Question

A nine-year bond has a yield of 15% and a duration of 12.094 years. If the bond's yield changes up by 15 basis points, what is the percentage change in the bond's price? (Negative amount should be indicated by a minus sign. Round your answer to 2 decimal places. Omit the "%" sign in your response.)

Change in bond's price

%

Answer 1

Solution:

As per the information given in the question

The Duration of the bond = 12.094 years

Interest rate = Yield = 15 %

The yield and price of a bond are inversely related. This relationship is explained by calculating the volatility of the bond.

Thus the volatility = Duration / ( 1 + yield )

= 12.094 / ( 1 + 0.15 ) = 12.094 / 1.15 = 10.5165 %

= 10.5165 %

Inference for volatility : For every one percentage change in the yield the bond price will change by 10.5165 % .

Thus,

For every one percentage increase in the yield or interest rate, price of the bond will decrease by the ( percentage of volatility * percentage of increase in interest rate )

For every one percentage decrease in the yield or interest rate, price of the bond will increase by the ( percentage of volatility * percentage of decrease in interest rate )

As per the information given in the question the yield increase by 15 basis points

Thus since the bond’s yield is increasing by 0.15 % , the price of the bond will decrease by

= 0.15 * 10.5165 %

= 1.5775 %

= 1.58 %

Thus the price of the bond will decrease by 1.58 %

Solution : Change in the bond’s price – 1.58 %