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Garygary · 2024年11月16日

absolute deviation

  1. CFA I
  2. Quantitative

NO.PZ2021061603000025

问题如下：

Annual returns and summary statistics for three funds are listed in the following exhibit:

The fund with the highest absolute dispersion is:

选项：

A.Fund PQR if the measure of dispersion is the range B.Fund XYZ if the measure of dispersion is the variance C.Fund ABC if the measure of dispersion is the mean absolute deviation

解释：

C is correct. The mean absolute deviation (MAD) of Fund ABC's returns is greater than the MAD of both of the other funds.

MAD=∑i=1n∣Xi−Xˉ∣nMAD = \frac{{\sum\limits_{i = 1}^n {\left| {{X_i} - \bar X} \right|} }}{n}, where Xˉ{\bar X} is the arithmetic mean of the series.

MAD for Fund ABC =

∣−20−(−4)∣+∣23−(−4)∣+∣−14−(−4)∣+∣5−(−4)∣+∣−14−(−4)∣5=14.4%\frac{{\left| { - 20 - ( - 4)} \right| + \left| {23 - ( - 4)} \right| + \left| { - 14 - ( - 4)} \right| + \left| {5 - ( - 4)} \right| + \left| { - 14 - ( - 4)} \right|}}{5} = 14.4\%

MAD for Fund XYZ=

∣−33−(−10.8)∣+∣−12−(−10.8)∣+∣−12−(−10.8)∣+∣−8−(−10.8)∣+∣11−(−10.8)∣5=9.8%\frac{{\left| { - 33 - ( - 10.8)} \right| + \left| { - 12 - ( - 10.8)} \right| + \left| { - 12 - ( - 10.8)} \right| + \left| { - 8 - ( - 10.8)} \right| + \left| {11 - ( - 10.8)} \right|}}{5} = 9.8\%

MAD for Fund PQR=

∣−14−(−5)∣+∣−18−(−5)∣+∣6−(−5)∣+∣−2−(−5)∣+∣3−(−5)∣5=8.8%\frac{{\left| { - 14 - ( - 5)} \right| + \left| { - 18 - ( - 5)} \right| + \left| {6 - ( - 5)} \right| + \left| { - 2 - ( - 5)} \right| + \left| {3 - ( - 5)} \right|}}{5} =8.8\%

A and B are incorrect because the range and variance of the three funds are as follows:


The numbers shown for variance are understood to be in "percent squared" terms so that when taking the square root, the result is standard deviation in percentage terms. Alternatively, by expressing standard deviation and variance in decimal form, one can avoid the issue of units. In decimal form, the variances for Fund ABC, Fund XYZ, and Fund PQR are 0.0317, 0.0243, and 0.0110, respectively.

我可以这样理解?

只有mean absolute deviation 才能计算absolute deviation

range 及variance 都不能计算absolute deviation/ 与absolute deviation无关

所以A & B 错, C 对

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1 个答案

品职助教_七七 · 2024年11月18日

嗨，从没放弃的小努力你好：


这道题要衡量的是absolute dispersion，也就是最大的离散程度。

range、variance和MAD都是衡量离散程度的指标，都需要考虑。

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加油吧，让我们一起遇见更好的自己！

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2024-08-06 10:23 1 · 回答

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2023-05-22 22:38 1 · 回答

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