Answer-first summary for fast verification
Answer: 0.00160
## Explanation The unbiased estimator for the sample variance is given by: \[ s^2 = \frac{\sum_{i=1}^{n} (X_i - \mu)^2}{n - 1} \] From the values in the table, the mean return \(\mu\) is calculated as: \[ \mu = \frac{21\% + 17\% + 11\% + 18\% + 13\%}{5} = \frac{80\%}{5} = 16\% \] Now calculate the squared deviations: - \((21\% - 16\%)^2 = (5\%)^2 = 0.0025\) - \((17\% - 16\%)^2 = (1\%)^2 = 0.0001\) - \((11\% - 16\%)^2 = (-5\%)^2 = 0.0025\) - \((18\% - 16\%)^2 = (2\%)^2 = 0.0004\) - \((13\% - 16\%)^2 = (-3\%)^2 = 0.0009\) Sum of squared deviations: \[ \sum (X_i - \mu)^2 = 0.0025 + 0.0001 + 0.0025 + 0.0004 + 0.0009 = 0.0064 \] Unbiased sample variance: \[ s^2 = \frac{0.0064}{5 - 1} = \frac{0.0064}{4} = 0.00160 \] Therefore, the correct unbiased sample variance is **0.00160**.
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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:
| Portfolio manager | Annualized total return |
|---|---|
| 1 | 21% |
| 2 | 17% |
| 3 | 11% |
| 4 | 18% |
| 5 | 13% |
What is the correct unbiased sample variance of the returns data?
A
0.00128
B
0.00160
C
0.00288
D
0.00360
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