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cy g. · 2024年01月17日

为什么不用加上risk free rate 4%

  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.

计算中为什么不用加上risk free rate 4%。

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1 个答案

lynn_品职助教 · 2024年01月17日

嗨，努力学习的PZer你好：


计算中为什么不用加上risk free rate 4%。


因为已经考虑了哈


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：


近似算：Spending+Inflation+management fee=nominal return


也可以用乘法算精确的：


（1+Spending）（1+Inflation）（1+ management fee）=（1+nominal return） 


这道题中distribution就是spending的部分。至于为什么不考虑rf，那这道题说明，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。

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努力的时光都是限量版，加油！

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