基于机会约束随机Index-DEA的投资组合效率评价

传统DEA和分散化DEA是两种常见的非参数评价方法，二者也被广泛应用于投资组合效率评价。已有相关研究通常将风险和期望收益视为投资组合的投入和产出指标，但该投入-产出假设与实际投资过程并不吻合。在实际投资过程中，真实投入应为投资组合的初始财富，产出则是其终端财富。基于新的投入-产出假设，本文对投资组合初始财富进行标准化，将终端财富转化为收益率形式，进而构造随机生产可能集和相应的机会约束随机Index-DEA模型。当投资组合收益率服从联合正态分布时，随机Index-DEA模型被转化为等价的确定性模型，从理论上证明该等价模型的凸凹性，并提出相应的求解算法。最后，利用该随机Index-DEA模型对我国30只开放式基金进行效率评价，验证所提出DEA模型和求解算法的有效性。

Estimation of Portfolio Efficiency Using a Chance-constrained Stochastic Index-DEA Approach

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.