Properties of Bond Duration
An annual coupon bond with a 5.2% yield to maturity has a Macaulay duration of 6.4. The expected change in a bond's price for a 50-basis-point decrease in its yield to maturity is _closest_ to:
That's right!
The expected change in a bond's price is calculated as follows:
$$\displaystyle \% \Delta PV^{Full} \approx - \text{AnnModDur} \times \Delta \text{Yield}$$
where
$$\displaystyle \% \Delta PV^{Full}$$ is the percentage change in a bond's price (including accrued interest), AnnModDur is the annual modified duration, and $$\displaystyle \Delta \text{Yield}$$ is the change in yield to maturity.
Modified duration is calculated from Macaulay duration and the bond yield as follows:
$$\displaystyle \text{ModDur} \approx \frac{\text{MacDur}}{(1+r)}$$
In this example,
$$\displaystyle \text{ModDur} = \frac{6.4}{(1+0.052)} \approx 6.08$$
$$\displaystyle \% \Delta PV^{Full} = -6.08 \times {-0.005} = 3.04 \% $$.
Incorrect.
This answer uses the bond's Macaulay duration rather than its modified duration to calculate the expected price change.
Incorrect.
This is the expected change in a bond's price for a 100-basis-point change in its yield to maturity.
3.0%.
3.2%.
6.1%.
