Enhanced Index Tracking with a Two-Stage Mixed Integer Programing Model and Pattern Search Algorithm

Document Type : Research Paper

Authors

1 Assistant Prof., Alzahra University, Tehran, Iran

2 Ph.D. Student in financial engineering, Faculty of Management University of Tehran, Iran

3 .Ph.D. Student in finance, Faculty of Management University of Tehran, Iran

Abstract

Index tracking is an important issue in portfolio theory. Index tracking is a passive approach in the portfolio optimization problem based on which finite stock should be selected to track the benchmark index. Enhanced index tracking is a selection of the portfolio with limited stock so that its return is maximized and track error is minimized without buying all stock in benchmark portfolio. The main aim of this paper was to propose a two-stage mixed integer model for enhancing portfolio performance. In order to show the approach performance, top 50 companies were traced. Return, tracking error, excess return and information ratio were used as Portfolio performance measurement. Genetic Algorithm and Pattern Search Algorithm were also used to solve the models.  The findings showed that the two-stage model was better than one stage model. Likewise, pattern search enjoyed higher performance than Genetic Algorithm in the two-stage model. Therefore, two-stage model had higher performance during pattern search algorithm compared to one stage model or Genetic algorithm.

Keywords

References

-          حجازی, رضوان. جعفری سرشت, داود و دلشادی, محمود (1390). » تشکیل صندوق شاخصی بهبود یافته با استفاده از الگوریتم ژنتیک «, فصلنامه بورس اوراق بهادار، شماره 14, صفحات 135 -157.
-          حنیفی، فرهاد. بحرالعلوم، محمدمهدی و جوادی، بابک (1388). » طراحی و تحلیل مقایسه‌ای الگوریتم‌های فرا ابتکاری جهت پیاده‌سازی سرمایه‌گذاری شاخص محور در بورس تهران «, فصلنامه چشم‌انداز مدیریت، شماره 32, صفحات 89 -108.
-          رضایی، علیرضا؛ رنجبران، سجاد (1386). آموزش الگوریتم ژنتیک در نرم‌افزار متلب. تهران، انتشارات آذر.
-          عباسی، ابراهیم. اکبری، صمد (1393). » کاربرد الگوریتم‌های تبرید شبیه‌سازی‌شده و ژنتیک در تشکیل صندوق شاخصی «. فصلنامه مهندسی مالی و مدیریت اوراق بهادار، شماره 20 , صفحات 135 -157.
-          محمدی قلعه­نی، مهدی؛ ابراهیمی، کیومرث (1391) » ارزیابی الگوریتمهای جستجوی مستقیم و ژنتیک در بهینه­سازی پارامترهای مدل غیرخطی ماسکینگام - یک سیلاب از کارون«، مدیریت آب و آبیاری، دوره 2 ، شماره 2، صفحات 1-12.
-          ورسه ای، محسن و شمس، ناصر (1389). » ارائه یک روش حل ابتکاری به‌منظور بهینه‌سازی حل مسئله سبد ردیاب شاخص و پیاده‌سازی آن برای اولین بار در بازار سهام تهران «، هشتمین کنفرانس بین‌المللی مدیریت.
                  -            Abbasi, Ebrahim; Akbari, Samad (2015), application of SA and genetic algorithm in index tracking, No 20, pp.135-157, (in persian).
                  -            Audet, C. & Dennis Jr, J. E. (2002). Analysis of generalized pattern searches. SIAM Journal on optimization, 13(3), 889-903.
                  -            Beasley, J. E. Meade, N. & Chang, T. J. (2003). An evolutionary heuristic for the index tracking problem. European Journal of Operational Research, 148(3), 621-643.
                  -            Canakgoz, N. A. & Beasley, J. E. (2009). Mixed-integer programming approaches for index tracking and enhanced indexation. European Journal of Operational Research, 196(1), 384-399.
                  -            Corielli, F. & Marcellino, M. (2006). Factor based index tracking. Journal of Banking & Finance, 30(8), 2215-2233.
                  -            de Paulo, W. L. Fontova, M. I. V. & de Souza, R. C. (2019). AN ANALYSIS OF A MEAN-VARIANCE ENHANCED INDEx TRACKING PROBLEM WITH WEIGHTS CONSTRAINTS.
                  -            Erdogan, E. Goldfarb, D. & Iyengar, G. (2004). Robust portfolio management.
                  -            Focardi, S. M. & Fabozzi 3, F. J. (2004). A methodology for index tracking based on time-series clustering. Quantitative Finance, 4(4), 417-425.
                  -            García, F. Guijarro, F. & Oliver, J. (2018). Index tracking optimization with cardinality constraint: a performance comparison of genetic algorithms and tabu search heuristics. Neural Computing and Applications, 30(8), 2625-2641.
                  -            Gilli, M. & Këllezi, E. (2002). The threshold accepting heuristic for index tracking. In Financial engineering, e-commerce and supply chain (pp. 1-18). Springer, Boston, MA.
                  -      Hanifi et al(2010), Implementation and aomparision analyses of metaheuristic for index tracking portfolio, Financial Management Perspective, No 20, pp.89-108(in persian).
                  -      Hejazi et all(2012), enhanced index traking with genetic algorithm, QUARTERLY JOURNAL OF SECURITIES EXCHANGE,No 14 ,pp.135-157(in persian).
                  -            Jansen R and Dijk H. (2002). "Index Tracking, cointegration and equity market regimes". International Journal Of Finance And Economics, Vol 10, 213-237
                  -            Konno, H. & Wijayanayake, A. (2001). Minimal cost index tracking under nonlinear transaction costs and minimal transaction unit constraints. International Journal of Theoretical and Applied Finance, 4(06), 939-957.
                  -            Kwon, R. H. & Wu, D. (2017). Factor-based robust index tracking. Optimization and Engineering, 18(2), 443-466.
                  -            Lam, W. S. & Lam, W. H. (2016). Mathematical modeling of enhanced index tracking with optimization model. J. Numer. Anal. Appl. Math, 1(1), 1-5.
                  -            Lewis RM and Torczon V (2000) Pattern search methods for linearly constrained minimization. SIAM Journal on Optimization. Pp. 917-941.
                  -            Lewis, R. M. Torczon, V. & Trosset, M. W. (1998). Why pattern search works (No. ICASE-98-57). Institute for computer applications in Science and engineering hampton va.
                  -            Mohammadi ghaleni, mehdi; Kiomars, Ebrahimi(2013), Evaluation of direct search and genetic algorithms in optimization of muskingum nonlinear model parameters - a flooding of Karoun river, journal of water and irrigation management, No2, pp.1-12, (in persian).
                  -            Rafaely, B. & Bennell, J. A. (2006). Optimisation of FTSE 100 tracker funds: A comparison of genetic algorithms and quadratic programming. Managerial Finance, 32(6), 477-492.
                  -            Rezaie alireza and Ranjbaran Sajad(2008), genetic algorithm learning, Azar publicaton(in persian).
                  -            Roll, R. (1992). A mean/variance analysis of tracking error. The Journal of Portfolio Management, 18(4), 13-22.
                  -            Rudolf, M. Wolter, H. J. & Zimmermann, H. (1999). A linear model for tracking error minimization. Journal of Banking & Finance, 23(1), 85-103.
                  -            Strong, R. (2008). Portfolio construction, management, and protection. Nelson Education.
                  -      varasai, mohsen; Naser, Shams (2011), present a solution based metahuristic algorithm for index traking in TSE, 8 th international management confroncess((in persian).
 

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History

  • Receive Date: 23 February 2019
  • Revise Date: 27 September 2019
  • Accept Date: 09 October 2019

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