FRM Part I · FRM Exam Part I · Properties of Interest Rates
A bond has a Macaulay duration of 6.00 years and a yield of 5% per annum with annual compounding. What is its modified duration?
Modified duration is Macaulay duration divided by one plus the periodic yield. With annual compounding at 5%, 6.00 divided by 1.05 equals about 5.71 years. Multiplying instead of dividing, or skipping the adjustment, gives incorrect values.
- A5.45 years
- B5.71 yearsCorrect
- C6.00 years
- D6.30 years
Explanation
Modified duration = Macaulay duration / (1 + y/m) = 6.00 / 1.05 = 5.714. Multiplying by 1.05 gives 6.30, which reverses the adjustment. Dividing by 1.10 (5.45) uses the wrong yield. Using 6.00 ignores the adjustment altogether.
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