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lz523 · 2025年06月18日

这题的BPV可以判断吗？C选项的BPV会不会差距有点多

  1. CFA III
  2. Fixed Income

NO.PZ2018120301000015

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.


Which portfolio in Exhibit 2 【fails to meet】 the requirements to achieve immunization for multiple liabilities?

选项：

A.

Portfolio A

B.

Portfolio B

C.

Portfolio C

解释：

Correct Answer: A

A is correct. The two requirements to achieve immunization for multiple liabilities are for the money duration (or BPV) of the asset and liability to match and for the asset convexity to exceed the convexity of the liability. Although all three portfolios have similar BPVs, Portfolio A is the only portfolio to have a lower convexity than that of the liability portfolio (31.98, versus 33.05 for the $20 million liability portfolio), and thus, it fails to meet one of the two requirements needed for immunization.

如题。

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1 个答案

发亮_品职助教 · 2025年06月20日

这道题是多期负债匹配，就是拿BPV找最优组合的。负债的BPV是：basis point value (BPV) of $10,505

三个资产组合的BPV都离这个数比较接近。组合A的BPV=10,524，和负债的差距是19，组合B的差距是1，组合C的差距是11.

这三个差距都很小，一般像BPV是五位数如本题的10505，误差在100以内的都算合适的。


因为BPV衡量利率变动1BP时，债券的value改变金额。拿C组合为例，和负债的BPV差异是11，意思是当利率变动1bp时，资产与负债的value改变金额差异为11元。

而一般的利率改变多的就是50bp左右，通常一次利率改变不会太大，所以一次利率改变，误差金额会控制在几百左右。

对于一个20million的组合，误差在几百左右时完全可以接受的。


从做题的角度看，反而组合B，这个最接近的具有迷惑性，因为会有考生看到B组合的BPV最接近，就直接选。其实不是，还要结合convexity数据判断。

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