Key Rate Durations

Standard duration answers "how does this bond's value change if yields move?" under a hidden assumption: that every maturity on the curve moves by the same amount at the same time. Real curves don't move that way — the 2-year and the 30-year regularly move by different amounts, sometimes in opposite directions. Key rate duration fixes this by measuring sensitivity to each maturity point separately, instead of collapsing the whole curve into one number.

Why one number isn't enough

Picture bumping the curve at exactly the 5-year point by 1 basis point, leaving the 2-year, 10-year, and 30-year points untouched, then smoothly blending that bump into its neighbors so the curve stays continuous. The resulting change in a bond's price, scaled appropriately, is that bond's 5-year key rate duration. Repeat at each maturity you care about (commonly 2, 5, 10, 30 years) and you get a full profile of where along the curve the bond's value is actually exposed.

A bullet bond maturing in 10 years has almost all its key rate duration concentrated at the 10-year point. A barbell portfolio — half in 2-year bonds, half in 30-year bonds — can have the same total duration as a 10-year bullet, but a completely different key rate profile: exposure concentrated at the short and long ends, with almost none in the belly.

Worked example

A portfolio has key rate durations (in years) of: 2y: 0.4, 5y: 1.1, 10y: 3.0, 30y: 0.5. Total duration is the sum: $0.4 + 1.1 + 3.0 + 0.5 = 5.0$.

Now the curve moves non-parallel: 2y up 20bp, 5y up 10bp, 10y flat, 30y down 15bp. The percentage price change is approximately:

$$\Delta P / P \approx -\sum_i KRD_i \times \Delta y_i$$ $$\approx -(0.4 \times 0.0020 + 1.1 \times 0.0010 + 3.0 \times 0 + 0.5 \times (-0.0015))$$ $$= -(0.00080 + 0.00110 + 0 - 0.00075) = -0.00115$$

A loss of about 0.115%. A single "duration 5.0" estimate using only, say, the 10-year move (which was flat) would have wrongly predicted zero change — the non-parallel move mattered, and only the key-rate breakdown captures it.

What this means in practice

Key rate durations are how curve trades — steepeners, flatteners, butterflies — are actually risk-managed: a trader expressing a view on the belly versus the wings needs to know the position's exposure at each maturity individually, not just its blended total. Portfolio managers running large fixed-income books report and limit risk by key-rate bucket precisely because total duration can look perfectly hedged while curve-shape risk sits unhedged underneath it.