How does the quantitative hedge fund Two Sigma make money?

Can’t speak for Two Sigma, but if they operate like most hedge funds, they collect annual fees and a performance fee based on …. their performance. This allows investors to invest with a hedge fund, the fund manager uses their capital to place bigger trades and both the investor and hedge fund profit, assuming all goes according to plan.

Of course, there are all sorts of problems if the hedge fund loses investor money (either -40% or all of it) or even in the hedge fund underperforms the overall S&P 500.

I recommend you look at a hedge funds performance NET of all fees and compare them to other hedge funds in a similar instruments (stocks/options, bonds, futures, etc) and compare them to the buy and hold of the S&P 500 (if you invested in $SPY on your own without fees).