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YAO Monica · 2022年04月28日

计算价格变动时,spread谁减谁,定增减方向

NO.PZ2019011002000004

问题如下:

Bond C is a 5-year corporate bond rated at AA. The table below shows the probabilities of a particular rating transitioning to another over the course of the following year.

Bond C will have a modified duration of 3.22 at the end of the year. According to the information above and assuming no default, how should the analyst adjust the bond’s yield to maturity (YTM) to assess the expected return on the bond over the next year?

选项:

A.

Add 0.091% to YTM

B.

Subtract 0.091% from YTM

C.

Subtract 0.120% from YTM

解释:

B is correct

解析:

考点:考察对Transition matrixes的理解和使用

表格最后一行显示了每一个评级下的Credit spread;由题干信息已知债券的Modified duration为3.22;

则从AA变动为AAA,债券价格的变动为:

-3.22×(0.60%-0.90%)=0.9660%

从AA变动为A,债券价格的变动为:

-3.22×(1.10%-0.90%)=-0.6440%

从AA变动为BBB,债券价格的变动为:

-3.22×(1.50%-0.90%)=-1.9320%

从AA变动为BB,债券价格的变动为:

-3.22×(3.40%-0.90%)=-8.050%

从AA变动为B,债券价格的变动为:

-3.22×(6.50%-0.90%)=-18.0320%

从AA变动为CCC,CC,C,债券价格的变动为:

-3.22×(9.50%-0.90%)=-27.69%

题干中的表格给出了AA级向每一个级别变动的概率,因此我们可以用概率乘以对应的债券价格变动:

0.015×0.966%+0.8800×0%+0.0950×(-0.644%)

+0.0075×(-1.9320%)+0.0015×(-8.050%)

+0.0005×(-18.0320%)+0.0003×(-27.69%)=-0.091%

则假设在没有违约的情况下,下一年的预期收益为YTM减去0.091%。

计算价格变动时,哪个spread减哪个spread有些疑惑,能否直接根据以下逻辑,定好方向后,再计算增减的程度。

评级上调:expected return on bond增,+%to YTM

评级下调:expected return on bond减, -%to YTM

1 个答案
已采纳答案

pzqa015 · 2022年04月30日

嗨,从没放弃的小努力你好:


用新的spread减去旧的spread,比如

从AA评级变为AAA,AAA的spread为0.6%,AA的spread为0.9%,所以,spread变化为0.6%-0.9%

从AAA评级变为AA,则spread的变化为0.9%-0.6%。

评级上调,△spread为负(spread变小了),modifed duration也为负(代表价格与收益率负向变动),所以,评级上调时△ytm(△P/P)为正;

评级下调,△spread为正(spread变大了),modified duration为负,所以,评级下调时,△ytm为负。


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努力的时光都是限量版,加油!

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