Companies with at least 30 percent women in leadership roles may boost their net profit margins by about 15 percent compared with those with no female leaders, according to a new report by the Peterson Institute for International Economics and EY.

The study, which examined data from about 22,000 companies in 91 countries, found the biggest gains took place when women were in the so-called C-suite, holding senior executive positions such as chief financial officer or chief operating officer. Companies run by a woman chief executive officer without other women in the C-suite or on the board of directors don’t perform particularly better or worse than male-run firms, the study found.

“Women in positions of leadership are associated with superior corporate performance,” said Marcus Noland, Peterson’s executive vice president and director of studies. “The most important finding of the study is the importance of having a pipeline” of women at the top.

Adding women to a board of directors had some effect on profitability, although it wasn’t “robust,” he added. But, the report said, “a more gender-balanced board might show greater interest in encouraging a more balanced executive team.”

The research considered 13,000 profitable companies, which had a median net profit margin of 6.4 percent, and found that the margin increased by more than 1 percentage point, or about 15 percent, when women filled at least 30 percent of leadership roles.

This effect was “even more striking” when unprofitable companies were included in the analysis, the report said. The combined 22,000 companies had a median net profit margin of just over 3 percent; those with 30 percent women in top roles posted profit margins as much as 6 percentage points more.

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Noland said that the more women present in leading roles, the higher a company’s profit margins appeared to be. But there’s no determining how many women are the optimal number, he said.

“We haven’t found the point of diminishing returns yet because we just don’t have any firms where there are lots of women,” he said.

Looking at women on boards, the report said, “there is no evidence that board quotas have any significant impact, positive or negative, on company performance.” One criticism of such quotas is that they could create the “golden skirt” phenomenon, where a scarce number of qualified women are stretched among multiple board positions. In quota countries such as Iceland, Norway and France, about 9 percent of women served on multiple boards, compared with 7 percent of men.

Still, both of those percentages were well below the average for all countries, where 13 percent of men and 12 percent of women sat on two boards. “Golden skirts are no more prevalent than golden pants,” the report said.

The Peterson Institute, a Washington-based non-profit that studies international policy, was named after Peter G. Peterson, former chairman of Lehman Brothers and co-founder of the Blackstone Group, in 2006. Previously it was the International Institute for Economics.