Modified duration
The approximate percentage change in a bond's price for a one-percentage-point change in its yield, in the opposite direction.
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How it is computed here
The Macaulay duration divided by (1 + y/2), with y the bond's estimated yield: a modified duration of 7.7 means about −7.7 % on the price for a one-point rise in yield and about +7.7 % for a one-point fall. Beside it the position panel shows the DV01, the money the position changes for a 0.01-point move in yield.
Worked example
- Macaulay duration ÷ (1 + yield ÷ 2) = 7.9284 ÷ 1.0264 = 7.724 years.
- A one-point rise in UST 4.625% 2036-08-15's yield lowers its price by about 7.72%, and a one-point fall raises it by about as much.
- In money, on 10,000 of face value, the position changes by 7.39 USD for each 0.01 point of yield: the DV01.
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
It is a straight-line estimate: for a large move the real change is smaller for a rise and larger for a fall, which is what convexity measures. It also assumes the whole yield curve moves together, which it rarely does; the key-rate durations say where along the curve a bond is sensitive. It describes sensitivity, not a forecast of rates, and it is our estimate from the Treasury curve, not a dealer quote.
The formula
- Dmod — the modified duration, in years;
- DMac — the Macaulay duration;
- y — the bond's yield to maturity, compounded twice a year;
- ΔP ⁄ P — the relative change of the price;
- Δy — the change of the yield, as a fraction (0.01 is one point);
- DV01 — the change of the price per 100 for a 0.01-point move in yield, in money.
A worked example on a real Treasury
The Treasury note UST 4.625% 2036-08-15: DMac = 7.9348 years and y = 5.2394 %, so 1 + y ⁄ 2 = 1.026197 and Dmod = 7.9348 ÷ 1.026197 = 7.732. A one-point rise in its yield lowers the price by about 7.73 %. DV01 = 7.732 × 95.896 × 0.0001 = 0.0741 per 100: on 10,000 of face value, 7.41 for every 0.01 point. The exact change for a full point is a little smaller, −7.38 %, because of convexity. All figures are our estimates from the Treasury curve of 1 October 2026, not dealer quotes.
What this page does not do
It does not say where yields will go, and it is exact only for tiny moves of the bond's own yield. A bond that is sold before maturity is worth whatever price it then has.
Compared with
- Macaulay duration — the time-weighted average it comes from
- Convexity — the curvature that corrects it for large moves
- Key-rate durations — which part of the curve the sensitivity sits on
Questions people ask
Does a duration of 7.7 mean I lose 7.7 % if rates rise?
Only roughly, and only for a one-point rise in this bond's own yield, all at once, from today's price. A smaller rise gives a smaller change; the exact figure for a full point is a little smaller (7.38 % here, see convexity); and the figure is an estimate from the Treasury curve.
What is the DV01?
The change in money for a 0.01-point move in yield: here 7.41 on 10,000 of face value. The change for a one-point move is about a hundred times that, less the convexity effect.
Sources
Last reviewed 2026-10-02 by Sphinx Risk.