A 9-year bond has a yield of 6.0% and a duration of 7.982 years. If the market yield changes by 35 basis points, what is the percentage change in the bond’s price?
To calculate the percentage change in the bond's price, we can use the modified duration formula. The formula is as follows:
Percentage Change in Price = - Modified Duration * Change in Yield
First, let's express the change in yield as a decimal:
Change in Yield = 35 basis points = 0.35%
Now, we can substitute the values into the formula:
Percentage Change in Price = - 7.982 * 0.35%
Calculating the percentage change in the bond's price:
Percentage Change in Price = -2.7937%
Therefore, the percentage change in the bond's price is approximately -2.7937%. Note that the negative sign indicates a decrease in price as the yield increases.
To find the percentage change in the bond's price, you can use the formula:
Percentage change in price = -Duration × Change in yield
First, let's convert the change in yield from basis points to a decimal. Since 1 basis point is equal to 0.01%, we can convert 35 basis points to a decimal by dividing it by 10000:
Change in yield = 35 / 10000 = 0.0035
Now we can substitute the values into the formula:
Percentage change in price = -7.982 × 0.0035
Multiply the two values:
Percentage change in price = -0.027937
Finally, to convert this decimal into a percentage, we multiply by 100:
Percentage change in price = -0.027937 × 100 = -2.7937%
Therefore, the percentage change in the bond's price due to a 35 basis point change in yield is approximately -2.7937%. Note that the negative sign indicates a decrease in price.