When Carol Bartz became the chief executive of Yahoo in 2009, her appointment was less seen as evidence of a corporate breakthrough for women than as evidence of another trend: the "glass cliff."

This phenomenon, coined by researchers, describes how women are recruited disproportionately into tough jobs, where the title may be big but the odds of success are quite small. And Yahoo was certainly that: The company was struggling to grow and diversify, its stock price was suffering, and within the past year it had navigated a failed acquisition offer from Microsoft and an attempt by investor Carl Icahn to replace its board. At the time, Yahoo's chairman called her "the exact combination of seasoned technology executive and savvy leader that the board was looking for."

Then, like a comparatively high ratio of female CEOs, Bartz was fired. (Over the phone, many will recall.)

Strategy&, the consulting firm formerly known as Booz & Company, released its 14th annual Chief Executive Study earlier this week, and it found that women are more often forced out of CEO jobs than men who hold the same position. The study showed that over the past decade, 38 percent of female chief executives who left their positions were sent packing (rather than leaving due to a retirement or merger), compared with 27 percent of male CEOs.

Gary Neilson, one of the study's co-authors and a senior partner at the firm, says his findings show something new about women's so-called glass cliff. "We don't think it's so much that they're put into challenging roles than that they're more often outsiders," he says.

His report discovered that women CEOs are comparatively more likely to hail from outside the company than their male peers are. Thirty-five percent of female chief executives between 2004 and 2013 were outsiders, compared with just 22 percent of men. (The study looked at incoming and outgoing CEOs over a period of 10 years for the world's 2,500 largest public companies, resulting in a sample of more than 100 women at the top.)

Being CEO as an outsider "is a tougher job," Neilson says. "They don't have as many connections in the company to understand how things work, and their performance is not as high" as those who've been groomed in-house. Research has shown, for instance, that external CEOs are 6.7 times more likely to be dismissed with a short tenure than homegrown ones.

While there are plenty of notable female CEOs who did rise through the ranks — just look at GM's Mary Barra, IBM's Virginia Rometty or PepsiCo's Indra Nooyi — Neilson says many companies still lack enough female senior executives just beneath the CEO level who are ready to take on the job.

"Maybe this is the chicken-or-the-egg thing," Neilson says, "but more women CEOs are outsiders because companies can't find them inside their own companies, or they may find them but they're not ready. So they go pick them off another company."

That should, of course, improve with time. Neilson's study found that in eight of the last 10 years, the share of women becoming CEOs has been higher than the share of those leaving the position. While women made up just 3.6 percent of new CEOs in 2013, the authors predict in their report that as many as a third of incoming CEOs will be female by the year 2040.

A greater focus on helping such candidates could accelerate that trend, Neilson says. "You can only steal so many other people" from other institutions, he says. "Companies need to move down a more aggressive path [on internally developing] women who may be quite capable leaders."

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