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Answer: $5.81
The table gives a weighted time sum of **2.6448**. Since the bond-equivalent yield is **14.0%**, the semiannual yield is **7.0%**, so the modified duration is: \[ D_{mod} = \frac{2.6448}{1.07} \approx 2.471 \] For a **26 bps drop** in yield, \(\Delta y = -0.0026\). The duration-based price change is approximately: \[ \Delta P \approx -D_{mod} \times P \times \Delta y \] \[ \Delta P \approx -2.471 \times 904.67 \times (-0.0026) \approx 5.81 \] So the bond price is expected to **increase by about $5.81**. **Correct answer: A) $5.81**
Author: Manit Arora
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714.2. A three-year bond $1,000.00 face value bond pays a 10.0% semi-annual coupon and has a semi-annual (aka, bond equivalent) yield of 14.0%. It's price is therefore $904.67. The chart below also shows cash flows as proportional weights:
| Face value | $1,000.00 |
| Semi-annual coupon | 10.0% |
| Semi-annual yield (YTM) | 14.0% |
| Semi-Annual Period (T) | d.f. | Cash flow | Weight (W) | Time * Weight (T*W) | |
|---|---|---|---|---|---|
| FV | PV | ||||
| 0.5 | 0.935 | $50.00 | $46.73 | 0.052 | 0.026 |
| 1.0 | 0.873 | $50.00 | $43.67 | 0.048 | 0.048 |
| 1.5 | 0.816 | $50.00 | $40.81 | 0.045 | 0.068 |
| 2.0 | 0.763 | $50.00 | $38.14 | 0.042 | 0.084 |
| 2.5 | 0.713 | $50.00 | $35.65 | 0.039 | 0.099 |
| 3.0 | 0.666 | $1,050.00 | $699.66 | 0.773 | 2.320 |
$1,300.00 | $904.669 | 1.000 | 2.6448 |
We can use modified duration to estimate the price impact of a small change in yield. Which of the following is NEAREST to a duration-based (i.e., linearly approximate) estimate of the bond's price change given a 26 basis point (0.26%) drop (shock down) to the yield?
A
$5.81
B
$6.00
C
$6.18
D
$7.25
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