Index tracking using Two-tail Mixed Conditional Value-at-risk in Tehran Stock Exchange

Document Type : Research Paper

Authors

1 Assistant Prof., Department of Finance and Insurance, Faculty of Management, University of Tehran, Tehran, Iran.

2 PhD Candidate, Department of Finance and Insurance, Faculty of Management, University of Tehran, Tehran, Iran.

Abstract

Objective: Passive management is an investing strategy that tracks a market value-weighted index or portfolio. It seeks to minimize the cost of investment fees and to avoid undesirable repercussions of the unpredictability of future trends. Active portfolio management tries to beat the market while passive portfolio management pursues a similar risk-return pattern to that of the market index. Index tracking is a passive investment strategy in the stock market that aims to make a portfolio using constituents of an index. It seeks to mimic its behavior without purchasing all of its constituents. This study aimed to track Tehran Exchange Dividend & Price Index (TEDPIX).
Methods: In this study, portfolios were tracked and their performances were examined by applying a two-tail mixed conditional value-at-risk model (main model). Optimizing TMCVaR is a linear program that minimizes the upper deviation and the downside deviation from the benchmark index. The investigated sample included the weekly data gathered from 2011/3/21 to 2018/20/3. The data was divided into 26-time frames including 52 in-sample data and 12 out-of-sample data.
Results: Statistical tests confirmed the portfolios resulting from the main model were successful in tracking the index. As a result, the investigated model was recognized as capable of tracking the index. However, due to the tracking error and information ratio, the two models were not statistically different. In the present study, the two models showed the same performance in tracking the index.
Conclusion: In this study, a linear mathematical programming model was proposed to form index tracking portfolios. The results showed that although the main model was successful in index-tracking it did not outperform the mean absolute deviation model in terms of reduction in tracking error and increasing information ratio.

Keywords

References

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. https://doi.org/10.1016/S0377-2217(02)00425-3
Boston Consulting Group, Global Asset Management (2019) Will These ’20s Roar?
Bruni, R., Cesarone, F., Scozzari, A., & Tardella, F. (2017). On exact and approximate stochastic dominance strategies for portfolio selection. European Journal of Operational Research, 259(1), 322–329. https://doi.org/10.1016/j.ejor.2016.10.006
Buckley, I. R. C., & Korn, R. (1998). Optimal Index Tracking Under Transaction Costs and Impulse Control. International Journal of Theoretical and Applied Finance, 01(03), 315–330. https://doi.org/10.1142/S0219024998000187
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. https://doi.org/10.1016/j.ejor.2008.03.015
Dose, C., & Cincotti, S. (2005). Clustering of financial time series with application to index and enhanced index tracking portfolio. Physica A: Statistical Mechanics and Its Applications, 355(1), 145–151. https://doi.org/10.1016/j.physa.2005.02.078
Eyvazloo, R., Shafizadeh, M. & Ghahramani, A. (2017). Index Tracking and Enhanced Indexing Using Co-integration and Correlation Approaches. Journal of Financial Researches, 19(3), 457-474. (in Persian)
Fallahpour, S. & Tondnevis, F. (2015). Application of an optimization model for constructing an index tracker portfolio and considering the uncertainty of model parameters by using of robust optimization approach. Journal of Financial Researches, 17(2), 325-340.
(in Persian)
Fallahpour, S. & Tondnevis, F. & Hashemi, A. (2015). The application of robust optimization for index tracking by using of single index model based on fifty active company index of tehran stock exchange. Journal of Financial Engineering and Securities Management (Portfolio Management), 6(24), 115-134. (in Persian)
French, K. R. (2008). Presidential Address: The Cost of Active Investing. The Journal of Finance, 63(4), 1537–1573. https://doi.org/10.1111/j.1540-6261.2008.01368.x
Goel, A., Sharma, A., & Mehra, A. (2018). Index tracking and enhanced indexing using mixed conditional value-at-risk. Journal of Computational and Applied Mathematics, 335, 361–380. https://doi.org/10.1016/j.cam.2017.12.015
Mansini, R., Ogryczak, W., & Speranza, M. G. (2007). Conditional value at risk and related linear programming models for portfolio optimization. Annals of Operations Research, 152(1), 227–256. https://doi.org/10.1007/s10479-006-0142-4
Markowitz, H. (1952). Portfolio Selection. The Journal of Finance, 7(1), 77–91. https://doi.org/10.1111/j.1540-6261.1952.tb01525.x
Meade, N., & Salkin, G. R. (1989). Index Funds—Construction and Performance Measurement. Journal of the Operational Research Society, 40(10), 871–879. https://doi.org/10.1057/jors.1989.155
Nabizade, A. Gharehbaghi, H. & Behzadi, A. (2017). Index Tracking Optimization under down Side Beta and Evolutionary Based Algorithms. Journal of Financial Researches, 19(2), 319-340. (in Persian)
Rockafellar, R. T., & Uryasev, S. (2000). Optimization of conditional value-at-risk. The Journal of Risk, 2(3), 21–41. https://doi.org/10.21314/JOR.2000.038
Rockafellar, R. T., & Uryasev, S. (2002). Conditional value-at-risk for general loss distributions. Journal of Banking & Finance, 26(7), 1443–1471. https://doi.org/10.1016/S0378-4266(02)00271-6
Roll, R. (1992). A Mean/Variance Analysis of Tracking Error. The Journal of Portfolio Management, 18(4), 13–22. https://doi.org/10.3905/jpm.1992.701922
Rudd, A. (1980). Optimal Selection of Passive Portfolios. Financial Management, 9(1), 57. https://doi.org/10.2307/3665314
Treynor, J. L., & Black, F. (1973). How to Use Security Analysis to Improve Portfolio Selection. The Journal of Business, 46(1), 66–86. Retrieved from http://www.jstor.org/stable/2351280
Wang, M., Xu, C., Xu, F., & Xue, H. (2012). A mixed 0–1 LP for index tracking problem with CVaR risk constraints. Annals of Operations Research, 196(1), 591–609. https://doi.org/10.1007/s10479-011-1042-9
Financial Research Journal
Volume 23, Issue 4
2022
Pages 545-563

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