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

过程 · 2021年04月10日

modified duration and credit spread duration of the EKN bond are equal 说明什么?

NO.PZ2019103001000069

问题如下:

Emma Gerber and Juliette Petit are senior and junior credit portfolio managers, respectively, for a European money management firm. They are discussing credit management strategies and preparing for an annual meeting with a major client.

One of their high-yield bond holdings is a 10-year bond issued by EKN Corporation (EKN). The bond has a price of 91.82, a modified duration of 8.47, and a spread duration of 8.47. For this bond, Petit speculates on the effects of an interest rate increase of 20 bps and, because of a change in its credit risk, an increase in the EKN bond’s credit spread of 20 bps. Petit comments that because the modified duration and credit spread duration of the EKN bond are equal, the bond’s price will not change (all else being equal) in response to the interest rate and credit spread changes.

Is Petit’s prediction correct that the EKN bond price will not change in response to the interest rate and credit spread changes, all else being equal?

选项:

A.

Yes

B.

No, the bond price should decrease

C.

No, the bond price should increase.

解释:

B is correct.

An increase in interest rates results in a decrease in the bond price. An increase in the credit spread also results in a decrease in the bond price. For the EKN bond, its modified duration shows the effect of the 20 bp increase in interest rates. The approximate percentage price change resulting from the increase in interest rates is –8.47 × 0.0020 = –1.694%. The spread duration shows the effect of the 20 bp increase in the credit spread. The approximate percentage price change resulting from the increase in the credit spread is –8.47 × 0.0020 = –1.694%. The combined effect is a total change of –3.388%, or a price decrease of roughly 3.4%.

请问,modified duration 和 credit spread duration一样的话,说明什么特别的问题吗?

2 个答案
已采纳答案

发亮_品职助教 · 2021年04月11日

嗨,努力学习的PZer你好:


请问,modified duration 和 credit spread duration一样的话,说明什么特别的问题吗?


就说明这是一个普通的固定利率公司债券。


注意,Modified duration与Spread duration是同源的


并不是说债券同时存在Modified duration和Spread duration,只是说,我们为了单独研究Spread变动对债券价格的影响,所以把Modified duration里面,关于Spread影响的部分单独拆出来,拆出来之后、专门起了个名就是Spread duration,专门研究Spread变动对债券价格的影响。


下面说一下,modified duration与Spread duration在分析时的路径:


我们说,债券的收益率Yield = benchmark yield + spread


当债券的收益率Yield发生改变时,会通过债券的Modified duration影响到债券的价格;用Modified duraton计算时,我们不会区分债券Yield的改变来自哪里,实际上,债券Yield的改变,即有可能来自Benchmark yield的改变,也有可能来自Spread的改变。但用Modified duration计算时不会区分来源,统一用△Yield × modified duration来计算。


那现在,我们为了专门研究债券Spread的改变对债券的影响,我们就引入了Spread duration概念,按住Benchmark yield不变,只让债券的Spread变动。


例如,债券的Spread变动1%时,通过Spread duration对债券价格的影响是:1% × Spread duration;这是从Spread duration的角度分析Spread改变对债券价格的影响。


那我们还可以从债券Modified duration的角度来分析Spread改变对债券价格的影响。按住Benchmark yield不变,让Spread 1%,本质上是让债券的Yield变动了1%,那此时通过Modified duration对债券的价格影响是:1% × modified duration。


我们发现,同样是债券的Spread变动1%,我们可以用spread duration与Modified duration两种方式来测量债券价格的变动幅度,且债券的价格变动只有一个数值,所以这两个方式衡量的债券价格变动应该是一样的,即:1% × modified duration = 1% × Spread duration;


所以我们发现,这里存在Modified duration = spread duration;


对于固定利率的公司债来说,是存在:Modified duration = spread duration。


但是,对于国债来说,由于不存在Spread,因此也就不存在Spread duration,所以国债的Modified duration ≠ Spread duration。

同时,对于浮动利率债券来讲,浮动利率债券的Modified duration≈0,而Spread duration≠0,因此浮动利率债券的Modified duration ≠ Spread duration。


这样的话,如果债券的Modified duration = spread duration,其实就说明这是一个普通的固定利率公司债。不过这道题告诉这个条件,并不是想让我们判断他是啥债券,这道题同时告诉Modified duration与Spread duration,其实是让我们辨析利率、Spread变动对债券价格的影响路径。

----------------------------------------------
虽然现在很辛苦,但努力过的感觉真的很好,加油!

mia · 2021年06月12日

老师讲的真的太好了!!!

闫珅考试必过 · 2022年01月27日

可是为啥明明只有一个20bp,最后的结果要把两个影响叠加呢

发亮_品职助教 · 2021年06月17日

谢谢~~~

尽人事知天命 · 2021年10月13日

真是专业

闫珅考试必过 · 2022年01月27日

哦没事啦,我看到题眼了