Standard Deviation (σ)
The Statistical Measure of Price Volatility and Dispersion
Standard Deviation (σ) is the workhorse statistic that quantifies how much prices scatter around their average over a given period. In trading, it's the go-to gauge for volatility: low σ means calm, tightly clustered prices; high σ signals wild swings and big dispersion. It's the math behind Bollinger Bands, volatility breakouts, and risk assessment – turning raw price chaos into a clean, comparable number. Simple, powerful, and essential for understanding how 'noisy' or 'explosive' the market really is.
The Core Formula – Dispersion in Numbers
Standard population formula (used in most trading platforms):
\sigma = \sqrt{\frac{1}{N} \sum_{i=1}^{N} (P_i - \bar{P})^2}
- P_i: Price (usually close) for each period
- \bar{P}: Simple average of prices over N periods
- N: Look-back length (commonly 20)
Some tools use sample std dev (divide by N−1) – minor difference for large N.
Reading Standard Deviation Levels
Volatility moods (relative – compare historically):
- Low σ: Prices tightly clustered – low volatility, potential squeeze.
- Rising σ: Volatility expanding – breakouts or trend acceleration likely.
- High σ: Wild swings – over-extension, possible exhaustion.
- Falling σ: Volatility contracting – consolidation or calm before storm.
In Bollinger Bands: ±2σ captures ~95% of price action in normal distributions.
Practical Trading Applications
Key uses:
- Bollinger Bands: SMA ± k×σ – dynamic S/R and squeeze signals.
- Volatility stops: Place stops at 2–3 × σ beyond structure.
- Position sizing: Risk fixed % using current σ for share calculation.
- Breakout filter: Only trade breakouts when σ rising from low levels.
- Regime detection: High σ = trend possible; low = range likely.
Parameter Choices
N controls sensitivity:
- Short (10–14): Fast – intraday volatility spikes.
- Classic (20): Standard for Bollinger and daily analysis.
- Long (50–100): Smooth macro volatility view.
σ vs ATR – Complementary Tools
Quick comparison:
- σ: Statistical dispersion around mean – assumes normal distribution.
- ATR: True range average – captures gaps, directionless volatility.
- Use both: σ for bands/squeezes, ATR for stops/sizing.
Strengths and Limitations
The Wins
- Clean statistical volatility measure.
- Foundation for Bollinger Bands and risk models.
- Comparable across assets (in relative terms).
- Works with normal distribution assumptions.
The Gotchas
- Assumes normality – markets have fat tails.
- Lagging – based on past dispersion.
- Ignores gaps (unlike ATR).
- Raw units – normalize for cross-asset work.
Your Standard Deviation Checklist
- Plot with period 20 on close prices.
- Add Bollinger Bands for visual context.
- Compare current σ to historical percentiles.
- Use rising/falling σ for regime clues.
- Combine with ATR for complete volatility picture.
- Backtest band touches and squeeze signals.
Key Takeaways
Standard Deviation quantifies price scatter around the mean – core volatility statistic.
Low σ = calm/clustered, high = wild/dispersed.
Powers Bollinger Bands, risk sizing, and regime detection.
Statistical and clean – but assumes normality and misses gaps.
Pair with ATR and trend tools – and volatility becomes crystal clear. Stay dispersed wisely and trade measured!
Related Terms
Standard Deviation (σ)
The Statistical Measure of Price Volatility and Dispersion
Standard Deviation (σ) is the workhorse statistic that quantifies how much prices scatter around their average over a given period. In trading, it's the go-to gauge for volatility: low σ means calm, tightly clustered prices; high σ signals wild swings and big dispersion. It's the math behind Bollinger Bands, volatility breakouts, and risk assessment – turning raw price chaos into a clean, comparable number. Simple, powerful, and essential for understanding how 'noisy' or 'explosive' the market really is.
Table of Contents
The Core Formula – Dispersion in Numbers
Standard population formula (used in most trading platforms):
\sigma = \sqrt{\frac{1}{N} \sum_{i=1}^{N} (P_i - \bar{P})^2}
- P_i: Price (usually close) for each period
- \bar{P}: Simple average of prices over N periods
- N: Look-back length (commonly 20)
Some tools use sample std dev (divide by N−1) – minor difference for large N.
Reading Standard Deviation Levels
Volatility moods (relative – compare historically):
- Low σ: Prices tightly clustered – low volatility, potential squeeze.
- Rising σ: Volatility expanding – breakouts or trend acceleration likely.
- High σ: Wild swings – over-extension, possible exhaustion.
- Falling σ: Volatility contracting – consolidation or calm before storm.
In Bollinger Bands: ±2σ captures ~95% of price action in normal distributions.
Practical Trading Applications
Key uses:
- Bollinger Bands: SMA ± k×σ – dynamic S/R and squeeze signals.
- Volatility stops: Place stops at 2–3 × σ beyond structure.
- Position sizing: Risk fixed % using current σ for share calculation.
- Breakout filter: Only trade breakouts when σ rising from low levels.
- Regime detection: High σ = trend possible; low = range likely.
Parameter Choices
N controls sensitivity:
- Short (10–14): Fast – intraday volatility spikes.
- Classic (20): Standard for Bollinger and daily analysis.
- Long (50–100): Smooth macro volatility view.
σ vs ATR – Complementary Tools
Quick comparison:
- σ: Statistical dispersion around mean – assumes normal distribution.
- ATR: True range average – captures gaps, directionless volatility.
- Use both: σ for bands/squeezes, ATR for stops/sizing.
Strengths and Limitations
The Wins
- Clean statistical volatility measure.
- Foundation for Bollinger Bands and risk models.
- Comparable across assets (in relative terms).
- Works with normal distribution assumptions.
The Gotchas
- Assumes normality – markets have fat tails.
- Lagging – based on past dispersion.
- Ignores gaps (unlike ATR).
- Raw units – normalize for cross-asset work.
Your Standard Deviation Checklist
- Plot with period 20 on close prices.
- Add Bollinger Bands for visual context.
- Compare current σ to historical percentiles.
- Use rising/falling σ for regime clues.
- Combine with ATR for complete volatility picture.
- Backtest band touches and squeeze signals.
Key Takeaways
Standard Deviation quantifies price scatter around the mean – core volatility statistic.
Low σ = calm/clustered, high = wild/dispersed.
Powers Bollinger Bands, risk sizing, and regime detection.
Statistical and clean – but assumes normality and misses gaps.
Pair with ATR and trend tools – and volatility becomes crystal clear. Stay dispersed wisely and trade measured!
Related Terms
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