All the money in the world can’t get you into some of the world’s best hedge funds.

Multibillion-dollar funds operated by Renaissance Technologies LLC, PDT Partners, WorldQuant LLC, Two Sigma Investments LP and other computer-driven “quant” firms have generated market-beating returns for years, according to people close to the firms, sparking heated investor interest. Renaissance’s Medallion fund, for example, has averaged annual gains of more than 35% since 1990, and was up about 10% this year through July 20, the people...