Answer: 6.53%

## Calculation Explanation **Step 1: Calculate the Mean** \[ \text{Mean} = \frac{(0.12 + 0.13 + 0.05 + 0.04 + 0.20)}{5} = \frac{0.54}{5} = 0.108 \text{ or } 10.8\% \] **Step 2: Calculate Deviations and Squared Deviations** | Stock | Return | X – Mean | (X – Mean)² | |-------|--------|----------|-------------| | A | 12% | 1.2% | 0.000144 | | B | 13% | 2.2% | 0.000484 | | C | 5% | –5.8% | 0.003364 | | D | 4% | –6.8% | 0.004624 | | E | 20% | 9.2% | 0.008464 | | Total | | | 0.017080 | **Step 3: Calculate Sample Standard Deviation** \[ \text{Sample Standard Deviation} = \sqrt{\frac{\sum(X - \text{Mean})^2}{n - 1}} = \sqrt{\frac{0.017080}{4}} = \sqrt{0.00427} = 0.0653 \text{ or } 6.53\% \] **Key Points:** - We use **n-1** in the denominator because this is a **sample** standard deviation (not population) - The sample standard deviation is an unbiased estimator of the population standard deviation - The calculation follows the formula: \( s = \sqrt{\frac{\sum(x_i - \bar{x})^2}{n-1}} \)

Author: Tanishq Prabhu