A bond has a modified duration of 6.5 years and an annual convexity of 350. If yields increase by 40 bps, the percentage price change is:A.–2.88%.B.–2.32%.C.–2.04%.
Question
A bond has a modified duration of 6.5 years and an annual convexity of 350. If yields increase by 40 bps, the percentage price change is:A.–2.88%.B.–2.32%.C.–2.04%.
Solution
To calculate the percentage price change of a bond due to a change in yield, we can use the formula:
ΔP/P = -DΔy + 0.5C*(Δy)^2
where: ΔP/P is the percentage price change, D is the modified duration, Δy is the change in yield, and C is the convexity.
Given in the problem, we have: D = 6.5 years, Δy = 40 bps = 0.40% = 0.004 (in decimal form), and C = 350.
Substituting these values into the formula, we get:
ΔP/P = -6.50.004 + 0.5350*(0.004)^2
Solving this equation gives us:
ΔP/P = -0.026 + 0.0028 = -0.0232
So, the percentage price change is -2.32%.
Therefore, the correct answer is B. –2.32%.
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