本文選題：投資組合評價　切入點：數(shù)據(jù)包絡(luò)分析　出處：《湖南大學(xué)》2012年碩士論文

【摘要】：本文構(gòu)建了基于矩特征的投資組合DEA評價模型，考慮了高階矩風(fēng)險對投資決策的影響。文章根據(jù)投資組合優(yōu)化模型，將二階矩(方差)、三階矩(偏度)和四階矩(峰度)特征作為DEA投入-產(chǎn)出指標構(gòu)建生產(chǎn)可能集，使建立的評價模型有理論根據(jù)與經(jīng)濟意義。在基于均值-方差的DEA評價模型的基礎(chǔ)上，考慮偏度風(fēng)險，并以下半偏度指標代替偏度指標，使得一向存在非凸規(guī)劃難題的三階矩投資組合模型成為凸規(guī)劃問題，滿足了投資組合模型生產(chǎn)可能集為凸集的要求，因此可以建立起相應(yīng)的基于均值-方差-下半偏度的DEA評價模型。并在此基礎(chǔ)上引入四階矩(峰度)指標建立基于均值-方差-下半偏度-峰度的DEA評價模型。 實證部分文章對27個投資組合在2009-2011年度的表現(xiàn)進行評價對比分析。實證分析表明投資組合收益率的非正態(tài)性特征非常明顯且從不同評價模型的評價結(jié)果對比分析中可以得到：每增加一個矩特征指標，，被評投資組合相對有效性都會發(fā)生變化，即效率排名發(fā)生變化。這意味著偏度、峰度對投資決策存在重要影響，且影響程度不同。在矩特征框架下，有效投資組合數(shù)目會增多，那些具有較大下半偏度、較低峰度的投資組合的效率排名得到提升，甚至從無效投資組合變?yōu)橛行顿Y組合；而那些具有較小下半偏度、高峰度的投資組合的效率排名不變，甚至出現(xiàn)排名下降。文章最后采用配對資料的符號秩和檢驗有效說明了三種評價模型下得到的效率排名存在顯著差別。 總之，基于矩特征的投資組合DEA評價模型考慮了資產(chǎn)收益率分布特征和收益-風(fēng)險關(guān)系，符合投資者效用偏好，評價結(jié)果更全面、更科學(xué)、更符合實際，對投資者的參考價值更大。
[Abstract]:This paper constructs a portfolio evaluation model based on DEA moment feature, considering the impact of higher moments risk on investment decision-making. According to the portfolio optimization model, the two order moment (variance), three moments (skewness) and four moments (kurtosis) features as the DEA input-output index construction production set the established evaluation model according to the theoretical and economic significance. Based on the evaluation of DEA mean variance model, considering the skewness risk and skewness index, below half instead of skewness index, the three order moment there has always been non convex programming problem portfolio model is a convex programming problem and meet the investment portfolio the model is a convex production possibility set requirements, so we can establish the corresponding evaluation DEA mean variance skewness model based on the second half. And on the basis of the introduction of the four order moment (kurtosis) index and mean variance skewness based on half - The DEA evaluation model of kurtosis.
The empirical part of the article on the performance of a portfolio of 27 in the year 2009-2011 to evaluate the comparative analysis. The empirical analysis shows that the portfolio return rate of non normality is very obvious and can be obtained from the comparative analysis of different evaluation model evaluation results: each additional moment feature index, was awarded the portfolio relative effectiveness will change, namely efficiency ranking changes. This means that the skewness, kurtosis have important influence on investment decisions, and the influence of different degree. In the moment features under the framework of the number of effective investment portfolio will increase, the second half of those with larger skewness, kurtosis of the low efficiency of investment portfolio ranking has improved, even from the invalid portfolio into the effective investment portfolio; while those with lower half peak efficiency of skewness portfolio ranking unchanged, even dropped. Finally, using the paired The symbolic rank sum test of the data effectively shows that there is a significant difference in the efficiency ranking obtained under the three evaluation models.
In a word, the DEA evaluation model based on moment characteristics considers the distribution characteristics and return risk relationship of assets return, which is consistent with the utility preference of investors. The evaluation result is more comprehensive, more scientific and practical, and has greater reference value for investors.

【學(xué)位授予單位】：湖南大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2012
【分類號】：F830.59

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