Research On DEA Models And Applications For Portfolio Evaluation On Considering Moment Characteristics

This thesis constructs DEA models to evaluate portfolio based on momentcharacteristics, considering the effects of the moment characteristics on theinvestment decisions. According to portfolio models, we select secondmoment(variance), third moment(skewness) and fourth moment(kurtosis) as theinput-output indexes to build production probable sets and DEA models, making themodels with theoretical basises and economic significances. Based on mean-varianceDEA evaluation model, we put lower semi-third moment instead of skewness,resolving the non convex programming problem that always exists and meeting thethird moment portfolio model’ frontier for concave function. So we can set upcorresponding DEA evaluation models based on third moment and fourth moment.The empirical part, we evaluate and analysis the performance of27portfolio inthe2009-2011. The empirical analysis shows that rate of return of portfolio isnon-normal distribution. From the evaluation results of three evaluation models, wecan get: moment characteristics have different effects on investors, namely,skewness and kurtosis having important and different influences on the investmentdecision-making. In the moment characteristics frameworks, the number of effectiveportfolio will increase. Those with larger lower semi-third moment and lowerkurtosis portfolio rank ascend, even from invalid decision making units into theeffective decision makig units and vice versa. Finally, we use the Wilcoxonsigned-rank test to examine the differences of evaluation results.In a word, the portfolio evaluation DEA models based on the momentcharacteristics consider the distribution characteristics of rate of return, risk-returnrelationship and the investors utility preference. The evaluation results are morecomprehensive, more scientific and more actual, and have larger reference value forinvestors.