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必过1030_ · 2022年05月24日

选项b的正确说法是什么？

  1. CFA III
  2. Fixed Income

NO.PZ2021120102000015

问题如下：

Which of the followingstatements about credit spread measures is most accurate?

选项：

A.

The DM is the yield spread over the MRR established upon issuanceto 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：

Cis correct.

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

选项b的正确说法是什么？

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1 个答案

pzqa015 · 2022年05月26日

嗨，努力学习的PZer你好：


如果MRR remain constant，那么Z-DM=DM

如果MRR曲线向上倾斜（隐含着未来的MRR大于现在的MRR），则Z-DM小于DM。原因如下

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次幂放大后，(1+(zn+ZDM)/m)^N才比(1+(MRR+DM)/m)^N大），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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