‎Data envelopment analysis (DEA) is a methodology widely used for evaluating the relative performance of portfolios under a mean–variance framework‎. ‎However‎, ‎there has been little discussion of whether nonlinear models best suit this purpose‎. ‎Moreover‎, ‎when using DEA linear models‎, ‎the portfolio efficiency obtained is not comparable to those on the efficient portfolio frontier‎. ‎This is because a separable piecewise linear boundary usually below the efficient frontier is considered the efficient frontier‎, ‎so the model does not fully explore the possibility of portfolio benchmarks‎. ‎In this paper‎, ‎and with use of the dual-Lagrangian function‎, ‎we propose a linear model under a mean–variance framework to evaluate better the performance of portfolios relative to those on the efficient frontier‎.