The literature on the risk-return performance of equity portfolios depending on their ESG score is mixed. While most studies use some variant of Fama-French, we optimize equity portfolios of the NYSE between 2018-2019 according to the Markovitz mean-variance framework depending on their ESG scores to better reflect the behavior of financial agents. We then systematically analyze the optimal and efficient portfolio performance and find that high ESG portfolios have lower volatility and even lower returns, resulting in lower Sharpe ratios. The lower performance of high ESG portfolios is homogeneous across the three ESG components and robust across specifications.