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MasterMath

Historical Volatility Calculator

Enter a series of closing prices and get the annualised volatility, along with what counts as a normal move and what counts as a bad day.

Currency and number format for

Annualised volatility

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Annualised volatility—
Per period—
Normal move—
Worst 1% move—
Return over the stretch—
Observations—

How this was worked out

    Indicative result. Nothing here is investment advice. Historical volatility describes the past; it is not a forecast.

    The formula

    volatility = standard deviation of log returns × √(periods per year)

    Where it comes from

    Historical volatility is the standard deviation of returns, scaled up to a yearly figure. It describes how widely the price has been swinging, which is the standard measure of risk in finance and the input every option model needs.

    How to work it out by hand

    1. Turn the prices into returns, using logarithms
    2. Work out the standard deviation of those returns
    3. Multiply by the square root of the number of periods in a year
    4. Multiply by 100 for a percentage

    What is worth knowing

    The square-root scaling is what lets daily and annual figures be compared, and it is also where the model shows its limits: it assumes returns are independent and normally distributed, and real markets have neither property. Extreme moves happen far more often than a normal distribution allows, which is why the worst-1% figure here should be read as a floor and not a bound. Two other cautions: volatility clusters, so a calm stretch understates what is coming and a turbulent one overstates it; and this is backward-looking. What options actually price is implied volatility, which is the market's guess about the future and routinely differs from this number.

    Frequently asked questions

    Is high volatility the same as risk?

    It is the standard proxy, but not the same thing. Volatility measures movement in both directions; permanent loss of capital is what most people mean by risk.

    Why multiply by the square root?

    Because variance adds over independent periods, so standard deviation grows with the square root of time. It is the convention that makes daily and annual figures comparable.

    What is a normal volatility figure?

    Broad equity indices typically run between 12 and 20% annualised, individual shares often 25 to 40%, and crypto far higher.

    Does this predict future volatility?

    No. It measures what has already happened. Volatility does cluster, so recent readings carry some information, but implied volatility is the market's actual forecast.