Question

A bond has a duration of seven years and a yield to maturity of 7.5 percent. If the yield to maturity changes to 12 percent, what should be the percentage price change of the bond?

Answer 1

Modified duaration :

Modified duration is a measurable change in the value of a security in response to a change in interest rates.

Modified duration = Duration / [ 1 + YTM ]
It specifies% change in Price in opposite direction due to 1% change in YTM.

Particulars	Values
Duration	7
YTM	7.5000%

Modified Duration = Duration / [ 1 + YTM ]
= 7 / [ 1 + 0.075 ]
= 7 / [ 1.075 ]
= 6.5116 %

I.e 1% change in disc rate leads to 6.5116 % change in Bond Price

Change in Disc Rate is 4.5 %
% Change in Bond price for change in disc rate by 4.5 % is [ 6.5116 % * 4.5 ]
I.e4.5 %change in Disc Rate leads to 29.3023 %

%Cahnge in Price is 29.30%