Document Type : Research Article
Authors
Department of Statistics, Islamic Azad University, Tehran North Branch
Abstract
Investment is the selection of assets to hold and earn more pro t for greater prosperity in the future. The selection of a portfolio based on the theory of constraint is classical data covering analysis evaluation and ranking Sample function. The in vestment process is related to how investors act in deciding on the types of tradable securities to invest in and the amount and timing. Various methods have been proposed for the investment process, but the lack of rapid computational methods for determining investment policies in securities analysis makes performance appraisal a long term challenge. An approach to the investment process consists of two parts. Major is securities analysis and portfolio management. Securities analysis involvesestimating the bene ts of each investment, while portfolio management involves analyzing the composition of investments and managing and maintaining a set of investments. Classical data envelopment analysis (DEA) models are recognized as accurate for rating and measuring efficient sample performance. Unluckily, this perspective often brings us to get overwhelmed when it's time to start a project. When it comes to limiting theory, the problem of efficient sample selection using a DEA models to test the performance of the PE portfolio is a real discontinuous boundary and concave has not been successful since 2011. In order to solve this problem, we recommend a DEA method divided into business units based on the Markowitz model. A search algorithm is used to introduce to business units and prove their validity. In any business unit, the boundary is continuous and concave. Therefore, DEA models could be applied as PE evaluation. To this end, 25 companies from the companies listed on the Tehran Stock Exchange for the period 1394 to 1399 were selected as the sample size of statistics in data analysis. To analyze
the data, after classi cation and calculations were analysed by MATLAB software, the simulation results show that performance evaluation based on constraint theory based on DEA approach and the Markowitz model presented in this paper is efficient and feasible in evaluating the portfolio of constraint theory.
Keywords
[2] K. P. Anagnostopoulos and G. Mamanis. A portfolio optimization model with three objectives and discrete variables. Computers & Operations Research, 37(7):1285{1297, 2010.
[3] R. D. Banker, A. Charnes, and W. W. Cooper. Some models for estimating technical and scale inefficiencies in data envelopment analysis. Management science, 30(9):1078{1092, 1984.
[4] D. W. Caves, L. R. Christensen, and W. E. Diewert. The economic theory of index numbers and the measurement of input, output, and productivity. Econometrica: Journal of the Econometric Society, pages 1393{1414, 1982.
[5] A. Charnes, W. W. Cooper, and E. Rhodes. Measuring the efficiency of decision making units. European journal of operational research, 2(6):429{444, 1978.
[6] Y. Chen and A. I. Ali. Dea malmquist productivity measure: New insights with an application to computer industry. European journal of operational research, 159(1):239{249, 2004.
[7] G. Cornuejols and R. Tutuncu. Optimization methods in nance, volume 5. Cambridge University Press, 2006.
[8] J. D. Cummins, G. Turchetti, et al. Productivity and technical efficiency in the italian insurance industry. Technical report, Wharton School Center for Financial Institutions, University of Pennsylvania, 1996.
[9] R. Fare, S. Grosskopf, M. Norris, and Z. Zhang. Productivity growth, technical progress, and efficiency change in industrialized countries. The American economic review, pages 66{83,1994.
[11] K. Fathi Vajargah, H. Mottaghi Golshan, and A. Arjomandfar. Optimization of estimates and comparison of their efficiency under stochastic methods and its application in nancial models. Advances in Mathematical Finance and Applications, 2022.
[12] K. Frajtova-Michalikova, E. Spuchakova, and M. Misankova. Portfolio optimization. Procedia Economics and Finance, 26:1102{1107, 2015. ISSN 2212-5671. doi: https://doi.org/10.1016/S2212-5671(15)00936-3. URLhttps://www.sciencedirect.com/science/article/pii/S2212567115009363. 4th World Conference on Business, Economics and Management(WCBEM-2015).
[13] H. Fukuyama and W. L. Weber. Efficiency and productivi ty change of non-life insurance companies in japan. Paci c Economic Review, 6(1):129{146, 2001.
[14] M. Izadikhah. Dea approaches for nancial evaluation-a literature review. Advances in Mathematical Finance and Applications, 7(1):1{37, 2022.
[15] T. Joro and P. Na. Portfolio performance evaluation in a mean{variance{skewness framework. European Journal of Operational Research, 175(1):446{461, 2006.
[16] C. B. Kalayci, O. Ertenlice, and M. A. Akbay. A comprehensive review of deterministic models and applications for mean-variance portfolio optimization. Expert Systems with Applications, 125:345{368, 2019.
[17] K. Kerstens, A. Mounir, and I. Van de Woestyne. Geometric representation of the mean{variance{skewness portfolio frontier based upon the shortage function. European Journal of Operational Research, 210(1):81{94, 2011.
[18] S. Malmquist. Index numbers and indifference surfaces. Trabajos de estadstica, 4(2):209{242,1953.
[19] H. Markowitz. Portfolio selection. The Journal of Finance, 7(1):77{91, 1952. ISSN 00221082, 15406261. URL http://www.jstor.org/stable/2975974.
[20] H. M. Markowitz. Foundations of portfolio theory. The journal of nance, 46(2):469{477,1991.
[21] H. M. Markowitz and G. P. Todd. Mean-variance analysis in portfolio choice and capital markets, volume 66. John Wiley & Sons, 2000.
[22] H. Wu, Y. Zeng, and H. Yao. Multi-period markowitz's mean{variance portfolio selection with state-dependent exit probability. Economic modelling, 36:69{78, 2014.
)