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Lunanana · 2020年06月02日

问一道题:NO.PZ2018062016000059

问题如下:

Which of the following statements is most accurate?

选项:

A.

The arithmetic mean is appropriate to estimate the average returns over multiple periods.

B.

The geometric mean is appropriate for assessing past performance.

C.

The geometric mean is always greater than or equal to arithmetic mean.

解释:

B is correct. For reporting historical returns,the geometric mean is more appropriate because it is the rate of growth or return we would have had to earn each year to match the actual,cumulative investment performance.

老师您好,请问讲义上有一句话“the arithmetic mean is the statistically best estimator of the next year's returns given only the three years of return outcomes",课程上何璇老师是讲过算术平均预测将来更靠谱,但是为何讲义上特意强调“ best estimator of the next year's return" 且只能是“only the three years". 求教。感谢!

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已采纳答案

星星_品职助教 · 2020年06月02日

同学你好,

这里的“only the three years"并不是强调的重点,可以忽略。重点是算术平均用来预测未来,几何平均用来衡量过去。

算术平均预测未来是因为算术平均本质是加权平均,权重是相等的1/n,如果用未来预测的概率做权重的话,算术/加权平均此时就被叫做expected value,也就是对于将来的平均预测值。

几何平均衡量过去是因为这种方法侧重于投资的最终价值,可以更好的解读每年的compound rate of return。这句话前一页讲义举的例子很好的说明了这一点,由于year end value和初始投资相同,所以几何平均更加准确的衡量出了增长率是0%,但是算术平均却是25%。