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dognmnm · 2023年02月22日

structure risk与cash flow yield

  1. CFA III
  2. Fixed Income

NO.PZ2018120301000014

问题如下：

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


Based on 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.

我想确认一下, 我们在讨论structure risk的过程中, 是不是跟CF yield没啥关系? 哪怕差很多也没关系对吧?

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1 个答案

发亮_品职助教 · 2023年02月27日

嗨，从没放弃的小努力你好：


我们在讨论structure risk的过程中, 是不是跟CF yield没啥关系? 


有关系。本质上Structural risk是由现金流分布不同引起的。就是资产的现金流和负债的现金流分布不一样，所以导致利率变动时，资产的表现和负债的表现不一致，于是导致Strucutral risk。所以，在判断免疫、比较Structural risk的时候，我们需要看现金流分布dispersion。


但因为债券Portfolio没有直接可以利用的Dispersion指标，判断起来比较麻烦。所以后面就找到了债券现金流dispersion和convexity的关系。

就是在债券Macaulay duration与cash flow yield保持不变的情况下，债券的现金流dispersion越大，那么对应的convexity越大；现金流dispersion越小， 对应的convexity就越小。

这样就把比较Dispersion，转换成了看债券的convexity指标。而convexity是债券直接可得的数据。


后面就直接利用convexity判断债券的structural risk。convexity越大，structural risk越大

但利用convexity比较有个前提，就是几个债券的Macaulay duration和cash flow yield要一样大， 这样比较convexity才有意义。因为几个债券的Macaulay duration和cash flow yield一样大时，才能保证convexity的大小完全受dispersion的影响，才能通过convexity判别structural risk大小。


我们教材出题，为了保证严谨，就把债券的cash flow yield和macaulay duration也给出来。目的是想让我们知道，几个portfolio的条件差不多，可以比较convexity数据。


注意，到目前为止，cash flow yield这个数据，也只是为了出题严谨给了指标，还没有利用cash flow yield来做题的情况出现。所以之后出现了CF yield，就当成是题干默认的条件，只是为了严谨并非是让我们利用它解题。


哪怕差很多也没关系对吧?


差很多的话，就说明convexity指标不可比，不能利用convexity大小判断structural risk大小。

这种情况不会出现，因为教材没有涉及在这样的背景下如何判断structural risk，所以基本上题目都是CF yield差不多的。

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