Estimation of fuzzy portfolio efficiency via an improved DEA approach

Abstract DEA (Data Envelopment Analysis) is a nonparametric approach that has been used to estimate fuzzy portfolio efficiency. In this paper, we propose an approach under the fuzzy theory framework that can both improve the DEA frontier and suggest a replicable benchmark for investors. We first construct an improved DEA model using the proposed approach and then investigate the relationships among the evaluation model based on a portfolio frontier, the traditional DEA model and the improved DEA model. We show the convergence of the improved DEA model under the fuzzy framework. The simulation indicates that the improved DEA frontier is closer to the portfolio frontier than to the traditional DEA frontier. More importantly, we incorporate the diversification DEA model and improved DEA model to analyze the performance of China’s open-end fund. The empirical results indicate that the improved DEA model not only provides a quicker way to assess the investment funds compared to the diversification DEA model but also makes up for the shortcoming of the traditional DEA model, which overestimates the fuzzy portfolio efficiency.

[1]  Sheridan Titman,et al.  On Persistence in Mutual Fund Performance , 1997 .

[2]  Mark M. Carhart.  On Persistence in Mutual Fund Performance , 1997 .

[3]  Helu Xiao,et al.  Estimation of portfolio efficiency via DEA , 2015 .

[4]  Lotfi A. Zadeh,et al.  Fuzzy Sets , 1996, Inf. Control..

[5]  Wei-Guo Zhang,et al.  Possibilistic mean-variance models and efficient frontiers for portfolio selection problem , 2007, Inf. Sci..

[6]  HuangXiaoxia.  Mean-risk model for uncertain portfolio selection , 2011 .

[7]  Kristiaan Kerstens,et al.  Benchmarking mean-variance portfolios using a shortage function: the choice of direction vector affects rankings! , 2012, J. Oper. Res. Soc..

[8]  W. Briec,et al.  Single-Period Markowitz Portfolio Selection, Performance Gauging, and Duality: A Variation on the Luenberger Shortage Function , 2002 .

[9]  Zhongfeng Qin,et al.  Portfolio selection based on fuzzy cross-entropy , 2009 .

[10]  Helu Xiao,et al.  DEA frontier improvement and portfolio rebalancing: An application of China mutual funds on considering sustainability information disclosure , 2017, Eur. J. Oper. Res..

[11]  John D. Lamb,et al.  Data envelopment analysis models of investment funds , 2012, Eur. J. Oper. Res..

[12]  Christer Carlsson,et al.  On Possibilistic Mean Value and Variance of Fuzzy Numbers , 1999, Fuzzy Sets Syst..

[13]  Martin Branda.  Reformulations of input-output oriented DEA tests with diversification , 2013, Oper. Res. Lett..

[14]  Robert LIN,et al.  NOTE ON FUZZY SETS , 2014 .

[15]  Martin Branda,et al.  Mean-value at risk portfolio efficiency: approaches based on data envelopment analysis models with negative data and their empirical behaviour , 2016, 4OR.

[16]  Christer Carlsson,et al.  A Possibilistic Approach to Selecting Portfolios with Highest Utility Score , 2001, Fuzzy Sets Syst..

[17]  Louis Aimé Fono,et al.  Moments and semi-moments for fuzzy portfolio selection , 2012 .

[18]  Kin Keung Lai,et al.  Mutual funds performance evaluation based on endogenous benchmarks , 2011, Expert Syst. Appl..

[19]  Kristiaan Kerstens,et al.  Multi-horizon Markowitz portfolio performance appraisals: A general approach , 2009 .

[20]  Martin Branda,et al.  Diversification-consistent data envelopment analysis with general deviation measures , 2013, Eur. J. Oper. Res..

[21]  Wei-Guo Zhang,et al.  On Possibilistic Variance of Fuzzy Numbers , 2003, RSFDGrC.

[22]  Richard C. Morey,et al.  Mutual fund performance appraisals: a multi-horizon perspective with endogenous benchmarking , 1999 .

[23]  Yian-Kui Liu,et al.  Expected value of fuzzy variable and fuzzy expected value models , 2002, IEEE Trans. Fuzzy Syst..

[24]  Hervé Leleu,et al.  Portfolio analysis with DEA: Prior to choosing a model , 2018 .

[25]  Kristiaan Kerstens,et al.  Mean-Variance-Skewness Portfolio Performance Gauging: A General Shortage Function and Dual Approach , 2007, Manag. Sci..

[26]  Weijun Xu,et al.  A possibilistic mean-semivariance-entropy model for multi-period portfolio selection with transaction costs , 2012, Eur. J. Oper. Res..

[27]  Ruiyue Lin,et al.  Mutual fund performance evaluation using data envelopment analysis with new risk measures , 2006, OR Spectr..

[28]  Didier Dubois,et al.  Possibility theory , 2018, Scholarpedia.

[29]  Jack L. Treynor.  How to Rate Management of Investment Funds , 2012 .

[30]  Elisabetta Allevi,et al.  Measuring the environmental performance of green SRI funds: A DEA approach , 2019, Energy Economics.

[31]  Paul Na,et al.  Portfolio performance evaluation in a mean-variance-skewness framework , 2006, Eur. J. Oper. Res..

[32]  Emmanuel Thanassoulis,et al.  Negative data in DEA: a directional distance approach applied to bank branches , 2004, J. Oper. Res. Soc..

[33]  Enriqueta Vercher,et al.  Fuzzy portfolio optimization under downside risk measures , 2007, Fuzzy Sets Syst..

[34]  Mukesh Kumar Mehlawat,et al.  Credibilistic mean-entropy models for multi-period portfolio selection with multi-choice aspiration levels , 2016, Inf. Sci..

[35]  Teng Ren,et al.  Maximum and minimum solutions for a nonlocal p-Laplacian fractional differential system from eco-economical processes , 2017 .

[36]  A. Basso,et al.  The role of fund size in the performance of mutual funds assessed with DEA models , 2014 .

[37]  Zhongbao Zhou,et al.  The Iterative Scheme and the Convergence Analysis of Unique Solution for a Singular Fractional Differential Equation from the Eco-Economic Complex System's Co-Evolution Process , 2019, Complex..

[38]  Preyas S. Desai,et al.  Efficiency of mutual funds and portfolio performance measurement: A non-parametric approach , 1997 .

[39]  Daiki Min,et al.  Efficiency of well-diversified portfolios: Evidence from data envelopment analysis , 2017 .

[40]  Antonella Basso,et al.  A Data Envelopment Analysis Approach to Measure the Mutual Fund Performance , 2001, Eur. J. Oper. Res..

[41]  Weijun Xu,et al.  Fuzzy multi-period portfolio selection optimization models using multiple criteria , 2012, Autom..

[42]  Sebastián Lozano,et al.  Data envelopment analysis of mutual funds based on second-order stochastic dominance , 2008, Eur. J. Oper. Res..

[43]  Wei-Guo Zhang,et al.  A multi-period fuzzy portfolio optimization model with minimum transaction lots , 2015, Eur. J. Oper. Res..

[44]  Martin Branda,et al.  Diversification-consistent data envelopment analysis based on directional-distance measures , 2015 .

[45]  Jack L. Treynor,et al.  MUTUAL FUND PERFORMANCE* , 2007 .

[46]  William L. Weber,et al.  Mutual fund efficiency and tradeoffs in the production of risk and return , 2016 .

[47]  A. Saeidifar,et al.  The possibilistic moments of fuzzy numbers and their applications , 2009 .

[48]  M. C. Jensen.  The Performance of Mutual Funds in the Period 1945-1964 , 1967 .

[49]  Peng Zhang,et al.  Multiperiod mean absolute deviation fuzzy portfolio selection model with risk control and cardinality constraints , 2014, Fuzzy Sets Syst..

[50]  Xiaoxia Huang,et al.  Mean-Entropy Models for Fuzzy Portfolio Selection , 2008, IEEE Transactions on Fuzzy Systems.

[51]  Wei Chen,et al.  Efficiency evaluation of fuzzy portfolio in different risk measures via DEA , 2017, Annals of Operations Research.

[52]  Xiaoxia Huang,et al.  Mean-risk model for uncertain portfolio selection , 2011, Fuzzy Optim. Decis. Mak..

[53]  Chaoqun Ma,et al.  Performance Evaluation of Portfolios with Margin Requirements , 2014 .