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

A bond has a Macaulay duration of 7.50 years and a yield to maturity of 5.00% per year, compounded semiannually. What is its modified duration, to two decimal places?

Modified duration is Macaulay duration divided by one plus the periodic yield. With semiannual compounding at 5%, the divisor is 1.025, so 7.50 / 1.025 equals about 7.32 years. Using 1.05 would ignore the semiannual compounding convention.

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

Explanation

Modified duration = Macaulay duration / (1 + y/m) = 7.50 / (1 + 0.05/2) = 7.50 / 1.025 = 7.317, or 7.32 years. Dividing by 1.05 (7.14) wrongly uses annual compounding. Multiplying by 1.025 (7.69) inverts the adjustment.

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