Affiliations: School of Mathematics, South China University of Technology, Guangzhou, China
Correspondence:
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Corresponding author. Xue Deng, School of Mathematics, South China University of Technology, Guangzhou, 510640, China. E-mail: dxue@scut.edu.cn.
Abstract: In this paper, a novel framework is proposed for fuzzy portfolio selection based on a combination between Data Envelopment Analysis (DEA) prospect cross-efficiency approach and the maverick index. Although DEA cross-efficiency evaluation is used to an effective tool for portfolio selection, no researcher has yet attempted to combine DEA cross-efficiency method with investors’ psychology in fuzzy portfolio selection. To address this problem, two novel prospect cross-efficiency models termed PCE (I) and PCE (II) are developed as the foundations for the construction of a novel fuzzy portfolio model. Because of the uncertain environment of financial market, the returns of assets are characterized as triangular fuzzy numbers. To make our models more comprehensive and practical, five criteria including mean, variance, semi-variance, skewness and entropy are employed in PCE models. Furthermore, based on the PCE evaluation, a novel mean-variance-maverick (MVM) framework is designed for fuzzy portfolio selection, in which the prospect cross-efficiency is viewed as return characteristic, maverick index and variance are considered as risk characteristics. The maverick index, as a novel risk measure, can be used as a good indicator for sensitivity to environment volatility in portfolio selection. Finally, a numerical example is provided to illustrate the effectiveness of our proposed models. The results show that our proposed approach can not only capture the risk attitudes of investors, but also permit well-diversified portfolios and higher risk-adjusted returns than other benchmark portfolios.
Keywords: Fuzzy portfolio selection, data envelopment analysis (DEA), risk attitude, prospect cross-efficiency, mean-variance-maverick model
