In 1999, Philippe Laffont opened a small tech hedge fund called Coatue that withstood the dot-com bust, thanks to smart investments in companies like Tencent and Apple. Today, he is one of the industry’s hottest managers—with $17 billion under management. 

Now, Mr. Laffont and his brother Thomas are making another big bet: a $700 million fund to back startups raising their earliest rounds of funding. It’s a massive fund on par with the biggest venture funds in the industry. It will inject major new capital into the industry. But it faces high expectations. To make money on a fund, you have to make back the money you spent and then some.