开发者:上海品职教育科技有限公司 隐私政策详情

应用版本:4.2.11(IOS)|3.2.5(安卓)APP下载

秋晨雨 · 2020年12月29日

问一道题:NO.PZ2019103001000032

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.

An upward shift in the yield curve on Strategy 2 will most likely result in the:

选项:

A.

price effect cancelling the coupon reinvestment effect.

B.

price effect being greater than the coupon reinvestment effect.

C.

coupon reinvestment effect being greater than the price effect.

解释:

A is correct.

An upward shift in the yield curve reduces the bond’s value but increases the reinvestment rate, with these two effects offsetting one another. The price effect and the coupon reinvestment effect cancel each other in the case of an upward shift in the yield curve for an immunized liability.

老师您好,这道题原题我可能没太看懂。原文说了Ng observes that the current fixed-income portfolio is structured to match the duration of each liability.,这句话的意思不是说投资组合和负债的duration没有match吗?既然没有match那么三个选项都选不出来啊

2 个答案

发亮_品职助教 · 2021年04月09日

嗨,爱思考的PZer你好:


老师我不太懂,何老师说structural risk =immunization risk,又说利率平行移动是immunization的充分非必要条件。这不就是说利率只要平行移动,都可以免疫吗


正确!(小幅)平行移动一定可以实现免疫。


这个Duration-matching(Immunization)就是针对平行移动设计的,让asset macaulay duration = liability macaulay duration = investment horizon就可实现免疫,所以知道,此时利率曲线发生小幅平行移动,Duration-matching一定成功,即本次资产的收益率不受影响、抵挡住了利率平行移动的影响。


为什么这里还是强调只能免疫一次。下一次又得rebalance


在这次利率变动之前,资产、负债Macaulay duration相等、已经满足了免疫条件,那这次资产其实就不会受到利率变动影响。

但是资产、负债的Macaulay duration是利率的函数,这次的利率变动影响到了资产、负债的Macaulay duration,利率变动之后,asset macaulay duration ≠ liability macaulay duration ≠ investment horizon。所以在利率变动之后,已经不满足免疫的条件了,为了让资产、负债能够继续实现免疫,我们就需要对资产进行Rebalance,使得资产、负债重新达到Macaulay duration相等的条件,使得资产、负债重回免疫。

----------------------------------------------
努力的时光都是限量版,加油!

发亮_品职助教 · 2020年12月30日

嗨,努力学习的PZer你好:


“原文说了Ng observes that the current fixed-income portfolio is structured to match the duration of each liability.,这句话的意思不是说投资组合和负债的duration没有match吗?”


不是的。

这句话是说,Ng同学观察到当前固定收益组合是Match每一个Liability的Duration的,也就是当前对每一个负债已经构建好了Duration-matching策略,所以当前是已经构建好了免疫策略的。但这句话其实和我们这道题没有啥关系。

所以继续往下看,题干又说,他们想换另外一个策略来做Immunization策略( different strategies to manage the interest rate risk ),题干提供了Strategy 1和Strategy 2这两个策略,然后他问平行移动时,Strategy 2的结果是啥。

从题干Strategy 2的描述看,他使用附息债券(coupon-bearing bonds)来做Duration-matching策略,所以我们知道Strategy 2达到了免疫状态,那这样的话,利率平行移动时,Strategy 2可以实现免疫,Price risk和Coupon reinvestment risk可以相互抵消,可以选出来A了,Price effect与Coupon reinvestment effect互相Cancel掉。


另外有一个细节,Stratege 2他使用了Continuouly matching duration。他其实保证了资产可以时时刻刻实现免疫。

我们知道,构建Duration-matching时,实际上是让资产的Mac.Duration等于负债的Mac.Duration,从而实现Immunization状态。

但是Duration是一个时间的函数,哪怕其他条件没有变化,仅仅是时间的流失,资产、负债的Mac.Duration也会发生变化,这样的话,虽然期初资产负债的Mac.Duration相等,他们实现了免疫,但是随着时间的流失,有可能资产、负债的Mac.Duration变动、他们不再相等,无法继续实现Immunization状态。

同时,Duration还是一个利率的函数,利率发生变动,Duration就会变动一次,所以哪怕期初我们让资产、负债的Mac.Duration相等,但利率变动一次之后,资产、负债的Mac.Duration可能就不再相等,这样也可能无法继续实现Immunization状态。

Stratege 2他使用了Continuouly matching duration,也就是他让资产、负债的Duration时时刻刻保持相等状态,也就是让他时刻实现Duration-matching策略。由此,我们知道,Strategy 2的策略也是时时刻刻免疫的。

不过,哪怕Strategy 2不是Continuouly matching duration,只要构建好Duration-matching策略,他就能抵御一次的利率平行移动,实现Prcie risk与Coupon reinvestment risk相互抵消。因此,哪怕Stratey 2不提Continuouly matching duration,本题说的利率平行移动,Strategy 2的结果依然是A选项。


-------------------------------
加油吧,让我们一起遇见更好的自己!


小锦鲤要加油 · 2021年04月08日

老师我不太懂,何老师说structural risk =immunization risk,又说利率平行移动是immunization的充分非必要条件。这不就是说利率只要平行移动,都可以免疫吗,为什么这里还是强调只能免疫一次。下一次又得rebalance