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Ausilio · 2024年05月27日

针对convexity的性质

  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.

老师好，这道题我理解了，但是针对convexity的性质我突然有一点问题。

我记得上课的时候何老师讲过，针对multiple liability的immunization，我们要在asset的convexity大于liability的convexity的组合当中找convexity最小的那个，但是convexity不是越大越好么？因为convexity有涨多跌少的优点——那么这里为什么是要在大的convexity里面找投资组合最小的portfolio呢？

对应的知识点是基础班的这一页


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1 个答案

发亮_品职助教 · 2024年05月27日

嗨，爱思考的PZer你好：


Convexity不是越大越好，具体要看投资的策略。


如果是做主动投资，追求的是高的收益率，这时候convexity越大越好，因为convexity大的可以享受涨多跌少的好处。并且，做主动投资时，我们还得基于未来利率发生波动的情况下，使用高convexity才有用。因为高convexity债券的涨多跌少好处，他的初始购买价格高，所以如果利率不改变的话，债券没办法享受convexity带来的涨多跌少，这相当于为高Convexity付出了购买成本，但没有享受到好处。


所以一般做主动投资，且基于未来利率变动的预期，才会是找Convexity越大的债券，越大越好。

主动投资下，如果预期未来利率不变，Convexity没办法享受涨多跌少，那高convexity的债券只会付出期初高的购买成本，拖累投资收益，所以这时候应该找convexity低、成本低的债券投资。


以上是主动投资，并非投资一定会找convexity高的。在Module 3会学。


但注意，本题是被动的投资，duration-matching策略。被动投资下，追求的不是高收益。Duration-matching的被动投资追求的是资产和负债的匹配，资产的变化和负债的变化尽可能一致。


所以，最好就是资产的convexity和负债的convexity比较接近。


在选Asset时，首先要资产的convexity大于负债的convexity（这是保证资产的现金流比负债现金流分散，可以包裹住负债的现金流），然后在此基础上，为了使得资产、负债变动一致，那就要保证资产与负债的convexity足够接近，即，minimize asset convexity。这是做duration-matching对convexity的要求。

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