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SuzieW · 2022年04月01日

老师，这道题怎么理解呢

  1. CFA I
  2. Quantitative

NO.PZ2021061603000027

问题如下：

The average return for Portfolio A over the past twelve months is 3%, with a standard deviation of 4%. The average return for Portfolio B over this same period is also 3%, but with a standard deviation of 6%. The geometric mean return of Portfolio A is 2.85%. The geometric mean return of Portfolio B is:

选项：

A.less than 2.85%. B.equal to 2.85% C.greater than 2.85%.

解释：

A is correct. The more disperse a distribution, the greater the difference between the arithmetic mean and the geometric mean。

所以标准差越大，算术平均和几何平均的差距越大。

A组合的标准差是4%，B的标准差是6%。B的标准差比A大，算数平均的几何平均的差距也要比组合A更大，所以几何平均应该是要小于2.85%，这样差距才会更大。

标准偏差越大，算数平均和几何平均的差距就越大，可是这道题并没有提到算数平均啊，只有portfolio a和b的几何平均，怎么比较呢。

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1 个答案

星星_品职助教 · 2022年04月02日

同学你好，

题干中的“average return”指的就是算术平均数。由于A和B算术平均相同（均为3%）。此时B的标准差又更大（6%＞4%），所以可知B的几何平均就会更小。选择A选项。


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