Question

A 9-year bond has a yield of 7.5% and a duration of 7.295 years. If the market yield changes by 100 basis points, what is the percentage change in the bond’s price? (Do not round intermediate calculations. Negative value should be indicated by a minus sign. Round your answer to 2 decimal places.)  

Answer 1

Solution:

As per the information given in the question

The Duration of the bond = 7.295 years

Yield = 7.5 % = 0.075

Calculation of Volatility of the bond :

The Volatility = Duration / ( 1 + Yield )

= 7.295 / ( 1 + 0.075 )

= 7.295 / 1.075

= 6.7860 %

Inference for volatility : For every one percentage change in the yield the bond price will change by 6.7860 % .

Thus, For every one percentage change in the Market yield, price of the bond will change by the ( percentage of volatility * percentage of change in yield )

As per the information given in the question the market yield changes by 100 basis points

Thus since the market yield is changing by 1 % , the price of the bond will change by

= 6.7860 % * 1

= 6.7860 %

= 6.79 % ( when rounded off to two decimal places )

Thus the price of the bond will change by 6.79 %