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Jinn · 2025年03月20日

老师求助

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NO.PZ201812310200000109

问题如下:

 Ibarra wants to know the credit spread of bond B2 over a theoretical comparable-maturity government bond with the same coupon rate as this bond. The foregoing credit spread is closest to:

选项:

A.

108 bps.

B.

101 bps.

C.

225 bps.

解释:

A is correct. The corporate bond’s fair value is computed in the solution to Question 8 as €1,101.24 The YTM can be obtained by solving the following equation for IRR:

1101.24= 60 1+IRR + 60 (1+IRR) 2 + 60 (1+IRR) 3 + 1060 (1+IRR) 4

The solution to this equation is 3.26%.

Valuation of a four-year, 6% coupon bond under no default (VND) is computed in the solution to Question 8 as 1,144.63. So, the YTM of a theoretical comparable-maturity government bond with the same coupon rate as the corporate bond B2 can be obtained by solving the following equation for IRR:

1144.63= 60 1+IRR + 60 (1+IRR) 2 + 60 (1+IRR) 3 + 1060 (1+IRR) 4

The solution to this equation is 2.18%. So, the credit spread that the analyst wants to compute is 3.26% – 2.18% = 1.08%, or 108 bps.

B is incorrect, because that is the spread over the four-year government par bond that has a YTM of 2.25% in Exhibit 2: 3.26% – 2.25% = 1.01%, or 101 bps. Although this spread is commonly used in practice, the analyst is interested in finding the spread over a theoretical 6% coupon government bond.

C is incorrect, because that is the YTM of the coupon four-year government bond in Exhibit 2.

之前有做过一道题也是就credit spread.

但是那道题的固定债券是这么求解的:

1、用算出来的FV作为等式左边,即 96.264=5/(1+YTM)^1+5/(1+YTM)^2+105/(1+YTM)^3

2、反求出YTM=6.4082%

3、用反求的YTM-coupon5=1.4082%


但是本道题我看解析的逻辑是:

1、用上面的1、2步算出YTM

2、还要再用VND再算一个YTM,

3、相减后才是credit spread.


我的具体问题是:

Q1: 为什么本体还要用VND再算一个YTM,以及计算公式是什么;

Q2: 什么情况下用我说的题目解法,什么情况下用本题的解决思路。感谢!

1 个答案

吴昊_品职助教 · 2025年03月21日

嗨,爱思考的PZer你好:


1、上面那道题:

三年期benchmark bond的YTM是5%是已知的。表格2给出的是par rate,par rate是债券价格等于面值时的YTM,此时YTM=coupon rate,由表格可知三年期的国债coupon rate=3%,因此,三年期国债YTM=5%。是因为题目表格直接给了国债的YTM,就不需要我们再额外计算了,所以可以直接相减。

2、而本题,同期限的国债YTM是需要利用折现反求的。

 (VND) is computed in the solution to Question 8 as 1,144.63,通过上一小问,我们可以得知VND=1144.63,即PV= -1144.63,FV=1000,N=4,PMT=60,反求出I/Y=2.18,拿着公司债的YTM减去同期限国债的YTM,就是Credit spread。


如果题目直接给出了同期限国债YTM,就只要算出公司债的YTM即可;如果题目没有给出同期限国债YTM,那么就需要算两个YTM,一个是公司债的,一个是国债的,两个YTM相减得到Credit spread。

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