The first woman to run a Wall Street firm could be a behavioral scientist, a mathematician or an engineer.

Three women with these backgrounds—Karen Peetz, president of Bank of New York Mellon; Mary Callahan Erdoes, chief of asset management at JPMorgan Chase; and Avid Modjtabai, head of consumer lending at Wells Fargo—are all currently within striking distance of the CEO suite.

Then again, none of them may get there. After all, no woman has ever been CEO at one of the 22 largest U.S. investment banks or financial firms, and none of these three female executives wanted to speculate on her chances.

Women have been close to the top of Wall Street firms before, only to get derailed or swatted away. Both Zoe Cruz, president of Morgan Stanley, and Sallie Krawcheck, head of Citigroup Global Wealth Management, lost their jobs following the financial crisis. Ina Drew, another contender, left JPMorgan Chase in 2012 amid the London Whale scandal. And earlier this year, Ruth Porat, Morgan Stanley’s chief financial officer, whom many considered a potential CEO, said she would instead decamp to Google for a $70 million paycheck.

Banks have certainly come a long way since the 1980s, when Goldman Sachs apologized after a Stanford University student said one of its recruiters asked her if she would have an abortion to save her job. Many banks now employ diversity chiefs and brag about affinity groups, parental leave, return-to-work programs, and Lean In Circles.

“I see more banks looking into increasing the level of senior women,” says Elisabetta Bartoloni, a partner at headhunting firm Heidrick & Struggles. They’re motivated in part by studies that have shown having diverse management helps companies achieve better results, she says.

But talk is cheap, and Wall Street’s woman problem runs deep. So deep, in fact, that it begins even before recruiting starts.

Consider this: 34 percent of MBA graduates are women. That’s up from 28 percent in 2002 but still far below the near parity in other fields such as medicine and law, according to the Forté Foundation, a consortium of business schools and companies, including Citigroup and Goldman Sachs. (An MBA is still a prerequisite for many investment-banking jobs.) And only about 20 percent of those female business school graduates say they’d even consider a career in financial services, compared with 36 percent of men, according to research by Universum Global. What’s more, that disparity has been increasing in recent years.

Selling women on a career in investment banking should begin as early as their freshman year in college, says Elissa Ellis Sangster, head of the Forté Foundation. “You’ve got to build the pipeline early,” she says.

When women do apply for banking jobs, they’re just as likely to get them as men are, says Matthew Bidwell, a professor of management at the University of Pennsylvania’s Wharton School who has studied gender in finance careers. However, he adds, “women are less likely to apply because they see that ‘there’s nobody like me’ at the senior levels.”

As women move to the middle ranks, things start to get even trickier. That’s when what’s called the leaky pipeline becomes especially evident, Bidwell says: “It’s not feeding them through quickly to the highest levels.”

One common explanation is that women drop out of Wall Street in their 30s to start families. That’s not borne out by reality, says Pamela Stone, a Hunter College sociology professor. In a study Stone co-authored last year, which looked at 25,000 Harvard Business School MBAs, only about 11 percent of women actually left their jobs to stay home with children. More often than not, Stone says, women at investment banks saw few opportunities for advancement and moved to other fields that let them have more of a life. “They need stay policies, not leave policies,” says Stone.