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Key rate duration estimates how much a bond or portfolio price responds when the benchmark yield changes at one chosen maturity. A profile of these sensitivities lets you estimate the effect of a curve twist by applying each maturity’s rate move to its own exposure. One total duration cannot show which part of the curve drives the result.
What the profile measures
Imagine repricing a bond after nudging only the two-year benchmark rate, with the other benchmark points held fixed. Repeat the exercise at other maturities. Each result is a key rate duration; together they form a map of interest rate exposure. CFA Institute’s Level I overview identifies this measure and says the key rate durations add to effective duration under a parallel shift.
The sum is useful as a check, but it discards the location of exposure. Two portfolios can have the same total duration yet respond differently when one part of the yield curve rises and another falls. CFA Institute also describes key rate durations as a way to assess sensitivity to changes in curve shape in its yield curve strategies overview.
An illustrative curve twist
Take an invented portfolio whose only material key rate durations are 3 at two years and 2 at ten years. Its total effective duration is 5 if the benchmark curve shifts in parallel. Now suppose the two-year benchmark yield rises by 40 basis points while the ten-year yield falls by 20 basis points. These are illustrative inputs, not observed market data.
- Convert the illustrative moves to decimals: the two-year change is +0.004 and the ten-year change is −0.002.
- The two-year contribution is −3 × 0.004, or −0.012. The ten-year contribution is −2 × (−0.002), or +0.004.
- Add the contributions: −0.008, an estimated price change of −0.8%.
The short-end rate rise has the larger effect, so the price estimate is negative despite the long-end rate fall. This is a local, first-order estimate: convexity and other changes can make the realised price move different, especially for a larger shock.
Where candidates go wrong
- Using one averaged yield move. Multiplying total duration by an average of the two yield changes assumes the same exposure at both maturities. The profile says otherwise.
- Losing the sign. A positive yield change contributes a negative price move; a negative yield change contributes a positive one.
- Confusing a sum with a profile. Effective duration summarises a parallel move. Keep each key rate duration when the curve reshapes.
When you revise this topic in the CFA programme, write the yield changes beside their matching key rates before calculating. The study methodology page is a separate starting point for organising practice around such sign and classification errors.
Sources
- Curve-Based and Empirical Fixed-Income Risk Measures | CFA Institute · cfainstitute.org · Retrieved
- Yield Curve Strategies | CFA Institute · cfainstitute.org · Retrieved
