How Can Index Funds Beat the Market?

Ben Stein loves Dimensional Fund Advisors. They "run the most amazingly successful, low-cost, unmanaged but somehow deep-value index funds I have ever found," he says, adding that "their returns are amazing, and they charge almost nothing." It's a bit weird: how can an index fund have "amazing" returns? Surely the whole point of an index fund is that it's more or less the same as the underlying index?

Michael Lewis has a huge article on DFA in the December issue of Portfolio, but even he seems a little unclear on exactly how Dimensional gets its returns.

If all financial advice is worthless and the only sensible strategy is to buy an index fund that tracks the market, why would anyone need a D.F.A. financial adviser? Why, for that matter, should anyone pay D.F.A. the 50 basis points it takes off the top of its oldest fund? D.F.A.'s answer to this is interesting: It can beat the index. The firm doesn't ever come right out and say, "We can beat the market," but over and over again, the financial advisers in attendance are shown charts of D.F.A.'s large-cap funds outperforming Standard & Poor’s 500-stock index and D.F.A.'s small-cap fund outperforming the Russell 2000.
In each case, the reason for D.F.A.'s superior performance is slightly different. In one instance, D.F.A. found a better way to rebalance the portfolio when the underlying index changes; in another, it came up with improvements in capturing small-cap risk. All these little opportunities can be (and are) rationalized as something other than market inefficiency, but they are hard to exploit, even with the help of D.F.A. The lesson of efficient-markets theory is that when anyone from Wall Street calls you up with financial advice, you should be very afraid. But it isn’t fear that prompts investors to embrace D.F.A. It’s greed.

It's a little more obvious why individual investors might choose DFA: they can talk to a human being who will reassure them on a regular basis that they're making extremely intelligent investment decisions. But the question of whether and how DFA manages to beat the market is still a very interesting one.

My theory, for what it's worth, is that most index-fund managers beat the market, but that they tend to keep the excess profits for themselves, rather than passing them on to investors. If you invest your money with Barclays or Vanguard, they will return to you the index, plus or minus a tiny fee. If they themselves make more than that, that's pure profit for them. Anecdotally, I've heard stories along these lines: that index-fund managers can be extremely aggressive in the pursuit of their own profits.

And then there's the whole issue of repos. An individual investor holding a basket of Dow stocks can't lend those stocks out to hedge funds. But a massive institutional investor can and does lend those stocks every day. Wouldn't you expect such lending activity to boost a fund's returns? Are repos the secret to making money running index funds? And if not, why not?