What is Volatility? Definition, Formula, and Example
Volatility is the statistical measure of how widely an asset's price disperses around its average, expressed as the annualized standard deviation of returns.
What is Volatility?
Volatility is the degree of variation in an asset's price over time, measured as the standard deviation of its returns and conventionally annualized. A stock with 20% annualized volatility is expected, with roughly 68% probability, to finish a year within plus or minus 20% of its current price. High volatility means wide, fast price swings; low volatility means tight, slow ones. Volatility is direction-agnostic: it measures the size of moves, not whether they are up or down. It is the single most important input into options pricing, position sizing, and risk management, and it is the reason a 2% daily move is routine for one stock and extraordinary for another.
How Volatility is Calculated
Historical (realized) volatility is computed from a series of periodic returns, usually daily log returns:
1. Compute each period's return: r_t = ln(P_t / P_t-1)
2. Compute the mean return over the sample.
3. Compute the sample standard deviation of those returns: sigma = sqrt( sum((r_t - mean)^2) / (n - 1) )
4. Annualize by multiplying by the square root of the number of periods per year: sigma_annual = sigma_daily x sqrt(252).
The 252 factor assumes returns scale with the square root of time, which is why annualizing by multiplying by 252 is wrong. A 30-day lookback is the market convention and matches the VIX methodology. Implied volatility is the forward-looking counterpart, backed out of option prices using a model such as Black-Scholes.
Worked Example
Take AAPL with daily closes of 190.00, 191.90, 189.15, 192.40, 191.00 over five days. The log returns are approximately 0.995%, -1.41%, 1.72%, -0.73%. The standard deviation of this sample is about 1.34%. Annualizing: 1.34% x sqrt(252) = about 21.3%. That is the realized volatility over that window. Now compare TSLA, which has historically printed daily standard deviations near 2.5%, annualizing to roughly 40%. Same market, same days, nearly double the risk per unit of capital. An options trader pricing a 30-day straddle on each name would demand roughly twice the premium on TSLA, because the expected range of outcomes is twice as wide.
When Traders Use It
Volatility drives nearly every quantitative decision. Options traders compare implied volatility against realized volatility to decide whether premium is rich or cheap, selling strangles when implied exceeds realized and buying when the reverse holds. Swing traders use it to set stop distances: a stop placed one average true range away survives normal noise, and average true range is itself a volatility measure. Risk managers scale position sizing inversely to volatility so that each position contributes equal dollar risk. Regime shifts matter too: volatility clusters, so a quiet tape that suddenly prints 2% daily moves signals a regime change that invalidates prior stop and target assumptions. You can screen for names whose volatility is expanding or contracting right now on the live scanner.
Limitations and Common Misconceptions
First, volatility is not risk in the everyday sense. A stock grinding down 0.5% per day for a year has low volatility and a catastrophic return. Second, annualized volatility assumes returns are independent and normally distributed; real returns have fat tails, so three-sigma moves happen far more often than the math implies. Third, realized volatility is backward-looking and says nothing about tomorrow; implied volatility is forward-looking but embeds supply, demand, and hedging flows, not just expected movement. Fourth, the square-root-of-time annualization breaks down during trending or mean-reverting regimes. Finally, low volatility is not safety: compressed volatility often precedes expansion, which is the entire premise of the TTM squeeze.