Five traders get together and decide to start a trading company, trading eachothers money. Each trader contributes 125k for a total of 625,000 Everyone's money is "locked in" for 1yr Everyone gets paid purly off their performance.
No, that is not a hedge fund. You're a proprietary trading company. If you're trading other people's money as well and each of them is an investing member in your firm, then that's still considered a prop trading firm. If you run people's money and they are not direct silent partners of the firm but are invested in the fund and the fund is run by the management company, then you are a hedge fund. The difference between a prop firm running other people's money and the way hedge funds are set up is relatively small, though.
Sounds like there are no sophisticated investors involved so you are definetly not a hedge fund. Prop shop, maybe, wear neon lycra each day and could be X-Men/Power Rangers Cygnus Atratus P.S. Please,Please,please see a lawyer that does securities law and have a proper structure in place and get independent back office people, trading can be stressfull enough on its own, without admin/legal headaches. It does not have to be a full Murex package, but a similar idea will save ur skin.