存在基数约束的投资组合效率评价方法

doi:10.16381/j.cnki.issn1003-207x.2017.02.019

中国管理科学 ›› 2017, Vol. 25 ›› Issue (2): 174-179.doi: 10.16381/j.cnki.issn1003-207x.2017.02.019

存在基数约束的投资组合效率评价方法

周忠宝¹, 金倩颖¹, 曾喜梅¹, 吴乾¹, 刘文斌^1,2

1. 湖南大学工商管理学院, 湖南长沙 410082;
2. Business School, University of Kent, Kent, CT2 7PE

收稿日期:2015-10-05 修回日期:2016-06-07 出版日期:2017-02-20 发布日期:2017-05-03
通讯作者: 金倩颖(1993-),女(汉族),浙江义乌人,湖南大学工商管理学院,在读博士,研究方向:金融工程与风险管理、系统优化与决策,E-mail:qianyingjin@hnu.edu.cn. E-mail:qianyingjin@hnu.edu.cn
基金资助:
国家自然科学基金面上项目（71371067）；国家自然科学基金重点项目（71431008）

Performance Evaluation of Portfolios with Cardinality Constraints

ZHOU Zhong-bao¹, JIN Qian-ying¹, ZENG Xi-mei¹, WU Qian¹, LIU Wen-bin^1,2

1. School of Business Administration, Hunan University, Changsha 410082, China;
2. Business School, University of Kent, Kent, CT2 7PE, England

Received:2015-10-05 Revised:2016-06-07 Online:2017-02-20 Published:2017-05-03

摘要/Abstract

摘要： 采用数据包络方法（DEA）评价投资组合效率的前提是有效前沿面为连续凹函数，然而存在基数约束的投资组合有效前沿面可能是非凹且不连续的函数，直接运用DEA方法对其进行评价是不合理的。本文首先给出了存在基数约束的投资组合效率的定义，考虑到其有效前沿面是由有限个连续凹函数分段构成的，提出了一种分段点搜索算法，构建分段DEA模型来评价投资组合效率。仿真分析表明，随着样本量的增加，本文提出的搜索算法得到的样本分段点逼近于真实分段点，分段DEA前沿面逼近于真实前沿面，DEA效率与真实效率相关性逐渐增大，从而说明了本文方法的可行性和有效性。

关键词: 投资组合效率, 基数约束, 有效前沿面, 分段点搜索方法, 数据包络分析

Abstract: Using Data Envelopment Analysis (DEA) to evaluate the performance of portfolios requires that the portfolio efficient frontier is continuous and concave. However, the efficient frontier on considering cardinality constraints may not be continuous or concave. Obviously, the direct use of DEA to evaluate the performance of portfolios with cardinality constraints is not reasonable. In this case, the definition of portfolio efficiencyis provided. Since the efficient frontier with cardinality constraints is a piecewise concave function, a numerical searching algorithm is put forward to obtain the sample segment points, which are used to group portfolios under cardinality constraints. The DEA model is then used to evaluate the performance of portfolios in each group. The simulation example indicates that, with the increase of sample size, the sample segment points converge to the real segment points, the DEA frontiers converge to the efficient frontier with cardinality constraints, the correlations between DEA efficiencies and portfolio efficiencies are becoming larger, which all indicate the feasibility and effectiveness of the proposed approach.

Key words: portfolio efficiency, cardinality constraints, efficient frontier, segment points search method, data envelopment analysis

中图分类号:

C931
F830

周忠宝, 金倩颖, 曾喜梅, 吴乾, 刘文斌. 存在基数约束的投资组合效率评价方法[J]. 中国管理科学, 2017, 25(2): 174-179.

ZHOU Zhong-bao, JIN Qian-ying, ZENG Xi-mei, WU Qian, LIU Wen-bin. Performance Evaluation of Portfolios with Cardinality Constraints[J]. Chinese Journal of Management Science, 2017, 25(2): 174-179.

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存在基数约束的投资组合效率评价方法

Performance Evaluation of Portfolios with Cardinality Constraints

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