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Start Learning → Browse All Articles →Before you can talk sensibly about a stock's volatility, you need a number for it — standard deviation is where that number usually comes from.
Standard deviation measures how spread out a set of numbers is around their average. Applied to a stock’s daily or periodic returns, it tells you how much those returns typically deviate from the average return over the period studied — a stock whose daily returns cluster tightly around its average has a low standard deviation, while one that swings widely from day to day has a high one. This is the statistical foundation underneath most of the volatility concepts traders use casually, including implied volatility and India VIX.
Standard deviation is used so widely in finance partly because it has convenient mathematical properties that make it easy to combine across time periods and portfolios, and partly because it’s intuitive: a number expressed in the same units as the returns themselves (typically as a percentage), rather than an abstract, hard-to-interpret statistic.
Because standard deviation is normally calculated from daily or other short-period returns, it is typically annualised for comparison purposes by multiplying by the square root of the number of trading periods in a year (roughly the square root of 252 for daily data), a convention worth knowing since raw daily standard deviation numbers look deceptively small compared with the annualised figures usually quoted for stocks and indices.
Standard deviation calculated from a stock’s actual past returns is what’s generally called historical volatility, distinct from implied volatility, which is derived from options prices and reflects the market’s expectation of future volatility rather than a measurement of what already happened. The two often move together but can diverge meaningfully around anticipated events.
Standard deviation treats upside and downside moves symmetrically, the same limitation that affects the Sharpe ratio, which is calculated directly from it. A stock that rallies sharply and one that crashes by the same magnitude contribute identically to its standard deviation, even though most traders experience those two outcomes very differently — a nuance worth remembering before treating standard deviation alone as a complete picture of a stock’s risk.