A 9-year bond has a yield of 10% and a duration of 7.194 years. If the market yield changes by 50 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.)

Hi, well in order to find what is going to happen with the price if the yield changes by +/- 50 basis points (which is +/-0.5%), we have to use the following formula.

[tex]PriceChange=-Duration*(\frac{bps}{10,000} )[/tex]

So, if the yield changes (rises) 50 basis points, everything should look like this:

[tex]PriceChange=-7.194*(\frac{50}{10,000} )=-0.0360[/tex]

So, if the yield rises 50 bps, the price would drop by -3.60%

Now, if the yield drops by 50 bps:

[tex]PriceChange=-7.194*(\frac{-50}{10,000} )=0.0360[/tex]

So, if the yield drops 50 bps, the price would rise by 3.60%

Please notice that this is just an approximation and the price hardly varies in the same percentage. I took the liberty to find this bond coupon (4.71% annual) given its duration, and I found out that if the yield goes up by 50 bps, the price drops -3.20% and if the yield goes down by 50 bps, the price would go up by 3.34%.

Please notice the attached excel sheet, you can change the yellow cell adding/substracting 0.5% to change the blue cells with the result of the green cell, then you can see how the price changes, in different magnitude, even if you use the same values substracting or adding.

Best of luck