How does standard deviation provide investors with a measure of historical volatility?

Standard deviation measures how widely returns have varied around their average over a historical period. It is calculated by taking each period’s return, measuring its deviation from the mean return, squaring those deviations, averaging them, and then taking the square root to return the measure to the same units as the original data. The result is a single statistic that summarises typical dispersion of returns, which investors interpret as volatility. A higher standard deviation indicates returns have been more spread out, implying greater uncertainty and risk; a lower standard deviation indicates returns have been more stable around the average. Measuring highs and lows alone does not capture the full distribution or how frequently returns deviate from the mean. Comparing price movements to a benchmark relates more to beta or tracking error, not standalone volatility. Analysing historical price movements is too broad and does not define the statistic. CISI questions typically focus on the precise interpretation: standard deviation quantifies the degree of fluctuation around the mean, providing a historical volatility measure that is comparable across assets and portfolios.