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I Yuan · 2022年03月03日

为什么我无论怎样都算不了0.79%这个答案?

NO.PZ2019012201000083

问题如下:

let’s consider the performance of the Russell 1000 between February 1990 and December 2016. The monthly arithmetic return was 0.878%, and the volatility, as measured by the standard deviation of return, was 4.199%. What is the geometric return?

选项:

A.

0.79%

B.

0.62%

C.

0.54%

解释:

We know that the expected compounded/geometric return of an asset (Rg) is approximately related to its expected arithmetic/periodic return (Ra) and its expected volatility (σ):

Rg=Raσ22R_g=R_a-\frac{\sigma^2}2

Rg=0.878%4.199%22=0.79%R_g=0.878\%-\frac{4.199\%^2}2=0.79\%

0.878%-(0.04199^2/2)=0.8771又或者0.878%-(4.199^2/2)=-7.938,后者是负数明显是错误的。麻烦解释一下。

1 个答案

笛子_品职助教 · 2022年03月04日

嗨,爱思考的PZer你好:


带百分号是算不出来的,因为百分号没法平方。在计算的时候,要把所有的百分号都去掉算,才不会错。


0.00878 - 0.5*(0.04199^2)=0.007898 = 0.79%


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虽然现在很辛苦,但努力过的感觉真的很好,加油!