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yiml · 2023年11月23日

这道题没看懂,能再讲一讲么?不是说2,3,4是可以用有效久期来衡量利率的敏感性么?为什么又是最不正确的呢?

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NO.PZ202209060200004702

问题如下:

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

选项:

A.Shrewsbury regarding Type I investors

B.Silver regarding Type I, II, III, and IV investors

C.Shrewsbury regarding Type II, III, and IV investors

解释:

Solution

B is correct. Silver is correct in that Type I clients can use a yield statistic for immunizing their liabilities, but he is incorrect in stating that Type II, III, and IV investors can use the same approach. An advantage to knowing the size and timing of cash flows is that yield duration statistics—that is, Macaulay duration, modified duration, money duration, and PVBP—can be used to measure the interest rate sensitivity of the liabilities. With Type II, III, and IV liabilities, a curve duration statistic known as effective duration is needed to estimate interest rate sensitivity. This statistic is calculated using a model for the uncertain amount and/or timing of the cash flows and an initial assumption about the yield curve.

A is incorrect because Shrewsbury is correct regarding Type I clients.

C is incorrect because Shrewsbury is correct regarding II, III, and IV clients.

请再讲一讲,谢谢。不是说2,3,4是可以用有效久期来衡量利率的敏感性么?为什么又是最不正确的呢?

2 个答案

yiml · 2023年11月25日

解答的太详细了,非常感谢!

pzqa31 · 2023年11月24日

嗨,从没放弃的小努力你好:


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:

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就算太阳没有迎着我们而来,我们正在朝着它而去,加油!

考拉 · 2024年01月22日

解析走心了!透彻