What Is Stock Volatility? Definition and Measurement
Stock volatility is a measure of how much a stock’s returns vary over time. The most common way to express it is the standard deviation of returns: the bigger the typical swing away from the average, the higher the volatility. A stock that moves 0.5% on most days is less volatile than one that regularly moves 3%, even if both end the year at the same price.
Volatility does not say whether a stock will rise or fall. It describes the size of the moves, in either direction.
Calculating it step by step
Take five daily returns for a hypothetical stock: +1%, -1%, +2%, 0% and -2%.
- Average return. The sum is 0%, so the mean is 0%.
- Deviation from the mean, squared. The squared deviations are 1, 1, 4, 0 and 4, which total 10.
- Variance. Divide by one less than the number of observations (the sample variance): 10 / 4 = 2.5.
- Standard deviation. The square root of 2.5 is about 1.58%. This is the daily volatility.
Real calculations use many more observations, usually a year or more of data, but the steps are the same.
Annualising
Volatility is usually quoted per year so that numbers can be compared. When returns are assumed to be independent from one period to the next, volatility grows with the square root of time. A common convention is 252 trading days in a year, so daily volatility is multiplied by the square root of 252, about 15.87. In the example, 1.58% x 15.87 is roughly 25%. Using weekly or monthly data, the multipliers are the square roots of 52 and 12.
That “square root of time” rule is an approximation. Real returns are not perfectly independent, so annualised figures are estimates.
Historical versus implied volatility
- Historical (realised) volatility is calculated from past returns, over a window you choose, such as 30 or 252 days.
- Implied volatility is backed out of options prices and reflects what the market expects over the life of the option. Cboe’s VIX index, for instance, is a measure of the implied volatility of S&P 500 index options over about 30 days.
The two can differ a lot, and neither is a forecast that is guaranteed to hold.
Volatility, beta and drawdown
These terms are often mixed up:
| Measure | What it describes |
|---|---|
| Volatility | Total variability of a stock’s returns |
| Beta | Sensitivity to the market’s moves; a beta of 1 means it has moved in line with the market |
| Maximum drawdown | The largest peak-to-trough fall over a period |
A stock can have high volatility and a low beta, if its movements are large but unrelated to the market. The reverse is also possible. Definitions of these and related terms appear in the site’s glossary of low volatility investing terms, and the investing FAQ answers common questions.
Common misunderstandings
- “Volatility means losses.” Volatility counts upward moves too. A stock that jumps 10% in a day contributes just as much to the statistic as one that drops 10%.
- “Low volatility means safe.” A calm stock can still lose value, and one-off events can cause sharp falls. Standard deviation does not capture all risk.
- “Returns are normally distributed.” Actual returns have fatter tails than the bell curve implies, so extreme days happen more often than a simple model suggests.
- “The number is fixed.” Volatility changes with time. Periods of calm are often followed by turbulence, and estimates depend on the window used.
Why investors measure it
Volatility is used to size positions, set risk budgets, compare funds, price options and design portfolios. Academic research has examined whether less volatile stocks earn returns that differ from what theory predicts, a topic covered on the home page and in related articles on this site. Regulators such as the U.S. Securities and Exchange Commission publish investor education on risk at Investor.gov.
Frequently asked questions
What is a high volatility for a stock?
There is no universal threshold. Compare against the stock’s own history, its sector and a broad index.
Is volatility the same as risk?
It is one measure of risk. Others include drawdown, downside deviation, liquidity and the possibility of permanent loss.
How is volatility different from variance?
Variance is the average squared deviation. Volatility is its square root, which puts the figure back into the same units as returns.
A note on use
This article is general education, not financial advice or a recommendation to buy or sell any security. Past volatility does not predict future results. For decisions about your own money, consult a licensed financial professional.