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?