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小菜菜 · 2024年07月16日

请问老师，这道题会涉及geometric return v.s arithmetic return 的考点吗？

  1. CFA III
  2. Asset Allocation

NO.PZ2022122801000008

问题如下：

A few months later, Carson receives a phone call from Hamidah. She’s now on the board of trustees of Artic Foundation for Medical Research (AFMR). AFMR was established to support various medical research initiatives. She is very excited and asks Carson to help identify the return objective of AFMR’s portfolio. Osaka notes the following:

• AFMR’s overall investment objective is to maintain its portfolio’s real purchasing power after distributions.

• The risk-free rate is 4.0%.

• An expected inflation rate is 3.5%.

• The portfolio’s standard deviation is 15.0%.

• The cost of earnings investment returns is 50 bp.

• AFMR targets a 5.5% annual distribution of assets.

AFMR’s return objective is closest to: (2020 mock PM)

选项：

A.

9.50%

B.

9.74%

C.

10.27%

解释：

The calculation is (1.055) (1.035) (1.005) – 1 = 9.74%.

AFMR’s assets should be invested with the objective of earning a nominal average annual return of 9.74%. This level reflects a spending rate of 5.5%, an expected inflation rate of 3.5% and a 50 bp cost of earning investment returns.

  1. 请问老师，这道题会涉及geometric return v.s arithmetic return 的考点吗？
  2. geometric return v.s arithmetic return 的知识点是哪个章节的哪个module的呢？想不起来了，一下子没有找到~
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Lucky_品职助教 · 2024年07月16日

嗨，努力学习的PZer你好：


同学你好：


这道题涉及到了计算geometric return的知识点，但是并不是geometric return 和 arithmetic return进行对比，在AA中几乎没有会需要计算 arithmetic return的知识点。


这道题考察的是，如何计算 目标收益率，return objective

总结一下对于目标是Support in perpetuity、并且Maintain the purchasing power（real value）的Endowment/Foundation，计算Required return时，公式是：

近似的算法：Spending+Inflation+management fee=nominal return

也可以用乘法算精确的：1+spending rate）×（1+inflation）×（1+cost of earning）=（1+nominal return） 

这两种算法，大概率考试的时候是让我们用乘法算精确的，也就是算geometric return，但是如果同学考试的时候用精确的算法答案不在选项中，那就再用近似的算法再算一下。


这道题中distribution就是spending的部分。

这个计算就不要考虑rf了，因为AFMR要求每年的distribution是5.5，意思就是说他的收益率最低最低要达到这个5.5，这5.5不是风险溢价，相当于是一个total return，无风险利率4已经包含在5.5中了，因此不再次加入计算了。


关于几何收益率这中计算方法，并不是一个独立的知识点，它是在一些例题中体现的，下面的截图就是其中之一。

同学在答题中，如果题干中出现了spending rate、通胀率和cost这三个值，那就要意识到我们需要通过这些已知条件，来通过几何收益率的方法来计算earning objective了。



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