The Rule of 16

Question

Implied volatility on a stock is 24% annualized. What one-day move is that pricing in, in percent? State the conversion rule, say where the magic number comes from, and name the most common way people misuse it.

Accepted Answer

The rule of 16. Volatility scales with the square root of time (variances add across independent days; vols don't). With 252 trading days in a year, sigma_textdaily = fracsigma_textannualsqrt252 approx fracsigma_textannual15.87 approx frac24%16 = mathbf1.5%. So 24 vol means the market prices a one-standard-deviation daily move of about 1.5%. The magic number is just sqrt252 approx 15.87, rounded to 16 because traders convert in their heads all day: vol 32 means 2% days, vol 16 means 1% days, vol 80 means 5% days. Two refinements worth volunteering: - A 1-sd move is not the "expected move". For a normal distribution the average absolute move is mathbbE|Z| cdot sigma approx 0.8,sigma, so 24 vol implies typical daily moves around 1.2%, with 1.5% being the one-sigma marker (about a third of days should exceed it). - Use trading days, not calendar days. Dividing by sqrt365 approx 19 understates the daily move; variance accrues when markets trade (weekends contribute little, which is also why desks mark vol around weekends and holidays). The misuse: treating the 1-sd move as a ceiling ("vol is 24, so it can't move more than 1.5%"). It's a distribution, not a budget; roughly one day in th

The Rule of 16

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