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CC · 2023年08月14日

CS计算

NO.PZ2019011002000008

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:

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

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：

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

经过计算YTM为：2.92%

则Credit spread为：4.75% - 2.92% = 1.83%

老师，这里在求CS时，1）为什么PV是负号啊？ PV和FV有一个是负号不可以么？

2）为什么最后FV=1000 ？？

3）这类题目，站在一个什么角度上，是投资者还是为发行人？

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1 个答案

pzqa31 · 2023年08月15日

嗨，努力学习的PZer你好：

有一个是负号就可以了，并不影响计算结果，负号只代表现金流流出而已。这道题是站在投资者角度，认为期初是花钱买了债券，所以是PV用了负号。从fair value的数量级可以看出，par=1000.

----------------------------------------------
就算太阳没有迎着我们而来，我们正在朝着它而去，加油！

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2024-04-30 21:14 1 · 回答

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2022-05-17 21:39 1 · 回答