Some investors are finding that companies with more women in top positions outperform. Now they're starting to wonder: How much does a female CEO add to market returns?

On one hand, a company led by a woman has reached the pinnacle of corporate diversity efforts, but on the other hand, some investors worry that women are too frequently appointed to helm struggling companies, running off the "glass cliff." Market returns bear out both points, showing that female CEOs frequently deliver strong performance, but are often handed a difficult job to start.

"It's the cynical view," said Alison Cook, a management professor at Utah State University, who has studied the glass cliff. Women may take a tough job because it's one of their only opportunities, while men may avoid it because they know "their chances of succeeding and being the hero are slim," she said.

To be sure, in 2016, it's still rare for a woman to helm an S&P 500 company. Only 5 percent of the companies in the index had a female CEO, according to data compiled by Bloomberg.

But the debate is taking on new significance as investors pour millions of dollars into funds and indexes with strategies based on corporate diversity. In the six months through June, assets linked to equity and debt products with a gender-based strategy climbed 150 percent to $560 million, according to investment firm Veris Wealth Partners.

The Pax Ellevate Global Women's Index Fund, backed in part by former Citigroup Inc. and Bank of America Corp. executive Sallie Krawcheck, reached over $100 million in assets this year. The fund invests primarily in companies that have at least 30 percent women on their boards and 25 percent women in senior management. In the two years through Aug. 31, the fund's institutional class shares returned 2.36 percent, compared to the MSCI World Index's 1.13 percent return over that period. "It's the least crowded trade with the most evidence," Krawcheck said in an interview.

Even Pax is struggling with whether companies that have women in the very top spot should get extra credit. When selecting companies for the fund, Krawcheck only gives companies with a female CEO a "smallish" benefit, compared to the weighting for women on boards or in senior management overall. The weighting in part reflects Krawcheck's own experience in the top echelons of Wall Street.

"There is, to my mind, absolutely no doubt that there's a glass cliff," Krawcheck said, noting she was brought into Citigroup as CEO of Smith Barney at a time when the business was struggling and the company needed a "different" approach. Women CEOs, are often asked to do an "impossible job" she said, citing the experience of CEOs like Yahoo! Inc.'s Marissa Mayer and General Motors Co.'s Mary Barra.

Female CEOs do tend to outperform according to data compiled by Bloomberg. Of the 16 female CEOs in the S&P 500 index who have held the job for at least three years, 75 percent have outperformed the index since they took over. That group includes PepsiCo Inc. CEO Indra Nooyi and Lockheed Martin Corp.'s CEO Marillyn Hewson.

Still, companies that appoint female CEOs often are underperforming. Almost 38 percent of the S&P 500 companies where women outperformed, had negative market returns in the year before she started or in her first year, according to data compiled by Bloomberg.

A 2015 Utah State study found that of the 52 female CEOs of Fortune 500 companies appointed between 1955 and 2014, 42 percent took over during a crisis or market downturn. That compares to 22 percent for a matched sample of male CEOs.

"It's a challenging question: Are females hired only when companies are doing worse, so they have a greater opportunity for outperformance?," said Karen Rubin, vice president of product for online trading algorithm development platform Quantopian Inc.

Rubin has been working since 2013 on an algorithm that tests investment in female CEOs. The strategy uses an equal-weighted portfolio that buys shares of a Fortune 1000 company when a female CEO is appointed and sells them when she leaves. The portfolio outperformed the S&P 500 index by 217 percent from 2002 to 2014.

"Historically, had you invested in female CEOs, you would have outperformed the market," Rubin said.

The results weren't just surprising to her, and observers have suggested that there could be other reasons behind the outperformance. So, she removed Yahoo from the test to see if the returns could be explained by the company's investment in Alibaba Group Holding Ltd. The portfolio still outperformed the S&P 500 by 197 percent. In another attempt, she removed consumer companies to respond to a critique that women were more likely to be CEOs in that sector, which has been performing well. She found the portfolio still outperformed the S&P 500 by 153 percent.

Women CEOs are often aware of the potential pitfalls of the cliff, said Trina Gordon, CEO of executive recruitment firm Boyden World Corp. in Chicago, and they tend to do a huge amount of due diligence before accepting the role. "They turn over every stone," Gordon said. "Female CEOs are very calculated risk-takers."

It's also possible that diverse CEOs are more sought after by struggling companies, because they possess leadership skills that are particularly valuable for a turnaround. "In a time of crisis you want someone who has that more consensus-building, participatory-type of leadership," Utah State's Cook said.