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Answer: $5.81
Use the duration approximation: \[ \Delta P \approx -D_{mod} \times P \times \Delta y \] The table gives Macaulay duration as the weighted average time: \[ D_{Mac} = 2.6448 \] For a semiannual bond-equivalent yield of 14.0%, the modified duration is: \[ D_{mod} = \frac{D_{Mac}}{1 + y/2} = \frac{2.6448}{1.07} \approx 2.4728 \] Now apply the yield change of -0.26% = -0.0026: \[ \Delta P \approx - (2.4728)(904.67)(-0.0026) \] \[ \Delta P \approx 5.81 \] Since yield falls, price rises, so the estimated price change is approximately **+$5.81**.
Author: Manit Arora
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Q-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:
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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