- Bond price
- 100
- Macaulay duration
- 4.4854 years
- Modified duration
- 4.376
- Convexity
- 22.6123
- Duration estimate
- -2.188 %
- Duration + convexity estimate
- -2.1598 %
- Exact repricing change
- -2.16 %
The same regular bond is repriced at each displayed annual yield; face value and cash flows stay fixed. This is an illustrative example.
View the chart values
| Series | Annual yield (%) | Bond price |
|---|---|---|
| Bond | 3 | 109.22218 |
| Bond | 3.5 | 106.82592 |
| Bond | 4 | 104.49129 |
| Bond | 4.5 | 102.21655 |
| Bond | 5 | 100 |
| Bond | 5.5 | 97.839981 |
| Bond | 6 | 95.734899 |
| Bond | 6.5 | 93.683204 |
| Bond | 7 | 91.683395 |
A local estimate of a price change
Modified duration supplies the linear part of the estimate. Convexity adds curvature. Both measures are calculated from the bond’s discounted regular cash flows, using the coupon frequency shown in the inputs. The exact comparison reprices those same cash flows at the shifted yield.
Enter the yield change in basis points
A change of 50 basis points is 0.005 in decimal yield, or half a percentage point. A positive change raises the yield. A negative change lowers it. The shifted yield must remain within the regular-bond model’s nonnegative-yield range.
Duration and convexity use the same yield convention. The yield change is a decimal inside the formula.
Use the comparison to learn the approximation
For a small yield move, the estimates usually sit close to exact repricing. For a larger move, neglected higher-order terms can matter. Embedded options, changing cash flows and nonparallel yield-curve changes require different modelling assumptions; this tool holds the regular cash flows fixed.