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Amber · 2020年01月20日

问一道题:NO.PZ2019103001000031

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.

Which duration measure should be matched when implementing Strategy 2?

选项:

A.

Key rate

B.

Modified

C.

Macaulay

解释:

C is correct.

An investor having an investment horizon equal to the bond’s Macaulay duration is effectively protected, or immunized, from the first change in interest rates, because price and coupon reinvestment effects offset for either higher or lower rates.

這題好怪...可以用coupon bearing bond嗎? 不好意思怎麼完全沒印象這章有出現用coupon bearing bond,而且這樣是ok的嗎?不是會出現mismatch 和無法immunisation,可以請老師幫忙解釋嗎?謝謝

1 个答案

发亮_品职助教 · 2020年01月20日

嗨,爱思考的PZer你好:


"可以用coupon bearing bond嗎? 怎麼完全沒印象這章有出現用coupon bearing bond,而且這樣是ok的嗎?"


完全没有问题的。

我们在匹配单期负债时,最理想、完美的Duration-matching策略,就是找零息债券来匹配。

但是有一个非常大的缺点,就是零息债券的期限非常少,尤其是国债只有几个特定期限的零息国债。

所以我们在匹配单期负债时,往往使用的是附息债券(Coupon-bearing bond)来做Duration-matching。

因为零息债券做Duration-matching是最完美的状态,所以我们用附息债券来匹配单期负债时,就是尽量让附息债券的表现模拟零息债券。



”不是會出現mismatch 和無法immunisation"


会出现。

因为只有零息债券来做单期匹配时完美的;而用附息债券的话,可能会出现不匹配的情景。所以为了降低附息债券匹配单期负债时不匹配的风险,我们就尽可能的让附息债券模拟零息债券匹配。

如何实现尽可能地模拟零息债券呢?这其实就是单期负债匹配里的第三个要求:Minimize convexity,最小化附息债券组合的Convexity数据。


理解如下:

Macaulay duration衡量的是债券现金流的平均到账时间,而现金流的Dispersion衡量的是债券现金流距离Macaulay duration的离散程度。

对于零息债券,因为只有一笔现金流,且发生在Macaulay duration那天,所以他的现金流离散程度为零。

而Convexity和现金流离散程度成正比,也就是Dispersion越大,债券的Convexity数据就越大,所以在相同的Duration下,零息债券的Convexity数据是最小的。

所以,在用附息债券匹配单期负债时,我们的要求是:

Asset Macaulay duration = Liability Macaulay duration

Asset PV = Liability PV

这两个要求和用零息债券一模一样没有区别。而第三个要求Minimize Convexity,就是让附息债券的现金流离散程度尽可能地小、尽可能地像零息债券。

在满足其他两个匹配条件的情况下,如果付息债券的Convexity足够小,那说明付息债券的现金流离Macaulay duration足够近,那就相当于现金流集中在单期负债到期日那天,这就相当于用零息债券来匹配单期负债。

总结下:绝大多数单期负债匹配,实际上是用Coupon-bearing bond来实现的,因为零息债券并不是所有的期限都有。在用Coupon-bearing bond做单期负债匹配时,为了消除附息债券的Mismatch风险、让匹配效果足够好,我们就尽可能地让附息债券模拟零息债券的表现,这就体现在单期负债匹配的第三个条件里:Minimize Convexity。


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