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Lisa Li · 2020年03月12日

问一道题：NO.PZ2019103001000033

  1. CFA III
  2. Fixed Income

问题如下：

Doug Kepler, the newly hired chief financial officer for the City of Radford, asks the deputy financial manager, Hui Ng, to prepare an analysis of the current investment portfolio and the city’s current and future obligations. The city has multiple liabilities of different amounts and maturities relating to the pension fund, infrastructure repairs, and various other obligations.

Ng observes that the current fixed-income portfolio is structured to match the duration of each liability. Previously, this structure caused the city to access a line of credit for temporary mismatches resulting from changes in the term structure of interest rates

Kepler asks Ng for different strategies to manage the interest rate risk of the city’s fixed-income investment portfolio against one-time shifts in the yield curve. Ng considers two different strategies:

Strategy 1: Immunization of the single liabilities using zero-coupon bonds held to maturity

Strategy 2: Immunization of the single liabilities using coupon-bearing bonds while continuously matching duration.

The effects of a non-parallel shift in the yield curve on Strategy 2 can be reduced by:

选项：

A.

minimizing the convexity of the bond portfolio.

B.

maximizing the cash flow yield of the bond portfolio.

C.

minimizing the difference between liability duration and bond-portfolio duration.

解释：

A is correct.

Minimizing the convexity of the bond portfolio minimizes the dispersion of the bond portfolio. A non-parallel shift in the yield curve may result in changes in the bond portfolio’s cash flow yield. In summary, the characteristics of a bond portfolio structured to immunize a single liability are that it (1) has an initial market value that equals or exceeds the present value of the liability, (2) has a portfolio Macaulay duration that matches the liability’s due date, and (3) minimizes the portfolio convexity statistic.

请问题目中不是说针对multiple liabilities吗？那么为何是选择convexity最小的状况呢？

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1 个答案

发亮_品职助教 · 2020年03月13日

嗨，从没放弃的小努力你好：


“请问题目中不是说针对multiple liabilities吗？那么为何是选择convexity最小的状况呢？”

 Strategy 2是：Immunization of the single liabilities using coupon-bearing bonds while continuously matching duration.

注意里面说的是Single liabilities（Liability是复数），他是把多期负债看成是多个单期负债的组合，所以先逐个匹配里面的单期负债，每一个单期负债都实现了匹配就相当于实现了这个多期负债的匹配。

所以他的描述是：Immunization of the single liabilities，对多个单期负债（Single liabilities）进行匹配。

于是，为了降低Structural risk（Non-parallel时，资产不匹配负债的风险），我们就要选择Convexity最小的债券。

注意，这种把多期负债拆成多个单期负债组合进行逐项匹配，只是匹配多期负债的一种思路，了解这种思路即可。

实际上在三级里面关于多期负债匹配，教给我们的方法是把多期负债当成一个Portfolio，从资产Porfolio层面来匹配多期负债Portfolio。满足的要求就是：

1、Asset PV ≥ Liability PV

2、Asset  BPV = Liability BPV

3、Asset convexity > Liability Convexity

在多期负债匹配里，我们对Convexity的要求是：资产的Convexity > 负债的Convexity。

Convexity达到以上条件，就已经可以实现匹配啦。但是，资产的Convexity数据不能太大，太大又会引入Structural risk。

于是，如果要实现最好的匹配效果，我们就让资产的Convexity尽可能的小。

这样的话，在多期负债匹配里，要实现最优的匹配，对Convexity的要求是：资产的Convexity > 负债的Convexity，且尽可能地降低资产Convexity。

这样的话，无论单期负债，还是多期负债，为了降低Structural risk，要求都是Minimize asset convexity，只不过在多欺负债里有个约束条件是资产的Convexity > 负债的Convexity。


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