Explanation:
Key rate duration measures the sensitivity of a bond's price to changes in specific key rates along the yield curve. When there is a parallel shift in the benchmark yield curve (meaning all rates change by the same amount), the sum of key rate durations equals the bond's effective duration.
Key Points:
- Effective duration measures price sensitivity to parallel shifts in the yield curve.
- Key rate durations decompose interest rate risk across different maturities on the yield curve.
- For parallel shifts, the combined effect of all key rate durations equals the effective duration.
- Modified duration assumes a flat yield curve and parallel shifts, but it's based on the bond's yield to maturity rather than the benchmark curve.
- Macaulay duration is a weighted average time to receive cash flows, not a direct measure of interest rate sensitivity.
Therefore, for parallel shifts in the benchmark yield curve, key rate durations collectively indicate the same interest rate sensitivity as effective duration.
