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阿弥陀佛 · 2021年04月15日

为何选择B呢

Silver tells Shrewsbury, “Managing fixed-income portfolios to meet obligations requires an understanding of the nature of the liabilities. Clients with liability types such as those listed in Exhibit 1 use yield statistics, such as Macaulay, modified duration, money durations, and the present value of a basis point (PVBP), when implementing immunization strategies.”

Exhibit 1

Classification of Liabilities

Liability TypeExampleCash Outlay AmountTimingIBond with no optionsKnownKnownIICallable bondKnownUncertainIIIStructured notesUncertainKnownIVDefined benefit planUncertainUncertain

Shrewsbury responds, “Only Type I clients can measure the interest rate sensitivity of liabilities using yield statistics. Those with Type II, III, and IV liabilities must use a curve duration statistic, such as effective duration, to estimate interest rate sensitivity.”



Q. Who is least likely correct with regard to the measures that clients in Exhibit 1 use when immunizing their liabilities?

  1. Shrewsbury regarding Type I investors
  2. Silver regarding Type I, II, III, and IV investors
  3. Shrewsbury regarding Type II, III, and IV investors


1 个答案

发亮_品职助教 · 2021年04月16日

嗨,爱思考的PZer你好:


为何选择B呢



这道题实际上有点涉及到1级的知识点。大概回忆一下,债券的Duration数据其实可以有2类,第一类叫做Yield statistics;第二类叫做Curve statistics


其中Yield statistics,都是基于债券自身收益率Yield算出来的。


例如,Modified duration就是对债券的折现公式进行求导算出来的,MD是债券收益率Yield的函数;

同理Convexity是对Duration进一步求导算出来的,他依然是债券自身Yield的函数。Macaulay duraiton也是通过债券自身的Yield算出来的,基于Modified duration算出来的Money duration与PBVP实际上也是间接地基于债券自身的Yield算出来的数据。


我们把这一类基于债券自身Yield的数据,称为Yield statistics。


如果债券想要有Yield statistics,那首先债券需要有一个有效的Yield,债券首先需要能写出来一个合格的折现公式。

其实只有固定利率债券,才有一个有效的折现公式,因为只有固定利率债券的现金流是确定的,才可以写出有效的现金流进行折现。


而浮动利率债券、含权债券,其实他们的现金流不确定,不确定的话就无法写出一个有效的折现公式,即,他们没有有效的Yield。所以,这一类债券其实没有Yield statistics,所以他们就无法算出基于自身Yield statistics,例如,含权债券的Modified duration就没有意义,Floating rate bond的Modified duration也无意义。


那要衡量这类债券的利率风险,我们就引入了Curve statistics,不再使用债券的自身Yield了,而是使用基准利率,即,基准利率变动1单位,债券的价格变动多少。这一类债券的Duration, convexity等数据,都是基于基准利率算出来的,如Effective duration,Effective convexity,以及基于Effective duration算出来的Money duration,PVBP.


那由于是基于基准利率,我们把这类参数称为Curve statistics。


所以,普通的固定利率债券,使用Yield statistics来衡量;含权债券,浮动利率债券使用Curve statistics。


在这个表1里面,只有Liability Type 1属于现金流确定、发生时间确定的固定利率债券,只有Type 1存在Yield statistics;

而Type 2/3/4,要么现金流金额不确定,要么发生时间不确定,没有有效的Yield statistics,我们只能算出来Curve statistics,因此针对后三个Liability,我们要使用Curve statistics数据。


于是,题干下面这句正确,选项AC就正确:

Shrewsbury responds, “Only Type I clients can measure the interest rate sensitivity of liabilities using yield statistics. Those with Type II, III, and IV liabilities must use a curve duration statistic, such as effective duration, to estimate interest rate sensitivity.


然后题干这句错误,他说表1里的Liability都能使用Yield statistics这点错误,只有Type 1可以使用Yield statistics:


Silver tells Shrewsbury, “Managing fixed-income portfolios to meet obligations requires an understanding of the nature of the liabilities. Clients with liability types such as those listed in Exhibit 1 use yield statistics, such as Macaulay, modified duration, money durations, and the present value of a basis point (PVBP), when implementing immunization strategies.”


讲义参考74、75页:

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虽然现在很辛苦,但努力过的感觉真的很好,加油!

Yiyun · 2024年05月30日

实话实说 发亮牛逼(づ ̄3 ̄)づ╭❤~

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