Do activist investors see female CEOs as easy targets?

That's the question raised by a recent New York Times story, which notes that of the 23 female S&P 500 CEOs, "at least a quarter" have been targeted by activist investors.

Three of those six women are battling one investor in particular--Nelson Peltz. A Fortune story delves into his activities and interests, asking, "Does Nelson Peltz have a problem with women?" Peltz is currently targeting PepsiCo, Mondelez, and Dupont, all of which have female CEOs. The Times says that 89 percent of Peltz's targets have been men.

There's another explanation besides gender, though, at least in the case of some of these CEOs. Perhaps women CEOs become the targets of activist investors not because they're women, but because women are more likely to be appointed to a CEO position when a company is already in hot water.

This phenomenon, known as the "glass cliff," was first identified by two psychology professors at the University of Exeter, Michelle Ryan and Alexander Hasam. "Women are more likely to be appointed to leadership positions that are associated with an increased risk of criticism and failure," write the pair on their web site. Specifically, their research shows that women are more likely to be installed in positions of leadership already associated with poor company performance.

If Ryan and Hasam's research is correct, it would stand to reason that women CEOs would be more likely to be targets for activist investors. In many cases, those investors were probably already chomping at the bit before the women became CEOs.

This does not seem to hold true for the three CEOs targeted by Peltz. Indra Nooyi, CEO of PepsiCo, took over a firm in relatively good shape but with its share of challenges. Irene Rosenfeld, it can be argued, was master of her destiny, spinning out Kraft’s international operations and then choosing to spin herself out with them, becoming CEO of the newly-created Mondelez in 2012.

Ellen Kullman's situation is a bit muddier: DuPont shares had been sliding for more than a decade when she took over DuPont in 2009, and quickly rebounded under her leadership.

But Mary Barra's predicament at GM is a textbook example of the glass cliff. When Barra was appointed CEO in December 2013, the company had recently emerged from a government bailout and was in the midst of an investigation over a faulty ignition switch that would eventually be blamed for 52 deaths.

Yahoo's troubles were just as well known. When Mayer came on board, she became the company's fifth CEO (if you count one whose title was interim CEO) in less than four years--hardly a sign of corporate health and stability. Just by staying at the helm for two and a half years, she's achieved a longer tenure than any of her four most recent predecessors.

Meg Whitman didn't exactly inherit a walk in the park at Hewlett-Packard: analysts openly carped about her selection, and her September 2011 appointment followed followed the brief tenure of Leo Apotheker, who had the dubious distinction of being the third HP CEO to be let go in six years.

Of course it is possible that activist shareholders might, on some level, think they'd be in for an easier or at least different kind of battle with a female CEO than with a male one. But in the cases of GM, Yahoo, and HP the gender of the CEO seems unlikely to rank very high on a list of investor's concerns.