مطالعه تطبیقی مدل بهینه سازی پرتفوی چند دوره ای چندهدفه در محیط اعتبار فازی با معیارهای متفاوت ریسک

نوع مقاله: مقاله پژوهشی

نویسندگان

1 گروه مدیریت مالی، واحد علی‌آباد کتول، دانشگاه آزاد اسلامی، علی‌آباد کتول، ایران

2 گروه مهندسی مالی، واحد علی‌آباد کتول، دانشگاه آزاد اسلامی، علی‌آباد کتول، ایران،

3 گروه مهندسی صنایع، ‌واحد تهران جنوب، دانشگاه آزاد اسلامی، تهران، ایران

4 گروه مدیریت مالی، واحد علی‌آباد کتول، دانشگاه آزاد اسلامی، علی آباد کتول، ایران

چکیده

هدف از پژوهش حاضر مقایسه تطبیقی مدل‌های بهینه‌سازی پرتفوی در محیط اعتبار فازی می‌باشد. به این منظور سه مدل بهینه‌سازی پرتفوی طراحی گردید. به‌جای در نظر گرفتن مدل تک دوره‌ای پرتفوی از مدل سه دوره‌ای استفاده گردید. معیارهای ریسک استفاده‌شده در مدل‌ها عبارت‌اند از ارزش در معرض خطر، ارزش در معرض خطر میانگین و نیم آنتروپی. همچنین به‌منظور نزدیک شدن مدل به دنیای واقعی سرمایه‌گذاری با در نظر گرفتن هزینه معاملات و سرمایه‌گذاری بخشی از ثروت در دارایی بدون ریسک علاوه بر محدودیت‌های اصلی، از محدودیت‌هایی نظیر، حداقل و حداکثر تخصیص ثروت به هر دارایی، ‌حداقل و حداکثر تعداد سهام موجود در پرتفوی و همچنین از آنتروپی نسبت برای رسیدن به حداقل درجه تنوع‌بخشی استفاده شد. هر سه مدل این پژوهش با استفاده از الگوریتم MOPSO اجرا گردید. نتایج حاصل از ارزیابی عملکرد پرتفوهای بهینه با در نظر گرفتن معیارهای شارپ و ترینر نشان داد، مدل Mean- AVaR نسبت به دو مدل Mean- Semi Entropy و Mean-VaR عملکرد بهتری دارد.

کلیدواژه‌ها


عنوان مقاله [English]

A Comparative Study of Multi-Objective Multi-Period Portfolio Optimization Models in a Fuzzy Credibility Environment Using Different Risk Measures

نویسندگان [English]

  • Amir Shiri Ghahi 1
  • Hosein Didehkhani 2
  • Kaveh Khalili Damghani 3
  • Parviz Saeedi 4
1 islamic azad university of aliabad
2 islamic azad university of aliabad
3 Department of Industrial engineering islamic azad university of tehran
4 islamic azad university of aliabad
چکیده [English]

The purpose of the present research is to compare portfolio optimization models in a fuzzy credibility environment, aimed for end-of-period wealth maximization and risk minimization. The investor’s risk was measured using the Value at Risk (VaR), Average Value at Risk (AVaR) and semi Entropy. In order to get closer to the real world investment model, while allowing for transaction costs and investing part of wealth in risk-free assets, in addition to the cardinal constraints, other constraints including the minimum and maximum amount of wealth assigned to each asset, and the minimum and maximum number of stocks present in portfolio were applied. The results of the multi-period models running by MOPSO algorithm indicated for the models Mean-AVaR, Mean-Semi Entropy, and Mean-VaR, respectively, performed better, in terms of Sharp and Treynor measures. 

کلیدواژه‌ها [English]

  • Portfolio Optimization
  • Fuzzy Credibility Theory
  • risk
  • MOPSO Algorithm
-      پور احمدی، زهرا و نجفی، امیرعباس، (1394). "بهینه‌سازی پویای سبد سرمایه‌گذاری با توجه به هزینه معاملات"، مهندسی مالی و مدیریت اوراق بهادار، (22)6، صص. 127-146.

-      کاظمی میان گسکری، مینا؛ یاکیده، کیخسرو و قلی زاده، محمدحسن، (1396). "بهینه یابی سبد سهام (کاربرد مدل ارزش درمعرض ریسک بر روی کارایی متقاطع)". راهبرد مدیریت مالی, (5)2,  صص.159-183. . doi: 10.22051/jfm.2017.12040.1155

-      همائی‌فر، ساغر و روغنیان، عماد، (1395). "به کارگیری الگوهای بهینه‌سازی پایدار و برنامه‌ریزی آرمانی در مسئله انتخاب سبد سرمایه‌گذاری چند دوره‌ای"، مهندسی مالی و مدیریت اوراق بهادار، (28)7، صص.153-167.

-      Andersson, F., Mausser, H., Rosen, D., & Uryasev, S. (2001). “Credit risk optimization with conditional value-at-risk criterion”. Mathematical Programming, 89(2), pp.273-291.

-      Artzner, P., Delbaen, F., Eber, J. M., & Heath, D. (1999). “Coherent measures of risk”. Mathematical finance, 9(3), pp.203-228.‏

-      Campbell, R., Huisman, R., & Koedijk, K. (2001). “Optimal portfolio selection in a Value-at-Risk framework”. Journal of Banking & Finance, 25(9), pp.1789-1804.‏

-      Chen, Z. (2005). “Multiperiod consumption and portfolio decisions under the multivariate GARCH model with transaction costs and CVaR-based risk control”. OR Spectrum, 27(4), pp.603-632.

-      Chen, Z., & Song, Z. (2012). “Dynamic portfolio optimization under multi-factor model in stochastic markets”. OR spectrum, 34(4), pp.885-919.

-      Chunhachinda, P., Dandapani, K., Hamid, S., & Prakash, A. J. (1997). “Portfolio selection and skewness: Evidence from international stock markets”. Journal of Banking & Finance, 21(2), pp.143-167.

-      Coello, C. A. C., Lamont, G. B., & Van Veldhuizen, D. A. (2007). “Evolutionary algorithms for solving multi-objective problems (Vol. 5). New York: Springer.

-      Cong, F., & Oosterlee, C. W. (2016). “Multi-period mean–variance portfolio optimization based on Monte-Carlo simulation”. Journal of Economic Dynamics and Control, 64, pp.23-38.

-      Consigli, G. (2002). “Tail estimation and mean–VaR portfolio selection in markets subject to financial instability”. Journal of Banking & Finance, 26(7), pp.1355-1382.

-      DeMiguel, V., Mei, X., & Nogales, F. J. (2016). “Multiperiod Portfolio Optimization with Multiple Risky Assets and General Transaction Costs”. Journal of Banking & Finance.

-      DeMiguel, V., Mei, X., & Nogales, F. J. (2016). “Multiperiod portfolio optimization with multiple risky assets and general transaction costs”. Journal of Banking & Finance, 69, pp.108-120.

-            Deng, X., & Li, R.(2012). “A portfolio selection model with borrowing constraint based on possibility theory”. Applied Soft Computing, 12(2), pp.754-758.

-      Dubois, D., & Prade, H. (2012). Possibility theory: an approach to computerized processing of uncertainty. “Springer Science & Business Media”.

-      Feinstein, C. D., & Thapa, M. N. (1993). “A Reformulation of a Mean-absolute Deviation Portfolio Optimization Model”. Management Science, 39(12).

-      Geyer, A., Hanke, M., & Weissensteiner, A. (2009). “A stochastic programming approach for multi-period portfolio optimization”. Computational Management Science, 6(2), pp.187-208.

-      Grootveld, H., & Hallerbach, W. (1999). “Variance vs downside risk: Is there really that much difference?” European Journal of operational research, 114(2), pp.304-319.

-      Guo, S., Yu, L., Li, X., & Kar, S. (2016). “Fuzzy multi-period portfolio selection with different investment horizons”. European Journal of Operational Research, 254(3), pp.1026-1035.

-      Gupta, P., Mehlawat, M. K., Inuiguchi, M., & Chandra, S. (2014). “Fuzzy Portfolio Optimization”. Springer-Verlag, Berlin.

-      Homaeifar, S., Roghanian, E. (2016). “The Application of Robust Optimization and Goal Programming in Multi Period Portfolio Selection Problem”.Financial Engineering and Portfolio Managemen, 7(28), pp.153-167. (In Persian)

-      Huang, X. (2006). “Fuzzy chance-constrained portfolio selection. Applied mathematics and computation”, 177(2), pp.500-507.

-      Huang, X. (2008). “Mean-variance model for fuzzy capital budgeting”. Computers & Industrial Engineering, 55(1), pp.34-47.

-      Huang, X. (2008). “Risk curve and fuzzy portfolio selection”. Computers & Mathematics with Applications, 55(6), pp.1102-1112.

-      Huang, X. (2008). “Mean-entropy models for fuzzy portfolio selection”. IEEE Transactions on Fuzzy Systems, 16(4), pp.1096-1101.

-      Kazemi miyangaskari, M., Yakideh, K., Gholizadeh, M. (2017). “Portfolio optimization (the application of Value at Risk model on cross efficiency)”. Financial Management Strategy, 5(2), pp.159-183. (In Persian)

-      Kapur, J. N. (1990). “Maximum Entropy Models in Science and Engineering”. Wiley Eastern Limited, New Delhi

-      Konno, H., & Yamazaki, H. (1991). “Mean-absolute deviation portfolio optimization model and its applications to Tokyo stock market”. Management science, 37(5), pp.519-531.

-      Li, D., & Ng, W. L. (2000). “Optimal dynamic portfolio selection: Multiperiod mean‐variance formulation”. Mathematical Finance, 10(3), pp.387-406.

-      Li, X., Qin, Z., & Kar, S. (2010). “Mean-variance-skewness model for portfolio selection with fuzzy returns”. European Journal of Operational Research, 202(1), pp.239-247.

-      Li, X., Zhang, Y., Wong, H. S., & Qin, Z. (2009). “A hybrid intelligent algorithm for portfolio selection problem with fuzzy returns”. Journal of Computational and Applied Mathematics, 233(2), pp.264-278.

-      Lin, C. C., & Liu, Y. T. (2008).”Genetic algorithms for portfolio selection problems with minimum transaction lots”. European Journal of Operational Research, 185(1), pp.393-404.

-      Liu, B. D. (2004). “Uncertain theory: An introduction to its axiomatic foundation. Berlin”: Springer-Verlag.

-      Liu, B., & Liu, Y. K. (2002). “Expected value of fuzzy variable and fuzzy expected value models”. Fuzzy Systems, IEEE Transactions on, 10(4), pp.445-450.

-      Liu, Y. J., & Zhang, W. G. (2015). “A multi-period fuzzy portfolio optimization model with minimum transaction lots”. European Journal of Operational Research, 242(3), pp.933-941.

-      Liu, Y. J., Zhang, W. G., & Xu, W. J. (2012). ‘Fuzzy multi-period portfolio selection optimization models using multiple criteria”. Automatica, 48(12), pp.3042-3053.‏

-      Liu, Y. J., Zhang, W. G., & Zhang, Q. (2016). “Credibilistic multi-period portfolio optimization model with bankruptcy control and affine recourse”. Applied Soft Computing, 38, pp.890-906.‏

-      Liu, Y.-J., Zhang, W.-G., & Zhang, P. (2013). “A multi-period portfolio selection optimization model by using interval analysis”. Economic Modelling, 33, pp.113-119.

-      Liu, Y.-J., Zhang, W.-G., & Zhang, Q. (2016). “Credibilistic multi-period portfolio optimization model with bankruptcy control and affine recourse”. Applied Soft Computing, 38, pp.890-906.

-      Markowitz, H., & Selection, P. (1959). “Efficient diversification of investments”. John Wiley and Sons, 12, pp.26-31.

-      Mehlawat, M. K. (2016). “Credibilistic mean-entropy models for multi-period portfolio selection with multi-choice aspiration levels”. Information Sciences, 345, pp.9-26.

-      Mossin, J. (1968). “Optimal multiperiod portfolio policies”. The Journal of Business, 41(2), pp.215-229.

-      Peng, J. (2011). “Credibilistic value and average value at risk in fuzzy risk analysis”. Fuzzy Information and Engineering, 3(1), pp.69-79.‏

-      Philippatos, G. C., & Wilson, C. J. (1972). “Entropy, market risk, and the selection of efficient portfolios”. Applied Economics, 4(3), pp.209-220.

-      Pourahmadi, Z., Najafi, A.A. (2015). “Dynamic Portfolio Optimization with Transaction Cost”. Financial Engineering and Portfolio Management, 6(24), pp.152-172. (In Persian)

-      Rachev, S. T., Stoyanov, S. V., & Fabozzi, F. J. (2008). “Advanced stochastic models, risk assessment, and portfolio optimization: The ideal risk, uncertainty, and performance measures (Vol. 149). John Wiley & Sons.‏

-      Rockafellar, R. T., & Uryasev, S. (2000). “Optimization of conditional value-at-risk”. Journal of risk, 2, pp.21-42.

-      Rockafellar, R. T., Uryasev, S., & Zabarankin, M. (2006). “Generalized deviations in risk analysis”. Finance and Stochastics, 10(1), pp.51-74.‏

-      Sadjadi, S. J., Seyedhosseini, S. M., & Hassanlou, K. (2011). “Fuzzy multi period portfolio selection with different rates for borrowing and lending”. Applied Soft Computing, 11(4), pp.3821-3826.

-      Speranza, M. G. (1993). “Linear programming models for portfolio optimization”. Finance, 14, pp.107–123.

-            Usta, I., & Kantar, Y. M. (2011). “Mean-variance-skewness-entropy measures: a multi-objective approach for portfolio selection”. Entropy, 13(1), pp.117-133.

-      Vercher, E., & Bermúdez, J. D. (2015). “Portfolio optimization using a credibility mean-absolute semi-deviation model”. Expert Systems with Applications, 42(20), pp.7121-7131.

-      Wei, S. Z., & Ye, Z. X. (2007). “Multi-period optimization portfolio with bankruptcy control in stochastic market”. Applied Mathematics and Computation, 186(1), pp.414-425.

-      Yao, H., Li, Z., & Li, D. (2016). “Multi-period mean-variance portfolio selection with stochastic interest rate and uncontrollable liability”. European Journal of Operational Research, 252(3), pp.837-851.

-            Zhang, W. G., Liu, Y. J., & Xu, W. J. (2012). “A possibilistic mean-semivariance-entropy model for multi-period portfolio selection with transaction costs”. European Journal of Operational Research, 222(2), pp.341-349.

-      Zhou, J., Li, X., & Pedrycz, W. (2016). “Mean-Semi-Entropy Models of Fuzzy Portfolio Selection”. IEEE Transactions on Fuzzy Systems, 24(6), pp.1627-1636.

-      Zhou, R., Cai, R., & Tong, G. (2013). “Applications of entropy in finance: A review”. Entropy, 15(11), pp.4909-4931.

-      Zhu, S. S., Li, D., & Wang, S. Y. (2004). “Risk control over bankruptcy in dynamic portfolio selection: A generalized mean-variance formulation”. IEEE transactions on Automatic Control, 49(3), pp.447-457.