Implied versus realized volatility
Lesson 13 · about 9 min
Implied volatility is what the market charges. Realized volatility is what the stock actually does. The difference between them, measured after the fact, is the profit or loss of every option position that was not purely directional. Understanding this gap is the difference between trading options and gambling with them.
Realized volatility
Realized (or historical) volatility is the annualised standard deviation of the stock's actual daily returns over some window, most commonly 20 or 30 trading days.
The calculation, so you know what the number is:
- Compute each day's log return: ln(today's close ÷ yesterday's close).
- Take the standard deviation of those returns over the window.
- Multiply by √252 (trading days in a year) to annualise.
If XYZ has moved an average of 1.3% per day over the last 20 days, its realized volatility is roughly 1.3% × √252 ≈ 20.6%. A quick mental version: annual volatility ≈ average daily move × 16.
The gap and who it pays
Options are priced on IV. Their value at expiration is determined by the actual path of the stock, which is realized volatility. So:
- If realized turns out lower than implied, options were overpriced. Sellers, on average, win. Buyers paid for movement they did not get.
- If realized turns out higher than implied, options were underpriced. Buyers win. Sellers collected too little for the risk.
On broad equity indices, implied has exceeded subsequent realized roughly 80% to 85% of the time historically, by a few volatility points on average. This is the volatility risk premium, and it is the reason systematic option selling has a positive long-run expectancy on average, and also the reason the losses, when they come, are concentrated in the 15% to 20% of periods when realized blows through implied.
On individual stocks the premium is smaller and less reliable, and around events it can invert badly.
A worked comparison
XYZ at $50, 30-day ATM straddle sold for $3.75 (IV 32%). Three scenarios for what XYZ actually does over the month, described by the realized volatility and the final price:
| Scenario | Realized vol | Path | Final price | Straddle value at expiry | Seller's P&L |
|---|---|---|---|---|---|
| Quiet | 18% | Small chop, drifts to $51 | $51.00 | $1.00 | +$2.75 |
| As priced | 32% | Moves around, ends $46.50 | $46.50 | $3.50 | +$0.25 |
| Wild | 55% | Gaps on news, ends $42 | $42.00 | $8.00 | −$4.25 |
In the "as priced" scenario the seller roughly breaks even, which is what "fairly priced" means. In the quiet scenario the seller keeps most of the premium. In the wild scenario a single month costs more than the previous two quiet months earned. That is the distribution premium sellers live with: many small wins, occasional large losses, and the whole thing only works if the small wins are numerous enough and the large losses are sized to be survivable.
For the buyer, the table is simply inverted, and the buyer's problem is that the quiet scenario is the most common one.
Key idea: Options are priced on implied and paid off on realized. Sellers profit when the stock moves less than priced; buyers profit when it moves more. On indices, implied has historically been higher than realized most of the time, but the exceptions are large.
Using the comparison before a trade
Before buying or selling premium, put IV next to recent realized:
| Situation | Reading | Lean |
|---|---|---|
| IV 32%, 20-day realized 18% | Market pricing a lot more movement than recent history | Selling premium has a cushion; buying needs a catalyst |
| IV 32%, 20-day realized 34% | Market pricing about what has been happening | No edge from volatility; direction has to carry the trade |
| IV 32%, 20-day realized 50% | Market pricing less movement than recent history | Buyers may be getting a bargain; sellers are underpaid |
The obvious warning: realized is backward-looking. A stock that has been quiet for 20 days and has earnings in 5 will show a low realized and a high implied, and the high implied is right. The comparison is a starting point for a question, not an answer.
Realized volatility and the daily breakeven
Module 3 gave the daily move a long option needs to cover its theta: roughly (2 × theta ÷ gamma)^½. For the 30-day ATM call that was about $0.89, or 1.8% of a $50 stock. Multiply by 16 and you get about 29%, near the option's IV of 32%. That is not a coincidence. The daily breakeven move for a long option is the daily move implied by its IV. A long option makes money on gamma when the stock's realized daily moves exceed the implied daily move, and loses to theta when they fall short.
So "should I buy this option?" is, on the volatility side, "do I think this stock will move more than 1.8% a day on average for the next month?" If the honest answer is "it has been moving 1.1%", the trade needs a reason to expect a change.
Try it: Pick a stock and compute its 20-day realized volatility from daily closes (a spreadsheet does it in one column). Compare to the 30-day ATM IV. Write one sentence on whether options look rich or cheap relative to recent movement, and one sentence on whether there is a reason (event, news) for the gap.
Recap
- Realized volatility is the annualised standard deviation of actual daily returns; roughly average daily move × 16.
- Sellers profit when realized comes in below implied; buyers profit when it comes in above.
- On indices, implied has historically exceeded realized most of the time (the volatility risk premium), with large, clustered exceptions.
- Compare IV to recent realized before any premium trade, and ask whether an upcoming event explains the gap.
- A long option's daily breakeven move is the daily move implied by its IV.
See it drawn
Original diagrams for the ideas on this page. Illustrative, not real market data.