# Standard Deviation

A statistical measure of price fluctuation. In volatility trading, standard deviation is often used to measure how stock price movements are distributed around the mean.

A statistical measure of price fluctuation. One use of the standard deviation is to measure how stock price movements are distributed about the mean. See also Volatility.

The square root of the mean of the squares of the deviations of each member of a population (in simple terms, a group of prices) from their mean. In a normal distribution (or bell curve), one standard deviation encompasses 68% of all possible outcomes.

It’s important to note, this is about options, not statistics. But you’d probably hear standard deviation a lot in a room full of options traders, so let’s clarify its meaning.

If we assume stocks have a simple normal price distribution, we can calculate what a one-standard-deviation move for the stock will be. On an annualized basis the stock will stay within plus or minus one standard deviation roughly 68% of the time. This comes in handy when figuring out the potential range of movement for a particular stock.

For simplicity’s sake, here we assume a normal distribution. Most pricing models assume a log normal distribution. Just in case you’re a statistician or something.

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