How do I convert basis points before using duration or convexity formulas?

Convert basis points into a decimal yield change before multiplying by duration or convexity terms. One basis point is 0.01%, which is 0.0001 in decimal form.

So 40 basis points equals 0.40%, or 0.0040 as a decimal. If modified duration is 6.25, a 40 basis point yield increase gives an approximate price change of:

-6.25 x 0.0040 = -0.0250 = -2.50%

Write dy = 0.0040 on your scratch work before calculating. That one line usually catches the factor-of-ten mistakes.