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moon · 2022年05月07日

B为什么错了,ZDM和DM的大小关系?

NO.PZ2021120102000015

问题如下:

Which of the following statements about credit spread measures is most accurate?

选项:

A.

The DM is the yield spread over the MRR established upon issuance to compensate investors for assuming an issuer’s credit risk.

B.

The Z-DM will be above the DM if the MRR is expected to remain constant over time.

C.

The yield spread for a corporate bond will be equal to the G-spread if the government benchmark yield curve is flat.

解释:

C is correct.

The yield spread is the simple difference between a bond’s all-in YTM and a current on-the-run government bond of similar maturity, while the G-spread is an interpolation of government benchmark yields. If the government bond yield curve is flat, these two measures will equal one another.

B为什么错了,ZDM和DM的大小关系?

2 个答案

lynn_品职助教 · 2022年05月26日

嗨,爱思考的PZer你好:


嗯嗯,同学,我上面的回答是回答了上一个同学的两个问题。


题目给出的条件是 “if the MRR is expected to remain constant over time.”

对的。

B选项的意思是如果预期MRR保持不变,则Z-DM大于DM。这句话是错误的,正确的结论是:如果MRR保持不变,Z-DM=DM。

第二个问题问ZDM和DM的大小关系?经过分析,如果MRR曲线向上倾斜(假设未来MRR上升),那么Z-DM是小于DM的。


为什么Zn 要大于MRR呢?为什么预期MRR上升?哪来的已知条件?

不是已知条件是假设哈。

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lynn_品职助教 · 2022年05月09日

嗨,努力学习的PZer你好:


1.      B选项的意思是如果预期MRR保持不变,则Z-DM大于DM。

a)      DM的定价公式(公式1)如下图:

b) Z-DM的定价公式(公式2)如下图:

首先公式1等于公式2。因为不论是用Z-DM折现求和,还是DM折现求和,得到的债券现在的价格是相等的,也就是说两张图片中的PV是一样的。其次,在任何一个求价格的公式中,对PV影响最大的一期现金流是最后一期,也就是要考虑FV的一期现金流。

那么我们可以进一步简化为让上面两个公式的最后一项相等。

=

如果预期future MRR上升,也就是Zn>MRR。

 

单独看分子:(Zn+QM)*FV>(MRR+QM)*FV

 

看分母:(1+(Zn+Z-DM)/m)^N也应该大于(1+(MRR+DM)/m)^N,并且幅度与分子保持一致(等式才能成立)

 

但由于分母有N次幂,所以,(Zn+Z-DM)/m并不会比(MRR+DM)/m大太多(N次幂会有放大作用)。

 

可以认为二者是接近相等的,那么既然(Zn+Z-DM)/m=(MRR+DM)/m。

 

由于Zn>MRR,Z-DM


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徐威廉 · 2022年05月25日

题目给出的条件是 “if the MRR is expected to remain constant over time.” 为什么Zn 要大于MRR呢?为什么预期MRR上升?哪来的已知条件?

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