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Maisie · 2022年09月03日

标准差计算

NO.PZ2022071202000024

问题如下:

Question

A risk manager would like to calculate the coefficient of variation of a portfolio. The following table reports the annual returns of the portfolio and of the risk-free rate over the most recent five years:

The coefficient of variation of the portfolio is closest to:

选项:

A.1.00. B.0.74. C.0.90.

解释:

Solution

A is correct. First calculate the sample mean return as follows:

ˉX=(4.0%-1.0%+7.0%+11.0%+2.0%)/5=23.0%/5=4.6%

Then calculate the sample standard deviation with the following formula:

s =[(0.00004+0.00314+0.00058+0.00410+0.00068) /(5-1) ] 1/2 = 4.62%

The coefficient of variation (CV) is calculated with the following formula:

CV = s/X=4.62%/4.6% = 1.0

B is incorrect. It is the Sharpe ratio, not the coefficient of variation. First calculate the mean annual risk-free return over the five years:

ˉRF=2.0%+1.5%+1.0%+1.0%+0.5%5 = 1.2%

Then calculate the Sharpe ratio with the following formula:

Sh = ˉRp-ˉRFsp=4.6%-1.2%4.62% = 0.74

C is incorrect. In the formula for the standard deviation, it uses n instead of “n - 1” in the denominator:

s = [(0.00004+0.00314+0.00058+0.00410+0.00068) /5 ] 1/2 = 4.13%

Then, calculate the CV:

CV = 4.13%/4.6% = 0.90

为什么这里标准差用的是sample而不是population呢?

1 个答案
已采纳答案

星星_品职助教 · 2022年09月03日

同学你好,

题干中的“the most recent five years”说明这只是该资产组合最近五年的数据,所以属于样本。

除非题干特殊做了说明,不然这类给出某几年数据的情况都按照样本处理。

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