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ditto · 2024年10月05日

为什么要相加第一步和第二步计算的

  1. CFA I
  2. Fixed Income

NO.PZ2023052301000041

问题如下：

An investor purchases an eight-year, 6.4% annual coupon eurobond priced at par and sells it after six years. Assuming interest rates rise by 100 bps immediately after purchase, the investor’s rate of return at the end of six years is:

选项：

A.

lower than 6.4%.

B.

equal to 6.4%.

C.

higher than 6.4%.

解释：

A is correct. The future value of reinvested coupon interest is

= FV(0.074,6,6.4,0,0) = 46.245.

The sale price of the bond at the end of six years is

= PV(0.074,2,6.40,100,0) = 98.202,

which results in a six-year horizon yield of 6.32%, which is lower than 6.40%:


B and C are incorrect, because interest rates have risen and the investor’s investment horizon is not long enough to offset the price decline with additional reinvestment return.

https://class.pzacademy.com/qa/155511

以上链接的计算步骤很清楚了，属于审题没有搞懂。

第一步计算的金额coupon都已经付掉了， 算价值不应该包含进去了吧， 为什么计算时候还有


这道题的解题思路是什么，背步骤很困惑

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笛子_品职助教 · 2024年10月06日

嗨，从没放弃的小努力你好：


第一步计算的金额coupon都已经付掉了， 算价值不应该包含进去了吧， 为什么计算时候还有

这道题的解题思路是什么，背步骤很困惑

Hello，亲爱的同学~

收益率的计算需要两个数值。

1）投资者的初始投资数值，这个数值在本题就是债券面值100。

2）投资者最终获得的现金金额，包括3个部分：

a）债券的本金。（如果未到期，就是提前卖出债券的金额）

b）债券的累计发放的coupon。

C）投资者拿到债券的coupon后，把这部分coupon再拿去投资的收益。

这部分被称为RI（reinivestment return ）

同学注意：无论coupon是否付掉，这个coupon都算投资者的收益。


结合本题：在第6年的时候，这三部分加起来是多少呢。

RI + coupon 的这部分金额 =  FV(0.074,6,6.4,0,0) = 46.245

债券的本金（这里未到期，是卖出债券的金额） =  98.202

这三部分加起来，就是在第6年，可以收回的金额，是46.245 + 98.202

这个46.245 + 98.202是投资者，投资6年，最终可以拿回来的钱。


而我们初始投资金额是100。


因此收益率 ：


同学的纠结点是coupon付掉了，债券本金里不含coupon。

而这里计算的是，投资者最后拿到了多少钱，债券本金只是三个部分（本金、coupon、coupon的RI）中的1个部分。


对以上答疑服务，只要同学有任何不理解的地方，都是可以随时继续追问的。

祝学习顺利，逢考必过~


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虽然现在很辛苦，但努力过的感觉真的很好，加油！

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