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椰子鸡 · 2023年11月01日

6% compounded quarterly为什么6%可以除以4

  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

</span>12\frac12

一季度复利一次按照我的理解得用（1+r）^4=1+6%

才能得出来每一个季度的rate

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已采纳答案

星星_品职助教 · 2023年11月02日

@椰子鸡 如题目要求计算的是annualized return，即将给出的季度收益率去做复利年化，就需要这样计算。

这类题目通常会直接给出期间利率，然后要计算年化的利率是多少，此时就不能直接乘以4。

品职助教_七七 · 2023年12月26日

嗨，努力学习的PZer你好：


@于薇

不可以，6%不是实际利率，必须要转化为实际的利率（本题的季度利率）来计算。

----------------------------------------------
努力的时光都是限量版，加油！

于薇 · 2023年12月25日

计算出第四期 Fv 133.33, 再折现到零期的时候，直接133.33/(1+6%)不可以吗?为什么要133.33/(1+1.5)折现四次呢？

星星_品职助教 · 2023年11月02日

同学你好，

本题中的6%又被称为“stated annual interest rate”，即名义上的报价利率。这个利率的得来是由实际的期间利率×计息频率得到的，不是复利得到的。

故得到实际期间利率的方式为 名义利率 / 计息频率。

根据本题的“compounded quarterly”，可知实际的期间利率为季度利率，也就是6% / 4 =1.5%。

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