Standard deviation is the square root of variance: the typical magnitude of deviation from the mean. In trading it is computed on a return series and serves as the canonical measure of volatility — the σ in Sharpe ratios, Bollinger Bands, and Black-Scholes.
Annualization scales σ by √N, where N is the number of periods per year (252 for daily trading days, ≈8,760 for hourly bars in 24/7 markets). The choice of N depends on the market schedule and the bar frequency of the source data.
Standard deviation assumes returns are roughly stationary and well-behaved. Real financial returns have fat tails — extreme moves happen more often than Gaussian theory predicts — so σ understates true tail risk.
Formula
σ = sqrt(Σ(x_i − x̄)^2 / (N − 1)) for a sample of size N
Example
Daily returns [0.01, -0.02, 0.00, 0.015, -0.005]. Mean = 0.0. σ ≈ 0.014 = 1.4%. Annualized σ ≈ 1.4% · √252 ≈ 22%.
How Noon Barbari uses Standard deviation
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Volatility & Sharpe calculator →Related terms
- Statistics
Variance
Average squared deviation from the mean. Square root is standard deviation.
- Statistics
Sharpe ratio
Excess return over the risk-free rate per unit of total volatility.
- Indicators
Bollinger Bands
A moving average flanked by ±k standard deviations of price. k = 2 by default.
- Indicators
Average true range (ATR)
Rolling average of the true range — the canonical volatility measure for stops.