Explanation:

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.

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?

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MManit

Last updated: April 18, 2026 at 11:32

$5.81

66.7%

$6.00

0.0%

$6.18

16.7%

$7.25

16.7%

Financial Risk Manager Part 1