SummaryThe new Basel III framework increases the banks’ market risk capital requirements. In this paper, we introduce a new risk management approach based on the unconditional coverage test to minimize the regulatory capital requirements. Portfolios optimized with our new minimum capital constraint successfully reduce the Basel III market risk capital requirements. In general, portfolios with value‐at‐risk and conditional‐value‐at‐risk objective functions and underlying empirical distribution yield better portfolio risk profiles and have lower capital requirements. For the optimization we use the threshold‐accepting heuristic and the common trust‐region search method.