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HG · 2021年04月02日

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。。。

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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

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。。。

1 个答案

发亮_品职助教 · 2021年04月02日

嗨,努力学习的PZer你好:


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。。。


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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就算太阳没有迎着我们而来,我们正在朝着它而去,加油!

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NO.PZ201812020100000702

2021-10-17 12:08 1 · 回答

NO.PZ201812020100000702 1.124. 1.205. A is correct. To maintain the effective ration match, the ration of the 10-yebonsale must equthe totweighteration of the 3-yeanlong-term bonpurchases. 9.51 = (ration of 3-yebon× Weight of 3-yebon + (ration of long-term bon× Weight of long-term bon x = weight of 3-yebon(1 – x) = weight of long-term bon9.51 = 2.88x + 21.30(1 – x) x = 0.64 or 64% The procee from the sale of the 10-yeCanagovernment bonshoulallocate64% to the 3-yebonan36% to the long-term bon 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 bon × (Convexity of the long-term bon – (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 请问1年期和long term组合可以吗

2021-04-14 22:27 1 · 回答

1.124. 1.205. A is correct. To maintain the effective ration match, the ration of the 10-yebonsale must equthe totweighteration of the 3-yeanlong-term bonpurchases. 9.51 = (ration of 3-yebon× Weight of 3-yebon + (ration of long-term bon× Weight of long-term bon x = weight of 3-yebon(1 – x) = weight of long-term bon9.51 = 2.88x + 21.30(1 – x) x = 0.64 or 64% The procee from the sale of the 10-yeCanagovernment bonshoulallocate64% to the 3-yebonan36% to the long-term bon 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 bon × (Convexity of the long-term bon – (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 本题用卖10年债券的procee买3年和长期债,感觉是属于llneutr而不是 ration neutr,这块不太理解,请教一下,谢谢

2020-12-04 10:19 1 · 回答