In my article last week on the "fat tail" distribution of stock returns, I took a look at what happens to a stock that has experienced the attack of a "5-sigma." As I noted, returns from stocks exhibit something known as a "fat tail" distribution, which means that normally unlikely outcomes happen more often than they should. Specifically, I looked at 5-sigma events, or events five standard deviations or more away from the mean -- events that normally have a 1-in-3,488,555 chance in happening.

When you're investing in the stock market, you have to be ready for these events, whether your stock is shooting skyward or plummeting faster than Denny Green's chances of coaching the Arizona Cardinals next year. The obvious follow-up questions, though, are:

  1. Can you predict a 5-sigma event coming?
  2. What happens to a stock after it has one of these huge moves?

I can see clearly now
If you're a regular reader of The Motley Fool, and perhaps a bit Foolish yourself, you probably know that Fools aren't too big on technical analysis. While some of us believe that it's downright alchemy, I tend to take the stance that it's just not my style. So my easy answer to predicting a 5-sigma move is "don't bother." I figure most people have as much chance of predicting this as they do of reliably predicting the next time the Green Bay Packers are going to win the Super Bowl (which some may say is a 5-sigma event in itself!).

If I'm dead wrong, though, and you can see these massive moves ahead of time, please, please let me know. Anybody who could do that could've turned $10,000 into $90,000 trading on Akamai's (NASDAQ:AKAM) 5-sigma moves over the past seven years. That's an 800% return on only seven trades!

Respond react
I figure the next best thing to being able to predict a 5-sigma event is knowing how to react to one. If I can't set up a system to key on 5-sigmas ahead of time, surely I can at least set one up to identify when a 5-sigma happens and then trade based on that. Unfortunately, at least based on the data I looked at, it doesn't look like this is a reliable system, either.

To check this out, I used some of the data I examined for my first article. This consisted of the price histories (as available from Yahoo! Finance) for the S&P 500, Akamai, OfficeMax (NYSE:OMX), Johnson & Johnson (NYSE:JNJ), First Marblehead (NYSE:FMD), and Best Buy (NYSE:BBY). In total, there were 133 5-sigma events from this group. From each 5-sigma move, I traced out 60 days and one year to track how well the stock did after it had the move.

Much to my chagrin, there was no reliable direction that prices headed after a 5-sigma for either 60 days or one year. Just slightly more than 50% of the observations reversed direction from the 5-sigma over the next 60 days, and just slightly less than 50% reversed directions in the following one-year period. Worse still is the fact that about 40% of the 60-day price reversals were double reversals and reversed direction again for the one-year period.

What's this mess mean? Basically, it means that it's fruitless to try to buy on every big drop or to sell on a big jump upward (or vice versa). In either case, you have about a 50/50 chance of being right, which are lousy odds no matter how you slice them.

What is interesting to note, though, is that, again based on this data, you can throw out the idea that you should buy a stock or avoid buying a stock based on a price spike in either direction. Back in November 2002, Akamai jumped 45.7% in one day. Time to sell? Hardly -- if you could put up with losing 21% over the next two months, you would've gained another 417% over the following year. Or maybe it was time to hop in on OfficeMax back in 2001 when it lost 10% in one day? Not so much -- it lost another 17% over the next 12 months. And there are just as many examples in the other direction as well -- if you took the cold plunge on Best Buy when it got smacked to the tune of 37% in one day back in '02, you would've been up 145% in the following year.

The human element
If you started reading this article hoping that I was going to give a sure-fire way to make serious money playing 5-sigma moves, you are probably now cursing me for gypping you out of your valuable time. Hold on a second there -- if you're a serious investor, you have to be ready to get your hands a little dirty!

The bottom line here is that you need to get past the price movement and figure out what caused it. Did the company just announce a great (or terrible) quarter? Is there legal action being taken against the company? Did it just announce a significant new product? If the catalyst for the move is something that makes the company behind the stock a more attractive business, it's probably worth your while to hang onto the stock, but if it's simply an overreaction to quarterly numbers, it could be time to grab your profit and call it a day.

I'd love a brainless, simple way to milk cash out of the stock market just as much as the next guy. Unfortunately, those opportunities simply do not exist. If you need a hands-off, autopilot way to invest your money, Vanguard offers a fantastic selection of index funds that will help you grow your money without having to pay much of anything in management fees. If you have the time and the desire to beat the market, though, why not get Foolish -- check out the new CAPS community, poke around the discussion boards, check out a trial of one of the newsletter services. We don't pretend to have any easy answers to outsized returns, but as David and Tom Gardner have shown, with a little elbow grease, you can make toast of the market.

Get your daily serving of sigma:

Akamai is a Motley Fool Rule Breakers selection. Best Buy is a Motley Fool Stock Advisor recommendation. Johnson & Johnson is an Income Investor pick. First Marblehead is a Hidden Gems selection.

When it comes to quant, Fool contributor Matt Koppenheffer is more Ferrell than Fibonacci, but his fascination with all that you can do in Excel is never-ending. He does not own shares of any of the companies mentioned. The Fool's disclosure policy always adds up.