Traditional DEA models and nonlinear (diversification) DEA models are often used in performance evaluation of portfolios. However, the diversification models are usually very complicated to compute except the very basic models. And the classic DEA models still need to be further justified and tested, since it is not clear whether they are over-linearised according to the diversification models. The existing studies on performance evaluation via the classic DEA models generally focus on the selection of inputs and outputs. In this work, we investigate theoretical foundation of DEA models for portfolios from a perspective of sampling portfolio. We show the classic DEA provides an effective and practical way to approximate the portfolio efficiency (PE). We further verify this approach through different portfolio models with various frictions and bounds on the market. Through the comprehensive simulations carried out in this study, we show that with adequate data sets, the classic DEA models can effectively sample portfolios to take into account sufficient diversification, and thus can be used as an effective tool in computing the PE for their performance assessments. This study can be viewed as a justification of the classic DEA performance assessments and the way to introduce other efficiency notions (like allocation efficiency, scale efficiency, etc) into assessment of portfolios.
