When Barbara Krumsiek took over as chief executive of a socially responsible investment firm 20 years ago, she came in armed with a “game plan.”

She hired a personal coach to help her work through any challenges of transitioning to the top job. Krumsiek, who was hired by the board from another firm, met with all of her direct reports and asked them what they needed from her in order to succeed and what tasks they regularly performed at work that they felt weren’t accurately reflected in their job description.

At the time, female CEOs were relatively rare and so Krumsiek knew she would need to be extremely well prepared in order to make a good first impression. “It’s a slightly higher bar, there’s a spotlight on you,” she said.

But despite her efforts, Krumsiek wasn’t able to convince everyone to buy into her leadership, at least initially. Some of her direct reports reacted enthusiastically to her appointment, some appeared outwardly positive, but maintained some skepticism, and some were just altogether unsatisfied.

“I try not to make gender an issue, but I try to be aware that it may possibly be,” she said. “Women have to win over some folks.”

White male leaders become less helpful

New research adds some context to Krumsiek’s experience. When companies appoint a woman or person of color as CEO, white men, on average, don’t appear to react very well, according to a study set to be published in the Academy of Management Journal’s April issue. Instead, the examination of 1,000 executives working at large and mid-sized public companies found that top white male leaders tended to become less helpful to other workers — particularly women and people of color — after the appointment of a minority-status CEO.

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“They actually identify less, psychologically, with the organization after the appointment of a minority CEO and that reduces their propensity to help their colleagues,” said James Westphal, a finance professor at the University of Michigan’s Ross School of Business and one of the authors of the study. “Our theory is that the appointment of minority CEOs triggers biases.”

The research adds nuance to the well-documented challenges women and people of color face rising in the ranks in corporate America. Despite an increasing awareness among business leaders of the importance of diversity, women and people of color are still often subject to subtle or even outright bias in the workplace that can make it more difficult for them to ascend the corporate ladder.

The white male leaders don’t have much to worry about, if they do feel threatened by women of color at the top. As of January 2018, just 27 of the leaders of Fortune 500 companies, or 5.4%, are women and just three, or 0.6%, are black (all of whom are male). (The 2016 departure of Xerox XRX, -5.25% CEO Ursula Burns left zero black female CEOs running Fortune 500 companies).

Coping with that bias on a daily basis not only affects workers’ careers, it may even affect their health and overall well-being, according to a recent study on the emotional tax women of color face in the workplace from Catalyst, an organization aimed at promoting women in the workplace. Pay inequities, lack of visibility in top roles and other, more subtle forms of bias often mean these workers feel guarded, limiting their ability to contribute to an organization.

Some women leaders second-guess how they are perceived

“I just have a lot of grace in my position,” said Felicia Felton, a 39-year-old HR & safety manager at a manufacturing company in Michigan. As an African-American woman, she often finds she’s the only woman or black person in management-level discussions. And she’s cognizant of how stereotypes and long-standing biases may contribute to the way she’s perceived. “I have to constantly think about ‘I don’t want to be the angry black woman’ because I am the only black woman,” she said.

When women and people of color climb all the way to the top of the corporate ladder, they’re often not set up for success. Women and people of color are more likely to be promoted to the highest levels during times of crisis, according to a 2014 study on the phenomenon known as the “glass cliff.” If they can’t turn the firm around quickly, these leaders are swiftly replaced by white men, the study found.

The forthcoming study from the University of Michigan and University of Texas researchers provides insight into other reasons minority CEOs might struggle in their role. If white male leaders in the company react to their appointment by doing less to help their colleagues that could, ironically, wind up reflecting poorly on the new leader.

“That will ultimately make it more difficult for the CEO to implement their strategy more successfully,” said Westphal.

What’s more, women and minority workers at the company suffer disproportionately in this dynamic, meaning that the elevation of one under-represented person could wind up indirectly hurting the trajectory of other women and people of color. Westphal suggests companies do more to proactively make sure top leaders don’t react negatively — even subconsciously — to the promotion of a woman or person of color to head the company. One idea: nudge managers to reach out to white male leaders when a new CEO is appointed, to encourage them to keep helping their colleagues, he said.

For her part, Felton said she hopes to diversify the pipeline of future leaders in her industry by mentoring African-American women with an interest in the field. “There’s still a lot of work to do obviously to bring that diversity to so many different levels.”