CFA 2010.06 MORNING MOCK 第26题 because, number, likely, return, 收益

ryanlb

CFA 2010.06 MORNING MOCK 第26题。

26. When using stock return data, a geometric mean return calculation is most likely preferred over a geometric mean calculation because:
A. return data can be negative.
B. return data can be less than one.
C. the geometric mean return is closer in value to the arithmetic mean.

答案为A. 为什么收益的数据可以为负的话，用geometric mean calculation就好呢？  我想问下C的说法对不对呢？

以下为CFA协会的解释。
Taking the nth root of a negative number when n is an even number cannot be done (unless one uses imaginary numbers). As returns can be negative, it might not be possible to find their geometric mean. However, returns cannot be lower than -100%. By adding one to each return, as is done in the geometric mean return calculation, we create a series of numbers greater than or equal to zero. The product of such terms must therefore also be positive and the nth root can always be found.

apf_traviscui

你这样想好了，都说是算术平均比几何平均大

如果你投资的话，在收益率都是正的时候你喜欢选择算术平均，因为算术平均算出来的数字更好看

但是收益率为负的时候，就会偏向集合平均，因为几何平均的算法是可以net of，就像是做绝对值一样，这样负的一堆收益率很有可能算出来就是正的或者是0，那是不是比算术平均来的好看呢？

所以收益率为负的时候，喜欢用几何平均