Bond Price Volatility Ea7D0B
1. **State the problem:** We need to find which bond, A or B, has the greater dollar price volatility for a 25 basis point (0.25%) change in interest rates.
2. **Formula used:** The dollar price change (DP) is estimated by the formula:
$$DP = - (\text{Modified Duration}) \times P \times \Delta y$$
where $P$ is the price of the bond and $\Delta y$ is the change in yield (interest rate).
3. **Given data:**
- Bond A: $P = 1000$, Modified Duration $= 6$
- Bond B: $P = 800$, Modified Duration $= 7$
- Change in yield $\Delta y = 0.25\% = 0.0025$
4. **Calculate dollar price change for Bond A:**
$$DP_A = -6 \times 1000 \times 0.0025 = -15$$
5. **Calculate dollar price change for Bond B:**
$$DP_B = -7 \times 800 \times 0.0025 = -14$$
6. **Interpretation:** The absolute value of dollar price change represents the price volatility. Bond A has a dollar price change of 15, Bond B has 14.
7. **Conclusion:** Bond A has the greater dollar price volatility for a 25 basis point change in interest rates.