Question

You have discovered that when the required rate of return on a bond you own fell by 0.5 percent from 8.7 percent to 8.2 percent, the fair present value rose from $975 to $985. The bond pays interest annually. What is the duration of this bond? Assume annual payments. (Do not round intermediate calculations. Round your answer to 1 decimal place. (e.g., 32.1))

Duration of this bond

years

Answer 1

Modified Duration measures the change in bond price with respect to change in YTM. But the direction of change is opposite. That is when YTM increases, bond price decreases. Similarly when YTM decreases, bond price increases.

% change in bond price = Modified Duration * % change in YTM

(985-975)/975 =  Modified Duration * .5%

1.025641025% =  Modified Duration ​​​​​​​* .5%

Modified Duration = 1.025641025/.5

= 2.05128205 years

Modified Duration = Duration/(1+YTM)

2.05128205 = Duration / 1.087

Duration =2.05128205 *1.087

= 2.2 years