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Felix Young · 2023年12月27日

老师好，想问个细节

  1. CFA III
  2. 机构IPS

NO.PZ2019100901000015

问题如下：

The Prometheo University Scholarship Endowment (the Endowment) was established in 1950 and supports scholarships for students attending Prometheo University. The Endowment’s assets under management are relatively small, and it has an annual spending policy of 6% of the five-year rolling asset value.

Formulate the investment objectives section of the investment policy statement for the Endowment

选项：

解释：

The mission of the Prometheo University Scholarship Endowment is to provide scholarships for students attending the university. In order to achieve this mission, the Endowment must maintain the purchasing power of the assets in perpetuity while achieving investment returns sufficient to sustain the level of spending necessary to support the scholarship budget. Therefore, the investment objective of the endowment should be to achieve a total real rate of return (after inflation) of at least 6% with a reasonable level of risk.

这里的 spending policy of 6% ，是指nominal 还是指 real return。根据答案里的回答，我理解应该是指real return？ 以后碰到相应的题目，除非有特别说明，否则一律理解为real return嘛？


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lynn_品职助教 · 2023年12月28日

嗨，爱思考的PZer你好：


这里的 spending policy of 6% ，是指nominal 还是指 real return。根据答案里的回答，我理解应该是指real return？ 以后碰到相应的题目，除非有特别说明，否则一律理解为real return嘛？


同学理解对了，就是real return。


现在的考纲删除了，实际在上一版的考纲中，我们会计算endowment的Required return（Nominal rate）。计算nominal rate就是以spending rate为起点的。

Nomial return = spending rate + inflation + expense

从公式可以看出，在spending rate的基础上，额外又加了inflation，所以spending rate自身就是real return。

这个内容了解即可，不属于现在的考纲，但是需要知道spending rate自己就是real return。


下面大概解释一下为什么spending rate是一个real rate。


Spending是这么描述的：spending policy of 6% of the five-year rolling asset value.


也就是说，这个基金每年花费asset value的6%。注意，asset value本身就是一个名义数值了，asset value里面已经含有Inflation了，

所以：

real rate 6% × 名义值asset value，相乘算出来的结果就已经是一个名义值了。


试想一下，如果6%是名义值，6%里面含有Inflation的话，那么：

名义值6% × 名义值asset value，这里面可以进一步拆分

名义值6%可以拆成（inflation + 实际spending rate），名义值asset value可以拆成（实际asset value）×（1+inflation），

于是：

名义值6% × 名义值asset value = （inflation + 实际spending rate） × （实际asset value）×（1+inflation）


这里面inflation会考虑2次，会出现inflation的平方项。显然这是不合理的。


所以，6%的Spending rate只能是一个real rate，只表示比例，不含有inflation。

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