Volatility comes in two flavours, and traders constantly compare them. Historical volatility tells you how much an asset has already moved. Implied volatility tells you how much the options market expects it to move going forward. The relationship between the two — and the gap that usually separates them — sits at the heart of options pricing, hedging, and volatility trading.
The VIX is the most famous implied-volatility measure: the market's expectation of 30-day S&P 500 volatility, distilled from a strip of index option prices. Knowing the difference between implied and realized volatility is the difference between reading the VIX as a forecast and mistaking it for a record of the past.
Historical (realized) volatility
Historical volatility (HV), also called realized volatility (RV), is purely backward-looking. It is the annualized standard deviation of past returns over a chosen window — 10, 20, 30, or more trading days. The steps are mechanical:
- Take daily logarithmic returns over the window.
- Compute their standard deviation (the typical daily dispersion).
- Annualize by multiplying by √252 (the approximate number of trading days in a year).
The result is a single percentage describing how turbulent the asset actually was. It contains no opinion about the future; it is simply a measurement. Because it is computed from data, two analysts using the same window and the same prices will get the same number.
Implied volatility
Implied volatility (IV) is forward-looking and is extracted from option prices. Option pricing models link an option's market price to an expected level of future volatility; solving the model in reverse — given the price, what volatility is "implied"? — produces IV. When options are expensive, IV is high; when they are cheap, IV is low.
The VIX generalizes this idea across many strikes rather than a single option. Instead of inverting one contract, it aggregates a wide range of out-of-the-money S&P 500 puts and calls into one 30-day, annualized expectation of volatility. The full methodology is covered in how the VIX is calculated. Other indices apply the same logic to different horizons and underlyings, which is why the VIX has cousins such as VIX9D and VVIX — see VIX vs VVIX and the broader VIX-related indicators.
Side-by-side comparison
| Attribute | Historical / Realized (HV/RV) | Implied (IV) |
|---|---|---|
| Definition | Annualized std. dev. of past returns | Future volatility implied by option prices |
| Direction in time | Backward-looking (a measurement) | Forward-looking (an expectation) |
| Data source | Past price history | Current option market prices |
| Objectivity | Objective — same inputs, same output | Market-set — shifts with supply/demand for options |
| Example metric | 20-day realized vol of the S&P 500 | The VIX (30-day implied vol of the S&P 500) |
| Primary use | Risk measurement, benchmarking actual moves | Pricing options, gauging expected moves, sentiment |
| Who watches it | Risk managers, quants | Option traders, hedgers, volatility traders |
The volatility risk premium: the gap between them
Compare IV today against the RV that actually unfolds over the following month, and a pattern emerges: implied volatility usually sits above subsequently realized volatility. That persistent spread is the volatility risk premium — effectively an insurance premium that option buyers pay and option sellers collect.
- When IV > subsequent RV (the common case), sellers of options and short-volatility strategies tend to profit, because the protection turned out to cost more than the danger that materialized.
- When RV > IV, buyers of options win, because an unexpected shock made realized moves larger than the market had priced.
This is the structural reason inverse-volatility products like SVXY can grind higher in calm markets, and why they get hurt in shocks — explored in UVXY vs SVXY and how to read the VIX. The shape of IV across strikes adds another layer; that asymmetry is the subject of volatility skew.
Worked example: turning VIX into an expected move
Because the VIX is an annualized percentage, you scale it to shorter horizons by dividing by the square root of the number of those periods in a year. This is the "square-root-of-time" rule.
VIX of 16 → expected S&P 500 moves
- Monthly: 16 ÷ √12 ≈ 16 ÷ 3.46 ≈ 4.6% one-standard-deviation move over the next month.
- Daily: 16 ÷ √252 ≈ 16 ÷ 15.9 ≈ 1.0% typical daily move.
- Interpretation: in roughly two-thirds of months, the index would be expected to finish within ±4.6% of where it started — if the VIX forecast is accurate.
These are one-standard-deviation estimates, not guarantees. They describe the market's expected dispersion; realized moves can and do fall outside the band, especially in the tails. To compare this implied figure against what actually happened, you would line it up against realized volatility over the same window — precisely the IV-versus-RV comparison this page is about.
Common pitfalls when comparing the two
The IV-versus-RV comparison is powerful, but it is easy to misread. A few cautions:
- Mismatched windows. Comparing a 30-day implied figure like the VIX against 10-day realized volatility is apples to oranges. Line up the horizons before drawing conclusions.
- Backward-looking RV lags. Realized volatility is a trailing average, so it rises only after turbulence has already occurred. It will always confirm a shock late, never predict it.
- IV is a risk-neutral expectation, not a forecast. The volatility embedded in option prices includes the risk premium, so it is systematically a touch above the market's true best guess of future movement. Treat the VIX as "expectation plus insurance cost," not a pure forecast.
- Single numbers hide the smile. One IV figure averages across strikes. The way IV differs strike by strike — cheaper calls, pricier downside puts — is itself information; see volatility skew.
Used carefully, the spread between what was implied and what was realized is one of the cleanest reads on whether options are rich or cheap, and on whether the market over- or under-estimated the danger ahead.
Putting it together
Historical volatility is the scoreboard; implied volatility is the betting line. Skilled volatility traders watch the spread between them rather than either number alone. A high VIX is only "expensive" relative to the realized volatility that follows it, and a low VIX is only "cheap" if turbulence is actually coming. For how the VIX relates to the index it forecasts, see VIX and S&P 500 correlation. This is educational information, not investment advice.
Frequently asked questions
What is the difference between implied and historical volatility?
Historical (or realized) volatility measures how much an asset's price actually moved in the past, calculated as the annualized standard deviation of its returns. Implied volatility is forward-looking: it is the volatility the market expects in the future, backed out from current option prices. The VIX is a well-known implied-volatility measure, representing the market's expectation of 30-day S&P 500 volatility.
Is the VIX implied or historical volatility?
The VIX is implied volatility. It is derived from the prices of a wide strip of S&P 500 index options and expresses the market's expectation of 30-day forward volatility, annualized. It is not calculated from past S&P 500 returns, which would be historical or realized volatility.
Why is implied volatility usually higher than realized volatility?
On average, implied volatility tends to sit above the volatility that subsequently occurs. That persistent gap is the volatility risk premium: option buyers pay extra for protection against uncertainty, and option sellers demand compensation for bearing tail risk. When realized volatility ends up exceeding what was implied, it is usually because an unexpected shock arrived.
How do I convert VIX into an expected daily or monthly move?
The VIX is an annualized percentage, so divide by the square root of the number of periods in a year. For a rough daily move, divide by the square root of 252 (about 15.9); for a monthly move, divide by the square root of 12 (about 3.46). For example, a VIX of 16 implies roughly a 1% daily move and about a 4.6% one-standard-deviation monthly move in the S&P 500.