FRM Part I · FRM Exam Part I · Interest Rates
A bond has a Macaulay duration of 7.20 years and a yield to maturity of 5.0% per year, compounded semiannually. What is its modified duration?
Modified duration is about 7.02. With semiannual compounding, Macaulay duration is divided by one plus the periodic yield, 1.025, so 7.20 / 1.025 = 7.02. Using the annual yield of 1.05 would understate it, and leaving it at 7.20 ignores the conversion.
- A7.02Correct
- B6.86
- C7.38
- D7.20
Explanation
Modified duration = Macaulay duration / (1 + y/m) = 7.20 / (1 + 0.05/2) = 7.20 / 1.025 = 7.02. Dividing by 1.05 (6.86) wrongly treats the yield as annually compounded. Multiplying by 1.025 gives 7.38, which is the wrong operation.
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