While the debate rages, the new financiers are building up piles of money not seen since the heady days of the Internet boom. But unlike the wealth of many dot-com billionaires, who saw their fortunes collapse with the technology bubble, the gains of hedge funds are not simply returns on paper that fluctuate with the direction of the stock market. Instead the gains are huge cash payouts that most managers then reinvest in their funds, betting that they will continue to beat the markets.

Image James Simons, left, earned $1.7 billion in 2006, more than any other hedge fund manager. Kenneth Griffin, right, made $1.4 billion. Credit... J.N. Bowles/Bloomberg News, right

Still, the performance of these managers is as varied as their strategies, ranging from complex computer models to the more old-fashioned version of betting the farm on a few stocks. None of the managers contacted for this article returned calls or would comment.

For its rankings on compensation, Alpha magazine includes the managers’ share of the firm’s management fees, usually 2 percent, and performance fees, or a share of the profits, which typically start at 20 percent.

That structure means that some hedge fund managers can still earn a huge income even with mediocre returns because of the huge size of the assets under management. Raymond T. Dalio, head of Bridgewater Associates, which has more than $30 billion in hedge fund assets, for example, took home $350 million last year even though his flagship Pure Alpha Strategy fund posted a net return of just 3.4 percent for the second consecutive year.

The magazine also includes gains made on hedge fund managers’ own capital in their funds. Mr. Simons, for instance, has more than $1 billion of his own money invested in his funds.

Topping Alpha’s list for the second consecutive year, Mr. Simons, a former code breaker for the Defense Department, uses computer-driven models to detect pricing anomalies in stocks, commodities, futures and options.

Even though he has some of the highest fees in the business — 5 percent of assets under management and 44 percent of profits — he trounces most of his competitors year after year. In 2006, the $6 billion Medallion fund posted gross returns of 84 percent; 44 percent after fees, explaining his $1.7 billion take.