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Falcon · 2020年03月18日

问一道题：NO.PZ2019011002000008

  1. CFA II
  2. Fixed Income

问题如下：

Bond B is a 5-year corporate bond with a fixed coupon rate of 7%. The coupon is paid annually. The bond is rated at AA.

Assume the fair value of the bond is 1098.14. The bond’s value assuming no default (VND) is 1187.22.

Li, a credit analyst in a wealth management firm, wants to know the credit spread of Bond B over a theoretical comparable-maturity government bond with the same coupon rate as this bond.

According to the information above, the credit spread is closest to:

选项：

A.

1.78%

B.

1.83%

C.

2.55%

解释：

B is correct.

考点：计算Credit spread

解析：

已知该公司债的Fair value是1098.14，并且该债券是5年期，Coupon rate为7%，根据债券定价，可以反求出其YTM:

l70(1+YTM)+70(1+YTM)2+70(1+YTM)3+70(1+YTM)4+1070(1+YTM)5=1098.14{l}\frac{70}{(1+YTM)}+\frac{70}{(1+YTM)^2}+\frac{70}{(1+YTM)^3}+\frac{70}{(1+YTM)^4}+\frac{1070}{(1+YTM)^5}\\=1098.14

反求出来的YTM为4.75%。

而有题干信息The bond’s value assuming no default (VND) is 1187.22，可知利用无风险利率对该债券折现出来的价值为1187.22，该价值就等于假设的期限相同Coupon rate相同国债的价格，通过该价格反求出来的YTM就是对应假设国债的YTM：

l70(1+YTM)+70(1+YTM)2+70(1+YTM)3+70(1+YTM)4+1070(1+YTM)5=1187.22{l}\frac{70}{(1+YTM)}+\frac{70}{(1+YTM)^2}+\frac{70}{(1+YTM)^3}+\frac{70}{(1+YTM)^4}+\frac{1070}{(1+YTM)^5}\\=1187.22

经过计算YTM为：2.92%

则Credit spread为：4.75% - 2.92% = 1.83%

这道题对应的知识点何老师课上讲的例题，credit spread=YTM公司债2.4%-YTM国债1.5%，YTM国债例题是用3年期国债的coupon rate=1.50%, 并不是用VND=104.4152算出来的（我按计算器算的是1.4844%），为什么这道题用VND算国债的YTM，例题却不用VND算出一个？？

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1 个答案

WallE_品职答疑助手 · 2020年03月18日

同学你好，

例题中 题目有给出” The supervisor asks Mr. Kapili if the credit spread over the yield on the 3-year benchmark bond, which is 1.50%,“，这一题并没有给出。

 

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NO.PZ2019011002000008 问题如下 BonB is a 5-yecorporate bonwith a fixecoupon rate of 7%. The coupon is paiannually. The bonis rateAA.Assume the fair value of the bonis 1098.14. The bons value assuming no fault (VN is 1187.22.Li, a cret analyst in a wealth management firm, wants to know the cret spreof BonB over a theoreticcomparable-maturity government bonwith the same coupon rate this bonAccorng to the information above, the cret spreis closest to: A.1.78% B.1.83% C.2.55% B is correct.考点计算Cret sprea析已知该公司债的Fair value是1098.14，并且该债券是5年期，Coupon rate为7%，根据债券定价，可以反求出其YTM:l70(1+YTM)+70(1+YTM)2+70(1+YTM)3+70(1+YTM)4+1070(1+YTM)5=1098.14{l}\frac{70}{(1+YTM)}+\frac{70}{(1+YTM)^2}+\frac{70}{(1+YTM)^3}+\frac{70}{(1+YTM)^4}+\frac{1070}{(1+YTM)^5}\\=1098.14l(1+YTM)70​+(1+YTM)270​+(1+YTM)370​+(1+YTM)470​+(1+YTM)51070​=1098.14反求出来的YTM为4.75%。而有题干信息The bons value assuming no fault (VN is 1187.22，可知利用无风险利率对该债券折现出来的价值为1187.22，该价值就等于假设的期限相同Coupon rate相同国债的价格，通过该价格反求出来的YTM就是对应假设国债的YTMl70(1+YTM)+70(1+YTM)2+70(1+YTM)3+70(1+YTM)4+1070(1+YTM)5=1187.22{l}\frac{70}{(1+YTM)}+\frac{70}{(1+YTM)^2}+\frac{70}{(1+YTM)^3}+\frac{70}{(1+YTM)^4}+\frac{1070}{(1+YTM)^5}\\=1187.22l(1+YTM)70​+(1+YTM)270​+(1+YTM)370​+(1+YTM)470​+(1+YTM)51070​=1187.22经过计算YTM为2.92%则Cret sprea4.75% - 2.92% = 1.83% N=5，PV=-1098.14，PMT=70，FV=1000 得到I/Y=4.6666N=5，PV=-1187.22，PMT=70，FV=1000 得到I/Y=2.8897算出来是4.6666-2.8897=1.78% 不是1.83%

2024-04-30 21:14 1 · 回答

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2023-08-14 18:58 1 · 回答

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2022-07-14 10:40 1 · 回答

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2022-05-17 21:39 1 · 回答