a bond has an annual modified duration of 7.140 and annual convexity of 66.200. The bond's yield-to-maturity is expected to increase by 50 basis points. The expected percent-Age price change is closest to:
A) −3.40%.
B) −3.49%.
C) −3.57%

Question

a bond has an annual modified duration of 7.140 and annual convexity of 66.200. The bond's yield-to-maturity is expected to increase by 50 basis points. The expected percent-Age price change is closest to: 
A) −3.40%.
B) −3.49%.
C) −3.57%

Quizplus · Accepted Answer

Using the formula for approximating the percentage price change due to a change in yield-to-maturity:

ΔP/P ≈ -MD*ΔY + 0.5*C*(ΔY)^2

where ΔY is the change in yield-to-maturity, MD is the modified duration, and C is the convexity.

Plugging in the values:

ΔP/P ≈ -7.140*(0.005) + 0.5*66.200*(0.005)^2

ΔP/P ≈ -0.0357 or -3.57%

Therefore, the expected percentage price change is closest to option B (-3.49%).

A Bond Has an Annual Modified Duration of 7