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yan · 2025年02月02日

这道题为什么A和B不对

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.

这道题为什么A和B不对

1 个答案

发亮_品职助教 · 2025年02月02日

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.


这句话错在upon issuance。

选项A的意思是:DM是基于MRR的一个spread,且是在债券发行时刻就确定的spread,是用来补偿投资者承担credit risk。整句话都正确,唯一错在“在债券发行时刻”


这句描述的其实是quoted margin。Quoted margin是在债券发行时刻,根据发行人credit risk确定的一个补偿,且quoted margin一旦确定之后,在债券的一生里面都不会改变,quoted margin决定债券的Coupon rate。

coupon rate = MRR + Quoted margin


而DM并不是在债券发行时刻就确定的spread,DM是会根据债券的信用风险随时调整。可以反应债券的实时信用风险。DM是决定了债券的折现率,其折现率为:MRR + discount margin。


选项B:

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


DM和Z-DM都是浮动利率债券的折现率。区别是,DM是基于当前时刻的1个MRR,而Z-DM是基于一条MRR curve,会涉及到多个未来预期的MRR。


假设债券是有4笔cash flow。我们现在找折现率。


对于DM来讲,这4笔cash flow的折现率一致,都是:

(MRR + DM)

其中MRR是当前市场的MRR


而对于Z-DM来讲,这4笔cash flow的折现率各不相同,要使用对应期限的MRR。


第一期cash flow的折现率是:

MRR1 + Z-DM(这个MRR1其实就是当前市场的MRR,和DM里面的MRR一样大)


第二期cash flow的折现率是:

MRR2 + Z-DM,这个MRR2是预测的未来第2期的MRR,如果是一条向上倾斜的MRR curve,那这个MRR2一定大于当前市场的MRR1(MRR2>MRR1)


第三期的cash flow折现率是:

MRR3 + Z-DM,如果是一条向上倾斜的MRR curve,MRR3 > MRR2 > MRR 1


第四期的cash flow折现率是:

MRR4 + Z-DM,如果是一条向上倾斜的MRR curve


MRR4 > MRR3 > MRR2 > MRR 1


债券的价格是唯一的,我们是利用债券价格,利用折现公式,反求DM和Z-DM。

所以,无论是(MRR+DM),还是(各期MRR+Z-DM)

这个分母的折现率应该一样大。因为同一个债券价格一样,分子现金流一样,则分母的折现率必定一样。


但问题是,如果是一个upward-sloping的MRR曲线,在Z-DM里面,只有第一期的MRR等于DM里面的MRR,Z-DM里往后各期的MRR都更大。


为了保证Z-DM里分母的折现率(各期MRR+Z-DM)还与(MRR+DM)相等,则Z-DM必须要更小,Z-DM小于DM。


这样的话,Z-DM里各期MRR更大,大于DM里的MRR,但加上更小的Z-DM,这两个均匀一下,相加才有可能等于(MRR+DM)


选项B就是对上述理念的进一步理解。

选项B说,if the MRR is expected to remain constant over time,即,假设未来各期的MRR都维持不变,也就是等于当前的MRR。这样的话,这是一条flat水平的MRR curve。


那么在计算Z-DM时,分母折现率里面的MRR都是同一个,都等于当前时刻的MRR。这其实和DM一样,因为DM里面各期的MRR也是同一个,等于当前时刻的MRR。


这样的话,算出来的Z-DM与DM一样大。结论应该是Z-DM will equal to DM.

而选项B说Z-DM will be above DM就是错误的。

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