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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？

  1. CFA III
  2. Fixed Income

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？

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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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