Steve Jacobs, CFA, is analyzing the price volatility of Bond Q. Q’s effective duration is 7.3, and its effective convexity is 91.2. What is the estimated price change for Bond Q if interestrates fall/rise by 125 basis points?

Estimated return impact if rates fall by 125 basis points:

≈ −(Duration × ΔSpread) + ½ Convexity × (ΔSpread)2
≈ −(7.3 × −0.0125) + ½(91.2)(0.0125)2
≈ +0.09125 + 0.007125
≈ +0.0983750
≈ +9.84%

Estimated return impact if rates rise by 125 basis points:

≈ −(Duration × ΔSpread) + ½ Convexity × (ΔSpread)2
≈ −(7.3 × +0.0125) + ½(91.2)(0.0125)2
≈ −0.09125 + 0.007125
≈ −0.084125
≈ −8.41%

公式里convexity 前面不需要乘1/2的， 为什么这里要乘1/2，求解惑。