We investigate the portfolio frontier and risk premia in equilibrium when an institutional investor aims to minimize the tracking error variance and to attain an ESG score higher than the benchmark's one (ESG mandate). Provided that a negative ESG premium for stocks is priced by the market, we show that an ESG mandate can reduce the mean-variance inefficiency of the portfolio frontier when the asset manager targets a limited over-performance with respect to the benchmark. Instead, for a high over-performance target, an ESG mandate leads to a higher variance. The mean-variance improvement is due to the fact that the ESG mandate induces the asset manager to over-invest in assets with a high mean-standard deviation ratio. In equilibrium, with asset managers and mean-variance investors, a negative ESG premium arises if the ESG mandate is binding for asset managers. A result that is borne out by the data.