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.