The Environment Agency Pension Fund (EAPF) has become the first scheme to commit its investments to the international target to limit global warming to two degrees.
A shareholder resolution forcing Chevron to halt spending on high-carbon assets has been rejected by 96% of shareholders.
Stranded carbon assets, poor staff management and concerns over working conditions pose significant financial risks to companies, Standard Life Investments (SLI) warns.
UK pension funds' approach to carbon holdings and sustainability risks is "very varied", ShareAction chief executive Catherine Howarth says.
The Prince of Wales has called on pension funds to use their power as institutional investors to bring environmental, social and governance (ESG) issues into mainstream investment.
Investors have exposed themselves to a $6trn (£3.9trn) "carbon bubble" by failing to address sustainability, research says.