Key-rate durations
How much a bond's price moves when only one part of the Treasury curve moves, at 2, 5, 10 or 30 years, instead of the whole curve at once.
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How it is computed here
For each key point, the Treasury par curve is moved by one basis point at that tenor (fading linearly towards the neighbouring key points), the zero curve is rebuilt and the bond is repriced; the change in price, per percent of the price, is the duration at that point. The four add up to the duration for a move of the whole curve, and the position panel shows that sum next to the modified duration.
Worked example
- Moving only one part of the Treasury curve by one point, UST 4.625% 2036-08-15's price changes by this many percent, in years of duration: 2-year point −0.02, 5-year point +0.04, 10-year point +7.77, 30-year point −0.01.
- The four add up to 7.78, next to a modified duration of 7.72: one is for a move of the whole Treasury curve, the other for a move of the bond's own yield.
- Most of it sits at the 10-year point, where the last payments are.
- A figure below zero comes from how the curve is rebuilt after moving one point: it is not an error, and it is why the four are read with their sum.
Real Treasuries valued today on the Treasury's par curve: our estimates, not dealer quotes, and no yield here is a return anyone is owed. The demo holds none; signed in with a Treasury of your own, this is worked on yours.
Where it misleads
They are never read one at a time. At the long ends of a curve a figure can come out slightly negative, because moving one point of a par curve and rebuilding it lowers the forward rates beyond it; that comes from how the curve is rebuilt, it is not an error, and it is why the sum is shown beside them. The sum can also differ a little from the modified duration: one is for a move of the whole curve, the other for a move of the bond's own yield.
The formula
- KRDk — the key-rate duration at point k (2, 5, 10 or 30 years), in years;
- P — the bond's full price;
- P(+1 bp at k), P(−1 bp at k) — the price after moving only point k of the par curve up or down by one basis point (0.01 points), the rest of the curve fading linearly to the neighbouring key points;
- Σ KRDk — the sum of the four, the duration for a parallel move.
A worked example on a real Treasury
For the Treasury note UST 4.625% 2036-08-15 on the curve of 1 October 2026: 2-year point −0.02, 5-year +0.04, 10-year +7.78, 30-year −0.01; sum 7.79, beside a modified duration of 7.73. Almost all the sensitivity sits at the 10-year point, where its last payments are: a one-point rise in only that part of the curve lowers the price by about 7.78 %, while the same move at the 2-year point changes it by almost nothing. The two small negative figures, at 2 and 30 years, come from how the curve is rebuilt after moving one point; they are not an error, and nothing should be concluded from them alone. All figures are our estimates, not dealer quotes.
What this page does not do
It does not say which part of the curve will move, or whether it will: it describes where the price would react if it did. It is measured on the par curve of the Treasury; it promises nothing and forecasts nothing.
Compared with
- Modified duration — the single figure for a move of the bond's own yield
- Convexity — the curvature for big moves
- Maturity ladder — when the principal of a holding falls due
Questions people ask
Why is one of the figures negative?
Because of how the curve is rebuilt. Moving a single point of a par curve lowers the forward rates beyond it, and a bond with payments out there gains slightly from that. It is a feature of the calculation, and it is why the four figures are read together with their sum.
Why is the sum 7.79 and the modified duration 7.73?
They answer two slightly different questions: the sum is the sensitivity to a move of the whole Treasury par curve, the modified duration is the sensitivity to a move of the bond's own yield. For a bond priced on the curve they are close, not identical.
Sources
Last reviewed 2026-10-02 by Sphinx Risk.