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CFA Level I · CFA Level I Exam · Yield-Based Bond Convexity and Portfolio Properties

A 5-year annual-pay bond has a Macaulay duration of 4.20 years and a yield to maturity of 5.00% (annual compounding). The bond's modified duration is closest to:

Modified duration is 4.00. It equals Macaulay duration divided by one plus the periodic yield, so 4.20 divided by 1.05 gives 4.00. Multiplying instead of dividing would produce 4.41, which is a common error.

  1. A3.89
  2. B4.00Correct
  3. C4.41

Explanation

Modified duration = Macaulay duration / (1 + yield) = 4.20 / 1.05 = 4.00. Multiplying by (1 + yield) gives 4.41, which reverses the adjustment. 3.89 results from subtracting the yield incorrectly (4.20 / 1.08).

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