What is volatility in investing? How it's measured and annualised

Volatility is the statistical measure of how widely an asset's price swings. A savings account has almost none; broad stock indices have historically shown annual volatility somewhere in the teens to low twenties of percent; individual stocks are usually higher; and major cryptocurrencies have often been several times more volatile than stock indices.

For investors it is the most common shorthand for risk: the wider the swings, the less certain the value of your holding at any future date — and the more nerve it takes to hold through the dips.

Take a series of periodic returns, measure their standard deviation, then scale it to a year:

σ                 = standard deviation of periodic returns
Annual volatility = σ(daily) × √252   (stock markets)
Annual volatility = σ(daily) × √365   (24/7 crypto)

The square-root rule comes from the fact that, if returns are independent, variance grows in proportion to time. Stocks trade on roughly 252 days a year; crypto trades every day, so crypto volatility is often annualised with 365 instead — check which convention a figure uses before comparing. Many analysts use log returns, which give almost identical results for small daily moves.

If a stock's daily returns have a standard deviation of 1.5%, its annual volatility is about 1.5% × √252 ≈ 1.5% × 15.9 ≈ 24%. As a rough rule — assuming returns are close to normally distributed — in about two years out of three the annual return lands within one standard deviation of its average. With an expected return of 8% and 24% volatility, that range is roughly −16% to +32%.

Volatility also eats into compound growth. A fall of 50% followed by a rise of 50% leaves you at 0.5 × 1.5 = 0.75 — down 25%, even though the average of the two returns is zero. The more an investment swings, the bigger this 'volatility drag' on its long-run growth.

Market returns are not normally distributed: extreme days happen far more often than the bell curve predicts, so volatility understates the risk of crashes. Volatility also clusters — turbulent periods tend to follow turbulent periods — so a figure measured over a calm year can be badly out of date a month later.

Historical volatility looks backward. Implied volatility, derived from option prices, looks forward; the VIX index, for example, measures the 30-day volatility the options market expects for the S&P 500. And volatility is not the same as the risk of permanent loss: a volatile but sound asset held long enough can be less risky than a 'stable' one that slowly loses value to inflation.