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Chartered Financial Analyst Level 1

Chartered Financial Analyst Level 1

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An analyst collects the following data for a 4% annual-payment bond with a current yield-to-maturity of 4.0%:

Annualized Yield to Maturity | Bond Price 3.9% | 100.45 4.0% | 100.00 4.1% | 99.56

The bond's annualized Macaulay duration is closest to:

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Explanation:

To calculate the Macaulay duration, the following steps are taken:

  1. Approximate Modified Duration (AppxModDur): AppxModDur=(PV+−PV−)2×ΔYield×PV0=(100.45−99.56)2×0.001×100=4.45\text{AppxModDur} = \frac{(PV_+ - PV_-)}{2 \times \Delta \text{Yield} \times PV_0} = \frac{(100.45 - 99.56)}{2 \times 0.001 \times 100} = 4.45AppxModDur=2×ΔYield×PV0​(PV+​−PV−​)​=2×0.001×100(100.45−99.56)​=4.45
  2. Macaulay Duration: The Macaulay duration is derived by multiplying the modified duration by (1+YTM)(1 + \text{YTM})(1+YTM): Macaulay Duration=AppxModDur×(1+0.04)=4.45×1.04=4.628≈4.63\text{Macaulay Duration} = \text{AppxModDur} \times (1 + 0.04) = 4.45 \times 1.04 = 4.628 \approx 4.63Macaulay Duration=AppxModDur×(1+0.04)=4.45×1.04=4.628≈4.63

Option C is correct because it accurately adjusts the approximate modified duration by the yield-to-maturity to arrive at the Macaulay duration. Options A and B are incorrect due to miscalculations in the adjustment process.

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