FRM Part I · FRM Exam Part I · Interest Rates
A bond has a Macaulay duration of 8.4 years and a yield to maturity of 5% per year, compounded annually. What is its modified duration?
Modified duration is 8.00. With annual compounding, modified duration equals Macaulay duration divided by one plus the yield, so 8.4 divided by 1.05 is 8.00. Multiplying by 1.05 or by 0.95 would be using the wrong adjustment.
- A8.00Correct
- B8.40
- C8.82
- D7.98
Explanation
Modified duration = Macaulay duration / (1 + y/m) with m = 1, so 8.4 / 1.05 = 8.00. Multiplying by 1.05 gives 8.82, which is the inverted formula. 7.98 results from multiplying by (1 - 0.05) instead of dividing by (1 + 0.05).
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