The Effect of Meta-Malmquist Index on Portfolio Optimization
الموضوعات : مجله بین المللی ریاضیات صنعتی
Z. Taeb
1
(Department of Mathematics, Yadegar Imam Branch, Islamic Azad University, Tehran, Iran.)
SH. Banihashemi
2
(Department of Mathematics, Faculty of Mathematics and Computer Science, Allameh Tabataba'i University, Tehran, Iran.)
الکلمات المفتاحية: efficiency score, portfolio optimization, Negative data, Meta Malmquist index, Conditional Value at Risk,
ملخص المقالة :
Since the change of conditional value at risk (CVaR) in different confidence levels is very effective in portfolio optimization, the meta-Malmquist index (MMI) is utilized. For this purpose, mean-CVaR models by MMI in the presence of negative data are introduced. Like Markowitz theory in mean-variance framework, we use Conditional Value-at-risk as a risk measure and propose our models without considering the skewness and kurtosis of assets return. In our study there are some negative data, so our models is based on Range Directional Measure (RDM) model that can be taken positive and negative data. In this paper efficiencies are obtained in all confidence levels by mean-CVaR models and MMI is calculated on confidence levels as periods in the presence of negative data. This method could help the investors to construct their profitable portfolio by using MMI index. We, also carry out an empirical study within Iran stock exchange market .
[1] N. Aghayia, M. Tavanab, A. B. Maleki, Malmquist productivity index with the directional distance function and uncertain data, Scintica Iranica 26 (2018) 3819-3834.
[2] D. Akhbarian, Overall profit Malmquist productivity index under data uncertainty, Financial innovation, (2020).
[3] P. Artzner, F. Delbaen, J. M. Ebner, D. Health, Coherent measures of risk, Journal of Mathematical Finance 9 (1999) 203-228.
[4] Sh. Banihashemi, S. Navidi, Portfolio performance evaluation in mean-CVaR framework:A comparison with nonparametric methods Value-at-Risk in mean-VaR analysis, Operations Research Perspective 4 (2017) 21-28.
[5] W. J. Baumol, An expected Gain-confidence Limit criterion for Portfolio Selection, Journal of Management Science 10 (1963) 174-182.
[6] A. Charnes, W. W. Cooper, E. Rhodes, Measuring efficiency of Decision Making Units, European Journal of Operational Research 2 (1978) 429-444.
[7] D. W. Caves, L. R. Christensen, W. E. Diewert, The economic theory of indexnumbers and the measurement of input, output and productivity, Econometrica 50 (1982) 1393-1414.
[8] R. F¨are, S. Grosskopf, M. Norris, Z. Zhang, Productivity growth, technical progress and efficiency changes in industrialized countries, American Economic Review 84 (1994) 66-83.
[9] D. S. Huang, S. S. Zhu, F. J. Fabozzi, M. Fukushima, Portfolio selection with uncertain exit time: a robust CVaR approach, Economic Dynamics and control 32 (2008) 594-623.
[10] M. M. John, G. E. Hafiz, Applying CVaR for decentralized risk Management of financial companies, Journal of Banking and Finance 30 (2006) 627-644.
[11] T. Joro, P. Na, Portfolio performance evaluation in a mean-variance-skewness framework, European Journal of Operational Research 175 (2006) 446-461.
[12] K. Kerstens, A. Mounir, I. V. Woestyne, Geometric Representation of the meanvariance-skewness portfolio frontier based upon the shortage function, European Journal of Operational Research 210 (2011) 81-94.
[13] K. Kobayashi, Y. Takano, K. Nakata, Bilevel cutting-plane algorithm for cardinalityconstrained mean-CVaR portfolio optimization, Journal of Global Optimization 81 (2021) 493-528.
[14] C. Liang, B. Liu, X. Xia, EP-CVaR risk measure approach and its application in portfolio optimization, Journal of Interdisciplinary Mathematics 20 (2017) 1073-1088.
[15] B. Liu, A new risk measure and its application in portfolio optimization: The SPP - CV aR approach, Economic Modelling 51 (2015) 383-390.
[16] H. Markowitz, Portfolio selection, Journal of finance 7 (1952) 77-91.
[17] H. Markowitz, Portfolio selection: Efficient diversification of investment, New York: Wiley, (1959).
[18] S. M. Mirsadeghpour, M. Sanei, Gh. Tohidi, Sh. Banihashemi, N. Modarresi, The effect of underlying distribution of asset returns on efficiency in DEA model, Journal of Intelligent & Fuzzy System 40 (2021) 10273-10283.
[19] M. R. Morey, R. C. Morey, Mutual fund performance appraisals: a multi-horizon perspective with endogenous benchmarking, Omega 27 (1999) 241-258.
[20] M. Yousefpour, The Biennial Malmquist Index in the of Negative Data, Mathematics and Computer Science (2014) 1-11.
[21] M. Nishimizu, J. M. Page, Total factor productivity growth, technological progress and efficiency change: Dimensions of productivity change in Yugoslavia, 1965-1978, The Economic Journal 92 (1982) 920-936.
[22] M. C. Portela, E. Thanassoulis, G. Simpson, A directional distance approach to deal with negative data in DEA: An application to bank branches, Operational Research Society 55 (2004) 1111-1121.
[23] M. C. Portela, E. Thanassoulis, Malmquisttype indices in the presence of negative data: An application to bank branches, Journal of Banking & Finance 34 (2010) 1472-1483.
[24] R. T. Rockafellar, S. Uryasev, Optimization of Conditional Value-at-Risk, Journal of Risk 2 (2000) 21-41.
[25] R. T. Rockafellar, S. Uryasev, Conditional Value-at-Risk for general loss distributions, Journal of Banking and Finance 26 (2002) 1443-1471.
