon rates?

Answer 1

a) Coupon =4%*1000 =40
YTM =7%
Number of years =10
Price of Bond =PV of Coupons+PV of Par Value =40*((1-(1+7%)^-10)/7%)+1000/(1+7%)^10 =789.2926

New YTM =7%-2%=5%
Price of Bond =PV of Coupons+PV of Par Value =40*((1-(1+5%)^-10)/5%)+1000/(1+5%)^10 =922.7827

Percentage Price of Bond =(922.7827-789.2926)/789.2926 =16.91%
When interest rates decreases price of bond increases and vice versa.

b) Bond D
Semi Annual Coupon =10%*1000/2 =50
Semi annual YTM =7%/2 =3.5%
Number of periods =10*2 =20
Price of Bond =PV of Coupons+PV of Par Value =50*((1-(1+3.5%)^-20)/3.5%)+1000/(1+3.5%)^20 =1213.19

New YTM =7%-2%=5%
Semi Annual YTM =5%/2 =2.5%
Price of Bond =PV of Coupons+PV of Par Value =50*((1-(1+2.5%)^-20)/2.5%)+1000/(1+2.5%)^20 =1389.73

Percentage Price of Bond =(1389.73-1213.19)/1213.19 =14.55%

Higher the coupon lower is the interest rate risk, lower the coupon rate higher is the interest rate risk.