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简敏敏 · 2021年02月20日

问一道题：NO.PZ2018062016000051 [ CFA I ]

  1. CFA I
  2. Quantitative

问题如下：

Having collected mean returns for the three stocks, the analyst is now concerned about evaluating dispersion.Which of the following statements is least accurate?

选项：

A.

Based on the variance,Stock A has the highest dispersion.

B.

Based on the range,Stock C has the lowest dispersion.

C.

Based on the mean absolute deviation(MAD),Stock B has the highest dispersion.

解释：

C is correct.

MAD(A)=(|-39-2.4|+|31-2.4|+|12-2.4|+|-4-2.4|+|12-2.4|)/5=19.12

MAD(B)=(|-35-4.4|+|25-4.4|+|15-4.4|+|0-4.4|+|17-4.4|)/5=17.52

MAD(C)=(|6-2|+|-8-2|+|11-2|+|-2-2|+|3-2|)/5=5.6

Based on the MAD,Stock A has the highest dispersion.

老师你好，A、B答案为什么是正确的？
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1 个答案

星星_品职助教 · 2021年02月20日

同学你好，

A选项中，衡量离散程度的指标是variance。variance是standard deviation的平方。所以观察题干表格的最后一行，Stock A 的standard deviation最大，所以对应的variance也最大。A选项描述正确。

B选项中，衡量离散程度的指标是Range，Range=最大值-最小值。Range A=31-（-39）=70；Range B=25-（-35）=60；Range C=11-（-8）=19。可以看处Stock C的range最小，B选项描述正确。

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