Variance
The Core Statistical Measure of Price Dispersion and Volatility
Variance is the granddaddy of volatility stats – it quantifies how spread out prices are around their average by averaging the squared deviations. In trading, it's the raw engine behind Standard Deviation (σ = √variance), powering Bollinger Bands, risk models, and dispersion analysis. High variance means wild price swings; low variance signals calm clustering. It's the pure, unrooted measure of 'how much prices are deviating' – essential for understanding market chaos, building adaptive systems, and sizing risk properly.
The Core Formula – Squared Deviations
Population variance (most trading platforms):
\text{Variance} = \frac{1}{N} \sum_{i=1}^{N} (P_i - \bar{P})^2
- P_i: Price (usually close) each period
- \bar{P}: Mean price over N periods
- N: Look-back window
Sample variance uses N−1 – minor difference for large N.
Interpreting Variance Levels
Volatility signals:
- Low variance: Prices hugging the mean – low volatility, potential squeeze.
- Rising variance: Dispersion increasing – volatility expansion, trend possible.
- High variance: Wide swings – over-extension or strong momentum.
- Falling variance: Calming down – consolidation brewing.
Since it's squared, units are price² – take square root for intuitive σ.
Practical Trading Applications
Where variance shines:
- Bollinger Bands: Width = k × √variance – dynamic volatility envelope.
- Risk models: Portfolio variance for diversification and exposure.
- Adaptive systems: Scale stops/position size with current variance.
- Regime detection: Rising variance from lows → breakout potential.
Parameter Choices
N controls responsiveness:
- Short (10–14): Fast volatility changes – intraday focus.
- Classic (20): Standard for Bollinger and daily analysis.
- Long (50+): Smooth macro dispersion view.
Variance vs Standard Deviation vs ATR
Quick distinctions:
- Variance: Squared dispersion – raw input for models.
- Std Dev (σ): √variance – same units as price, intuitive.
- ATR: Range-based volatility – includes gaps, directionless.
Use variance when feeding models; σ for visualization.
Strengths and Limitations
The Wins
- Pure statistical dispersion – foundation of modern volatility tools.
- Essential for Bollinger, risk parity, and adaptive strategies.
- Clean input for quantitative models.
- Works across any price series.
The Gotchas
- Squared units (price²) – less intuitive than σ.
- Assumes normality – markets have fat tails/outliers.
- Lagging and gap-blind (unlike ATR).
- Sensitive to period choice.
Your Variance Quick-Start
- Plot variance with N=20 on closes.
- Compare to historical levels for context.
- Use as input for Bollinger width or risk scaling.
- Watch rising/falling variance for regime clues.
- Take square root for price-unit volatility (σ).
- Combine with ATR for complete picture.
Key Takeaways
Variance is squared price dispersion around the mean – raw volatility power.
Low = calm clustering, high = wild swings.
Drives Bollinger Bands, risk models, and adaptive systems.
Statistical purity – but take √ for intuitive σ.
Pair with ATR and trend tools – and dispersion becomes your edge. Stay squared and trade measured!
Variance
The Core Statistical Measure of Price Dispersion and Volatility
Variance is the granddaddy of volatility stats – it quantifies how spread out prices are around their average by averaging the squared deviations. In trading, it's the raw engine behind Standard Deviation (σ = √variance), powering Bollinger Bands, risk models, and dispersion analysis. High variance means wild price swings; low variance signals calm clustering. It's the pure, unrooted measure of 'how much prices are deviating' – essential for understanding market chaos, building adaptive systems, and sizing risk properly.
Table of Contents
The Core Formula – Squared Deviations
Population variance (most trading platforms):
\text{Variance} = \frac{1}{N} \sum_{i=1}^{N} (P_i - \bar{P})^2
- P_i: Price (usually close) each period
- \bar{P}: Mean price over N periods
- N: Look-back window
Sample variance uses N−1 – minor difference for large N.
Interpreting Variance Levels
Volatility signals:
- Low variance: Prices hugging the mean – low volatility, potential squeeze.
- Rising variance: Dispersion increasing – volatility expansion, trend possible.
- High variance: Wide swings – over-extension or strong momentum.
- Falling variance: Calming down – consolidation brewing.
Since it's squared, units are price² – take square root for intuitive σ.
Practical Trading Applications
Where variance shines:
- Bollinger Bands: Width = k × √variance – dynamic volatility envelope.
- Risk models: Portfolio variance for diversification and exposure.
- Adaptive systems: Scale stops/position size with current variance.
- Regime detection: Rising variance from lows → breakout potential.
Parameter Choices
N controls responsiveness:
- Short (10–14): Fast volatility changes – intraday focus.
- Classic (20): Standard for Bollinger and daily analysis.
- Long (50+): Smooth macro dispersion view.
Variance vs Standard Deviation vs ATR
Quick distinctions:
- Variance: Squared dispersion – raw input for models.
- Std Dev (σ): √variance – same units as price, intuitive.
- ATR: Range-based volatility – includes gaps, directionless.
Use variance when feeding models; σ for visualization.
Strengths and Limitations
The Wins
- Pure statistical dispersion – foundation of modern volatility tools.
- Essential for Bollinger, risk parity, and adaptive strategies.
- Clean input for quantitative models.
- Works across any price series.
The Gotchas
- Squared units (price²) – less intuitive than σ.
- Assumes normality – markets have fat tails/outliers.
- Lagging and gap-blind (unlike ATR).
- Sensitive to period choice.
Your Variance Quick-Start
- Plot variance with N=20 on closes.
- Compare to historical levels for context.
- Use as input for Bollinger width or risk scaling.
- Watch rising/falling variance for regime clues.
- Take square root for price-unit volatility (σ).
- Combine with ATR for complete picture.
Key Takeaways
Variance is squared price dispersion around the mean – raw volatility power.
Low = calm clustering, high = wild swings.
Drives Bollinger Bands, risk models, and adaptive systems.
Statistical purity – but take √ for intuitive σ.
Pair with ATR and trend tools – and dispersion becomes your edge. Stay squared and trade measured!
Related Terms
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