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Frances · 2024年06月29日

为什么不能大于

  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。

解析看得懂，B 的A和G差距更大，但为什么非得是小于呢，远远大于不行吗？standard deviation大只说明波动大，A和G差距大呀。

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1 个答案

品职助教_七七 · 2024年06月30日

嗨，爱思考的PZer你好：


A一定大于G，所以G只能比A低，也就是小于。不可能偏向大于的方向。

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