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和棋 · 2022年01月30日

没有理解B选项说的是什么意思

  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.

没有理解B选项说的是什么意思

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1 个答案

pzqa015 · 2022年02月01日

嗨，爱思考的PZer你好：


B选项说，如果未来MRR保持不变，则Z-DM比DM大，这句话是错误的，正确的结论是：如果MRR保持不变，Z-DM=DM，如果MRR曲线向上倾斜（未来MRR上升），那么Z-DM是小于DM的，原理如下：

用DM的定价公式如下图

用Z-DM的定价公式如下图

一方面，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。另一方面，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。

 

那么我们可以进步简化为让上面两个公式的最后一项相等，也就是

(((MRR+QM）*FV)/m+FV)/(1+(MRR+DM)/m)^N=(((zN+QM)*FV)/m+FV)/(1+(zn+ZDM)/m)^N

如果预期future MRR上升，也就是zN＞MRR。

单看分子：(zN+QM)*FV＞(MRR+QM）*FV

看分母：(1+(zn+ZDM)/m)^N也应该大于(1+(MRR+DM)/m)^N，

但由于分母有N次幂，所以，(zn+ZDM)/m并不会比(MRR+DM)/m大太多（N次幂起到放大作用）

可以认为二者是接近相等的，那么既然二者相等，由于zn＞MRR，ZDM一定是小于DM的

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