Algorithmic hedge funds trade on statistical models successfully. I work for one at the moment, and over the long term they expect to make 15-20% per year. We have no traders and there's no intervention - it's purely the statistical model that determines how and when to trade.

So it can be done, but you need a brain the size of a planet. (I don't have a brain the size of a planet, so I don't build the models)