effective duration and effective convexity to calculate price change effective, change, price

drexelyu0

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? Fall Rise A) +9.84% −8.41% B) +10.20% −8.06% C) +10.55% −7.70% 我根据公式算出来的是C, 但schweser 的答案是 A 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。

sololonely

我研究生课程学这部分的时候是有1/2，对于LEVEL1 里面没有1/2感到很奇怪。然后翻了下课程课件，发现教授在某一页下面注释里写着Sometimes see effective convexity reported as half this amount (building in the factor of ½
from the formula on the previous page for P taking into account convexity ).
我想大概是有1/2更精确吧

sololonely

找到一点：LOS 58.i上方有句话说这个了，often the measure is calculated in a way that requires an analyst to divide the measure by two to get the correct convexity adjustment. 我想这就是effective convexity

sololonely

看了2014年版的notes，LOS 55 k 明确写了有1/2的

mophic

这个effective duration实际就是债券价格曲线在某一收益率的泰勒展式，应该是有1/2的