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必过1030_ · 2019年12月15日

问一道题:NO.PZ2019103001000070

问题如下:

Gerber explains the concept of empirical duration to Petit and makes the following points.

Point 1: A common way to calculate a bond’s empirical duration is to run a regression of its price returns on changes in a benchmark interest rate.

Point 2: A bond’s empirical duration tends to be larger than its effective duration.

Point 3: The price sensitivity of high-yield bonds to interest rate changes is typically higher than that of investment-grade bonds.

Which of Gerber’s points about empirical duration is correct?

选项:

A.

Point 1

B.

Point 2

C.

Point 3

解释:

A is correct.

A bond’s empirical duration is often estimated by running a regression of its price returns on changes in a benchmark interest rate.

选项三为什么不对?

1 个答案

发亮_品职助教 · 2019年12月16日

嗨,努力学习的PZer你好:


”Point 3: The price sensitivity of high-yield bonds to interest rate changes is typically higher than that of investment-grade bonds.”


他说:High-yield bond对Interest rate的敏感度高于Investment-grade bond对Interest rate的敏感度。

他刚好说反了,Investment-grade bond对利率的敏感度更高。


这点是原版书给的结论,记住即可:Investment-grade portfolios have more exposure to interest rate risk than high-yield portfolios.



理解如下:

债券的Yield可以理解成为:基准利率 + Spread,即:Yield = interest rate + spread

Interest rate的变动,会影响到债券的收益率YTM的大小,进而会影响到债券的价格。

也就是债券价格对Interest rate的敏感度,是通过Yield这个媒介传递的。

如果说Interest rate和Spread的变动没有啥联系的话,Interest rate变动多少,Yield就变动多少,进而通过Duration影响到债券的价格;

在这种情况下,Interest rate变动1%,对于High-yield bond和Investment-grade bond来说,Yield都变动1%,这是理想状态下。


但现实中,往往Interest rate与Spread的变动呈现Negative correlation关系。

也就是经济变好的时候,Interest rate会上升,同时High-yield bond的违约概率降低、Spread降低。

这样Interest rate虽然上升,但Spread下降,所以High-yield bond的Yield并没有变动多少,反应到债券价格上,就是Interest rate变动较大,但High-yield bond债券的价格没有变动多少。这就对应High-yield bond对利率的敏感度较低。

同理,当经济变差的时候,Interest rate会下降,High-yield bond的违约概率上升、Spread上升,这样Interest rate虽然下降,但是Spread上升,所以High-yield bond的Yield没有变动多少,反映到债券价格上就是:Interest rate变动较大,而High-yield bond债券的价格没有变动多少。也对应High-yield bond对Interest rate的敏感度较低。

而对于Investment-grade bond来说,Yield中Spread的影响相对就很小了,Interest rate和Spread的这种Negative correlation的影响没有High-yield bond大,所以对于Investment-grade bond,Interest rate变动时,Yield就会跟着变动,反映出来就是:Interest rate变动时,Investment-grade的价格变动较大,即IG bond对利率的敏感度更大。



从上面这个角度,还能得到一个结论:债券的Empircal duration实际上低于债券的Effective duration。

Effective duration是理论值:Interest rate变动时,债券的价格变动幅度;

Empirical duration是债券的实际价格变动与Interest rate回归出来的敏感度:实际上Interest rate与Spread因为变动相反,两者互相能抵消一点,所以债券价格的变动幅度没有理论值大,于是反映出了的Empirical duration小于Effective duration。


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虽然现在很辛苦,但努力过的感觉真的很好,加油!