One of California's, and the nation's, biggest pension funds said Wednesday it will push companies to add more women to their boards and to disclose more about their carbon emissions, setting out strong markers for the 9,000 companies in its global portfolio.

In votes to be cast at upcoming shareholder annual meetings, the California State Teachers' Retirement System (CalSTRS) will vote against the entire board of directors at companies that do not have at least one woman, the $318 billion retirement system said in a press release.

It also will vote against nominating committee members of boards that are not at least 30% female. Those standards could especially pressure non-U.S. or European company boards, said Aeisha Mastagni, who oversees CalSTRS' stewardship strategies, in an interview.

"It's 2022 and we've been talking about the value of diversity for long enough," she said.

In addition, CalSTRS said it will vote against directors at companies that have not disclosed direct and indirect greenhouse gas emissions, known as Scope 1 and 2 emissions. A rule recently passed by U.S. Securities regulators, which must still be finalized, has similar requirements.

Some climate activists have also pressed companies to go further and to disclose emissions from suppliers and customers, known as Scope 3. Mastagni said that would be a good regulatory change but the first two types at least will help investors judge corporate emission reduction plans.

Mastagni said the new policies would likely increase the frequency of CalSTRS' votes against directors from 54% last year.

Other big asset managers such as Goldman Sachs also have called for more boardroom diversity and climate disclosures, as investors pour money into funds that use environmental, social and governance (ESG) criteria to pick securities.

CalSTRS is the second-largest U.S. public retirement system after the $476 billion California Public Employees' Retirement System. Both have helped push reforms such as last year's drive that elected dissidents to Exxon Mobil Corp's board.