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dream66 · 2025年04月28日

根据single liability match条件看，没动为啥选C

  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.

从BPV、convexity看，应该选B吧，没理解为啥选C

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1 个答案

发亮_品职助教 · 2025年04月28日

这道题是匹配多期负债multiple liabilities（题干条件20 million portfolio of liabilities），并非是提问里面说的single liability哈。

Multiple liabilities的匹配条件是：

asset BPV = Liability BPV

Asset convexity > liability convexity，且minimize asset convexity。


注意关于convexity的要求，是在资产convexity大于负债convexity的基础上，找资产convexity更小的。

因为资产的convexity越大，说明越偏离负债的convexity。而convexity代表cash flow的分散程度，资产convexity越大则说明资产的现金流与负债的现金流分布的差异越大。

这个差异越大的影响就是：在利率曲线发生非平行移动时，两者的表现就越不一样，会有更大概率出现资产与负债不匹配的情况，即structural risk越大。


所以结论就是：在资产、负债的BPV和convexity满足基本条件的情况下，资产的convexity越大，非平行移动时不匹配的风险（structrural risk）越大


这道题的负债BPV=10505，三个备选资产的BPV都比较接近，所以从BPV的角度看，3个组合符合要求。

负债的convexity=33.05，Portfolio A=31.98，组合A不满足条件排除。


组合B和组合C都满足条件，所以两个组合都可以做duration-matching。但是，组合C的convexity过大，所以structural risk最大。这道题问的就是哪个组合的structural risk最大，直接选Portfolio C。如果这道题让选最优的匹配组合，则应该选组合B。

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