Advanced Financial Management (AFM)MCQQuestion 5885 of 506
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A bond has a Macaulay Duration of 4.80 years and currently yields 8.00% per annum. What is the Modified Duration of the bond, and what is the estimated percentage change in bond price if yield increases by 50 basis points (+0.50%)?

Select Your Answer (Keyboard: A, B, C, D)
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Correct Answer

✅ Option A — Modified Duration = 4.44 years; Price change = -2.22%

All Options:

  • AModified Duration = 4.44 years; Price change = -2.22% ✓
  • BModified Duration = 4.80 years; Price change = -2.40%
  • CModified Duration = 5.18 years; Price change = -2.59%
  • DModified Duration = 4.44 years; Price change = +2.22%

Detailed Solution & Explanation

Bond Duration and Price Volatility:
1. **Modified Duration (MD)**:
MD=Dmac1+y=4.801+0.08=4.4444 yearsMD = \frac{D_{mac\displaystyle \text{mac}}}{1 + y} = 4.801+0.08=4\displaystyle \frac{4.80}{1 + 0.08} = 4.4444  years\displaystyle \text{ years}
2. **Percentage Price Change** for a 50 bps (0.0050) rise in yield:
ΔPP≈−MD×Δy=−4.4444×0.0050=−0.0222 or −2.22%ΔPP\displaystyle \frac{\Delta P}{P} ≈−MD\displaystyle \approx -MD ×\displaystyle \times Δ\displaystyle \Delta y = -4.4444 ×\displaystyle \times 0.0050 = -0.0222  or −2\displaystyle \text{ or } -2.22\%
Hence, **Option A** is the correct answer.

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