Transparent method
The formula
Worked example
Example inputs
How to interpret the result
Duration alone approximates a bond's price sensitivity to interest rates using a straight line, and that approximation gets worse the larger the rate move being considered. Convexity is the correction for that curve. For a large rate shock, duration alone can meaningfully misstate the actual price change, while adding convexity brings the estimate back closer to the bond's true, curved price behavior.
Before you rely on it
What to check
Use duration alone only for small rate changes, and add the convexity adjustment whenever the scenario involves a larger shift.
The common error
Where people go wrong with bond convexity calculator
Relying on duration by itself for a large interest-rate move. The straight-line approximation increasingly diverges from the bond's actual price response as the assumed rate change grows larger.
Sensitivity evidence
How yield to maturity changes the estimated convexity
| Yield to maturity | Estimated convexity | Estimated bond price | Price change for +1% yield |
|---|---|---|---|
| 4.0% | 75.5 | $1,082 | -7.5% |
| 5.0% | 73.6 | $1,000 | -7.4% |
| 6.0%worked example | 71.8 | $926 | -7.3% |
| 7.0% | 69.9 | $858 | -7.2% |
| 8.0% | 68.1 | $796 | -7.1% |
Every input, tested
Which input moves the estimated convexity most
| Input | Tested from | To | Estimated convexity at each end | Swing |
|---|---|---|---|---|
| Years to maturity | 7.0 years | 13.0 years | 39.8 to 108.2 | 68.4 (95%) |
| Annual coupon rate | 4.0% | 6.0% | 75.3 to 68.8 | 6.5 (9.1%) |
| Yield to maturity | 5.0% | 7.0% | 73.6 to 69.9 | 3.7 (5.1%) |
| Payments per year | 1 | 3 | 72.6 to 71.5 | 1.1 (1.5%) |
| Face value | $900 | $1,100 | 71.8 to 71.8 | none |
Two variables at once
Estimated convexity by yield to maturity and annual coupon rate
| Yield to maturity \ Annual coupon rate | 3.0% | 5.0% | 7.0% |
|---|---|---|---|
| 4.0% | 82.9 | 75.5 | 70 |
| 5.0% | 81.2 | 73.6 | 68.1 |
| 6.0% | 79.5 | 71.8 | 66.2 |
| 7.0% | 77.8 | 69.9 | 64.3 |
| 8.0% | 76.1 | 68.1 | 62.4 |
Step by step
The worked example, input by input
| Input | Value used |
|---|---|
| Face value | $1,000 |
| Annual coupon rate | 5.0% |
| Yield to maturity | 6.0% |
| Years to maturity | 10.0 years |
| Payments per year | 2 |
| Estimated convexity | 71.8 |
| Estimated bond price | $926 |
| Price change for +1% yield | -7.3% |
Where the inputs come from
Face value, coupon rate, yield to maturity, years to maturity and payments per year define the bond. Convexity measures how the bond's duration changes as yields change, and it is used to improve the price estimate for larger yield moves. Take the yield from the bond's quote and use the same coupon frequency as the actual bond. The tool also computes the price and an estimated price change for a one percentage point rise in yield.
Using the estimated convexity in a real decision
Higher convexity is good for the holder: the price falls less when yields rise and rises more when they fall. Longer, lower-coupon bonds have higher convexity.
When the result stops applying
The estimate assumes a parallel shift and a fixed set of cash flows, so it does not apply to callable or mortgage-backed bonds with negative convexity. It is still an approximation for very large yield changes. Convexity does not measure credit risk. Two bonds with the same duration can have different convexity, which affects how they react.
What to compare it with
Start with the first-order estimate on the bond duration and DV01 calculators, and check the exact price at a new yield on the bond price page. The portfolio duration calculator handles several bonds. Compare with a zero-coupon bond, which has the highest convexity for its maturity.
People also ask
Frequently asked questions
What does convexity mean for a bond?
It measures how much the bond's duration changes as yields move, giving a more accurate picture of price changes for large yield moves.
Is higher convexity better?
For an investor, yes. A bond with higher convexity gains more when yields fall and loses less when they rise, other things equal.
What is negative convexity?
A property of callable and mortgage-backed bonds whose price gains are capped when yields fall because the issuer can call or borrowers can prepay.