Convert the yield move
One hundred basis points is one percentage point, or 0.01 in decimal yield. The formula requires 0.01, not 100 and not 1. Keep the positive sign because this scenario raises the yield.
Calculate the two terms
The duration term is −5 × 0.01 = −0.05. The convexity term is one-half × 40 × 0.01² = 0.002. Adding gives −0.048, or −4.8%. The curvature correction is positive here because convexity is positive and the yield change is squared.
| Term | Fractional price change | Percentage price change |
|---|---|---|
| Duration | −0.05 | −5.0% |
| Convexity | +0.002 | +0.2% |
| Combined | −0.048 | −4.8% |
Reverse the yield move
For a 100-basis-point decline, the duration term becomes +0.05 while the convexity term remains +0.002. The estimated gain is 5.2%. These are local approximations using supplied sensitivity measures, not exact prices of an identified security. Use cash-flow repricing when the full bond inputs are available.