Question

3) The Macaulay duration of a bond portfolio is 6.23 years, (assuming they pay coupon annually) and the yield to maturity of the bond portfolio is 14%. What is the approximate change in the value of the bond if interest rates increase by 3 percentage points (3%)?

Increase by 18.55%

Decrease by 18.55%

Increase by 16.39%

Decrease by 16.39%

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	6.23
YTM	14.0000%

Modified Duration = Duration / [ 1 + YTM ]
= 6.23 / [ 1 + 0.14 ]
= 6.23 / [ 1.14 ]
= 5.4649 %

I.e 1% change in disc rate leads to 5.4649 % change in Bond Price

Change in Disc Rate is 3 %
% Change in Bond price for change in disc rate by 3 % is [ 5.4649 % * 3 ]
I.e3 %change in Disc Rate leads to 16.3947 %

There is inverse relation between YTM and Bond Price, If yield increases, Price will decrease and Vice versa.

Option D is correct.

Pls comment, if any further assistance is required.