NO.PZ201812020100000702
问题如下：
Based on Exhibit 1, the gain in convexity from Hirji’s suggestion is closest to:
选项：
A.0.423.
B.1.124.
C.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
为什么在调整convexity时要保证组合Duration不变？
而且，按照题目中的意思，我觉得前面的同学提到需要cash-neutral还挺有道理的。
