FRM Part I · FRM Exam Part I · Applying Duration, Convexity, and DV01
A 4-year zero-coupon bond has a yield of 6.00% per year, compounded annually. Using modified duration, what is the approximate percentage price change if the yield rises by 25 basis points?
A zero-coupon bond's Macaulay duration equals its 4-year maturity, so modified duration is 4/1.06, about 3.774. Multiplying by the 0.25% yield rise gives a price decline of roughly 0.94%. Using 4 directly would overstate the fall at 1.00%.
- A-0.89%
- B-0.94%Correct
- C-1.00%
- D+0.94%
Explanation
The Macaulay duration of a zero equals its maturity, 4 years. Modified duration = 4 / 1.06 = 3.774. The price change is about -3.774 × 0.0025 = -0.943%, or -0.94%. Using Macaulay duration directly gives -1.00%, which ignores the yield adjustment.
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