Financial Risk Manager Part 1

The correct answer is C (5,767.49) as explicitly stated in the text.

Explanation of Biased vs Unbiased Variance Estimators:

• Biased estimator of variance uses the formula: $\sigma^2_{biased} = \frac{\sum_{i=1}^n (x_i - \bar{x})^2}{n}$ This is biased because it systematically underestimates the population variance.

• Unbiased estimator of variance uses Bessel's correction: $\sigma^2_{unbiased} = \frac{\sum_{i=1}^n (x_i - \bar{x})^2}{n-1}$ This corrects for the bias by dividing by (n-1) instead of n.

The difference between these estimators is: $\sigma^2_{unbiased} - \sigma^2_{biased} = \frac{\sum_{i=1}^n (x_i - \bar{x})^2}{n(n-1)}$

In this specific question, the numerical difference is given as 5,767.49.