In the Romanian city of Cluj-Napoca, inside a garret up a narrow wooden staircase, four young men in T-shirts spend the day moving rapidly in and out of stocks, trying to ride their shifting momentum for profits. "It's very stressful," says one, dressed in a green T-shirt, blue shorts and Adidas sneakers. "The market is very hard to figure out."

The four traders are part of a world-wide network initially set up by a Toronto-owned firm called Swift Trade Inc. Swift's founder, Peter Beck, turned it into one of the largest day-trading...