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为了求职冲呀 · 2022年03月03日

请问为什么会和SD有关系？

  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。

老师您好，看了您给其他学院的解答，本题目考点：

A>G>H


但是不理解为什么这道例题和SD会相关，何老师在本章中也没有讲过SD。不理解sd和其他算数平均几何评论的关联点，请问应该去看那个方面或者章节的知识点呢？

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1 个答案

星星_品职助教 · 2022年03月03日

同学你好，

本章在两个地方提到了这点。

第一张截图中的 more disperse可以理解为standard deviation越大；

第二张截图中，公式里的 s 就是sample standard deviation。

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