Standard Deviation

Standard deviation is a statistical measure of how widely values are spread around their average. In technical analysis it is applied to closing prices over a set number of bars to measure volatility: when prices swing far from their average, standard deviation is high; when they hold close to it, standard deviation is low. It is used less as a signal of its own than as a building block, most famously in Bollinger Bands.

How it is calculated

Mean = SMA(N) of the close
Standard deviation = square root of ( sum of (close - mean)² over N bars / N )

Take the simple moving average over N bars (20 is common). For each bar, square the difference between the close and that average, add the squares up, divide by N and take the square root. Squaring makes large moves count much more than small ones.

The result is in price units. A $500 stock and a $20 stock will have very different readings even if they are equally volatile, so to compare stocks, divide by the price: 100 × standard deviation / price gives volatility as a percentage.

How to read it

• High and low volatility. Rising standard deviation means price is moving away from its average quickly, in either direction. Falling standard deviation means the market is calm and range-bound.
• Contraction before expansion. Volatility tends to alternate. Unusually low readings, compared with the stock’s own history, often come before a larger move. They do not say which way.
• Tops and bottoms. Market tops are often accompanied by high volatility as traders swing between greed and fear. Many bottoms form after a volatile sell-off, once volatility starts to fall back.
• Distance from the average. If closes were normally distributed, about 68% would fall within one standard deviation of the mean and about 95% within two. Prices have fatter tails than that, so moves of three or more standard deviations happen more often than the textbook suggests.

Settings and common mistakes

• Period. 20 bars is the usual setting and matches Bollinger Bands. Shorter periods react quickly; longer ones show the volatility regime.
• Comparing raw values. Always normalize by price before comparing stocks or long periods of one stock’s history.
• Confusing it with historical volatility. Standard deviation of price measures the spread of closes around their average, and a steady trend alone raises it. Historical volatility is the standard deviation of daily returns, annualized, and is the measure used for options and risk.
• Expecting a direction. High volatility is not bearish and low volatility is not bullish. Combine it with a trend or momentum indicator.

Live chart: SPY (S&P 500 ETF), daily, with the 20-day standard deviation of the close. The chart updates every trading day.

Screen for it on MarketInOut

Standard deviation is stddev(period) in our formula language, in price units. Stocks in a long-term uptrend whose 20-day standard deviation has fallen to a six-month low:

exch(nyse,nasdaq) and type(stock) and price > 1 and advol(21) > 1
and stddev(20) new_low 126 and price > sma(200)

Quiet stocks, with a standard deviation under 1% of the price, that are pushing to a one-month high:

exch(nyse,nasdaq) and type(stock) and price > 1 and advol(21) > 1
and 100 * stddev(20) / price < 1 and price > sma(200) and price new_high 21

Related: Bollinger Bands, Average True Range, Moving averages.