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

A bond has a Macaulay duration of 7.5 years and a yield to maturity of 5% per year compounded semiannually. What is its modified duration?

Modified duration is 7.32 years. It equals Macaulay duration divided by one plus the periodic yield, so 7.5 divided by 1.025. Dividing by 1.05 ignores semiannual compounding, and multiplying instead of dividing overstates the figure.

  1. A7.32 yearsCorrect
  2. B7.50 years
  3. C7.14 years
  4. D7.69 years

Explanation

Modified duration = Macaulay duration / (1 + y/m) = 7.5 / 1.025 = 7.317 years. Using 1.05 (annual compounding) gives 7.14, which ignores the semiannual frequency. Multiplying by 1.025 instead of dividing gives 7.69.

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