A key problem is that portfolio managers, even of ESG funds, typically assign very little weight to a company’s climate performance, according to a comprehensive analysis (pdf) in August by economists at EDHEC Business School in France. The analysts found that market cap is still by far the most important factor in whether a company is included in a fund, and at what volume. Other “ESG” issues like equitable pay for female employees also tend to outrank climate considerations. The upshot, the report said, is that any climate-labeled fund not using climate data for at least half of its stock weighting determinations “should be considered to be at a significant risk of greenwashing.”

Ratings firms that assign the ESG scores underlying these portfolios also sometimes rely on a misleading interpretation of corporate data that is more concerned with how a company will be affected by climate change than vice-versa, according to a recent Bloomberg investigation.

But the green paint job may soon get a closer look from regulators: The US Securities and Exchange Commission is already investigating Deutsch Bank’s asset management arm over allegations that it may have overstated its products’ ESG credentials, and regulators in the US, Europe, and elsewhere are considering new rules for ESG disclosure and labeling.