Question

A(n) eight-year bond has a yield of 9% and a duration of 7.211 years. If the bond's yield increases by 75 basis points, what is the percentage change in the bond's price? (Input the value as a positive value. Do not round intermediate calculations. Round your answer to 2 decimal places.) The bond's pric (Click to select) increased by decreased by

Answer 1

Solution:

As per the information given in the question

The Duration of the bond = 7.211 years

Interest rate = Yield = 9 %

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 )

= 7.211 / ( 1 + 0.09 ) = 7.211 / 1.09 = 6.6156 %

= 6.6156 %

Inference for volatility : For every one percentage change in the yield the bond price will change by 6.6156 % .

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 75 basis points

Thus since the interest rate is increasing by 0.75 % , the price of the bond will decrease by

= 0.75 * 6.6156 %

= 4.9617

= 4.96 %

Thus the price of the bond will decrease by 4.96 %

The solution is decreased by 4.96 % .