Volatility is how widely and how quickly an asset's price swings. In finance it has a precise meaning. FINRA, the US broker-dealer regulator, defines it as "the annualized standard deviation of returns." A volatility of 60% means much larger typical swings than 15%. Volatility measures the size of moves only, not their direction. A highly volatile asset can rise sharply as easily as it falls.
Two kinds of volatility
Historical (realised) volatility
Historical volatility looks backwards. It measures how much returns actually varied over a past window, such as the last 30 or 90 days.
Implied volatility
Implied volatility looks forwards. FINRA describes it as "a measure of the expected volatility in the price of an underlying security" that is "calculated from current market options prices rather than from historical data." When traders pay more for options, implied volatility rises. This happens because the market expects bigger moves.
The two often differ. A quiet past month can sit alongside high implied volatility if traders expect an event, such as a policy decision or a data release.
How historical volatility is calculated
The usual method has four steps:
- Take daily closing prices and compute each day's return. Analysts often use log returns: the natural log of today's close divided by yesterday's.
- Compute the standard deviation of those daily returns over the chosen window.
- Annualise it by multiplying by the square root of the number of trading periods in a year. The common convention is 252 trading days for stock markets. Crypto trades every day, so 365 is common there.
- Express the result as a percentage.
The square root is there because variance grows in proportion to time, so standard deviation grows with the square root of time. The method assumes each day's return is roughly independent of the last.
Worked example. Suppose an asset's daily returns have a standard deviation of 2%.
- On a 365-day crypto basis: 2% × √365 ≈ 2% × 19.1 ≈ 38% annualised.
- On a 252-day stock basis: 2% × √252 ≈ 2% × 15.9 ≈ 32% annualised.
The same price history gives a different headline number depending on the convention. When you compare volatility figures, check which basis each one uses.
To go the other way, divide an annual figure by the same square root to get a rough typical daily move.
The VIX: the market's best-known volatility gauge
The Cboe Volatility Index (VIX) is the most widely quoted implied-volatility measure. Cboe describes it as "a leading measure of market expectations of near-term volatility conveyed by S&P 500 Index (SPX) option prices." In a post dated 24 April 2023, Cboe says the VIX tracks "constant, 30-day expected volatility" of the S&P 500. It adds that the reading is "a non-directional, annualized expectation for the standard deviation of the S&P 500."
Cboe gives its own example of how to read a level: "the VIX Index at 16 means an expected +/- 16% annual move for the S&P 500, which would equal a daily range of +/- ~1%." That is the same square-root conversion as above: 16 ÷ √252 ≈ 1.0.
The VIX says nothing about whether stocks will rise or fall. It shows only how large the market expects moves to be.
Volatility versus beta
Volatility and beta measure different things. In FINRA's words, "Beta measures how a stock moves relative to the market movement, not the total volatility of a stock." The benchmark index has a beta of 1. A beta of 1.2 means a stock has historically moved more than the index. An asset can be very volatile and still have a low beta if its swings are unrelated to the wider market.
How big is that daily swing in annual terms?
Enter a daily standard deviation of returns and the number of trading days in a year to see the annualised volatility.
| Standard deviation of daily returns | Trading days per year used to annualise | Annualised volatility |
|---|---|---|
| 2 % | 365 days | 38 % |
| 2 % | 365 days | 38 % |
| 2 % | 252 days | 32 % |
- The daily standard deviation and the day count are your own inputs, not figures from any source.
- The square-root rule assumes each day's return is roughly independent of the last.
This only converts a daily figure into an annual one: it does not compute the standard deviation from prices, forecast future moves, show direction, or say how much swing suits you.
Volatility and risk
FINRA's investor guidance puts the link plainly: "The more dramatic the swings, the higher the level of volatility—and potential risk." Volatility is not the same as the chance of permanent loss. It does mean a wider range of outcomes over a given period, including large drawdowns. Without price movement there would be no gains either. How much swing an investor can tolerate is a personal judgement, and this article does not give advice on it.
FINRA also warns that volatile markets attract fraud, including schemes promising "risk-free" returns.
Why crypto volatility behaves differently
Crypto assets are widely regarded as more volatile than broad stock indices. Research on how crypto interacts with traditional markets has changed that picture in recent years.
In a blog post dated 11 January 2022, IMF staff (Tobias Adrian, Tara Iyer and Mahvash S. Qureshi) reported these findings:
- The correlation between Bitcoin and S&P 500 returns was 0.01 in 2017–19. It "jumped to 0.36 for 2020–21, indicating the assets increasingly moved together."
- "Bitcoin volatility explains about one-sixth of S&P 500 volatility during the pandemic."
- "Bitcoin volatility explains about one-tenth of the variation in S&P 500 returns."
These figures cover 2017–2021. They show that crypto swings and stock-market swings became more connected in that period. They do not show how the two markets relate today.
Two practical differences also matter for anyone reading crypto volatility figures:
- Continuous trading. Crypto markets trade around the clock, so volatility is usually annualised on 365 days rather than 252. Stock figures and crypto figures are not directly comparable unless they use the same basis.
- No closing gaps, but no pause either. Stock markets can gap between one session's close and the next open. Crypto has no close, so large moves can happen at any hour, including weekends.
Volatility and leverage
Leverage multiplies the effect of every price move on the margin posted. This is simple arithmetic:
- With 10x leverage, a 5% move against a position equals a 50% loss of the margin.
- A 10% move against it can wipe out the full margin.
Leveraged positions are usually closed by liquidation before the margin reaches zero, once losses hit a maintenance threshold that varies by product. Higher volatility makes moves of that size more frequent and less predictable. This is why volatility matters more for leveraged derivatives than for unleveraged holdings.
Key points
- Volatility is the annualised standard deviation of returns. It measures the size of moves, not their direction.
- Historical volatility uses past prices. Implied volatility is drawn from option prices.
- The annualisation basis (252 or 365 days) changes the headline figure, so compare like with like.
- The VIX reflects 30-day expected volatility of the S&P 500. A reading of 16 implies roughly a ±1% daily range.
- Beta measures how an asset moves relative to a market, not its total volatility.
- Leverage scales the effect of volatility on margin.
Limitations: the crypto correlation figures come from a single 2022 IMF analysis covering 2017–2021 and may not reflect current conditions.
