Parameter uncertainty in estimation of portfolio efficiency: Evidence from an interval diversification-consistent DEA approach

Abstract Traditional data envelopment analysis (DEA) and diversification-consistent DEA, as the data-driven relative performance evaluation approaches, are widely used in the estimation of portfolio efficiency. To some extent, diversification-consistent DEA is more favored by researchers compared with traditional DEA for it deals fully with portfolio diversification. However, the existing studies assume that decision-makers can accurately estimate the statistical characteristics of portfolio returns and ignore the impact of parameter uncertainty on the portfolio efficiency and its ranking. In this paper, we construct three diversification-consistent DEA models under the mean-variance framework. We treat the expectation and covariance of portfolio return as interval values to characterize the parameter uncertainly in the proposed DEA models. And the bi-level programming models and the corresponding equivalent models are also provided to obtain the lower and upper bounds of portfolio efficiency. We select 30 American industry portfolios and perform some empirical analyses under different datasets to find out which model has better robustness in dealing with the impact of parameter uncertainty on the portfolio efficiency and its ranking. Finally, we provide some robustness tests to further verify the consistency of our findings.

[1]  Sohrab Kordrostami,et al.  Measuring the efficiency of two-stage network processes: A satisficing DEA approach , 2020 .

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

[3]  R. G. Dyson,et al.  Data envelopment analysis, operational research and uncertainty , 2010, J. Oper. Res. Soc..

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

[5]  A. Charnes,et al.  Deterministic Equivalents for Optimizing and Satisficing under Chance Constraints , 1963 .

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

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

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

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

[10]  John D. Lamb,et al.  Resampling DEA estimates of investment fund performance , 2012, Eur. J. Oper. Res..

[11]  Adel Hatami-Marbini,et al.  Dual-role factors for imprecise data envelopment analysis , 2017, Omega.

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

[13]  Chung-Cheng Lu.  Robust data envelopment analysis approaches for evaluating algorithmic performance , 2015, Comput. Ind. Eng..

[14]  SeJoon Park,et al.  A stochastic simulation-based holistic evaluation approach with DEA for vendor selection , 2017, Comput. Oper. Res..

[15]  Mehdi Toloo,et al.  Robust optimization with nonnegative decision variables: A DEA approach , 2019, Comput. Ind. Eng..

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

[17]  Mehrab Esmaeili,et al.  An Enhanced Russell Measure in DEA with interval data , 2012, Appl. Math. Comput..

[18]  Joe Zhu,et al.  Hedge fund performance appraisal using data envelopment analysis , 2005, Eur. J. Oper. Res..

[19]  Maria Grazia Scutellà,et al.  Robust portfolio asset allocation and risk measures , 2013, Ann. Oper. Res..

[20]  Dimitris K. Despotis,et al.  Data envelopment analysis with imprecise data , 2002, Eur. J. Oper. Res..

[21]  William W. Cooper,et al.  Chapter 13 Satisficing DEA models under chance constraints , 1996, Ann. Oper. Res..

[22]  R. Banker,et al.  A Monte Carlo comparison of two production frontier estimation methods: Corrected ordinary least squares and data envelopment analysis , 1993 .

[23]  Desheng Dash Wu,et al.  Stochastic DEA with ordinal data applied to a multi-attribute pricing problem , 2010, Eur. J. Oper. Res..

[24]  P. W. Wilson,et al.  Sensitivity Analysis of Efficiency Scores: How to Bootstrap in Nonparametric Frontier Models , 1998 .

[25]  Sheridan Titman,et al.  Short-Term Reversals: The Effects of Past Returns and Institutional Exits , 2017, Journal of Financial and Quantitative Analysis.

[26]  Helu Xiao,et al.  Time-Consistent Investment and Reinsurance Strategies for Insurers Under Multi-Period Mean-Variance Formulation with Generalized Correlated Returns , 2019, Journal of Management Science and Engineering.

[27]  Donald Goldfarb,et al.  Robust Portfolio Selection Problems , 2003, Math. Oper. Res..

[28]  Richard O. Michaud,et al.  Efficient Asset Management: A Practical Guide to Stock Portfolio Optimization and Asset Allocation , 1998 .

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

[30]  Samarjit Kar,et al.  Fuzzy mean-variance-skewness portfolio selection models by interval analysis , 2011, Comput. Math. Appl..

[31]  Raymond Kan,et al.  Optimal Portfolio Choice with Parameter Uncertainty , 2007, Journal of Financial and Quantitative Analysis.

[32]  Narasimhan Jegadeesh,et al.  Evidence of Predictable Behavior of Security Returns , 1990 .

[33]  Helu Xiao,et al.  Estimation of cardinality constrained portfolio efficiency via segmented DEA , 2018 .

[34]  Herminia I. Calvete,et al.  A new approach for solving linear bilevel problems using genetic algorithms , 2008, Eur. J. Oper. Res..

[35]  B. Halldórsson,et al.  An Interior-Point Method for a Class of Saddle-Point Problems , 2003 .

[36]  Richard O. Michaud.  The Markowitz Optimization Enigma: Is 'Optimized' Optimal? , 1989 .

[37]  R. Thaler,et al.  Does the Stock Market Overreact , 1985 .

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

[39]  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.

[40]  Ying-Ming Wang,et al.  The upper and lower bound evaluation based on the quantile efficiency in stochastic data envelopment analysis , 2017, Expert Syst. Appl..

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

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

[43]  Antonella Basso,et al.  Constant and variable returns to scale DEA models for socially responsible investment funds , 2014, Eur. J. Oper. Res..

[44]  Toshiyuki Sueyoshi,et al.  Stochastic DEA for restructure strategy: an application to a Japanese petroleum company , 2000 .

[45]  Kenneth C. Land,et al.  Chance‐constrained data envelopment analysis , 1993 .

[46]  S. Dempe,et al.  On the solution of convex bilevel optimization problems , 2015, Computational Optimization and Applications.

[47]  W. Cooper,et al.  Idea and Ar-Idea: Models for Dealing with Imprecise Data in Dea , 1999 .

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

[49]  Helu Xiao,et al.  Performance evaluation of portfolios with fuzzy returns , 2019, RAIRO Oper. Res..

[50]  Chiang Kao,et al.  Interval efficiency measures in data envelopment analysis with imprecise data , 2006, Eur. J. Oper. Res..

[51]  Kalyanmoy Deb,et al.  Using Karush-Kuhn-Tucker proximity measure for solving bilevel optimization problems , 2019, Swarm Evol. Comput..

[52]  Joe Zhu,et al.  Computational tractability of chance constrained data envelopment analysis , 2019, Eur. J. Oper. Res..

[53]  S. Dempe.  Annotated Bibliography on Bilevel Programming and Mathematical Programs with Equilibrium Constraints , 2003 .

[54]  Mehdi Toloo,et al.  Robust Russell and enhanced Russell measures in DEA , 2018, J. Oper. Res. Soc..

[55]  Ruiyue Lin,et al.  Dynamic network DEA approach with diversification to multi-period performance evaluation of funds , 2017, OR Spectr..

[56]  Jian-Bo Yang,et al.  Interval efficiency assessment using data envelopment analysis , 2005, Fuzzy Sets Syst..

[57]  H. Simon,et al.  Models of Man. , 1957 .

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

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

[60]  Stephan Dempe,et al.  Foundations of Bilevel Programming , 2002 .

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

[62]  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..

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

[64]  Qi Zeng,et al.  Stock Returns and the Miller-Modigliani Valuation Formula: Revisiting the Fama-French Analysis , 2012 .

[65]  William W. Cooper,et al.  Chance constrained programming approaches to technical efficiencies and inefficiencies in stochastic data envelopment analysis , 2002, J. Oper. Res. Soc..

[66]  William W. Cooper,et al.  Stochastics and Statistics , 2001 .

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

[68]  Lorenzo Garlappi,et al.  Portfolio Selection with Parameter and Model Uncertainty: A Multi-Prior Approach , 2004 .

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

[70]  Helu Xiao,et al.  Forecasting stock price movements with multiple data sources: Evidence from stock market in China , 2020 .

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