
Answer-first summary for fast verification
Answer: 5.05%.
**Explanation:** The correct answer is **B** (5.05%). 1. **Modified Duration Calculation:** For a zero-coupon bond, the Macaulay duration equals its time to maturity (5 years). The modified duration is calculated as: \[ \text{Modified Duration} = \frac{\text{Macaulay Duration}}{1 + \text{Yield}} = \frac{5}{1.02} = 4.901961 \] 2. **Percentage Price Change:** The percentage change in price due to a yield change is given by: \[ \text{Percentage Change} = -\text{Modified Duration} \times \Delta Y + \frac{1}{2} \times \text{Convexity} \times (\Delta Y)^2 \] Substituting the values for a 1% decrease in yield (\\(\Delta Y = -0.01\\)): \[ \text{Percentage Change} = -4.901961 \times (-0.01) + \frac{1}{2} \times 28.835 \times (0.01)^2 = 0.04901961 + 0.0014418 = 0.0504614 \approx 5.05\% \] 3. **Why Not A or C?** - **A (4.76%)** incorrectly subtracts the convexity adjustment instead of adding it. - **C (5.14%)** applies the convexity adjustment to the Macaulay duration instead of the modified duration.
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An analyst evaluates a zero-coupon bond with the following characteristics:
A
4.76%.
B
5.05%.
C
5.14%.