Document Type : Research Article
Authors
1 Department of Mathematics and Computer Sciences, Kharazmi University, Tehran, Iran
2 Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran
3 Department of Accounting, Finance and Economics, Griffith University, Brisbane, QLD, Australia
Abstract
Data envelopment analysis (DEA) is a methodology widely used for evaluating the relative performance of portfolios under a mean–variance framework. However, there has been little discussion of whether nonlinear models best suit this purpose. Moreover, when using DEA linear models, the portfolio efficiency obtained is not comparable to those on the efficient portfolio frontier. This is because a separable piecewise linear boundary usually below the efficient frontier is considered the efficient frontier, so the model does not fully explore the possibility of portfolio benchmarks. In this paper, and with use of the dual-Lagrangian function, we propose a linear model under a mean–variance framework to evaluate better the performance of portfolios relative to those on the efficient frontier.
Keywords
indices, FinancUver-Czech J Econ Financ, (2012), 62(2), 10624.
[2] W. Briec, K. Kerstens, and O. Jokung,Mean-Variance-Skewness Portfolio Performance
Gauging: A General Shortage Function and Dual Approach, Management Science, (2006),
53, pp. 153-149.
[3] F. Choobineh, D. Branting, A Simple Approximation for Semi variance, European Journal
of Operational Research, (1986), Vol. 27, pp. 364-370.
[4] G. Hanoch, H. Levy , The efficient analysis of choices involving risk, Review of Economic
Studies, (1969), 36 (3) 335346.
[5] G. Iazzolino, M. E. Bruni, S. Veltri, D. Morea, and G. Baldissarro,The impact of ESG
factors on financial efficiency: An empirical analysis for the selection of sustainable firm
portfolios, Corporate Social Responsibility and Environmental Management, (2023), 30(4),
1917-1927.
[6] M. C. Jensen , The performance of mutual funds in the period, 19451968. Journal of Finance,
(1968), 23, 389416.
[7] T. Joro, P. Na ,Portfolio performance evaluation in a meanvarianceskewness framework,
European Journal of Operational Research, (2006), 175(1), 446461.
[8] P. D. Kaplan, R. H. Alldredge ,Semi variance in Risk-Based Index Construction: Quantidex Global Indexes, The Journal of Investing,(1997), Vol. 6, pp. 82-87.
[9] K. Kerstens, A. Mounir , and I. V. Woestyne ,Geometric Representation of the MeanVariance Skewness Portfolio Frontier Based Upon the Shortage Function, European Journal
of Operational Research, (2011), 210, pp. 81-94.
[10] Q. Y. E. Lim, Q. Cao, and C. Quek, Dynamic portfolio rebalancing through reinforcement
learning, Neural Computing and Applications, (2022), 34(9), 7125-7139.
[11] W. Liu, Z. Zhou, D. Liu, and H. Xiao,Estimation of portfolio efficiency via DEA, Omega,
(2015), 52, 107118.
[12] S. Lozano, E. Gutierrez ´ ,Data envelopment analysis of mutual funds based on second-order
stochastic dominance, European Journal of Operational Research, (2008), 189(1), 230244.
[13] S. O. Lozza, E. Angelelli, and D. Toninelli ,Set-portfolio selection with the use of
market stochastic bounds, Emerging Markets Finance and Trade, (2011), 47(5): 524.
[14] Y. Ma, R. Han, and W. Wang, Portfolio optimization with return prediction using deep
learning and machine learning, Expert Systems with Applications, (2021), 165, 113973.
[15] H. Markowitz, Portfolio selection, The Journal of Finance, (1952), 7(1), 7791.
[16] H. Markowitz, Portfolio Selection: Efficient Diversification of Investments, New York:
Yale University Press, John Wiley,(1992), Vol. 119, pp. 165-166.
[17] M. R. Morey, R. C. Morey ,Mutual fund performance appraisals: a multi-horizon perspective with endogenous benchmarking, Omega, International Journal of Management Science,(1999), 27, 241258.
[18] W. F. Sharpe , Mutual fund performance, Journal of Business,(1966), 39(1), 119138.
[19] W.F. Sharpe, J.A. Gordon, and V.B. Jeffry, Investment, 5th. Ed, Prentice HallCollege
Div,(1995).
[20] H. Soleimani, H. R. Golmakani, and M. H. Salimi ,Markowitz-based portfolio selection
with minimum transaction lots, cardinality constraints and regarding sector capitalization
using genetic algorithm, Expert Systems with Applications,(2009), 36, 50585063.
[21] J. Tobin, Liquidity Preference as Behavior Toward Risk, Review of Economic Studies, (1958),
25, pp.65-86.
[22] J. Treynor ,How to rate management of investment funds, Harvard Business Review,(1965),
43(1), 6375.
[23] A. L. Turner, and E. J. Weigel, Daily Stock Market Volatility: 1928-1989, Management
Science,(1992), 38, pp. 1586-1609.
[24] P. Wolfe, A duality theorem for non-linear programming, Quarterly of applied mathematics,
(1961), 19(3), 239-244.
[25] A. Yoshimoto , The meanvariance approach to portfolio optimization subject to transaction
costs, Journal of the Operations Research Society of Japan,(1996), 39(1), 99117.
[26] Z. Zhou,H. Xiao,Q. Jin and W. Liu,DEA frontier improvement and portfolio rebalancing:
An application of China mutual funds on considering sustainability information disclosure,
European Journal of Operational Research,(2017), 121.
)