High priests have ways to keep a good gig to themselves … magic rites, forbidden knowledge, and secret terms. It doesn’t matter whether they are psychiatrists, witch doctors or investment analysts.

In our field—investments—we’ve been considering the secrets of volatility. 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.

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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.

By the way, this volatility that we just unraveled is for the S&P 500 index itself. You could do the same for the Dow or any other index. You can do exactly the same thing for any stock. But be clear, this is NOT the oft-quoted VIX, which hogs the news. The VIX is found with the same kind of math, but it measures the movement of options on the S&P 500 index. Options are much more volatile than stocks, and unlike many others, I do not consider VIX nearly as valid a market indicator as regular volatility. But we’ll do VIX tricks some other time.

But the question is, why would we want to know this kind of “standard deviation” volatility, anyway? As it turns out, the volatility is interesting and very useful if you are planning short-term trading or options trading.  For us, it is the standard deviation itself that is the better focus, because it is significant. Very significant.

It all comes back to the good, old “bell curve.”  While individual stocks, not to mention the market as a whole, are somewhat less than perfect copies of theory, they do behave with pretty fair predictability that we can turn to our own uses. Very often, how much a stock returns is related to its standard deviation.

Source: Russell

On the grand scale of the S&P 500, this relationship has held up well over decades. About 68% of returns fell within one standard deviation of the mean, and 95% of the time returns were within two standard deviations.

For stocks, the relationship is a little flukier, but still very sturdy. This is why technical analysts like to look at Bollinger bands. They are lines on stock charts that are drawn exactly one standard deviation above and below a moving average.

I use Bollinger bands a lot. First of all, they tell me what range a stock is likely to move in. Second, they tell me if a movement exceeds the range of its standard deviation, and that matters because big moves are often followed by an opposite reaction.

But hey, that’s enough for this section. Let’s move on to the next article, and I’ll show you. I’ve been hinting that there’s a volatility tool with some predictive power—this is the one.

To sum up, we have a new volatility definition:

“Volatility” unless otherwise noted usually means annualized standard deviation68% of market returns tend to fall within 1 standard deviation of the mean95% tend to fall within two standard deviationsThe standard deviation changes as the stock or index becomes more or less active, but “historical volatility” is normally calculated from the past 60 days. Other periods may be used as well.

Respectfully,

Lynn Carpenter

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