So far, it’s been all plain English. But the witch doctors aren’t going to let us off that easily. We’ve seen volatility as a matter of “jumpiness” visible to the naked eye, as dollars and cents (ATR), as percent (Zigzag), as a relationship to an index (beta) and finally we come to “plain” volatility. And in the way of witch doctors, it turns out that plain old volatility is the most complicated version yet. Well, it’s time to bust their game.

Here’s something to get you started. The volatility of the S&P 500 is 20% at present. That seems pretty clear. It would mean that the S&P goes up and down by 20%, no?

Hah! Gotcha! Would you believe around 1.2% a day, but only on days when the market is open, not all year? The volatility that you hear quoted is actually an annualized daily standard deviation. Don’t faint. You have just read the hard part, and we’re not going to let the geeks wear us down.

Plain volatility, also called historical volatility or actual volatility is just a number that summarizes average daily movements then translates them to an annual basis with some standard statistical maneuvers.

Just a quick aside here, this current volatility level is very high, as you can see in the following chart of S&P volatility from 1928 to 2000:

To put this new volatility concept in simple terms, we’ll use some recent history. Lately, the S&P has had an average closing price of 1407. Some days it was higher, some it was lower. I could figure out how much it deviated from the average each day with simple math. If the average is 1407 and it closed at 1403, there’s a 4-point difference that day. I could even add up a series of deviations and figure out how much the average deviation is.

A standard deviation is pretty much the same simple process with frosting on top. Instead of doing the math straight, the statistician squares each deviation (4 x 4 =16, for instance), adds all these squares up, figures the average of that number, then “unsquares” the answer—that is, he takes the square root of his squared average.

There you have it, “standard deviation,” which sounds expensive, but is really nothing more than a simple average done with squares of numbers instead of the unadorned numbers.

Such a drill on the S&P lately would lead you to 1.2% daily standard deviation. To get from there to the stated historical volatility this daily variation is hocus-pocused one more way. It is annualized. (If you really want to know how…. the statisticians would take the number of trading days in a year, say 250, find the square root of that number and multiply it by the standard deviation.)

And thus, 1.2% a day or so in average movement, in either direction, turns into 20% stated volatility.