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孙胖胖学CFA · 2024年08月04日

structure risk 和 multiple liabilities duration matching 的条件冲突吗？

  1. CFA III
  2. Fixed Income

NO.PZ2023032703000022

问题如下：

Serena Soto is a risk management specialist with Liability Protection Advisors. Trey Hudgens, CFO of Kiest Manufacturing, enlists Soto’s help with three projects.

The second project for Soto is to help Hudgens 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. Soto 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：

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’ duration 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.

multiple liabilities duration matching 的第三个条件是covexity of assets are greater than those of liabilities. 这里c 选项符合这个标准，但是structure risk最大，所以这两者并不冲突对吗？

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发亮_品职助教 · 2024年08月05日

不冲突。先要满足资产的convexity更大，大于负债的convexity。在这个基础上才考虑尽可能降低资产convexity。


其实只要资产与负债的BPV相等，且资产的Convexity大于负债的convexity，只要满足这2个条件就已经实现了duration-matching了，利率曲线的平行移动已经能够实现免疫了。


在以上的基础下，再额外要求资产的convexity尽可能地小，是为了额外保证在非平行移动时，依然能够实现免疫，有最小的structural risk。


只要资产的convexity小于负债convexity，直接排除。

然后2个组合BPV满足条件，他们的convexity在大于负债convexity的基础上，asset convexity更小的组合是最优。

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