What is annualized volatility
Annualized volatility is the standard deviation of an asset's returns, scaled so that it describes the spread of returns over a full year.
Standard deviation measures how far individual returns usually sit from their average. A higher figure means prices have moved more widely. It does not tell you the direction of those moves.
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Volatility formula
The usual steps are:
- Take closing prices at a fixed interval, such as daily or weekly.
- Turn them into returns. Many analysts use log returns: r_t = ln(P_t / P_prev).
- Calculate the standard deviation of those returns. This gives σ_period.
- Scale it to a year: σ_annual = σ_period × √N, where N is the number of such periods in a year.
The square root is used because variance, which is standard deviation squared, grows in proportion to time when returns are independent. Standard deviation therefore grows with the square root of time.
Worked example (hypothetical)
Take a hypothetical index and use its daily closing prices:
- You compute daily log returns and get a daily standard deviation, σ_d.
- Stocks and indices trade only on exchange days, so N is the count of trading days in a year.
- Annualized volatility = σ_d × √N.
If the asset were a crypto coin that trades every day, N would be the count of calendar days. The same daily σ_d would then give a higher annual figure. This is why you should always check which N a source used.
Where you see the term
- Options quotes. Implied volatility is quoted as an annualized figure. See Delta (options).
- Fund factsheets and risk reports. Volatility often appears next to annualized return and CAGR. It is also an input to ratios such as the Sharpe ratio.
- News. Phrases like "volatility jumped" or "realized volatility fell" usually refer to annualized numbers.
- Charting platforms. MetaTrader includes a Standard Deviation indicator. It measures the spread of prices over the last bars of the chart. It is not annualized and it is not based on returns. See Technical analysis.
Precise definition and edge cases
- Historical (realized) volatility is calculated from past returns. Implied volatility is backed out from option prices and reflects what the market expects.
- The square-root-of-time rule assumes that returns are independent and that variance stays constant. Real markets show volatility clustering, autocorrelation and fat tails. Under these conditions, the scaled figure can understate how large extreme moves really are.
- Sample choices change the result. These include the length of the lookback window, whether you use simple or log returns, sample or population standard deviation (Bessel's correction), and how you treat gaps over weekends and holidays.
- Price jumps distort short-window estimates. Examples include a flash crash or a black swan event.
High volatility in a leveraged CFD or forex position means losses can build quickly. A volatility figure describes past or expected movement. It is not a forecast of price. For more on sizing positions against volatility, see Risk management.
Related terms
Frequent questions
What does annualized volatility mean in simple terms?
It shows how widely an asset's returns have spread, or are expected to spread, expressed on a yearly scale.
Why multiply by the square root of N and not by N?
Variance adds up over time when returns are independent. Standard deviation is the square root of variance, so it scales with the square root of time.
Is high annualized volatility good or bad?
It is neither. It measures how large moves are, not which way they go. It does mean that losses can be larger and arrive faster.
Is implied volatility the same as historical volatility?
No. Historical volatility comes from past prices. Implied volatility comes from current option prices and reflects market expectations.