Financial Risk Manager Part 1

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An analyst gathers monthly data about the returns of a stock for the past five years. If the mean monthly return is 6% and the standard deviation of the series of returns is 1.8%, then what is the standard deviation of the mean over the period?

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NNikitesh

Last updated: February 2, 2026 at 10:22

0.45%

0.23%

0.52%

1.39%

Explanation:

The standard deviation of the sample mean (also called standard error of the mean) is calculated using the formula:

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

Where:

σ = population standard deviation = 1.8%
n = number of observations

Since we have monthly data for 5 years:

Number of months = 5 years × 12 months/year = 60 months

Calculation:

\text{Standard Error} = \frac{1.8\%}{\sqrt{60}} = \frac{1.8\%}{7.746} = 0.232\% \approx 0.23\%

This represents the standard deviation of the sample mean, which measures how much the sample mean is expected to vary from the true population mean. The correct answer is 0.23%.

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