| The existing DEA portfolio performance evaluation researches have many insufficient in theoretical basises and practical applications,which lack of guidance in actual investment.The main limitations include the following several aspects:(1)The traditional DEA portfolio assessment literatures always regard the risk as input and expected return as output.However,in the actual investment,the input should be their own initial wealth,while the output should be the terminal value of portfolios held by investors.Obviously,the existing input-output processes of investment do not coincide with the actual situation.(2)Traditonal DEA cannot provide investors with practical and workable benchmark and investment strategy,since the benchmark provided by DEA are risk and expected return,whereas investors are still not clear how to adjust the asset allocation to achieve it.(3)The existing DEA portfolio evaluation researches generally assume that the asset returns with accurate parameter estimation,ignore the asset return parameter uncertainty.The actual investment environment is extremely complex,the characteristic parameters of the asset returns,such as mean and covariance matrix,are often difficult to accurately estimate,which also leads to the fact that there are large errors between the traditional DEA evaluation results and the actual performances.(4)Most of stock selection and portfolio optimization researches via DEA usually regard financial data as the input and output indicators to analyze the stock investment value.However,the listed company financial statement informations have the characteristics of information lag,especially the high-frequency trading is prevalence now,thus the tradtional stock selection and portfolio optimization method are lack of timeliness apparently.Along the above research background,the purpose of this paper is to provide theory and method supports for the application of DEA method in performance evaluation of portfolio,offer a new thought of modeling for investors to investment strategy optimization,provide some advices for individual investors/institutional investors to invest and control financial risks.Based on DEA approach,this paper mainly discusses the relative performance of portfolios under different situation,portfolio benchmark improvement and portfolio optimization.The main research results include the following aspects:Firstly,this paper systematically analyzes the input-output process of investment problem,and then constructs stochastic investment possibility sets and their deterministic estimations.Based on the deterministic estimations of stochastic investment possibility sets,the diversification DEA model and traditional DEA model with certainty parameter are constructed to evaluate portfolio performance,respectively.The relationship among diversification DEA frontier,traditional DEA frontier and the real frontier are discussed.Also,we prove that the diversification model and traditional DEA model are both convergence in theory.The simulation analysis shows that the evaluation models are applicability.It also provides theoretical support for the empirical analysis in this paper.In addition,we randomly select 50 open-ended funds from China fund market to verify the effectiveness and universality of the proposed model.Secondly,this paper firstly discusses DEA portfolio benchmark problem under the mean-variance portfolio optimization framework.We provide an iteration algorithm for improving DEA frontier and investment strategy,which provides investors with a realizable portfolio benchmark and the corresponding portfolio reblancing strategy.We design out-of-sample evaluation approach to test the portfolio rebalancing strategy whether has the role of benchmarking in the actual investment or not.These results show that the portfolio rebalancing strategy can improve the out-of-sample performance of original portfolio.In addition,this paper applies DEA portfolio benchmarking approach to discuss the performance evaluation of fund in China.We construct fund disclosure index of sustainable development,analyze influence of disclosure index of sustainable development to fund performance,put forward valuable investment suggestions for the fund managers,and also provide certain reference basis for our country to construct sustainable development green fund.Thirdly,this paper discusses the parameters uncertainty of asset retruns impact on portfolio evaluation results,combinates tradtional DEA model and the Bootstrap-DEA model,investigates the portfolio benchmark.Under the direction distance function measure,the Bootstrap-DEA portfolio evaluation model is constructed.Then,we design portfolio benchmarking approach to build a more robust DEA portfolio frontier,and provide investors with a more robustness and workable investment benchmark.The out-of-sample tests show that the portfolio rebalancing strategy consturcted here is more robustness in the actual investment.In addition,this paper combines the above portfolio benchmarking approach and the traditional portfolio optimizationl theory to build a new type of investment strategy.The empirical results show that the performance of constructed investment strategy is better than those of traditional investment strateges in the actual investment.Finally,this paper analyzes the individual stocks investment of input-output process strictly,constructs the corresponding DEA model based on the history of the stock price data,combines the relative efficiency value of assets acquired DEA and its historical returns to design different stock selection schemes.Under the different stock selection schemes,we include the DEA relative efficiency value of the assets into the investment strategy optimization and build a more useful investment strategy.The out-of-sample tests show that DEA-based investment strategy has better performance than those of traditional investment strategies,which also makes up for the limitation of the traditional investment strategy in out-of-sample evaluation,and enrichs the portfolio optimization theory partly. |
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