Understanding Standard Deviation in Stock Returns

Hard Statistical Concepts And Returns Measures Of Dispersion

A financial analyst recently gathered the following monthly returns of a stock over the last year: 4%, -2%, 6%, 3%, -1%, 5%, 2%, 0%, 7%, -3%, 4%, 1%. The analyst is now attempting to assess the volatility of this stock by determining the standard deviation of its monthly returns.

To calculate the standard deviation, the analyst first finds the mean return for the period. After calculating the mean return, she squares the deviations of each monthly return from the mean, averages those squared deviations (populations standard deviation), and then takes the square root of that average. How is the standard deviation mathematically defined?

Which of the following statements correctly defines the standard deviation in the context of the stock's returns?

The standard deviation is the square root of the average squared deviations of returns from the mean, calculated as $ ext{SD} = rac{ ext{Sum of } (X_i - ar{X})^2}{N}$, where $N$ is the number of returns.

The standard deviation is the average of the absolute deviations of returns from the mean, calculated as $ ext{SD} = rac{ ext{Sum of } |X_i - ar{X}|}{N}$.

The standard deviation is the square of the variance of the returns, represented as $ ext{SD} = ext{Var}^{2}$.

Hint

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