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

返回

yan · 2025年02月04日

这道题没有看懂，请解释一下B和C

  1. CFA III
  2. Fixed Income

* 问题详情，请 查看题干

NO.PZ202209060200004602

问题如下：

According to the information in Exhibit 1 and assuming Berendsen retires in four years, the fixed-income portfolio most likely:

选项：

A.should have a shorter duration.

B.needs a higher cash flow yield.

C.has currently achieved zero replication.

解释：

Solution

C is correct. The portfolio’s Macaulay duration of approximately 4.0 matches the time horizon of the liability and can be calculated as follows:

[(Portfolio weightBond 1 × DurationBond 1) + (Portfolio weightBond 2 × DurationBond 2) + (Portfolio weightBond 3 × DurationBond 3)] ÷ 3 = 3.99.

When compared with the single liability due in four years, the portfolio has the same return and duration characteristics of a single zero-coupon bond maturing in four years. The interest rate risk has been immunized, which is known as zero replication.

A is incorrect because the portfolio’s current duration matches the duration of the liability, or retirement date.

B is incorrect because the cash flow yield matches the required investment return. Although not equivalent to investment return, it is likely the portfolio’s return will meet the required rate of return.

这道题没有看懂，请解释一下B和C

添加评论
1 个答案

发亮_品职助教 · 2025年02月05日

这道题就是基于duration-matching考查相关结论的。


选项B说组合needs a higher cash flow yield。

cash flow yield就是债券组合的内部收益率。对于单个债券来讲，内部收益率是YTM，对于债券组合来讲，对标的收益率就是cash flow yield。

在分析的时候，两者起到的作用是一样的。


只要组合达到duration-matching，债券组合就锁定了（lock in）一个收益率，无论利率如何改变，组合利率免疫都能实现这个收益率。这个锁定的收益率其实就是债券组合的cash flow yield。

这块需要注意，duration-matching的债券组合投资收益率确定、稳定，这个稳定，或者说锁定的收益率是其期初时刻的cash flow yield.


题干下面这句说，只要债券未来4年能实现4%的收益率，则资产足够cover负债：

If the fixed-income portfolio achieves an average annual investment return of at least 4% for the next four years, the proceeds of its liquidation will be enough to purchase an annuity sufficient to provide the funds needed to supplement your Social Security benefits.


这个4%相当于是实现cover负债需要达成的最低收益率。

所以，我们这道题就需要看一下，这个duration-matching的资产组合，他锁定的cash flow yield有没有到达4%。如果比4%小，则说明资产收益率太小，期末不足以cover负债。如果资产的cash flow yield大于等于4%，则说明资产的收益足够大，期末一定可以cover负债。


这道题的cash flow yield信息在表格1下面的脚注：

Note 2: Portfolio cash flow yield: 4.15%

即，组合锁定的收益率是4.15%，比最低标准4%要高。所以期末时刻，资产一定可以cover负债。

选项B说，我们需要一个更高的cash flow yield，这个就是错的。4.15%的收益率已经够了。


选项C说，组合已经实现了zero-replication（has currently achieved zero replication），这个说法正确。

因为zero replication就是duration-matching的同义词。选项C翻译过来是说，组合已经实现了duration-matching。


通过计算，我们发现组合的macaulay duration=3.99≈4，而负债的到期日=4years。已经实现了macaulay duration = investment horizon = 4。已经达成duration-matching，所以c说zero replication没有问题。


关于duration matching是zero replication的同义词，这点在基础课有提过哈。

简单说一下如何理解，之后把两者当成一回事。


在single liability duration matching时，负债有一笔cash flow，可以看成是零息债券。我们使用付息债券组合去cover这笔零息债券。


如何实现精准cover呢？其实就是，当利率改变时，无论是平行or非平行，只要付息债券组合的表现与零息债券（负债）一致，表现完全同步，那就代表资产时时刻刻cover了负债。


这种资产表现与负债的同步，就是在模拟零息债券（负债）的表现，这种模拟，就称为zero-replication，zero是零息负债的含义，replication是模拟。这是这个名字的含义。

  • 1

    回答

  • 0

    关注

  • 7

    浏览
相关问题

NO.PZ202209060200004602 问题如下 Accorng to the information in Exhibit 1 anassuming Berenen retires in four years, the fixeincome portfolio most likely: A.shoulhave a shorter ration. B.nee a higher cash flow yiel C.hcurrently achievezero replication. SolutionC is correct. The portfolio’s Macaulration of approximately 4.0 matches the time horizon of the liability anccalculatefollows:[(Portfolio weightBon1 × rationBon1) + (Portfolio weightBon2 × rationBon2) + (Portfolio weightBon3 × rationBon3)] ÷ 3 = 3.99.When comparewith the single liability e in four years, the portfolio hthe same return anration characteristiof a single zero-coupon bonmaturing in four years. The interest rate risk hbeen immunize whiis known zero replication.A is incorrebecause the portfolio’s current ration matches the ration of the liability, or retirement te.B is incorrebecause the cash flow yielmatches the requireinvestment return. Although not equivalent to investment return, it is likely the portfolio’s return will meet the requirerate of return. 老师好，大案里这个[(Portfolio weightBon1 × rationBon1) + (Portfolio weightBon2 × rationBon2) + (Portfolio weightBon3 × rationBon3)] ÷ 3 = 3.99.具体是怎么算出来的啊？我用allocation那三个百分比配合macauly ration算，算得应该是4.0143，是我哪里用的有问题吗

2024-05-26 11:54 1 · 回答

NO.PZ202209060200004602 问题如下 Accorng to the information in Exhibit 1 anassuming Berenen retires in four years, the fixeincome portfolio most likely: A.shoulhave a shorter ration. B.nee a higher cash flow yiel C.hcurrently achievezero replication. SolutionC is correct. The portfolio’s Macaulration of approximately 4.0 matches the time horizon of the liability anccalculatefollows:[(Portfolio weightBon1 × rationBon1) + (Portfolio weightBon2 × rationBon2) + (Portfolio weightBon3 × rationBon3)] ÷ 3 = 3.99.When comparewith the single liability e in four years, the portfolio hthe same return anration characteristiof a single zero-coupon bonmaturing in four years. The interest rate risk hbeen immunize whiis known zero replication.A is incorrebecause the portfolio’s current ration matches the ration of the liability, or retirement te.B is incorrebecause the cash flow yielmatches the requireinvestment return. Although not equivalent to investment return, it is likely the portfolio’s return will meet the requirerate of return. 解析说When comparewith the single liability e in four years, the portfolio hthe same return anration characteristiof a single zero-coupon bonmaturing in four years. The interest rate risk hbeen immunize whiis known zero replication.但zero replication (immulization)条件有三种，目前只有mration 4满足，其他条件如PV, convexity我没有在原文中找到啊，况且解析说的same return 也不算三个免疫条件中的一种啊

2024-01-22 00:18 1 · 回答

NO.PZ202209060200004602问题如下 Accorng to the information in Exhibit 1 anassuming Berenen retires in four years, the fixeincome portfolio most likely:A.shoulhave a shorter ration.B.nee a higher cash flow yielC.hcurrently achievezero replication.SolutionC is correct. The portfolio’s Macaulration of approximately 4.0 matches the time horizon of the liability anccalculatefollows:[(Portfolio weightBon1 × rationBon1) + (Portfolio weightBon2 × rationBon2) + (Portfolio weightBon3 × rationBon3)] ÷ 3 = 3.99.When comparewith the single liability e in four years, the portfolio hthe same return anration characteristiof a single zero-coupon bonmaturing in four years. The interest rate risk hbeen immunize whiis known zero replication.A is incorrebecause the portfolio’s current ration matches the ration of the liability, or retirement te.B is incorrebecause the cash flow yielmatches the requireinvestment return. Although not equivalent to investment return, it is likely the portfolio’s return will meet the requirerate of return.zero replication 什么意思？就是免疫成功的意思么？

2023-11-24 18:44 1 · 回答

NO.PZ202209060200004602 问题如下 Accorng to the information in Exhibit 1 anassuming Berenen retires in four years, the fixeincome portfolio most likely: A.shoulhave a shorter ration. B.nee a higher cash flow yiel C.hcurrently achievezero replication. SolutionC is correct. The portfolio’s Macaulration of approximately 4.0 matches the time horizon of the liability anccalculatefollows:[(Portfolio weightBon1 × rationBon1) + (Portfolio weightBon2 × rationBon2) + (Portfolio weightBon3 × rationBon3)] ÷ 3 = 3.99.When comparewith the single liability e in four years, the portfolio hthe same return anration characteristiof a single zero-coupon bonmaturing in four years. The interest rate risk hbeen immunize whiis known zero replication.A is incorrebecause the portfolio’s current ration matches the ration of the liability, or retirement te.B is incorrebecause the cash flow yielmatches the requireinvestment return. Although not equivalent to investment return, it is likely the portfolio’s return will meet the requirerate of return. 请问这个portfolio的cash flow yiel是加权平均算吗？

2023-07-14 16:11 1 · 回答