Explanation

The standard deviation of the mean (also known as the standard error) is calculated using the formula:

$$\text{Standard Error} = \frac{\sigma}{\sqrt{n}}$$

Where:

• $\sigma$ = population standard deviation = 15%
• $n$ = sample size = 25

Substituting the values:

$$\text{Standard Error} = \frac{15\%}{\sqrt{25}} = \frac{15\%}{5} = 3.0\%$$

Key Points:

• The standard error measures the variability of the sample mean around the population mean
• It decreases as the sample size increases (due to the square root in the denominator)
• The mean weekly return of 7% is not used in this calculation, as we're only concerned with the variability of the mean, not its value
• This is a fundamental concept in statistics and is particularly important in risk management for understanding the precision of estimated parameters