Abstract: Traditional DEA and diversification DEA are two common nonparametric evaluation approaches, which are widely used in the estimation of portfolio efficiency. However, the existing studies have generally regarded the risk and expected return as the input and output indicators of portfolios, which is obviously inconsistent with the actual investment process. Actually, the input should be the initial wealth of portfolio, while the output should be the terminal wealth. Under this input-output framework, this paper unitizes the initial wealth of portfolios, converts the terminal wealth into the form of return rate. Further, the stochastic production possibility set and the chance-constrained stochastic Index-DEA model are both constructed. When the return rates of portfolios follow a joint normal distribution, the stochastic Index-DEA model can be transformed into an equivalent deterministic DEA model. The convexity of the equivalent model is proved theoretically, and the corresponding algorithm is also provided in this paper. Finally, the chance-constrained Index-DEA model is applied to evaluate the efficiency of 30 growth open-ended funds in China, so as to verify the effectiveness of the proposed model and algorithm.

Key words: chance-constrained; index-DEA; portfolio; efficiency evaluation