Historical Volatility Calculator (Annualized)

How it works

Log return rₜ = ln(Pₜ ÷ Pₜ₋₁) · σ = sample standard deviation of rₜ (divide by n − 1) · annualized volatility = σ × √k, with k = 252 trading days, 365 days, 52 weeks or 12 months · one-year ±1 SD range ≈ last price × e^(±σ annual)

Historical (realized) volatility measures how much an asset’s price has actually moved. It is the standard deviation of its periodic log returns, scaled to a year by the square root of the number of periods per year — the convention used by exchanges, option pricing models and risk systems. Stocks are usually annualized with 252 trading days and crypto with 365 calendar days. Compare it with implied volatility to judge whether options look cheap or expensive; as a rough guide, broad stock indexes run at 15–20% a year, single stocks at 25–50% and bitcoin often above 50%.

Worked example

The eleven daily closes 100, 102, 101, 105, 107, 104, 108, 110, 109, 112 and 115 give 10 log returns (the first is ln(102 ÷ 100) = 1.980%). Their sample standard deviation is 2.233% per day, so the annualized volatility is 2.233% × √252 = 35.45%. A one-standard-deviation day is about ±2.57 on a 115 stock, and a ±1 SD year spans roughly 80.67 to 163.94.

Sources: Wikipedia — Volatility (finance)

Frequently asked questions