Hedge funds are supposed to do what they say they will do. Some have the goal you stated and others do not. Most hedge funds are scams in that they figure to underperform reasonable benchmarks because of their high fees. Renaissance Technologies is one notable exception having averaged roughly 74 percent a hear before fees for over 20 years. Since the only investors left are the founders and key employees, the high fees of something like 5/45 are misleading. Renaissance has produced more billion than any business I know of Ray Dalio who has the world's largest fund has the goal you laid out and always has a bunch of un/low corelation bets. Tepper, Ackman, Druckenmiller (and the old Steve Cohen) are more likely to bet directionally on their opinions.
I'm pretty sure that these "annual earnings" include the rolled personal investment funds that those managers keep in the fund. Much of these "annual earnings" are due to compounded personal funds. From what I understand it's not necessarily the 2/20 management and performance fees generating those fantastic numbers.