Convexity
How much a bond's duration itself changes as its yield changes: the curvature that makes a price rise more for a fall in yield than it falls for an equal rise.
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How it is computed here
The second derivative of the price with respect to the yield, divided by the price, in years squared, computed from the estimated yield and the payment calendar. The position panel uses it in its exact one-point figure: it reprices every payment at the yield moved by one point, so convexity is included, and shows that figure under the DV01.
Worked example
- Duration alone says a one-point rise in UST 4.625% 2036-08-15's yield lowers its price by 7.72%.
- Convexity of 72.32 adds back ½ × 72.32 × 0.01² = 0.36%, so about −7.36%.
- Repricing every payment at the yield plus one point gives a change of −7.37%: −705.12 USD on 10,000 of face value.
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
Convexity matters for big moves and long bonds and is almost nothing for small moves. It is a number in years squared, not a percentage, and it says nothing about which way yields will go. The figure is our estimate from the Treasury curve, not a dealer quote.
The formula
- ΔP ⁄ P — the relative change of the price;
- Dmod — the modified duration;
- Δy — the change of the yield, as a fraction (0.01 is one point);
- C — the convexity, in years squared;
- d²P ⁄ dy² — the second derivative of the price with respect to the yield.
A worked example on a real Treasury
The Treasury note UST 4.625% 2036-08-15 has Dmod = 7.732 and C = 72.43. Duration alone says a one-point rise in its yield (Δy = 0.01) lowers the price by 7.732 %. Convexity adds ½ × 72.43 × 0.01² = 0.36 %, so about −7.37 %. Repricing all twenty payments at 6.2394 % gives a full price of 88.817 against 95.896: a change of −7.079, or −7.38 %; on 10,000 of face value, −707.91. A one-point fall in yield, repriced the same way, adds +8.11 %: the curve bends, so the same move down is worth more than the same move up costs. 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 which yield move to expect, and it is not a measure of quality: it is the curvature of the price against the yield, which the market already includes in the price.
Compared with
- Modified duration — the straight-line sensitivity convexity corrects
- Macaulay duration — the average time of the payments
- Key-rate durations — where along the curve the sensitivity sits
Questions people ask
Why is a fall in yield worth more than an equal rise costs?
Because the price curve bends. For the example bond, a one-point rise costs 7.38 % and a one-point fall adds 8.11 %: the same move in opposite directions, with an asymmetry that duration alone cannot show.
Is a higher convexity better?
It means the price curve bends more. That is part of how bonds are priced, so it is not a free advantage, and nothing here says which bond to hold: it describes how the price reacts.
Sources
Last reviewed 2026-10-02 by Sphinx Risk.