Only one woman named CEO of a major company in North America in 2015

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Just four percent of S&P 500 CEOs are women. Only 19 percent of those companies' board members are women.

Yet even among the discouraging stats about the number of women in corporate leadership roles, this one stands out: Exactly one of the 87 new CEOs named to lead the largest public companies in the United States or Canada in 2015 was a woman, according to a new report.

The study, released Tuesday by the strategy consulting division of PwC, examined the 2,500 largest global companies and found that among the 359 permanent or interim CEOs named in 2015, only 10 of them - worldwide - were female. At 2.8 percent of all new CEOs, that's the lowest rate since 2011, according to the study.

In the United States or Canada, PwC said, the rate of new female CEOs declined for the third year, and dipped to its lowest point since 2004, when PwC began tracking the number. Just 1.1 percent of the new CEOs named to the job last year were women in PwC's analysis of North American companies — down from 4 percent in 2014, 4.7 percent in 2013, and 7.3 percent in 2012. (The distinction, PwC said, went to Andrea Greenberg, who was named CEO of MSG Networks in September after it was spun off from Madison Square Garden.)

At a time when the issue of gender diversity seems to be gaining more attention than ever — investors are pushing for it, companies are disclosing more data on it, and Sheryl Sandberg has sparked the whole "Lean In" moment — the numbers come as something of a surprise. "We were very surprised as well," said Per-Ola Karlsson, a partner with PwC, in an interview. "It was definitely a step back."

So what explains the decline? There's not an easy answer, Karlsson said. At least in the United States, the decline doesn't appear to be due to a lopsided number of CEO changes in certain industries traditionally dominated by men, such as energy or utilities. While that may have contributed to the decline in the global figure, he said, the industry mix in North America has held steady.

It's also not likely due to more companies turning outside for their next CEO, a trend the study examines. If anything, PwC's research shows that women chief executives are more likely to be recruited from the outside than male CEOs. While it may be a sign companies are anxious to cast a wide net and consider women for the top job, Karlsson said, it also means "companies themselves have failed to develop their own female candidates."

The most likely explanation is simply the law of small numbers. While the number of CEO turnovers wasn't much different from past years, the extremely low number of women who continue to get the top job means the percentage can easily swing from one year to the next. While Karlsson thinks this year's U.S. number is a "fluke," he says, "the trend we see in North America is obviously discouraging."

There was a bright spot in the study for female leaders: From 2004 to 2015, outgoing female CEOs were 27 percent more likely to be have been forced out of their jobs than men. In 2015, there was no statistically significant difference between the two. Perhaps the "glass cliff" — the phrase given for how often women are put into jobs with a high chance of failure — is getting less steep. The glass ceiling, meanwhile, seems very much intact.