NO.PZ2023091601000018
问题如下：
The CIO of a global macro fund is assessing the performance of the
international portfolio managers of the fund. The CIO gathers the annualized
total returns of a sample of the managers as presented in the following table:
The CIO calculates
the central moments of these returns. What is the correct unbiased sample
variance of the returns data?
选项：
A.0.00128
0.00160
0.00288
0.00360
解释：
B is correct. The
unbiased estimator for the sample variance is given by:
From the values in
the table, μ is obtained as (21%+17%+11%+18%+13%)/5 = 16%. Therefore,
S2=
[(21% − 16%)2 + (17% − 16%)2 + (11% − 16%)2 +
(18% − 16%)2 + (13% − 16%)2]/(5-1)=0.00160
A is incorrect.
This is a biased estimate as it divides by n=5 and not by n-1=4
C is incorrect.
This uses a μ that is adjusted with n-1, resulting in 20%, while also dividing
the numerator of the sample estimator by 5 and not 4.
D is incorrect.
This uses a μ that is adjusted with n-1, resulting in 20%.
