Question

A bond has a modified duration of 16.44 and has a YTM of 0.08 when interest rates change by -80 basis points. What is the expected change in price for the bond given this information?

A. 0.1367
B. 0.1260
C. 0.1425
D. 0.1204
E. 0.1315

Answer 1

Using the modified duration of 16.44 and the change in interest rates of -80 basis points, the expected change in price is calculated to be approximately 13.15%, which corresponds to Option E: 0.1315. The closest option to 0.13152 is Option E: 0.1315

Step-by-step explanation:

To calculate the expected change in the price of the bond given a change in interest rates, we use the modified duration and the change in interest rate (in decimal form). The formula is:

Percentage change in price = - (Modified Duration) × Change in interest rate

We are given that the bond has a modified duration of 16.44 and the interest rates change by -80 basis points. Since 1 basis point is 0.01% or 0.0001 in decimal, -80 basis points is -0.008 in decimal. Applying the formula:

Percentage change in price = - (16.44) × (-0.008) = 0.13152

The closest option to 0.13152 is Option E: 0.1315, representing an approximate 13.15% increase in bond price.