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awen · 2023年08月22日

解释一下复利公式怎么推导出来

  1. CFA III
  2. Capital Market Expectations

NO.PZ2022122601000073

问题如下：

Fiske prefers to forecast the average annual return for US large-cap equities over the next 10 years using the Grinold–Kroner model and the data in Exhibit 2.

Using the data in Exhibit 2 and Fiske’s preferred approach, the estimated expected annual return for US large-cap equities over the next 10 years is closest to:

选项：

A.7.9% B.7.6% C.7.4%

解释：

Correct Answer: B

The Grinold–Kroner model formula is E(R) = D/P ‒ ∆S + i + g + ∆P/E

First, compute the compound annual growth rate of the P/E: (15.0/15.6)1/10 – 1 = ‒0.4%.

Next, compute, as a percentage, the expected return per the Grinold–Kroner model formula:

E(R) = 2.1 ‒ (‒1.0) + 2.3 + 2.6 – 0.4 = 7.6

中文解析：

Grinold-Kroner模型公式为E(R) = D/P -∆S + i + g +∆P/E

首先，计算市盈率的复合年增长率:(15.0/15.6)1/10 - 1 = - 0.4%。

接下来，根据Grinold-Kroner模型公式，以百分比计算预期收益:

E(r) = 2.1 - (- 1.0) + 2.3 + 2.6 - 0.4 = 7.6

(15.0/15.6)1/10 – 1 = ‒0.4%.

这公式怎么推导呢？看不懂

（1+r)^10=(1+current rate)(1+future rate)?也不对啊，不会推

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源_品职助教 · 2023年08月22日

嗨，爱思考的PZer你好：


举个例子，如果15.0和15.6之间相隔了2年。

那么15.0/15.6就代表了从第0年到第2年的总变动率。假设两年中平均的年化变动率为R

那么（1+R）^2=15.0/15.6，所以R=(15.0/15.6)^1/2-1

同理，实际题目里是相隔了是相隔了10年，那么把上述式子里的1/2替换成1/10即可


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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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