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Hao · 2019年12月10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.

为什么B不对,对价格的影响不是比reinvestment的影响要大吗

1 个答案

发亮_品职助教 · 2019年12月10日

嗨,从没放弃的小努力你好:


“为什么B不对,对价格的影响不是比reinvestment的影响要大吗”


Strategy 2说是已经达到:Single liability的Immunization,也就是达到了单期负债的免疫状态。然后题目问,对于这样的Portfolio资产,他的Price risk和Reinvestment risk之间的大小关系。

这道题,其实考察的是对Immunization(Duration-matching)最根本原理的理解。

结论就是:当资产达到Immunization状态时,资产的Price risk和Coupon reinvestment risk两者的影响完全相互抵消。所以直接选A。



具体理解如下:

让债券的Price risk和Reinvestment risk完全抵消,就是做资产匹配负债最根本的原理。

Immunization(免疫策略),就是指资产匹配负债时,利率的变动不会影响资产的投资收益,进而不影响资产匹配负债。所以称为对利率的免疫(Immunization)


利率变动时,通过两个方面影响债券的投资收益;

第一是:债券期间现金流的再投资收益(Reinvestment risk);

第二是:提前卖出债券时,债券卖出价格不确定带来的Capital gain or capital loss(Price risk);

利率的变动,通过影响债券的Coupon再投资收益、以及债券卖出时的Capital Gain/Loss来影响债券的投资收益。

当利率上升时,债券的Coupon再投资收益上升;同时,因为利率上升,债券卖出时的价格降低,有Capital Loss;

当利率下降时,债券的Coupon再投资收益下降,同时,因为利率下降,债券卖出时的价格上升,有Capital gain;

发现,虽然利率变动会影响到债券期间现金流的再投资收益,以及债券卖出时的价格,但是Price risk和Coupon reinvestment risk对债券投资收益的影响方向是时刻相反的。

既然利率变动时,两个影响的方向是相反的,如果两者能完全抵消,那说明利率变动时,影响债券投资收益的两个风险完全抵消,则债券的投资收益就不受利率变动影响了、债券的投资收益就是一个稳定的预期收益。

也就是说,债券的投资收益对利率的变动免疫,达到Immunization状态,用这样有稳定预期收益的债券资产去匹配单期负债,是非常靠谱、保险的策略。


这就是我们做单期负债匹配的基本原理:

让债券资产的Macaulay duration = 债券资产的投资期 = 负债的Due date(负债的Macaulay duration),债券资产的Price risk和Reinvestment risk相互抵消,有稳定的收益预期。用这样的资产去Cover负债,实现单期负债匹配。

所以题目问,实现Immunization的Strategy 2,他的Price risk和Reinvestment risk大小如何比,我们知道两者是完全可以抵消掉的。


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