Concept

Standard Deviation

Standard Deviation, also known as stdev, sigma, is a Statistics concept. First implementations are in the build queue: the write-up leads, the indicators follow.

What is standard deviation?

Standard deviation, often abbreviated stdev and written with the Greek letter sigma, is the classic statistical measure of dispersion: the square root of the average squared distance between each observation and the mean. A small value means the data hug their average; a large value means they scatter widely. In trading it is the workhorse estimate of variability, applied to closing prices, returns, indicator readings, and equity curves alike.

Technical analysis uses it in two distinct ways that are worth keeping separate. Applied to returns, standard deviation is the conventional definition of volatility, the quantity that realized volatility estimators refine and that risk models scale by. Applied to prices around a moving average, it becomes a band-width generator, most famously in Bollinger Bands, where envelopes sit a chosen number of deviations from the mean and adapt automatically as dispersion expands and contracts.

Traders care because standard deviation converts "how much does this thing move" into a single comparable number, enabling normalization (z-scores), position sizing, and adaptive indicator widths. Its main caveat is the assumption baggage: it weights large deviations quadratically, and financial returns are fat-tailed and skewed, so sigma-based rules of thumb (like two deviations covering roughly 95% of outcomes) borrowed from the normal distribution tend to understate how often extreme moves occur.

How it's calculated

The rolling population form below is what most charting platforms compute for indicator purposes.

mean = ( sum of x_i for i = 1..n ) / n

variance = ( sum of (x_i - mean)^2 for i = 1..n ) / n

stdev = sqrt(variance)

sample form: variance_s = ( sum of (x_i - mean)^2 ) / (n - 1)

x_i: input values over the window, typically closes or period returns

n: lookback period (default 20 on many platforms)

mean: arithmetic average of the window

stdev: standard deviation of the window

Charting platforms usually use the population divisor n; statistics texts favor the sample divisor n - 1. On common lookbacks the difference is small but real.

Standard deviation of prices and standard deviation of returns are different quantities with different uses; annualized volatility multiplies the per-period return stdev by the square root of the number of periods per year.

How traders use it

As a volatility gauge: rolling standard deviation of returns summarizes how turbulent an instrument currently is, feeding volatility-targeted sizing and regime filters.
As band construction: Bollinger-style envelopes plot a moving average plus and minus k deviations, widening in turbulent periods and tightening in quiet ones, with the tightening itself watched as a squeeze precursor.
As normalization: dividing a deviation from the mean by the standard deviation yields a z-score, letting traders compare stretch across instruments and eras on a common scale.
As projection scaffolding: some frameworks extend deviations from an anchor to frame expected travel, as in standard deviation projections and VWAP bands.
With limitations in view: sigma is backward-looking, sensitive to the lookback choice, distorted by single outliers, and calm readings say nothing about the risk of a sudden regime change.

Standard deviation vs neighboring measures

ATR: ATR averages true ranges, capturing intrabar travel and gaps in price units without reference to a mean; standard deviation measures dispersion around an average and squares deviations, so the two can disagree about how volatile a market feels.

Z-Score: A z-score is a derived quantity: the current deviation from the mean expressed in standard deviations. Sigma measures spread; the z-score locates one observation within that spread.

Realized Volatility: Realized volatility is standard deviation applied specifically to returns, usually annualized, with refinements (intraday sampling, alternative estimators) aimed at measuring the same dispersion more efficiently.

Related concepts · Normalization & distribution

Z-score5 Distribution-of-returns Profiling5 Percentile Rank4 Min-max Scaling2 Sigmoid/softmax Transforms2 Distribution Moments2 Outlier Detection2 Winsorization0 Normality Testing0

Concept family

Statistics

46 concepts mapped · 46 in the Library

Standard Deviation FAQ

What lookback should I use?

It depends on the horizon you care about: 20 periods is the common charting default, while risk work often uses longer windows. Shorter windows react faster but jump around more.

Population or sample formula?

Most charting platforms use the population divisor n, while statistics convention prefers n - 1 for samples. Be consistent, and expect small numeric differences between tools.

Does the two-sigma rule hold for markets?

Only loosely. The 95% figure assumes normally distributed data, and market returns have fat tails, so moves beyond two or three deviations happen more often than the normal model predicts.

Should I compute it on prices or returns?

Returns for volatility and risk work, since prices trend and violate the stable-mean assumption. Price-based standard deviation is mainly used inside band indicators around a moving average.

Why did my standard deviation spike after one big bar?

Squaring deviations makes the measure outlier-sensitive: one extreme observation can dominate the window until it rolls out of the lookback, which also produces an artificial drop when it exits.

Build Standard Deviation your way.

Quant writes, tests, and refines it with you — then it runs on LuxAlgo charting or ports to TradingView.