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Leo 昊子 · 2022年01月22日

名义季度利率和实际季度利率

  1. CFA I
  2. Quantitative

NO.PZ2017092702000009

问题如下：

A perpetual preferred stock makes its first quarterly dividend payment of $2.00 in five quarters. If the required annual rate of return is 6% compounded quarterly, the stock’s present value is closest to:

选项：

A.

$31.

B.

$126.

C.

$133.

解释：

B is correct.

The value of the perpetuity one year from now is calculated as: PV = A/r, where PV is present value, A is annuity, and r is expressed as a quarterly required rate of return because the payments are quarterly. PV = $2.00/(0.06/4) PV = $133.33. The value today is (where FV is future value) PV = FV(1 + r)–N

PV = $133.33(1 + 0.015)–4

PV = $125.62 ≈ $126

这道题在计算第一个PV时，用6%/4，但这里的6%题目里说的是stated annual rate，得到的应该是“名义季度利率” 而题目说了是按quarterly计算复利，所以我先求出EAR，再除以4，得到了“实际季度利率”，比1.5%稍微大一丢丢。 然后计算年金PV，用A除以r，这里的r我理解应该用的是是实际季度利率而不是名义季度利率，请问哪里错了？
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1 个答案

星星_品职助教 · 2022年01月23日

同学你好，

没有名义季度利率的概念。

6%/4=1.5%就是季度利率，或者理解为你说的“实际季度利率”。对于这道题而言，直接这样去计算就可以了。不用继续转化。

换个角度来说，6%的名义报价利率是根据季度利率1.5%×4得到的。这种简便形式没有考虑1.5%在每个季度的复利效果，所以不能拿来直接计算。

拿来直接计算的方法就是直接用季度利率。在有的题目中，还要将这个季度利率转化为EAR。

没有EAR再除以4的这种算法，要理解“名义”和“有效/真实”利率的区别在于复利。一个复利的利率再按照单利直接除以4就什么都不是了。


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