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七七 · 2024年07月22日

continuously compounded long-term equity returns计算

  1. CFA III
  2. Capital Market Expectations

NO.PZ2020012201000007

问题如下：

Alena,CFA, was updating her firm’s projections for US equity returns.If she believed that in the long run that the US labor input would grow by 0.9% perannum and labor productivity by 1.5%, that inflation would be 2.1%, that the dividend yield would be 2.25%, and that there would be no further growth in P/E, what is likely to have been her baseline projection for continuously compounded long-term US equity returns?

选项：

A.

6.75%

B.

5.5%

C.

5.85%

解释：

A is correct

解释：

在长期，一国股票市场的CAPITAL APPRECIATION的增长率等于该国GDP的增长率(本题P/E增长率为0也证实了这一点)。那么本题CAPITAL APPRECIATION就等于计算该国GDP的增长率。此后再加上股息增长率就可以得到股权市场的增长率。

Her baseline projection is likely to have been 6.75% = 0.9% + 1.5% + 2.1% + 2.25%

依照公式可得：. 6.75% = 0.9% + 1.5% + 2.1% + 2.25%

请问这里continuously compounded long-term US equity returns中的continuously compounded体现在哪里？和直接问long-term US equity returns的求解思路有没有差别？

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源_品职助教 · 2024年07月24日

嗨，努力学习的PZer你好：



比如题目说年初投资资产价格是1，问年末资产价值是多少

那就是要用1*e^6.75去计算年末的资产价值

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源_品职助教 · 2024年07月22日

嗨，从没放弃的小努力你好：



在本题中，并没有体现出来。这里的continuously compounded，其实是指代如果按6.75%的增长率进行计算的时候，要用e^6.75%去计算而已（题目本身并不体现这一点）。

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