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  Indra K. Nooyi. Marissa Mayer. Ellen J. Kullman. Irene B. Rosenfeld. Meg Whitman. Mary T. Barra.
  
  What do these women have in common? They are the chief executives of some of the nation’s largest companies: PepsiCo, Yahoo, DuPont, Mondelez, Hewlett-Packard and General Motors. But they also share something else. In recent years their companies have been targeted by activist investors and other vocal shareholders seeking to make changes.
  
  Is that a coincidence?
  
  While women have made strides in cracking the glass ceiling, they still account for a small fraction of chief executives at public companies. Only 23 women lead companies in the Standard & Poor’s 500-stock index. Yet at least a quarter of them have fallen into the cross hairs of activist investors.
  
  What could explain this phenomenon? Are companies led by women truly more likely to be poor performers in need of change? Or do activist investors — all of them men — see women as softer targets?
  
  Patricia Sellers, a senior editor at Fortune magazine who runs the magazine’s Most Powerful Women franchise, recently raised the question online, “Does Nelson Peltz have a problem with women?” Mr. Peltz, a longtime activist investor, has singled out Ms. Nooyi of Pepsi, Ms. Kullman of DuPont and Ms. Rosenfeld of Mondelez.
  
  Starboard Value, another activist fund, has set its sights on Yahoo and Ms. Mayer. J. Kyle Bass, the investor who predicted the subprime mortgage bubble, has been publicly pressing Ms. Barra at G.M. to increase its dividend, which she did last week, but not by as much as Mr. Bass was seeking. Ms. Whitman of HP put Ralph V. Whitworth on her board in 2011, in part to keep him from waging a proxy contest against the company.
  
  It goes without saying that activist investors have mostly waged campaigns against male chief executives because of the dearth of women at the top ranks of large companies. Of Mr. Peltz’s 28 activist investments in companies since his fund’s inception, only three have been run by women. That means 89 percent have been led by men. And not all activist investors can be lumped together. For example, the activist investor Daniel S. Loeb pushed to install Ms. Mayer as C.E.O. of Yahoo after dislodging the existing chief executive, a man.
  
  Still, the anomaly remains, raising the question of whether activists are singling out companies led by women.
  
  Every activist investor I asked about this was outraged by the very question, insisting that a company’s performance, not the sex of the chief executive, was the only factor in their calculus to pursue an investment or activist campaign.
  
  Depending on how you slice the data, over the last several decades companies led by women have, at times, outperformed their peers — and at other times they have underperformed, with no clear trend. Still, some studies have shown that gender diversity at the top of companies generally leads to increased performance. (Other studies suggest female chief executives are more risk-averse, which may make them more likely to outperform their male counterparts in an economic downturn. But it is hard to generalize given the small sample of female C.E.O.s.)
  
  There may be a subconscious gender bias among activist investors, supported by recent research.
  
  Academics at the University of Utah and Washington University in St. Louis conducted a study published in 2012 in which they showed a prospectus for an initial public offering to a group of 222 M.B.A. students, 45 of whom were women. One group was shown the prospectus with a male chief executive listed as leading the company. The other group was shown the same prospectus, but with a woman listed as the C.E.O.
  
  The outcome was all too predictable. “Despite identical personal qualifications and firm financials, female founder/C.E.O.s were perceived as less capable than their male counterparts, and I.P.O.s led by female founder/C.E.O.s were considered less attractive investments,” the study found.
  
  Researchers have also shown that executives who are women may be expected to be more likely to compromise and less likely to fight, which, for an activist seeking a role on the board, may make it a more attractive target.
  
  Sheryl Sandberg, the chief operating officer of Facebook, recently pointed to a study at Yale University about the role of gender and power. “Social role theory states that because men and women occupy different social roles, they behave in predictably different ways in line with these roles. Specifically, because women are more likely than men to be in nurturing roles (e.g., mother, caretaker), they may behave in ways that are more communal and less aggressive,” the study said.
  
  The researchers found “that a female C.E.O. who talked disproportionately longer than others in an organizational setting was rated as significantly less competent and less suitable for leadership than a male C.E.O. who talked for an equivalent amount of time. Importantly, this effect was found among both male and female perceivers.”
  
  It is also true that more women are fired from top positions than men. A 2013 study conducted by a unit of PricewaterhouseCoopers found that “among C.E.O.s leaving once over the past 10 years, a higher share of women have been forced out than men (38 percent of women vs. 27 percent of men).”
  
  So perhaps subconscious perceptions and cultural attitudes are tilting the scales of investors. Or, activist attention on female C.E.O.s is now akin to being treated like one of the boys.
  
  When I approached several female chief executives to get their opinions, none wanted to discuss it, whether on the record or off. They suggested that women should be judged on their merits and didn’t want to play into any sort of gender narrative.
  
  Still, one chief executive, before she quickly hung up, said: “You’re onto something.”