FRM Part I · FRM Exam Part I · Properties of Interest Rates
A 2-year bond pays a 5% annual coupon on a face value of 100 and has a yield of 5% per annum with annual compounding, so it trades at par. What is its Macaulay duration?
The Macaulay duration is about 1.952 years. It is the present-value-weighted average time of the cash flows: (1×4.7619 + 2×95.2381)/100. Because the bond pays a coupon at year 1, duration is below the 2-year maturity.
- A1.952 yearsCorrect
- B2.000 years
- C1.859 years
- D1.500 years
Explanation
PV of the coupon at year 1 = 5/1.05 = 4.7619 and PV of the year-2 cash flow = 105/1.1025 = 95.2381. Duration = (1×4.7619 + 2×95.2381)/100 = 1.952 years. The 1.859 option is the modified duration (1.952/1.05), and 2.000 is the maturity, which applies only to a zero-coupon bond.
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