The present study is an attempt toward evaluating the performance of portfolios and asset selection using cross-efficiency evaluation. Cross-efficiency evaluation is an effective way of ranking decision making units (DMUs) in data envelopment analysis (DEA). The most widely used approach is to evaluate the efficiencies in each row or column in the cross-efficiency matrix with equal weights into an average cross-efficiency score for each DMU and consider it as the overall performance measurement of the DMU. This paper focuses on the evaluation process of the efficiencies in the cross-efficiency matrix and proposes the use of ordered weighted averaging (OWA) operator weights for cross-efficiency evaluation. The OWA operator weights are generated by the minimax disparity approach and allow the decision maker (DM) or investor to select the best assets that are characterized by an orness degree. The problem consists of choosing an optimal set of assets in order to minimize the risk and maximize return. This method is illustrated by application in mutual funds and weights are obtained via OWA operator for making the best portfolio. The finding could be used for constructing the best portfolio in stock companies, in various finance organization, and public and private sector companies. 1. Introduction In financial literature, a portfolio is an appropriate mix of investments held by an institution or private individuals. Evaluation of portfolio performance has created a large interest among employees also academic researchers because of huge amount of money being invested in financial markets. The theory of mean-variance, Markowitz [1] is considered the basis of many current models and this theory is widely used to select portfolios. This model is due to the nature of the variance in quadratic form. Other problem in Markowitz model is that increasing the number of assets will develop the covariance matrix of asset returns and will be added to the content calculation. Due to these problems sharp one-factor model is proposed by Sharpe [2]. This method reduces the number of calculations requiring information for the decision. Data envelopment analysis (DEA) has proved the efficiency for assessing the relative efficiency of decision making units (DMUs) employing multiple inputs to produce multiple outputs [3]. M. R. Morey and R. C. Morey [4] proposed mean-variance framework based on Data Envelopment Analysis, which the variance of the portfolios is used as an input to the DEA and expected return is the output. Joro and Na [5] introduced mean-variance-skewness
References
[1]
H. M. Markowitz, “Portfolio selection,” Journal of Finance, vol. 7, pp. 77–91, 1957.
[2]
W. F. Sharpe, “Capital asset prices: a theory of market equilibrium under conditions of risk,” Journal of Finance, vol. 19, pp. 425–442, 1964.
[3]
A. Charnes, W. W. Cooper, and E. Rhodes, “Measuring the efficiency of decision making units,” European Journal of Operational Research, vol. 2, no. 6, pp. 429–444, 1978.
[4]
M. R. Morey and R. C. Morey, “Mutual fund performance appraisals: a multi-horizon perspective with endogenous benchmarking,” Omega, vol. 27, no. 2, pp. 241–258, 1999.
[5]
T. Joro and P. Na, “Portfolio performance evaluation in a mean-variance-skewness framework,” European Journal of Operational Research, vol. 175, no. 1, pp. 446–461, 2006.
[6]
T. R. Sexton, R. H. Silkman, and A. J. Hogan, “Data envelopment analysis: critique and extensions,” in Measuring Efficiency: An Assessment of Data Envelopment Analysis, R. H. Silkman, Ed., pp. 73–105, Jossey-Bass, San Francisco, Calif, USA, 1986.
[7]
R. H. Green, J. R. Doyle, and W. D. Cook, “Preference voting and project ranking using DEA and cross-evaluation,” European Journal of Operational Research, vol. 90, no. 3, pp. 461–472, 1996.
[8]
J. Wu, L. Liang, and Y. C. Zha, “Preference voting and ranking using DEA game cross efficiency model,” Journal of the Operations Research Society of Japan, vol. 52, no. 2, pp. 105–111, 2009.
[9]
W.-M. Lu and S.-F. Lo, “A closer look at the economic-environmental disparities for regional development in China,” European Journal of Operational Research, vol. 183, no. 2, pp. 882–894, 2007.
[10]
W.-M. Lu and S.-F. Lo, “A benchmark-learning roadmap for regional sustainable development in China,” Journal of the Operational Research Society, vol. 58, no. 7, pp. 841–849, 2007.
[11]
J. Wu, L. Liang, D. Wu, and F. Yang, “Olympics ranking and benchmarking based on cross efficiency evaluation method and cluster analysis: the case of Sydney 2000,” International Journal of Enterprise Network Management, vol. 2, pp. 377–392, 2008.
[12]
J. Wu, L. Liang, and F. Yang, “Achievement and benchmarking of countries at the Summer Olympics using cross efficiency evaluation method,” European Journal of Operational Research, vol. 197, no. 2, pp. 722–730, 2009.
[13]
J. Wu, L. Liang, and Y. Chen, “DEA game cross-efficiency approach to Olympic rankings,” Omega, vol. 37, no. 4, pp. 909–918, 2009.
[14]
J. Doyle and R. Green, “Efficiency and cross-efficiency in DEA: derivations, meanings and uses,” Journal of the Operational Research Society, vol. 45, no. 5, pp. 567–578, 1994.
[15]
J. R. Doyle and R. H. Green, “Cross-evaluation in DEA: improving discrimination among DMUs,” INFOR, vol. 33, pp. 205–222, 1995.
[16]
L. Liang, J. Wu, W. D. Cook, and J. Zhu, “The DEA game cross-efficiency model and its nash equilibrium,” Operations Research, vol. 56, no. 5, pp. 1278–1288, 2008.
[17]
Y.-M. Wang and K.-S. Chin, “The use of OWA operator weights for cross-efficiency aggregation,” Omega, vol. 39, no. 5, pp. 493–503, 2011.
[18]
Y.-M. Wang and C. Parkan, “A minimax disparity approach for obtaining OWA operator weights,” Information Sciences, vol. 175, no. 1-2, pp. 20–29, 2005.
[19]
W. F. Sharpe, “Investment,” in Envelopment Analysis, Management Science, vol. 30, pp. 1078–1092, Prentice-Hall, 3rd edition, 1985.
[20]
A. Charnes, W. W. Cooper, A. Y. Lewin, and L. M. Seiford, Eds., Data Envelopment Analysis: Theory, Methodology and Applications, Kluwer Academic Publishers, Boston, Mass, USA, 1994.
[21]
R. R. Yager, “On ordered weighted averaging aggregation operators in multi- criteria decision making,” IEEE Transactions on Systems, Man and Cybernetics, vol. 18, no. 1, pp. 183–190, 1988.
[22]
M. O'Hagan, “Aggregating template or rule antecedents in real-time expert systems with fuzzy set logic,” in Proceedings of the 22nd Annual IEEE Asilomar Conference on Signals, Systems and Computers, pp. 681–689, Pacific Grove, Calif, USA, 1988.
[23]
R. D. Banker, A. Charnes, and W. W. Cooper, “Some models for estimating technical and scale inefficiencies in data envelopment analysis,” Management Science, vol. 30, no. 9, pp. 1078–1092, 1984.
[24]
W. D. Cook, L. Liang, and J. Zhu, “Measuring performance of two-stage network structures by DEA: a review and future perspective,” Omega, vol. 38, no. 6, pp. 423–430, 2010.
[25]
J. C. Paradi, S. Rouatt, and H. Zhu, “Two-stage evaluation of bank branch efficiency using data envelopment analysis,” Omega, vol. 39, no. 1, pp. 99–109, 2011.
[26]
C. Kao, “Malmquist productivity index based on common-weights DEA: the case of Taiwan forests after reorganization,” Omega, vol. 38, no. 6, pp. 484–491, 2010.
[27]
H. Chang, H. L. Choy, W. W. Cooper, and T. W. Ruefli, “Using Malmquist Indexes to measure changes in the productivity and efficiency of US accounting firms before and after the Sarbanes-Oxley Act,” Omega, vol. 37, no. 5, pp. 951–960, 2009.
[28]
F. Fiordelisi and P. Molyneux, “Total factor productivity and shareholder returns in banking,” Omega, vol. 38, no. 5, pp. 241–253, 2010.
[29]
M. Asmild, J. C. Paradi, and J. T. Pastor, “Centralized resource allocation BCC models,” Omega, vol. 37, no. 1, pp. 40–49, 2009.
