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苏·Xu · 2023年03月02日

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。

解析看了,不是很理解,麻烦详细讲解一下,谢谢。

1 个答案

星星_品职助教 · 2023年03月03日

同学你好,

本题考察样本的离散程度越大,算术平均和几何平均的差距也越大。

分析思路为:

1)根据标准差,Portfolio B的离散程度(6%)>Portfolio A的离散程度(4%)

2)根据“离散程度越大,算术平均和几何平均的差距也越大”,由于Portfolio B的离散程度更大,所以Portfolio B所对应的算术平均和几何平均的差距,也必须要大于Portfolio A算术平均和几何平均的差距;

3)结合①Portfolio A和B的算术平均相等(均为3%)②Portfolio A的几何平均为2.85%。可知此时Portfolio B的几何平均一定要小于2.85%。这样才能使得Portfolio B算术平均和几何平均的差距要更大。

-----

此后提问需要具体写明解析里不理解的地方是什么。


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