By Bill Snyder | Stanford Business contributor

CEO salaries are higher than ever. But finding the right person to fill that job is harder than ever, especially when a board must replace a visionary founder.

The market for top-flight talent is now so tight that nearly 100 directors of Fortune 250 companies estimate that fewer than four people -- including those both inside and outside their company -- would be capable of stepping into the CEO role today and running it at least as well as their current CEO, according to a survey by researchers at Stanford Graduate School of Business and the Rock Center for Corporate Governanceat Stanford University.

"I have never seen the CEO labor market tighter. With traditional industries such as retail, restaurant, and packaged goods under such pressure to transform, the pool of available candidates is small. There is no such thing as 'stepping' into a CEO role," one of the directors told the researchers.

"These findings have profound implications for talent development and CEO compensation," says David Larcker, the James Irvin Miller Professor of Accounting at Stanford Graduate School of Business, who led the research. "How you groom senior executives, how you plan for a CEO transition, and how you structure CEO pay really hinge on just how available replacement talent is."

The survey, conducted this summer, queried 113 directors and 18 executive recruiters and compensation experts.

Tightening Pipeline

The shallow pool of top-flight talent was evidenced by the difficulty major companies, including Symantec, General Electric, Walt Disney, and Uber, have had replacing their chief executives, says Nick Donatiello, a lecturer in corporate governance at the business school. Walt Disney, for example, recently extended the contract of CEO Robert Iger for another year as it struggles to fill the top job. Symantec has gone through four CEOs in the past decade. "Frankly, there is a lot of pressure on directors to get it right. This likely results in directors being risk averse, which of course only serves to narrow their view of who might be acceptable," says Nicholas Donatiello, one of the researchers in the study.

The directors were also asked how difficult it would be for their company's major competitor to find a new CEO: Sixty-eight percent said fewer than five people could fill the job, and when it comes to finding a CEO to turn around a troubled company in their industry, 58% said the choice was also limited to five.

Finding a qualified CEO is more difficult in some industries and types of companies than others.

"Visionary founders" such as Amazon's Jeff Bezos, Elon Musk of Tesla, and Warren Buffett of Berkshire Hathaway would be harder to replace than CEOs of large, well-established public companies, the directors indicated.

They said that just two people could replace Bezos, and three could replace Buffett or Musk. But the talent pool likely includes 15 people who could replace David Taylor of Procter & Gamble or IBM's Virginia Rometty, while 14 people would be qualified to fill the shoes of Mary Barra of General Motors or Ian Read of Pfizer.

While it's not surprising that it is more difficult to replace a founder than a professional CEO, the difference between the two is surprisingly large, the researchers commented.

Finding qualified high-level executives is by far the most challenging in the technology industry, followed by traditional retail, financial services, and the automotive sector, the directors indicated.

Impact on Pay

Although the survey did not deal directly with executive pay packages, the talent shortage and soaring compensation are obviously related issues, says Larcker. "These numbers [of qualified CEOs] are shockingly small and put issues such as CEO compensation in an entirely new light. If only a limited number of people are qualified to run large public companies, it helps to explain why today's pay packages are so large," he says.

But money may not be enough incentive to compensate for the stress of today's management jobs. "It is one of the most extreme roles out there today and becoming less desirable based on the political landscape. A person taking the job for the money is going to fail as CEO," said one of the directors in the survey.

Whether big salaries are the best way to corral talent isn't clear and wasn't the point of the survey, notes Brian Tayan, a researcher at the business school. "We're not saying high compensation levels are efficient, but if directors perceive the talent pool as very tight, they're not likely to let $1 million be a barrier."

Since CEO tenure is decreasing and the pool of available CEOs is small, directors need to be certain that their companies have real succession plans in place and that they take care to groom less senior executives for higher-level jobs, Larcker says.

The clear consensus of the directors surveyed was that the corporate environment moves faster and is less forgiving of mistakes in selecting the CEO than in the past. As one respondent said succinctly: "Talent is scarce, the job is tough, and the runway for success narrower every day."

This story first appeared on Insights by Stanford Business.