Definition
Volatility
Volatility is the standard deviation of returns over a stated horizon. The annualised volatility formula (√252 vs √365), realized vs implied, and why it is not the same thing as loss.
Volatility is the standard deviation of an asset's or strategy's returns over a stated horizon, and the horizon is part of the number: a 2% daily standard deviation is roughly 31.7% annualised for equities (√252 trading days) and 38.2% for crypto that trades 365 days a year. It measures how widely returns are dispersed around their average, counting upside and downside moves equally, and it is the denominator of the Sharpe ratio, so a strategy measured over a calm window will look better than the same strategy measured through a storm.
- Also known as
- standard deviation of returns · realized volatility · annualised volatility
How it is calculated
σ = √( Σ(rᵢ − r̄)² ÷ (n − 1) ) — sample standard deviation of period returns
σ_annual = σ_daily × √252 (equities, trading-day calendar)
σ_annual = σ_daily × √365 (crypto, 24x7)
Example: 2% daily → 2% × 15.87 ≈ 31.7% (equities), 2% × 19.10 ≈ 38.2% (crypto)
Vol-target size = Target σ ÷ Realized σ (fraction of full position)
Worked example: Daily σ of 2% → 2% × √252 ≈ 31.7% annualised for equities, 2% × √365 ≈ 38.2% for 24x7 crypto. Targeting 10% annual σ with realized 20% → hold 50% of full size.
The horizon is the whole meaning
A volatility figure without its horizon is not a number. Daily, weekly and annual standard deviations of the same return series differ by the square root of the number of periods, so the conventional annualisation multiplies daily σ by √252 for markets with a trading calendar and by √365 for markets that never close. The √T rule assumes returns are independent from one period to the next; when they are not, the annualised figure is only an approximation. Realized volatility is computed from past returns, implied volatility is backed out of option prices, and the two routinely disagree — implied is a forecast, realized is a measurement.
It clusters, and it sits under the Sharpe ratio
Realized volatility is persistent: a high-volatility day is far more likely to be followed by another high-volatility day than by a calm one, which is why forecasting models treat it as a time series rather than a constant. Because volatility is the denominator of the Sharpe ratio, the same strategy scores higher when the measurement window happens to be quiet, without any change in the strategy. Volatility targeting turns this around: position size is set to target σ ÷ realized σ, so exposure shrinks when markets get rough and grows when they calm. QANTERION's Sharpe ratio calculator takes annualised volatility as its input, so a daily figure has to be scaled by √252 or √365 first.
How it gets misread
Volatility is routinely read as a synonym for loss, but the standard deviation counts a 5% up day exactly as it counts a 5% down day; a strategy that only ever surprises to the upside still has high volatility. It is also read as a proxy for drawdown, which it is not: a low-volatility strategy whose small losses arrive in a row can sit in a deeper drawdown than a high-volatility one whose losses are scattered, because drawdown depends on the order of returns and volatility ignores it.
Sources
- The Sharpe Ratio — The Journal of Portfolio Management (author's reprint, Stanford University)
- Modeling and Forecasting Realized Volatility — National Bureau of Economic Research (Andersen, Bollerslev, Diebold & Labys), Working Paper 8160
Definitions are educational. Nothing here is investment advice, and no metric described on this page predicts future results.
Definitions are the easy part
Knowing what drawdown means is not the same as having a system that halts on it. QANTERION applies these limits while a strategy runs.