Question

1. A 6% coupon 20-year bond was bought 8 years ago is priced now to offer a 6% yield to maturity. You believe that in one year, the yield to maturity will be 5%. What is the change in price the bond will experience in dollars from now to one year later? In percentage?

Answer 1

Assuming face value of 1000

Case 1: Assuming annual coupon payments, Price now=(6%*1000)/(6%)*(1-1/1.06^12)+1000/1.06^12=1000

Price 1 year later=(6%*1000)/(5%)*(1-1/1.05^11)+1000/1.05^11=1083.064

Change in price=1083.064-1000=83.064

% change=83.064/1000=8.3064%

Case 2: Assuming semi-annual coupon payments, Price now=(6%*1000/2)/(6%/2)*(1-1/1.03^24)+1000/1.03^24=1000

Price 1 year later=(6%*1000/2)/(5%/2)*(1-1/1.025^22)+1000/1.025^22=1083.827

Change in price=1083.827-1000=83.827

% change=83.827/1000=8.3827%