Question

A bond currently sells for $1,080, which gives it a yield to maturity of 6%. Suppose that if the yield increases by 25 basis points, the price of the bond falls to $1,025.

a) What is the duration of this bond?

b) Given the duration in a), what will be the bond price if the yield decreases by 25 basis points and the current bond price is $1,080?

Answer 1

Answer a

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

(1025-1080)/1080 * 100= Modified Duration *.25%

5.092592592 %= Modified Duration*.25%

Modified Duration = 5.092592592% /.25%

= 20.37

Duration = Modified Duration*(1+YTM)

= 20.37*1.06

= 21.59

​​​​​​​Answer b

When the yield decreases by 25 basis points, price of the bond rises by 5.092592592 %.

New bond price = 1080 + 1080*5.092592592 %

= 1080 + 54.9999999936

= ​​​​​​​1135