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FRM Part I · FRM Exam Part I · Applying Duration, Convexity, and DV01

A 6-year zero-coupon bond has a yield to maturity of 4% per year, compounded annually. Using modified duration, what is the approximate percentage price change if the yield rises by 25 basis points?

The price falls by about 1.44%. The zero-coupon bond's Macaulay duration is 6 years, so modified duration is 6 divided by 1.04, or 5.769. Multiplying by the 0.25% yield rise gives roughly -1.44%. Using 6 directly would give -1.50%.

  1. A-1.50%
  2. B-1.44%Correct
  3. C+1.44%
  4. D-0.72%

Explanation

A zero-coupon bond has Macaulay duration equal to its maturity, 6 years. Modified duration = 6 / 1.04 = 5.769. The price change is about -5.769 x 0.0025 = -1.44%. Using Macaulay duration directly gives -1.50%, which skips the adjustment for yield.

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