The percentage change in the price of a bond due to a change in interest rates can be estimated using the modified duration. The formula for the approximate percentage change in the bond price is a. -3.89 percent
Percentage Change in Price≈−Modified Duration×Change in Yield
Percentage Change in Price≈−Modified Duration×Change in Yield
Where:
Modified Duration is a measure of the bond's sensitivity to interest rate changes.Change in Yield is the change in yield to maturity.
In this case:
Modified Duration = 6 years (given)
Change in Yield = 50 basis points = 0.50% (convert basis points to a percentage by dividing by 100)
Percentage Change in Price≈−6×0.005
Percentage Change in Price≈−6×0.005
Percentage Change in Price≈−0.03
Percentage Change in Price≈−0.03
So, the percentage change in the price of the bond is approximately -0.03 or -3%.
Therefore, the correct answer is:
a. -3.89 percent
Consider a bond with a duration of 6 years having a yield to maturity of 8 percent, and interest rates are expected to rise by 50 basis points. What is the percentage change in the price of the bond?
a. −3.89 percent
b. 3.45 percent
c. −2.88 percent
d. 2.88 percent
e. −3.45 percent