The rule of 16: turning implied volatility or the VIX into a daily move
Implied volatility is quoted as a yearly number, which makes it hard to picture. The rule of 16 turns it into something you can use: divide implied volatility by 16 and you get the move the options market expects in a single trading day. A VIX of 16 means the S&P 500 is priced to move about 1% a day. A stock with 48% implied volatility is priced to move about 3% a day.
Why 16
Volatility grows with the square root of time, not in a straight line. There are about 252 trading days in a year, and the square root of 252 is 15.87, which rounds to 16. So a yearly volatility divided by 16 is a one-day volatility:
The answer is one standard deviation, the same measure this site uses for every expected move. On a normal day the stock should finish inside that move about two times in three, and outside it about one time in three.
Quick table
| Implied volatility (or VIX) | Expected daily move |
|---|---|
| 12% | ±0.75% |
| 16% | ±1.00% |
| 20% | ±1.25% |
| 24% | ±1.50% |
| 32% | ±2.00% |
| 48% | ±3.00% |
| 64% | ±4.00% |
| 80% | ±5.00% |
Weeks and months
The same square-root rule stretches to longer periods. A week is about 5 trading days and a month about 21, so:
- One week: divide implied volatility by about 7. A 48% stock is priced to move about 6.8% in a week.
- One month: multiply implied volatility by about 0.29. The same stock is priced to move about 13.9% in a month.
Notice that a month is not 21 times a day. Because volatility grows with the square root of time, a month is only about 4.6 times a single day.
How it lines up with the expected move on this site
This site counts calendar days, not trading days: the expected move from 8 days out is implied volatility times the square root of days divided by 365. Over a week or more the two ways of counting give almost the same answer (7 calendar days and 5 trading days differ by under 2%). For a single day they differ more, which is why expiries under 8 days away use the price of the at-the-money straddle instead. The straddle is what traders actually pay for the move, so it needs no day counting at all. The methodology page has both formulas.
Where the rule breaks
- Earnings and other events. An expiry's implied volatility spreads the earnings jump across every day to expiry. Dividing by 16 gives an average day, not the earnings day, which is usually much bigger. The earnings guide shows how to pull the event out.
- Which implied volatility. Each strike has its own. Use the at-the-money figure for the expiry you care about, not a blended or 30-day number, unless a 30-day number is what you want (the VIX is one).
- Real moves are lumpier. Quiet days are more common than a normal curve suggests, and so are very big days. Expect more moves of 3 standard deviations or more than the textbook 1 in 370.
- Options usually overestimate. Implied volatility tends to run above the volatility that actually follows, so stocks usually move a bit less than the rule of 16 says. Our track record measures exactly this for every stock we follow.
A useful second number
The rule of 16 gives one standard deviation, not the typical size of a move. If options are priced right, the average day's move, up or down, comes to about 80% of that figure. So a VIX of 20 implies a 1.25% standard deviation but an average S&P 500 day of about 1.0%. When you compare the rule with what actually happened, compare like with like: the average move against 80% of the rule, or the share of days inside the range against two in three.