FRM Part I · FRM Exam Part I · Properties of Interest Rates
A bond has a Macaulay duration of 8.4 years and a yield of 5% per year compounded semiannually. What is its modified duration, to two decimals?
Modified duration is about 8.20. With semiannual compounding, Macaulay duration is divided by one plus the yield per period, 1.025, so 8.4 divided by 1.025 gives roughly 8.195. Using 1.05 would be wrong because the compounding frequency is semiannual.
- A8.20Correct
- B8.00
- C8.61
- D8.40
Explanation
Modified duration = Macaulay duration / (1 + y/m) = 8.4 / 1.025 = 8.195, about 8.20. Dividing by 1.05 wrongly uses annual compounding. Multiplying by 1.025 inverts the adjustment. 8.40 applies no adjustment.
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