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biguo · 2024年03月21日

Multiple liabilities

  1. CFA III
  2. Fixed Income

NO.PZ2018120301000014

问题如下：

Thesecond project for Serena is to help Trey immunize a $20 million portfolioof liabilities. The liabilities range from 3.00 years to 8.50 years with aMacaulay duration of 5.34 years, cash flow yield of 3.25%, portfolio convexityof 33.05, and basis point value (BPV) of $10,505. Serena suggested employing aduration-matching strategy using one of the three AAA rated bond portfoliospresented in Exhibit 2.


Basedon Exhibit 2, the portfolio with the greatest structural risk is:

选项：

A.

Portfolio A

B.

Portfolio B

C.

Portfolio C

解释：

Correct Answer: C

C is correct. Structural risk arises from the design of the duration-matching portfolio. It is reduced by minimizing the dispersion of the bond positions, going from a barbell structure to more of a bullet portfolio that concentrates the component bonds’ durations around the investment horizon. With bond maturities of 1.5 and 11.5 years, Portfolio C has a definite barbell structure compared with those of Portfolios A and B, and it is thus subject to a greater degree of risk from yield curve twists and non-parallel shifts. In addition, Portfolio C has the highest level of convexity, which increases a portfolio’s structural risk.

我想请问一下，这个的考虑顺序是什么呢？先是看BPV吗？Asset和liabilities BPV 想等，这三个是不是都和liabilities差不多？所以都可以吗？ 然后是看convexity？大于liabilities的convexity里选个最小的？因为越大的convexity风险越大？那这里为什么还需要看barbell和bullet ladder ed呢？怎么看怎么比呢 像这种情况，会用到cfyield吗？ 另外，我想请问一下，这里为什么要convexity大于liability，但是越小越好，但是其实涨多跌少是个好性质呢，不是越大越好吗？谢谢

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4 个答案

pzqa31 · 2024年04月19日

嗨，努力学习的PZer你好：


Structural risk的大小，可以由债券资产的Convexity数据来判断，在满足Duration-matching的基础上，Convexity越大的资产，Structual risk越大；

也就是在收益率曲线非平行移动时，资产不能匹配负债的风险就越大。Portfolio A不满足multiple liability的条件，也就谈不上strutual risk的问题了。

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cherry · 2024年05月01日

您的意思是在满足multi liab条件下才有资格谈structure risk是吗？

cherry · 2024年04月17日

那A convexity都没有包裹住liability的convexity，那不是更有structure risk


pzqa31 · 2024年03月23日

嗨，爱思考的PZer你好：


然后同学说到的涨多跌少的性质，那是针对单个债券的性质而言，这里我们要看的是整体上asset匹配liability的问题，所以看重的是现金流的分散程度。

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pzqa31 · 2024年03月23日

嗨，努力学习的PZer你好：


是的，对于Multiple liability，首先是Asset convexity要大于Liability convexity，理解上是资产的现金流要包裹住负债，因此资产的Convexity要大于负债的Convexity；然后，或者也可以说和第一个条件同时满足Asset Convexity大于Liability Convexity，这时候，理论上都能做到Match multiple liability；最后，Asset Convexity在大于Liability convexity的基础上，asset convexity又最小的那个资产组合是最优的，因为Structural risk最小，能在一些非平行移动时，也能较好的Match multiple liability。


然后关于第二给条件，资产的convexity大于Liability，咱们课上讲过，convexity和dispersion,也就是现金流的分散程度是同向的，咱们讲义上提供过相关的公式，所以这里我们可以认为，convexity越大，现金流越分散，所以这里的意思其实就是要求asset的现金流能够包裹住liability的现金流，为什么要这样呢？因为multiple liability较于single liability而言，负债结构更加复杂，做免疫更困难，因为如果到期只有一笔负债现金流，最简单的方法就是买一个零息债券就可以完美匹配了。但是multiple liabitliy不可以。所以这里才会要求asset的现金流更分散，那才可以更加安全的应对未来多个时间点的负债（现金流支出）。但是呢，如果Convexity太大的话，也会引入Structural risk的问题，所以这里在实现第二个条件的前提下，又要求了convexity最小。

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