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EvanWu · 2021年09月03日

关于convexity的问题

  1. CFA III
  2. Fixed Income

* 问题详情，请 查看题干

NO.PZ201812020100000304

问题如下：

Based on Exhibit 2, relative to Portfolio C, Portfolio B:

选项：

A.

has higher cash flow reinvestment risk.

B.

is a more desirable portfolio for liquidity management.

C.

provides less protection from yield curve shifts and twists.

解释：

B is correct.

Portfolio B is a laddered portfolio with maturities spread more or less evenly over the yield curve. A desirable aspect of a laddered portfolio is liquidity management. Because there is always a bond close to redemption, the soon-to-mature bond can provide emergency liquidity needs. Barbell portfolios, such as Portfolio C, have maturities only at the short-term and long-term ends and thus are much less desirable for liquidity management

single liability里面convexity越小duration match越好这个没问题，但是在multiple liability中的convexity不是说convexity asset 要比convexity liability大才好吗？所以应该怎么判断convexity大小对duration match的影响呢？

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已采纳答案

pzqa015 · 2021年09月03日

嗨，努力学习的PZer你好：


同学你好

在多笔现金流免疫中，第三个条件是资产的convexity大于负债的convexity，同时，在所有大于负债convexity的资产中，选择convexity最小的portfolio.

之所以这样做，是因为convexity越小，免疫策略的structural risk越小。从两个方面理解这个原理。

1、convexity可以代表现金流的离散程度，convexity越大，则现金流越离散。

那么如果资产的convexity大于负债的convexity，说明资产现金流比负债更离散，或者可以理解为资产的现金流可以包住负债的现金流。

比如负债有3、5年期，资产有1、3、5、7年期，那么这样的资产现金流是比负债现金流离散的，可以包住负债现金流。

这样做是为了避免最后一期负债没有对应的资产现金流可以cover，如果资产现金流比负债更分散，那么负债的最后一笔现金流，肯定可以通过资产的coupon或者sale price来覆盖的，这样免疫策略才会成功。

2、现金流越离散，那么面对收益率曲线的非平行移动，portfolio value的变化就越不可控，使得免疫策略失败，这就是structural risk。

我们要选择尽量与负债现金流离散程度一样的，使得即使收益率曲线非平行移动，资产与负债的value变化也尽量相近，这样才会最大程度保证免疫策略的成功。


那么我们到底应该如何判断convexity对duration match的影响呢？

我们在选择portfolio时，资产现值大于等于负债现值（大于最好，等于也可）、资产BPV等于负债BPV（或者接近）这两个条件首先要满足，如果这两个条件都不满足，就不用看convexity了；在满足这两个条件后，我们根据资产convexity大于负债convexity，并从所有满足convexity条件的portfolio中选择convexity最小的。最理想的状态是让资产的convexity与负债的convexity也相等，但现实中是很难实现的，所以退而求其次选择最接近的。

满足这三个条件的portfolio是duration match效果最好的。

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