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mino酱是个小破货 · 2024年07月11日

老师，PV01也不等啊，why？

  1. CFA III
  2. Fixed Income

* 问题详情，请 查看题干

NO.PZ202209060200004703

问题如下：

Based on the data in Exhibit 2, will the client discussed most likely be able to immunize its DB plan given the interest rate scenario described by Silver?

选项：

A.Yes

B.No, because of the differences in money duration

C.No, because of the differences in convexity and dispersion

解释：

Solution

C is correct. The money duration of the assets and liabilities are equal: 517,342,000 × 12.66 = 6,548,381,000, and 500,000,000 × 13.10 = 6,548,381,000. For parallel changes, the equal money durations and PV01 imply that assets and liabilities would move in tandem. Silver expects a bear steepener; that is, long rates will rise faster than short rates. In a bear steepener, long rates rise faster than short rates in a non-parallel fashion. Given that the assets have lower convexity and dispersion than the liabilities, they will underperform; that is, the liabilities would change by a greater amount than the assets.

A is incorrect because Silver expects a bear steepener; that is, long rates will rise faster than short rates. In a bear steepener, long rates rise faster than short rates in a non-parallel fashion. Given that the assets have lower convexity and dispersion than the liabilities, they will underperform.

B is incorrect because the differences in convexity and dispersion are unfavorable; that is, they are lower for the assets than for the liabilities. If the opposite were the case, then the liabilities would be immunized.

麻烦问下老师，PV01（asset）不等于PV01（lia），BPV=PV01的概念吗？按理来说，Money duration*0.01%不就是BPV吗？好奇怪，谢谢老师

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发亮_品职助教 · 2024年07月11日

这是协会官网补充的题目，这道题的表格数据有错，且题型有点问题。

PV01和BPV的数据应该是统一的，虽然差100倍，但是本源都是用money duration算的。


这道题不要管PV01这一行数据。需要利用表格的Market value×modified duration×0.0001算一下资产、负债的BPV。算下来之后会发现两者基本一致。所以仅仅从BPV的角度看，是满足Multiple liability duration-matching


这道题的问题是在于，资产的convexity 21.40小于负债的convexity 22.51，从这点上看不满足duration-matching，所以duration-matching失效。哪怕是利率曲线的平行移动，资产与负债都无法实现duration-matching。更何况本题是非平行移动的利率假设，那就更不可能实现duration-matching了。


由于convexity不满足匹配条件，所以本题没有满足duraiton-matching，本题的非平行移动（a bear steepening）不会实现duration-matching。

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