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biguo · 2024年03月26日

Convexity相关

  1. CFA III
  2. Fixed Income

NO.PZ2018120301000016

问题如下：


Basedon Exhibit 2, relative to Portfolio C, Portfolio B:

选项：

A.

has higher cash flow reinvestment risk.

B.

is a more desirable portfolio for liquidity management.

C.

provides less protection from yield curve shifts and twists.

解释：

Correct Answer: B

B is correct. Portfolio B is a laddered portfolio with maturities spread more or less evenly over the yield curve. A desirable aspect of a laddered portfolio is liquidity management. Because there is always a bond close to redemption, the soon-to-mature bond can provide emergency liquidity needs. Barbell portfolios, such as Portfolio C, have maturities only at the short-term and long-term ends and thus are much less desirable for liquidity management.

我还是不太理解，convexity越大是否相对更好呢？更能抵御twist变化？究竟什么时候要选convexity大的债券呢？

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3 个答案

pzqa31 · 2024年03月27日

嗨，爱思考的PZer你好：


涨多跌少是债券本身自带的一个性质，任何债券都有这个性质，这个性质其实主要体现在债券的收益率上，这个从公式上就能看出来：

如果不考虑convexity：△P/P=-mod D*△y

如果考虑convexity:△P/P=-mod D*△y+1/2*C*(△y)2

这里探讨的基本都是收益相关的问题。

这个性质咱们从一级债券性质就开始学了，其实并不是三级的重点，因为三级侧重的是投资策略，所以你看基本题目也是侧重免疫、收益率曲线变化对投资组合的影响等等。

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努力的时光都是限量版，加油！

pzqa31 · 2024年03月27日

嗨，爱思考的PZer你好：


总结一下哈，在免疫里咱们提到convexity的地方：

对于single liability，由于负债是零息债，所以convexity=0，那么对应的immunization portfolio只要选convexity最小的就行。

对于multiple liability，由于负债不是零息债了，所以convexity是＞0的，那么就要从资产convexity大于负债convexity的资产中选一个convexity最小的。

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努力的时光都是限量版，加油！

biguo · 2024年03月27日

谢谢！免疫的我明白。那什么时候是会用到convexity大涨多跌少很好的这个性质呢？

pzqa31 · 2024年03月27日

嗨，爱思考的PZer你好：


这道题不是问免疫，是问的收益率曲线非平行移动下，哪钟portfolio value波动更小（protection from yield curve shifts and twists)。yield curve shift and twist是指收益率曲线的非平行移动，由于laddered portfolio现金流分散更均匀，所以不同时间点收益率变动不同带来的reinvestment risk更有可能相互抵消，所以，在面对收益率曲线非平行移动时，laddered portfolio可以提供更好的protectation,这是原版书的结论。

这道题跟convexity大小没关系，要根据现金流发生结构判断哪个是laddered。


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虽然现在很辛苦，但努力过的感觉真的很好，加油！

biguo · 2024年03月27日

那什么情况下考虑convexity？选convexity大的债券？

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