Use one consistent conversion
A percentage point is a difference between two percentages. Moving a yield from 5% to 6% is a one-percentage-point increase, which equals 100 basis points and a decimal yield change of 0.01. It is not a decimal change of 1.
| Basis points | Percentage points | Decimal change |
|---|---|---|
| 1 | 0.01 | 0.0001 |
| 25 | 0.25 | 0.0025 |
| 50 | 0.50 | 0.0050 |
| 100 | 1.00 | 0.0100 |
Distinguish the level from the change
The yield level of 5% is 0.05 as a decimal. A 50-basis-point increase in that yield is a change of 0.005, producing a new decimal yield of 0.055. Keep the level and change in separate variables so the starting yield is not added twice.
Convert before squaring
In the convexity term, square the decimal change. For 100 basis points, 0.01² is 0.0001. Squaring 100 first and treating the result as a decimal creates a completely different scale. A quick magnitude check catches this error before you interpret the price estimate.