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王思祺 · 2020年08月14日

问一道题：NO.PZ2015120601000001

  1. CFA I
  2. Fixed Income

问题如下：

An analyst expects that a company’s net sales will double and the company’s net income will triple over the next five-year period starting now. Based on the analyst’s expectations, which of the following best describes the expected compound annual growth?

选项：

A.

Net sales will grow 15% annually and net income will grow 25% annually.

B.

Net sales will grow 20% annually and net income will grow 40% annually.

C.

Net sales will grow 25% annually and net income will grow 50% annually.

解释：

A is correct.

Using the general time value of money formula, for sales, solve for r in the equation 2 = 1 × (1+r)5. For income, solve 3 = 1 × (1+r)5. Alternatively, using a financial calculator, for sales, enter N = 5, PV = 1, PMT = 0, FV = −2 and compute I/Y. For income, change the FV to −3 and again solve for I/Y. The solution for sales is 14.87%; and for income is 24.57%.

老师老师，想请教一下，为什么用上面拿道题算是用的是两个YTM的平均数，而下面要用spread？比如下面的用（1.3%+2.7%）/2不可以吗

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3 个答案

吴昊_品职助教 · 2020年08月17日

同学你好：

第一题，题目直接给出的是四只债券的定价，没有区分国债和公司债。那我们认为他们是一类债券，只是年限和coupon rate不同。分别求得两年期和五年期的平均收益率后，然后利用线性插值法算出三年期债券的收益率。有了三年期债券的收益率，再反求出三年期，coupon rate为4%，半年付息债券的价值。

第二题，给出的四只债券，区分了国债和公司债，我们不能直接把两类不同的债券的收益率放在一起，直接求平均收益率。而是要分别算出三年期spread和六年期spread，利用线性插值法算出四年期的spread，再加上四年期国债收益率，从而得到四年期公司债收益率。

两道题思路不一样，虽然都是线性插值，但是第一题线性插值求的是三年期收益率，第二题线性插值求的是四年期的spread。

星星_品职助教 · 2020年08月17日

@王思祺

好的，我转给固收的助教

星星_品职助教 · 2020年08月14日

同学你好，

这道题你在一道数量的题库题下面截了三个固收的图，是不是想问的应该是下面的固收问题？

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