Volatility (σ)
Standard deviation of returns — the most common dispersion-based risk measure.
Definition
Volatility is the standard deviation of returns over a period, almost always annualised. It captures how much returns deviate from their mean — both up and down. Realised (historical) volatility is computed from observed data; implied volatility is extracted from option prices and reflects the market's forward-looking view. Volatility is symmetric (it punishes upside surprises equally) which is why Sortino and downside deviation exist as alternatives.
Formula
sigma = sqrt( (1/(N-1)) * sum_{i=1}^N (R_i - R_mean)^2 )
Annualisation:
sigma_annual = sigma_period * sqrt(periods_per_year)
daily -> sqrt(252)
weekly -> sqrt(52)
monthly -> sqrt(12)Worked example
SPY daily returns over the past year have a standard deviation of 0.012 (1.2%). Annualised volatility = 0.012 * sqrt(252) = 0.190 or 19%. By comparison BTC daily sigma might be 0.04, annualised ~63%, illustrating crypto’s far higher risk profile.
How ARIA Analyst uses it
ARIA estimates volatility with both EWMA (RiskMetrics) and GARCH(1,1) models and uses the higher of the two as a conservative input to Monte Carlo and position sizing.
Related terms
Sharpe Ratio
Risk-adjusted return measured as excess return per unit of total volatility.
Value at Risk (VaR)
The maximum loss expected over a given horizon at a given confidence level.
Beta (β)
Sensitivity of an asset to moves in a benchmark — typically the broad market.
Monte Carlo Simulation
A probabilistic technique that simulates thousands of random scenarios to estimate the distribution of outcomes.
See Volatility (σ) in action on any asset
ARIA Analyst computes Volatility (σ) automatically as part of a hybrid multi-agent investment report — 5 deterministic scoring agents plus AI augmentation (ML ensemble, Bull vs Bear debate, 10 Deep Search agents on Premium). Get yours in seconds.
Try ARIA Analyst free →