A mere 5 percent of the chief executives of the world’s biggest companies are women. And they are more likely to be sacked than their more numerous male colleagues

Consulting firm Strategy& (formerly Booz & Co.) reports that 38 percent of the female CEOs who left their jobs over the past 10 years were forced to go, compared with 27 percent of the men. This is the latest finding from the research on top management at the world’s 2,500 largest public companies that Strategy& has been conducting since 2000.

A clue as to why women are more likely to be fired than men is provided by another statistic in the study: 35 percent of female CEOs are hired from outside the company, compared with just 22 percent of male ones.

Outsiders generally have a higher chance of being kicked out, and generate lower returns to shareholders. Businesses that are already troubled are more likely to turn to outsiders; and outsiders are less likely to have a support network of friends who can rally around them when times get tough.

Michelle Ryan, an organizational psychologist at the University of Exeter in England, says women face nothing less than a “glass cliff” — they get their best shot at the top job by taking the helm of a firm in trouble. In practice, outsiders of either sex face the same precipice. But since women are still fairly exotic creatures in the C-suite, they attract disproportionate publicity when they hit problems.

Carly Fiorina, dropped as HP’s boss in 2005, made things worse by inviting such publicity. But the same is not true of, say, Ginni Rometty, the lower-profile boss of IBM (promoted from within the company in 2012), who is under fire over the firm’s performance.

The new research is not entirely pessimistic. Over the past 10 years the balance of incoming vs. outgoing female CEOs, as a proportion of all changes of boss, has risen significantly. Strategy& predicts that women will make up as many as a third of incoming CEOs by 2040.

It appears that the demand for female bosses exceeds supply — hence firms’ willingness to bring them in from outside. This points to an obvious solution: Companies should work harder on creating a pipeline of female future CEOs. This would reduce both the pressure to raid rival firms and the chances of women failing when they at last reach the top.

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