Question

A bond with a yield to maturity of 3% and a coupon rate of 3% has 3 years remaining until maturity. Calculate the duration and the modified duration for this bond assuming annual interest payments and a par value of $1,000. Why is the duration of this bond higher than the 3-year 10% coupon bond yielding 10% we looked at in the notes that had a duration of 2.7 years? If the required market yield on this bond increases to 4%, what approximate per- cent change in the bond price would you have based on the modified duration?

Answer 1

As yield to maturity is equal to coupon rate, price is equal to par=1000

Macaulay Duration or Duration=(1*3%*1000/1.03+2*3%*1000/1.03^2+3*3%*1000/1.03^3+3*1000/1.03^3)/1000=2.9135

Modified Duration=Macaulay Duration/(1+yield)=2.9135/1.03=2.8286

Duration decreases with increase in coupon rate and increase in yield to maturity

% change=-Modified Duration*change in yields=-2.8286*(4%-3%)=-2.8286%