Robinhood Is Gambling on Babies, 401(k)s to Get Everyone Trading

On a recent nostalgia trip through the Stanford University campus, Vlad Tenev, class of 2008, now chief executive officer of Robinhood Markets Inc., pops by a coffee kiosk owned by one of his former fraternity brothers. Students mill around, oblivious to the billionaire founder in their midst. But Tenev is acutely aware of them, or at least what they represent to his popular brokerage app.

“We try very hard to always stay relevant to the next generation. We don’t want to get stuck just being, like, a millennial company,” says Tenev, who’s 38. “So, you know, I’m trying ...