In investing, you regularly hear that the odds are stacked against the little guy. How can you compete with a billionaire hedge fund manager who has access to better information, faster computers, and more analysts than you do?

One way: piggyback their trades. This is easier than some think. All investment managers with more than $100 million under management are required to report their portfolio holdings to the SEC every quarter. They're called 13-F filings. Track these filings closely, and you can see exactly what some of the world's best investors have been buying and selling.

Here are what four of them have been up to lately.

Warren Buffett (and other Berkshire managers)
As was widely reported earlier this week, Buffett's Berkshire Hathaway (NYSE: BRK-B) purchased a massive $11 billion stake in IBM (NYSE: IBM) over the past several months. Here's what Buffett told CNBC on Monday:

I don't think there's any company that's done a better job of laying out where they're going to go and then having gone there. They have laid out a road map and I should have paid more attention to it five years ago, where they were going to go in the five years ending in 2010. Now they've laid out another road map for 2015. They've done an incredible job. First, Lou Gerstner, when he came in, he saved the company from bankruptcy. I read his book a second time, actually, after I read the annual report. You know, "Who Said Elephants Can't Dance?" I read it when it first came out and then I went back and reread it. And then we went around to all of our companies to see how their IT departments functioned and why they made the decisions they made. And I just came away with a different view of the position that IBM holds within IT departments and why they hold it and the stickiness and a whole bunch of things.

Many have been shocked by the investment, as Buffett has famously steered clear of technology investments. I think there are two points to keep in mind. One, IBM is more of a consulting and service business than a technology business. Two, Buffett's avoidance of technology investments was never driven by a steadfast abhorrence of the industry; it was driven by a self-admitted lack of understanding -- something that can change and evolve with time and learning. Asked if the constant ridicule for avoiding tech stocks in the late 1990s bothered him, here's what he once told a group of reporters:

Nothing bothers me like that. You can't do well in investing unless you think independently. And the truth is, you are neither right nor wrong because people agree with you. You're right because your facts and reasoning are right. In the end that's what counts.

Berkshire also purchased new stakes in Intel, General Dynamics, and CVS Caremark during the quarter, but the positions were relatively small, likely coming from either Todd Combs or Ted Weschler -- two investors hired to manage money for Berkshire with the possibility of eventually succeeding Buffett.

David Einhorn
Einhorn, known best for shorting companies and making as much noise as possible about it, did a fair amount of buying in the most recent quarter, opening new positions in CBS and Legg Mason, and adding to his stakes in General Motors, Microsoft, and Apple (Nasdaq: AAPL), among others.

Here's what Einhorn had to say about CBS in his most recent letter to shareholders:

CBS stands to benefit from growing retransmission fees (payments) by cable operators for the right to carry CBS stations. We believe this income stream could amount to several hundred million dollars of new earnings to CBS annually. The company has also been early and aggressive in pursuing high margin incremental deals with online video streaming services like Netflix to monetize its content library. CBS will also benefit from a broader recovery in advertising markets and what looks to be a big upcoming political cycle. CBS is repurchasing stock and has reduced debt.

And GM:

GM is being priced by the market as a cyclical company trading at less than 6x this year's earnings. While some may see it as normal to value cyclicals at low multiples of peak earnings, we believe that 2011 is not a peak and, in fact, is below mid-cycle. Prior to the crisis, U.S. auto sales ran between 15 and 19 million units for many years. While sales have bounced from the recession low to about 13 million units, GM is poised to grow earnings from both a return to mid-cycle volumes, which we estimate to be 15 million units, and from a coming major refresh of its North American product portfolio.

David Tepper
Tepper, who made one of the largest Wall Street fortunes in history buying bank stocks in early 2009, dumped many of those bets -- and a sizable amount of his overall portfolio -- over the summer.

Tepper sold his entire position in Bank of America (NYSE: BAC) and Wells Fargo, while cutting back on his bet on Citigroup. He also exited Pfizer, Hewlett-Packard (NYSE: HPQ), Merck, and UnitedHealth, while trimming his stake in Microsoft.

It's hard to know exactly what happened, but this looks like unfortunate timing. Financial stocks had imploded in value when Tepper sold them this summer, likely erasing much of the gains earned in 2009 and 2010 that made him famous. Easy come, easy go.

John Paulson
Paulson, who also made billions buying bank stocks in 2009 after earning another fortune shorting the housing market, sold a good chunk of his financial bets during the quarter as well. Paulson sold about a quarter of his stakes in Citigroup and Wells Fargo, though he added to his giant bet on Bank of America. He also upped his positions in Alcoa (NYSE: AA) and MGM (NYSE: MGM).

Paulson was relatively unknown before scoring outrageous paydays from 2007-2010. That made some question whether he was truly a new hedge fund king, or a one-hit wonder. As of October, his main fund was down 32% year to date -- you can be the judge.