Which statement correctly distinguishes variance and standard deviation in risk measurement?

• A. Variance is the average squared deviation of returns; standard deviation is the square root of variance
• B. Variance and standard deviation measure liquidity
• C. Variance is the square root of standard deviation
• D. Standard deviation is the average deviation from the mean

Answer: (A)

Measuring how far returns typically stray from the average is at the heart of risk. Variance captures this dispersion by averaging the squared deviations from the mean, so it expresses risk in squared units. Standard deviation takes the square root of that variance, bringing the measure back to the same units as the returns themselves and making it easier to interpret. That’s why the statement describing variance as the average squared deviation and standard deviation as the square root of variance is the correct distinction. The other descriptions mix up concepts—variance is not a liquidity measure, standard deviation is not the average deviation from the mean, and variance is not the square root of standard deviation.