The market has handed investors some nice, consistent returns over the long run, but in the short term, it can often be as unpredictable as an episode of Adventures in Hollyhood. In a pair of articles, I explored the market's so-called "fat tail" distribution -- the tendency of stocks to make huge moves that seem extremely statistically improbable. Since then, I've been following "five-sigma moves," or one-day price moves that are five standard deviations or more from a stock's average one-day change.

Keep in mind that we're looking at the price change relative to the stock's historical volatility, and not just the same old jittery "most active" stocks. So even though stocks like Ciena, Dendreon, and Solarfun Power saw some big movement last week, you're not going to see them on this list because of their higher average volatility.

Here's a taste of a few of the 5-sigmas from the past week:





CAPS Rating (out of 5)

Washington Group (NYSE:WNG)





CT Communications (NASDAQ:CTCI)










Advanced Medical Optics (NYSE:EYE)





Peru Copper (AMEX:CUP)





Sources: Yahoo! Finance, author's analysis, and CAPS as of June 1.

It's important to note that when I looked at stocks that made five-sigma moves in the past, they didn't always move in a predictable fashion following the event. In other words, not all of the stocks that jumped way up turned back down, nor did all of the stocks that fell through the floor start to bounce back up.

The key is to figure out whether the big move was due to a legitimate change in the company's fortunes, or whether it was simply investor overreaction. To get a better idea of which of these stocks might be worth a deeper look, I got some help from The Motley Fool's new CAPS investing community.

All hail King Copper
Last Tuesday, Peru Copper investors let out a deep sigh and collectively hit the sell button.

On May 24, the word was out that "Blue Horseshoe" (of Wall Street fame) was looking into Peru Copper. The company issued a press release after the close on Thursday, saying it had entered into an exclusivity agreement with an unnamed third party regarding the potential sale of the company. The stock shot up 10% the following day on volume that was roughly five times the three-month average.

As it turns out, Blue Horseshoe wasn't biting. The company followed up with a press release on Tuesday, stating that the exclusivity period had expired without producing a deal. Disappointment ensued, and the stock sank 20% on similarly high volume.

The company is still in the exploration stage, but it has generated some buzz because its primary mining target, copper, is so hot right now. As the price of copper itself soars, the stocks of copper-mining companies like Southern Copper (NYSE:PCU) have been consistently hitting 52-week highs. And with the massive $26 billion buyout of Phelps Dodge by Freeport-McMoRan (NYSE:FCX), Peru Copper shareholders certainly have reason to believe that their $660 million company could be a serious takeover candidate.

The company is currently working with UBS to figure out its next move. It claims it's keeping all of its options open -- in addition to considering an outright sale of the company, it's also mulling bringing in a partner to help with development of the Toromocho Project, or raising capital to do the development itself.

CAPS players have largely supported the stock and believe it could be worth a lot more than it's currently selling for. All-Star Jeffreyw posits:

Peru Copper is undervalued at $5/share. As copper prices and demand increase, the market will fairly value [the company] (around $10/share) or it will be bought by another company for close to fair value.

UofMNorthman also points out that the stock has a thin following on Wall Street and calls it "a diamond in the rough."

So far, 154 CAPS players have chimed in on Peru Copper, and there's always room for more. Take a stroll on over to CAPS and let the community know what you think of the opportunity at Peru Copper. And while you're at it, check out some of the other five-sigma stocks mentioned above -- or a few of the other 4,500 stocks on CAPS.

More CAPS Foolishness:

Fool contributor Matt Koppenheffer enjoys his weekly statistical rendezvous even more than he likes watching Computer and Big Triece mix it up on Hollyhood. He does not own shares of any of the companies mentioned. The Fool's disclosure policy knows it's Anacot Steel that Blue Horseshoe really likes.