A share trades at $184 with 32% annualised volatility. What is a one standard deviation daily move in dollars, and what would a two sigma day look like?

A share trades at $184 with 32% annualised volatility. What is a one standard deviation daily move in dollars, and what would a two sigma day look like?

Approach: Convert the annual figure to a daily percentage by dividing by the root of the number of trading days, then apply that percentage to the share price.

$3.68. Divide the annual volatility by 16 to get the daily volatility, since the square root of time factor sqrt(252) is 15.87 and 16 is the working approximation: 32%/16 = 2.0% a day. Two percent of $184 is $3.68, so that is the one sigma move. Using the exact sqrt(252) gives 32/15.8745 = 2.016% a day, or $3.71, so the shortcut runs 0.8% low, which is well inside the error on the volatility input itself. A two sigma day is $7.36, and under a normal assumption a move of that size or larger arrives on about 4.6% of days, so roughly one trading day a month.

Follow-up: The stock gaps $11 overnight. How many standard deviations is that, and what frequency does the normal model assign to it?

Key concepts: daily volatility, square root of time, one sigma move.