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张欣佳 · 2024年05月23日

unsmooth data 的 variance 不是应该高于smooth data的variance吗？

  1. CFA III
  2. Capital Market Expectations

NO.PZ2022122601000036

问题如下：

Lastly, Perumal focuses on forecasting the expected returns of investing in direct real estate. He analyzes the previous ten years of multifamily residential real estate returns data. He is skeptical that the volatility of the observed returns reflects smoothing. Perumal uses a publicly traded REIT index to unsmooth the return stream and appropriately reflect the risk (as measured by standard deviation) of investing in multifamily residential real estate (the variance of the REIT index for the measurement period is 16; λ equals 0.8).

Perumal’s unsmoothed standard deviation for multifamily properties for the investment period is closest to:

选项：

A.12 B.18 C.24

解释：

Correct Answer: A

Var(r)={(1+λ)/(1-λ)}*var(R)

Var(r)={(1+0.80/(1-0.8)}*16=144

Standard deviation=12

中文解析：

Var (r) ={(1 +λ)/(1 -λ)}* Var(右)

Var (r) = {(1 + 0.80 / (1 - 0.8)} * 16 = 144

标准差= 12

这样smooth 后的风险才被低估了？这么思考有什么问题？

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1 个答案

笛子_品职助教 · 2024年05月24日

嗨，从没放弃的小努力你好：


Hello，亲爱的同学~

同学的思考是没有问题的。

本题unsmooht 方差是144，而可观察到的smooth的方差是16。

144大于16，符合同学说的这个规律。

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努力的时光都是限量版，加油！

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