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moon · 2021年12月21日

为什么要用real return来和spending rate相比,而不是 nominal rate?

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.

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. 



为什么要用real return来和spending rate相比,而不是 nominal rate?

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发亮_品职助教 · 2021年12月21日

嗨,努力学习的PZer你好:


为什么要用real return来和spending rate相比,而不是 nominal rate?


因为Spending rate自己就是Real rate的概念。所以我们需要拿spending rate和Portfolio的Real return来比较。


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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