بهینه‎سازی سبد سهام با تلفیق کارایی ‌متقاطع و نظریۀ بازی‎ها

نوع مقاله : مقاله علمی پژوهشی

نویسندگان

1 کارشناس ارشد مدیریت صنعتی، دانشکدۀ ادبیات و علوم انسانی، دانشگاه گیلان، رشت، ایران

2 استادیار گروه مدیریت، دانشکدۀ ادبیات و علوم انسانی، دانشگاه گیلان، رشت، ایران

چکیده

­مسئلۀ بهینه­سازی سبد سهام، یکی از مهم‎ترین مسائل سرمایه‎گذاری است. اغلب مدل­های ریاضی که برای حل این مسئله ارائه شده‎اند، بر مبنای سوابق بازده سهم‎‌ها به حل مسئله پرداخته‎اند. به تازگی، استفادۀ کارایی متقاطع حاصل از مدل­های تحلیل پوششی داده­ها به­جای سوابق بازده، در کانون توجه قرار گرفته است. در این پژوهش جدول کارایی متقاطع که مجموعۀ نشانگرهایی از وضعیت­ هر شرکت در شرایط محتمل آینده است، به­عنوان جدول بازده در یک بازی دو نفرۀ جمع صفر بین سرمایه­گذار و بازار در نظر گرفته می‌شود. در این بازی فرض می­شود سرمایه­گذار قادر است شرکت مد­نظر را برای سرمایه‎گذاری برگزیند و بازار می‎تواند وضعیت را به­نفع هر یک از شرکت­ها که خواست، برگرداند. فرض جمع صفر، یک تقابل بین سرمایه­گذار و بازار را تداعی می‌کند که مناسب روحیۀ احتیاط در برابر بازار است­. سبد بهینۀ سهام را احتمالات بهینۀ حاصل از حل مدل بازی برای انتخاب سیاست بهینۀ خریدار مشخص می‌کند. نتایج نشان می­دهد عملکرد روش پیشنهادی در مقایسه با عملکرد سبد بازار قابل قبول است.

کلیدواژه‌ها


عنوان مقاله [English]

Portfolio optimization by synthesis of cross efficiency and Game theory

نویسندگان [English]

  • Mahshid Goodarzi 1
  • keikhosro Yakideh 2
  • Gholamreza Mahfoozi 2
1 MSc of Industrial Management, University of Guilan, Rasht- Iran
2 Assistant Prof. of Management, University of Guilan, Rasht- Iran
چکیده [English]

Portfolio optimization problem is one of the most important investment problems. Most of the mathematical models, presented for solving this problem are based on historical returns of stocks. Utilizing cross efficiencies, calculated by data envelopment analysis models, instead of historical returns, has attracted considerations just recently. In this paper table of cross efficiencies that is a collection of indicators about future possible state of each corporation, is considered as a return matrix of a zero- sum game between the investor and the market. It is assumed in this double game that the Investors can choose the corporation to invest and market can turn the conditions in favor of each of the corporations. Assuming a zero-sum reflects a confrontation between investors and the market which is right for spirit of caution against market. Optimal portfolio determines by the optimum possibilities that is achieved through solving the game in favor of the investor. Results show that the Performance of proposed method is acceptable in compare with market portfolio.

کلیدواژه‌ها [English]

  • Portfolio optimization
  • Cross efficiency
  • Game theory
Acerbi, C. & Tasche, D. (2002). Expected shortfall: a natural coherent alternative value of risk. Journal of Economic Notes, 3(2), 79-88.
Afshar Kazemi, M., Khalilaraghi, M. (2012). Portfolio selection in Tehran Stock Exchange by combining data envelopment analysis and planning. Journal of financial knowledge securities analysis, 5(1), 49-63. (in Persian)
Barbod, M. (2010). Portfolio selection models are designed with DEA. Master's Thesis, Tehran: Allameh university. (in Persian)
Bowlin, W. F. (2000). An analysis of the financial performance of defense business segments using data envelopment analysis. Journal of Accounting and Public Policy, 18(4), 287-310.
Chang, T. J., Yang, S. C. & Chang, K. J. (2009). Portfolio optimization problems in different risk measures using genetic algorithm. Expert Systems with Applications, 36(7), 10529-10537.
Charnes, A., Cooper, W. W., Golany, B., Seiford, L., & Stutz, J. (1985). Foundations of data envelopment analysis for Pareto Koopmans efficient empirical production functions. Journal of econometrics, 30(1-2), 91-107.
Chen, H. H. (2008). Stock selection using data envelopment analysis. Industrial Management & Data Systems, 108(9), 1255-1268.
Cooper, W. W., Park, K. S., & Pastor, J. T. (1999). RAM: A range adjusted measure of inefficiency for use with additive models, and relations to other models and measures in DEA. Journal of Productivity Analysis, 11(1), 5–42.
Doyle, J., & Green, R. (1994). Efficiency and cross-efficiency in DEA: Derivations, meanings and uses. Journal of the operational research society, 45(5), 567-578.
Drechsel, J. (2010). Cooperation in supply chains. In Cooperative lot sizing games in supply chains (pp. 55-61). Springer Berlin Heidelberg.
Edirisinghe, N. C. P., & Zhang, X. (2008). Portfolio selection under DEA-based relative financial strength indicators: case of US industries. Journal of the Operational Research Society, 59(6), 842-856.
Elahi, M., Yoosefi, M. (2014). Mean-variance portfolio optimization approach using the Search Algorithm for hunting. Journal of financial research, 16(1), 37-56. (in Persian)
Goh, J., Zhang, W., Lim, K., Sim, M. (2012). Portfolio­ value-at-risk optimization for asymmetrically distributed asset returns. European Journal of Operational Research, 221, 397-406 .
Jones, C. P. (2007). Investments: analysis and management. John Wiley & Sons.
Jorion, P. (1997). Value at risk: the new benchmark for controlling market risk. Irwin Professional Pub..
Kazemi, A. (1995). Politics poll. Tehran: Ministry of Foreign Affairs. (in Persian)
Kisiala, J. (2015). Conditional Value-at-Risk: Theory and Applications. Dissertation Presented for the Degree of MSc in Operational Research, University of Edinburgh.
Liebrman, J., Hielier, F. (2007). Operation Research. Tranlation: Yazdi &Vaziri. Tehran: Javan.
Lim, S., Oh, K. W. & Zhu, J. (2014). Use of DEA cross-efficiency evaluation in portfolio selection: An application to Korean stock market. European Journal of Operational Research, 236(1), 361-368.
Markowitz, H. (1952). Portfolio selection. The journal of finance, 7(1), 77-91.
Mehregan, M. (2007), Decision with multiple objective. Tehran: Tehran University. (in Persian)
Momeni, M. (2014). New issues in Operations Research. Tehran University.
(in Persian)
Neumann, J. V. (1928). On the theory of game of strategy, in contributions to the theory of games. Vol. IV, Anals of Mathematic Studies, (40), 13-42.
Osborne, M. J. (2004). An introduction to game theory. New York: Oxford University Press.
Rockafellar, R.T., Uryasev, S. (2002). Conditional value-at-risk for generalloss distributions. Journal of Banking and Finance, 26 (7), 1443–1471.
Rockfeller T, Uryasev S, (2000), Optimization of conditional value-atrisk. Journal of Risk, 2(3), 21–24.
Seyed Esfahani, M., Biazaran, M., Gharakhani, M. (2011). A game theoretic approach to coordinate pricing and vertical co-op advertising in manufacturer–retailer supply chains. European Journal of Operational Research, 211 (2), 263-273.
Shakeri, A. (2014). Microeconomics. Tehran: New publishing. (in Persian)
Sharpe, W. F. (1964). Capital asset prices: A theory of market equilibrium underconditions of risk. The journal of finance, 19(3), 425-442.
Tavasoli, Gh. (2012). Sociological Theories. Tehran: Samt. (in Persian)
Valinejad Shoubi, M., Shakiba, A. & Amirsoleimani, O. (2013). Application of Cost Allocation Concepts of Game Theory Approach for Cost Sharing Process, Research Journal of Applied Sciences, Engineering and Technology, 5(12), 3457-3464.
Vantsel, Y. (1995). Game theory and its application to strategic decision-making. Translation: Roshandel & Tayeb. Tehran: Ghoomes. (in Persian)
Woodside-Oriakhi, M., Lucas, C. & Beasley, J.E. (2011). Heuristic algorithms for the cardinality constrained efficient frontier. European Journal of Operational Research, 213 (3), 538-550.
Yeganegi Dasjerdi, V. (2010). Game theory (1). Tehran: Encyclopedia of urban Economies. (in Persian)