IDEAS home Printed from https://ideas.repec.org/a/eee/ecofin/v59y2022ics1062940821002175.html
   My bibliography  Save this article

Two new mean–variance enhanced index tracking models based on uncertainty theory

Author

Listed:
  • Yang, Tingting
  • Huang, Xiaoxia

Abstract

The enhanced index tracking (EIT) problem is concerned with selecting a tracking portfolio that achieves an excess return over a given benchmark with a minimum tracking error. This paper explores the EIT problem by providing two new mean–variance EIT models based on uncertainty theory where stock returns are treated as uncertain variables instead of random variables and stock return distributions are estimated by experts instead of from historical data. First, this paper formulates an uncertain enhanced index tracking (UEIT) model and analyzes the characteristic of the UEIT frontier. Then to reduce the tracking portfolio’s risk, this paper adds a risk index (RI) constraint to the UEIT model and proposes a UEIT-RI model. Next, by comparing the UEIT and UEIT-RI models this paper gives the advantages of the two models. Investors can choose the model according to their preferences. Finally, this paper conducts numerical examples to illustrate the application of the two models and the analysis results.

Suggested Citation

  • Yang, Tingting & Huang, Xiaoxia, 2022. "Two new mean–variance enhanced index tracking models based on uncertainty theory," The North American Journal of Economics and Finance, Elsevier, vol. 59(C).
    • Handle: RePEc:eee:ecofin:v:59:y:2022:i:c:s1062940821002175
    DOI: 10.1016/j.najef.2021.101622
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S1062940821002175
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.najef.2021.101622?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Huang, Xiaoxia & Yang, Tingting, 2020. "How does background risk affect portfolio choice: An analysis based on uncertain mean-variance model with background risk," Journal of Banking & Finance, Elsevier, vol. 111(C).
    2. Hodges, Stewart D, 1976. "Problems in the application of portfolio selection models," Omega, Elsevier, vol. 4(6), pages 699-709.
    3. Gruber, Martin J, 1996. "Another Puzzle: The Growth in Activity Managed Mutual Funds," Journal of Finance, American Finance Association, vol. 51(3), pages 783-810, July.
    4. Alexander, Gordon J. & Baptista, Alexandre M., 2010. "Active portfolio management with benchmarking: A frontier based on alpha," Journal of Banking & Finance, Elsevier, vol. 34(9), pages 2185-2197, September.
    5. Zhilin Kang & Xun Li & Zhongfei Li & Shushang Zhu, 2019. "Data-driven robust mean-CVaR portfolio selection under distribution ambiguity," Quantitative Finance, Taylor & Francis Journals, vol. 19(1), pages 105-121, January.
    6. Huang, Xiaoxia & Ying, Haiyao, 2013. "Risk index based models for portfolio adjusting problem with returns subject to experts' evaluations," Economic Modelling, Elsevier, vol. 30(C), pages 61-66.
    7. Gnägi, M. & Strub, O., 2020. "Tracking and outperforming large stock-market indices," Omega, Elsevier, vol. 90(C).
    8. Jin, Xiu & Chen, Na & Yuan, Ying, 2019. "Multi-period and tri-objective uncertain portfolio selection model: A behavioral approach," The North American Journal of Economics and Finance, Elsevier, vol. 47(C), pages 492-504.
    9. Caporin, Massimiliano & Lisi, Francesco, 2013. "A Conditional Single Index model with Local Covariates for detecting and evaluating active portfolio management," The North American Journal of Economics and Finance, Elsevier, vol. 26(C), pages 236-249.
    10. Guastaroba, G. & Mansini, R. & Ogryczak, W. & Speranza, M.G., 2016. "Linear programming models based on Omega ratio for the Enhanced Index Tracking Problem," European Journal of Operational Research, Elsevier, vol. 251(3), pages 938-956.
    11. Xiaoxia Huang & Hao Di, 2020. "Uncertain portfolio selection with mental accounts," International Journal of Systems Science, Taylor & Francis Journals, vol. 51(12), pages 2079-2090, September.
    12. Alexander, Gordon J. & Baptista, Alexandre M., 2008. "Active portfolio management with benchmarking: Adding a value-at-risk constraint," Journal of Economic Dynamics and Control, Elsevier, vol. 32(3), pages 779-820, March.
    13. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    14. Xiaoxia Huang & Guowei Jiang, 2021. "Portfolio management with background risk under uncertain mean-variance utility," Fuzzy Optimization and Decision Making, Springer, vol. 20(3), pages 315-330, September.
    15. de Paulo, Wanderlei Lima & de Oliveira, Estela Mara & do Valle Costa, Oswaldo Luiz, 2016. "Enhanced index tracking optimal portfolio selection," Finance Research Letters, Elsevier, vol. 16(C), pages 93-102.
    16. Sant’Anna, Leonardo Riegel & Caldeira, João Frois & Filomena, Tiago Pascoal, 2020. "Lasso-based index tracking and statistical arbitrage long-short strategies," The North American Journal of Economics and Finance, Elsevier, vol. 51(C).
    17. Wang, Xuting & Huang, Xiaoxia, 2019. "A risk index to model uncertain portfolio investment with options," Economic Modelling, Elsevier, vol. 80(C), pages 284-293.
    18. Sant’Anna, Leonardo R. & Filomena, Tiago P. & Caldeira, João F., 2017. "Index tracking and enhanced indexing using cointegration and correlation with endogenous portfolio selection," The Quarterly Review of Economics and Finance, Elsevier, vol. 65(C), pages 146-157.
    19. Georg Pflug & David Wozabal, 2007. "Ambiguity in portfolio selection," Quantitative Finance, Taylor & Francis Journals, vol. 7(4), pages 435-442.
    20. Tversky, Amos & Kahneman, Daniel, 1986. "Rational Choice and the Framing of Decisions," The Journal of Business, University of Chicago Press, vol. 59(4), pages 251-278, October.
    21. Rudolf, Markus & Wolter, Hans-Jurgen & Zimmermann, Heinz, 1999. "A linear model for tracking error minimization," Journal of Banking & Finance, Elsevier, vol. 23(1), pages 85-103, January.
    22. Canakgoz, N.A. & Beasley, J.E., 2009. "Mixed-integer programming approaches for index tracking and enhanced indexation," European Journal of Operational Research, Elsevier, vol. 196(1), pages 384-399, July.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Tingting Yang & Xiaoxia Huang, 2022. "A New Portfolio Optimization Model Under Tracking-Error Constraint with Linear Uncertainty Distributions," Journal of Optimization Theory and Applications, Springer, vol. 195(2), pages 723-747, November.
    2. Huang, Jinbo & Li, Yong & Yao, Haixiang, 2018. "Index tracking model, downside risk and non-parametric kernel estimation," Journal of Economic Dynamics and Control, Elsevier, vol. 92(C), pages 103-128.
    3. Huang, Jinbo & Li, Yong & Yao, Haixiang, 2022. "Partial moments and indexation investment strategies," Journal of Empirical Finance, Elsevier, vol. 67(C), pages 39-59.
    4. Yang, Tingting & Huang, Xiaoxia, 2022. "Active or passive portfolio: A tracking error analysis under uncertainty theory," International Review of Economics & Finance, Elsevier, vol. 80(C), pages 309-326.
    5. Ruchika Sehgal & Aparna Mehra, 2019. "Enhanced indexing using weighted conditional value at risk," Annals of Operations Research, Springer, vol. 280(1), pages 211-240, September.
    6. Huang, Xiaoxia & Ma, Di & Choe, Kwang-Il, 2023. "Uncertain mean–variance portfolio model with inflation taking linear uncertainty distributions," International Review of Economics & Finance, Elsevier, vol. 87(C), pages 203-217.
    7. Li, Xuepeng & Xu, Fengmin & Jing, Kui, 2022. "Robust enhanced indexation with ESG: An empirical study in the Chinese Stock Market," Economic Modelling, Elsevier, vol. 107(C).
    8. Ruchika Sehgal & Aparna Mehra, 2023. "Quantile Regression Based Enhanced Indexing with Portfolio Rebalancing," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 21(3), pages 721-742, September.
    9. Patrizia Beraldi & Maria Elena Bruni, 2022. "Enhanced indexation via chance constraints," Operational Research, Springer, vol. 22(2), pages 1553-1573, April.
    10. Li, Bo & Zhang, Ranran, 2021. "A new mean-variance-entropy model for uncertain portfolio optimization with liquidity and diversification," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    11. Palomba, Giulio & Riccetti, Luca, 2012. "Portfolio frontiers with restrictions to tracking error volatility and value at risk," Journal of Banking & Finance, Elsevier, vol. 36(9), pages 2604-2615.
    12. Stucchi, Patrizia, 2015. "A unified approach to portfolio selection in a tracking error framework with additional constraints on risk," The Quarterly Review of Economics and Finance, Elsevier, vol. 56(C), pages 165-174.
    13. Strub, O. & Baumann, P., 2018. "Optimal construction and rebalancing of index-tracking portfolios," European Journal of Operational Research, Elsevier, vol. 264(1), pages 370-387.
    14. Li, Bo & Huang, Yayi, 2023. "Uncertain random portfolio selection with different mental accounts based on mixed data," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    15. Filippi, C. & Guastaroba, G. & Speranza, M.G., 2016. "A heuristic framework for the bi-objective enhanced index tracking problem," Omega, Elsevier, vol. 65(C), pages 122-137.
    16. Gnägi, M. & Strub, O., 2020. "Tracking and outperforming large stock-market indices," Omega, Elsevier, vol. 90(C).
    17. Lorenzo Reus & Rodolfo Prado, 2022. "Need to Meet Investment Goals? Track Synthetic Indexes with the SDDP Method," Computational Economics, Springer;Society for Computational Economics, vol. 60(1), pages 47-69, June.
    18. Chen, Qi-an & Hu, Qingyu & Yang, Hu & Qi, Kai, 2022. "A kind of new time-weighted nonnegative lasso index-tracking model and its application," The North American Journal of Economics and Finance, Elsevier, vol. 59(C).
    19. Doering, Jana & Kizys, Renatas & Juan, Angel A. & Fitó, Àngels & Polat, Onur, 2019. "Metaheuristics for rich portfolio optimisation and risk management: Current state and future trends," Operations Research Perspectives, Elsevier, vol. 6(C).
    20. Giulio PALOMBA & Luca RICCETTI, 2013. "Asset Management with TEV and VaR;Constraints: the Constrained Efficient;Frontiers," Working Papers 392, Universita' Politecnica delle Marche (I), Dipartimento di Scienze Economiche e Sociali.

    More about this item

    Keywords

    Enhanced index tracking; Portfolio selection; Uncertainty theory; Risk index;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:ecofin:v:59:y:2022:i:c:s1062940821002175. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/620163 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.