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SKY天天 · 2025年06月17日

有两个疑问，具体见下，谢谢。6.04%计算出来的收益率是nominal的吗？/如何区分nominal和real rate

  1. CFA III
  2. 机构IPS

NO.PZ2019100901000016

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.

Prometheo University recently hired a new chief investment officer (CIO). The CIO directs her small staff of four people to implement an investment policy review. Historically, the endowment has invested 60% of the portfolio in US equities and 40% in US Treasuries. The CIO’s expectation of annual inflation for the next 10 years is 2.5%.

The CIO develops nominal 10-year return assumptions for US Treasuries and US equities, which are presented in Exhibit 1.

Discuss whether the current investment policy is appropriate given the Endowment’s annual spending policy.

选项：

解释：

GUIDELINE ANSWER:

●●The policy is not appropriate.

●●The expected real return of 3.54% is less than the spending policy rate of 6%.

●●Therefore, the current allocation and investment objectives are not sustainable.

The nominal expected return on the current portfolio, according to the nominal return assumptions in Exhibit 1, is 6.04% per year (0.6 × 7.4% + 0.4 × 4.0% = 6.04%). The expected real return is approximately 3.54% (6.04% – 2.5% = 3.54%), which is below the 6% spending rate and the stated objective of a 6% real return. Therefore, this real return is not sufficient to meeting the spending policy, which makes the Endowment’s goals unsustainable. The Endowment will need to change its asset allocation to earn higher returns and/or lower its spending policy rate.

1.我的答题如下，可以在根据我的计算思路吗？6.04%和答案中的一样，但是比较的基准我是在要求的6%spengding rate的基础上加上了通胀的2.5%，所以是8.5%和6.04%，请问这样可以吗？得出的结论是一样的，都是not appropriate approach.谢谢老师，麻烦解答一下。

Equity return=7.4%*60%=4.44%

Treasuries=4.0%*40%=1.6%

so the total return of the investment portfolio is the 4.44%+1.6%=6.04%

According to the endowment 's spending rate is 6%,andThe CIO’s expectation of annual inflation for the next 10 years is 2.5%.So the endowment at least have the min return is 6%+2.5%=8.5%,which is higher than the endowment's investment return=6.04%,so this is not the appropriate approach

2.另外，在做题的时候，怎么区分或者自己识别nominal rate和real rate?

 

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1 个答案

Lucky_品职助教 · 2025年06月17日

嗨，从没放弃的小努力你好：


你的计算中投资组合总回报 6.04% 的计算是正确的，但将 6% 的支出率与 2.5% 通胀直接相加得到 8.5% 作为比较基准的思路存在偏差。支出率 6% 是基于资产名义价值的年度支出比例，属于名义范畴，而判断其可持续性需考虑实际回报 ，名义回报 6.04% 扣除 2.5% 通胀后实际回报为 3.54%，该实际回报低于支出率所隐含的实际购买力维持需求，因此无法支撑长期支出。


区分名义利率与实际利率时，可从定义入手。名义利率未扣除通胀，直接反映货币数量的增长比例；实际利率则是扣除通胀后的真实购买力增长，通常通过 “名义利率 - 通胀率” 计算，且在涉及购买力维持、长期资产保值等场景中，需重点关注实际利率是否能满足目标。

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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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