Abstract: Using Data Envelopment Analysis (DEA) to evaluate the performance of portfolios requires that the portfolio efficient frontier is continuous and concave. However, the efficient frontier on considering cardinality constraints may not be continuous or concave. Obviously, the direct use of DEA to evaluate the performance of portfolios with cardinality constraints is not reasonable. In this case, the definition of portfolio efficiencyis provided. Since the efficient frontier with cardinality constraints is a piecewise concave function, a numerical searching algorithm is put forward to obtain the sample segment points, which are used to group portfolios under cardinality constraints. The DEA model is then used to evaluate the performance of portfolios in each group. The simulation example indicates that, with the increase of sample size, the sample segment points converge to the real segment points, the DEA frontiers converge to the efficient frontier with cardinality constraints, the correlations between DEA efficiencies and portfolio efficiencies are becoming larger, which all indicate the feasibility and effectiveness of the proposed approach.

Key words: portfolio efficiency, cardinality constraints, efficient frontier, segment points search method, data envelopment analysis