Historical Volatility (HV)
What is Historical Volatility?
Historical volatility (HV) measures how much a security’s price has fluctuated over a past period. It quantifies the dispersion of returns around their average and is used to assess the asset’s past riskiness. HV describes magnitude of movement, not direction or likelihood of loss.
How HV Is Calculated
- Choose a return type and sampling frequency:
- Common practice: use daily returns; longer windows (e.g., 30, 90, 252 days) change responsiveness.
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Use log returns (ri = ln(Pi / Pi-1)) for consistency, though simple returns can also be used.
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Compute returns for the chosen period.
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Calculate the sample standard deviation of those returns:
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s = sqrt( (1/(n-1)) * Σ(ri − r̄)² ), where r̄ is the mean return.
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Annualize if needed:
- σannual = sd_period * sqrt(N)
- For daily returns, N ≈ 252 trading days. For weekly returns, N ≈ 52.
Interpretation and Key Points
- HV indicates the typical size of price moves around the mean—not the direction.
- Higher HV = larger price swings and generally higher risk (and opportunity).
- Lower HV = smaller, more stable deviations from average price.
- HV does not predict future volatility; it summarizes past behavior.
- Choice of window matters: short windows react quickly but are noisy; long windows are smoother but slower to reflect change.
- Trending markets can show large cumulative price moves yet low HV if the price moves smoothly around a moving average.
Practical Uses
- Risk assessment: help set position sizing, stop-loss levels, and margin requirements.
- Options analysis: compare HV with implied volatility (IV) to spot potentially over- or underpriced options.
- Technical indicators: HV is an input for tools like Bollinger Bands (bands expand/contract with volatility).
- Strategy selection: traders may prefer high-volatility environments for momentum or options strategies and low-volatility environments for mean-reversion or income strategies.
Practical Considerations
- Time window selection should reflect the investment horizon and strategy.
- Sampling frequency (intraday vs daily vs weekly) affects measured volatility.
- Annualization assumes returns are independent and identically distributed; this may not hold in practice.
- Use HV alongside other metrics (IV, drawdown history, liquidity) for a fuller picture.
- Compare HV to peers or historical norms for the same asset to judge whether current volatility is typical.
Quick Takeaways
- HV = standard deviation of past returns; measures magnitude of past price movements.
- It’s a retrospective measure—useful for assessing past risk and informing risk management.
- Compare HV with implied volatility to inform options decisions.
- Select period and return type deliberately; different choices yield different HV readings.