It isn’t just your imagination: activist hedge funds do go after companies led by woman CEOs more often.

That’s a fact, borne out by new research. But the underlying causes are less clear, although female CEOs look as if perhaps they do a better job representing their investors in activist campaigns.

Also true: female CEOs whose companies are targeted by activist hedge funds themselves do worse out of the deal. They lose more in total compensation and are more likely to be replaced than their male peers, found Bill Francis and Qiang Wu of Rensselaer Polytechnic Institute and Yinjie Shen of Cleveland State University.

Activist hedge funds, which take stakes in companies and then push them to adopt new strategies or even new management, have become a massive force in financial markets, controlling more than $120 billion and launching two-thirds more major campaigns against companies with large market caps in the first half of this year compared with the same period last year.

A notable number of activists have taken after female-led companies, such as Carl Icahn’s 2015 stake in then-CEO Ursala Burns’ Xerox or Nelson Peltz’s run at Indra Nooyi’s PepsiCo.

The data backs up the impression formed by anecdote.

“Using a comprehensive dataset, we first confirm that activist hedge funds indeed regard female CEOs as preferred targets,” the study's authors write.

In a given year, a female CEO has a 5.7 percent chance of her company being targeted by activists, 54 percent higher than the 3.7 percent incidence for male CEOs, the data shows. The study, which covered 2003 to 2014, examined more than 2000 hedge fund activist events.

As of now, just over 5.2 percent of Fortune 500 company CEOs are woman.

The raw numbers actually understate the extent to which female CEOs face activist campaigns. An exercise matching female CEOs to male ones with similar work and company characteristics found they were actually 78 percent more likely to face an activist campaign on an apples-to-apples comparison.

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