Standard deviation measures the dispersion of returns around their average, providing a statistical measure of volatility and risk. Higher standard deviation indicates greater price volatility and risk, while lower values suggest more stable price behavior. Standard deviation is a fundamental component of risk assessment and portfolio optimization.

Standard deviation calculations consider the frequency and magnitude of price movements to quantify uncertainty levels. This measure assumes normal distribution of returns, which may not hold during extreme market conditions. Understanding standard deviation helps assess risk levels and compare volatility across different investments and timeframes.

Real-world example: A stock with 20% annual standard deviation experiences more volatile price swings than one with 10% standard deviation, indicating roughly twice the price uncertainty and risk level for similar expected returns.