Today we begin a series examining three high-growth stocks that have quadrupled in two years in the Motley Fool Rule Breakers portfolio. First up is NYSE Group (NYSE:NYX), which was profiled by David Gardner in the February 2005 issue and is currently up 356% since then.

The investment thesis
NYSE Group joined David's rebellious band as Archipelago Holdings, which, fittingly enough, was causing the New York Stock Exchange more than a little trouble. As David wrote in the initial report:

"Archipelago's business, primarily its management of the largest electronic stock market, ArcaEx, puts it in direct competition with the NYSE. Archipelago has been getting in the Exchange's hair for some time now, and is now a public company with a successful stock. Rules are being broken."

And cash was flowing. In the three years leading up to its selection for the portfolio, Archipelago had grown revenue by an average of 15.3% a year. Meanwhile, cash on hand improved from $51 million in 2002 to approximately $173 million by early 2005.

Fighting the good fight proved to be fruitless for the NYSE. So, three months after David first singled out Archipelago, the masters of the Big Board bid $400 million to join forces with their upstart rival.

Why he still holds
But the stock's run hasn't stopped. By March 2006, the shares had improved 270% from the original Rule Breakers buy-in price. What drove the gains? Technology. NYSE's chief executive said at the time of the merger's completion that electronic trading would dictate the future of the brokerage business. ArcaEx, it turns out, had no peer.

And yet more opportunity awaits, if you believe David. He envisions massive consolidation in which just a handful of exchanges will manage trillions in daily trading. Actually, he puts it more elegantly than that. Here's an excerpt from a post of his on the Rule Breakers message boards, reacting to the news that the Chicago Mercantile Exchange (NYSE:CME) agreed to pay $8 billion to merge with the parent of the Chicago Board of Trade, CBOT Holdings (NYSE:BOT):

"I really do believe this will continue with the logical end in sight being a worldwide global market. There may always be small offshoots in small countries, say, or something like 'The Philadelphia Stock Exchange,' but the consolidation of markets is a trend I would bet on."

Find your four-bagger
Statements like that last one sum up what Rule Breakers is all about: Identifying big trends and the firms best positioned to cash in on them.

That was Archipelago. Superior technology -- unique to its industry -- combined with superior management to capture more than 3% of the trading volume of the NYSE and 22% of the Nasdaq Stock Market (NASDAQ:NDAQ) before the firm was acquired. Electronic trading was shaking the foundations of the stock trading business; logic dictated that returns would follow.

And they have. As you embark on your own quest for the next four-bagger, remember the lessons of Archipelago. Don't just speculate. Instead, seek leaders with obvious and identifiable advantages in important and growing markets. In the past decade, (NASDAQ:AMZN), Starbucks (NASDAQ:SBUX), and eBay (NASDAQ:EBAY) have been three prime examples of this strategy at work. These are the kind of firms that have transformed thousands into millions.

For more on NYSE Group, or to see every Rule Breakers recommendation to date, click here to get 30 days of free access to the entire portfolio right now.

Fool contributor Tim Beyers only breaks the rules in his portfolio. Wimp. Tim didn't own shares in any of the companies mentioned in this article at the time of publication. Get the skinny on all of the stocks in Tim's portfolio by checking his Fool profile. Amazon, Starbucks, and eBay are Motley Fool Stock Advisor picks. The Motley Fool's disclosure policy is a rebel on Wall Street.