这个题的问法容易让人产生误解啊，我会求36%和64%，这个我都想到了，但是他问gain from convexity，难道不是说spread的变化通过convexity的增加而带来的gain吗？我以为是total convexity=0.36*0.118+0.64*2.912=1.91，然后再用0.5*C*y^2,求出convexity部分的收益呢。。。感觉说的不严谨，get不到出题人的意思。。。-有问必答-品职教育专注CFA ESG FRM CPA 考研等财经培训课程

这个题的问法容易让人产生误解啊，我会求36%和64%，这个我都想到了，但是他问gain from convexity，难道不是说spread的变化通过convexity的增加而带来的gain吗？我以为是total convexity=0.36*0.118+0.64*2.912=1.91，然后再用0.5*C*y^2,求出convexity部分的收益呢。。。感觉说的不严谨，get不到出题人的意思。。。

* 问题详情，请查看题干

NO.PZ201812020100000702

问题如下：

Based on Exhibit 1, the gain in convexity from Hirji’s suggestion is closest to:

选项：

0.423.

1.124.

1.205.

解释：

A is correct.

To maintain the effective duration match, the duration of the 10-year bond sale must equal the total weighted duration of the 3-year and long-term bond purchases.

9.51 = (Duration of 3-year bond × Weight of 3-year bond) + (Duration of long-term bond × Weight of long-term bond)

x = weight of 3-year bond

(1 – x) = weight of long-term bond

9.51 = 2.88x + 21.30(1 – x)

x = 0.64 or 64%

The proceeds from the sale of the 10-year Canadian government bond should be allocated 64% to the 3-year bond and 36% to the long-term bond:

9.51 = (64% × 2.88) + (36% × 21.30)

Gain in convexity = (Weight of the 3-year) × (Convexity of the 3-year) + (Weight of the long-term bond) × (Convexity of the long-term bond) – (Weight of the 10-year) × (Convexity of the 10-year)

Gain in convexity = (64% × 0.118) + (36% × 2.912) – (100% × 0.701) = 0.42284 or 0.423

嗨，努力学习的PZer你好：

这是一个题型，就是把Bullet portfolio调整成Barbell portfolio，然后专门计算前后Convexity的增加值。

需要算出新的Portfolio convexity，然后减去旧的Portfolio Convexity，求出来额外的增加值。

其实在基础班也有这种题目，和Gain in convexity配套的还有计算Give-up in yield。

Give-up in yield就是调整成Convexity更大的组合时，组合收益率的损失。因为Convexity是要付出成本的，调整之后，肯定会导致Portfolio的Yield降低。

这个Give-up in yield的算法就是：新Portfolio的Yield，减去旧Portfolio的Yield。

可以参考如下讲义：

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