Research On Technical Efficiency Evaluation Methods And Applications For Portfolios On Considering Market Frictions

Within the classical framework of economics, the definition of technicalefficiency of portfolio is proposed based on the portfolio frontier. However, inpractice, the portfolio optimization models are usually very complicated, and thus theanalytical solutions of the frontiers are very difficult to obtain. By using riskmeasures as inputs, return measures as outputs, under the assumption that the realfrontier is a concave function, we adopt DEA model to evaluate technical efficienciesof portfolios, and extend this approach for evaluating the technical efficiencies ofportfolios on considering market frictions. We study three kinds of models onconsidering transaction costs, trading constraints and margin constraints, respectively.Transaction costs include linear transaction costs, the V-shape transaction costs andpiece-wise linear transaction costs. Trading constraints include the upper and lowerbound constraints, total volume of trading constraints. Margin constraints includecash deposit constraints and mortgage constraints. According to the correspondingportfolio optimization models, the technical efficiencies of portfolios on consideringdifferent market frictions are defined. Based on the proof that the productionpossibility set is convex, we adopt DEA models to approximate the real frontiers andevaluate the technical efficiencies of portfolios on considering market frictions.We use the definitions(based on the real frontier) and the DEA models(based onDEA efficient frontier) to evaluate technical efficiencies of portfolios on consideringmarket frictions, respectively. The results of these two approaches have greatcorrelation, and the correlation increases with the increase of the number of decisionmaking units, indicating that DEA models are reasonable and feasible.