Question

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

1.
Price at 7%=1000*4%/7%*(1-1/(1+7%/2)^(2*10))+1000/(1+7%/2)^(2*10)=786.8140

Price at 5%=1000*4%/5%*(1-1/(1+5%/2)^(2*10))+1000/(1+5%/2)^(2*10)=922.0542

% change=922.0542/786.8140-1=17.1883%

If rate falls, price increases and vice versa

2.
Price at 7%=1000*10%/7%*(1-1/(1+7%/2)^(2*10))+1000/(1+7%/2)^(2*10)=1213.1860

Price at 5%=1000*10%/5%*(1-1/(1+5%/2)^(2*10))+1000/(1+5%/2)^(2*10)=1389.7291

% change=1389.7291/1213.1860-1=14.5520%

Higher coupon bonds have lower interest rate risk compared to that of lower coupon bonds