IDEAS home Printed from https://ideas.repec.org/p/wpa/wuwpge/0510012.html
   My bibliography  Save this paper

Tracking Error: a multistage portfolio model

Author

Listed:
  • Diana Barro

    (Department of Applied Mathematics - University of Venice)

  • Elio Canestrelli

    (Department of Applied Mathematics - University of Venice)

Abstract

We study multistage tracking error problems. Different tracking error measures, commonly used in static models, are discussed as well as some problems which arise when we move from static to dynamic models. We are interested in dynamically replicating a benchmark using only a small subset of assets, considering transaction costs due to rebalancing and introducing a liquidity component in the portfolio. We formulate and solve a multistage tracking error model in a stochastic programming framework. We numerically test our model by dynamically replicating the MSCI Euro index. We consider an increasing number of scenarios and assets and show the superior performance of the dynamically optimized tracking portfolio over static strategies.

Suggested Citation

  • Diana Barro & Elio Canestrelli, 2005. "Tracking Error: a multistage portfolio model," GE, Growth, Math methods 0510012, University Library of Munich, Germany.
    • Handle: RePEc:wpa:wuwpge:0510012
    Note: Type of Document - pdf; pages: 25
    as

    Download full text from publisher

    File URL: https://econwpa.ub.uni-muenchen.de/econ-wp/ge/papers/0510/0510012.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Ron Dembo & Dan Rosen, 1999. "The practice of portfolio replication. A practical overview of forward and inverse problems," Annals of Operations Research, Springer, vol. 85(0), pages 267-284, January.
    2. R. T. Rockafellar & Roger J.-B. Wets, 1991. "Scenarios and Policy Aggregation in Optimization Under Uncertainty," Mathematics of Operations Research, INFORMS, vol. 16(1), pages 119-147, February.
    3. Barro, Diana & Canestrelli, Elio, 2005. "Dynamic portfolio optimization: Time decomposition using the Maximum Principle with a scenario approach," European Journal of Operational Research, Elsevier, vol. 163(1), pages 217-229, May.
    4. Cesari, Riccardo & Cremonini, David, 2003. "Benchmarking, portfolio insurance and technical analysis: a Monte Carlo comparison of dynamic strategies of asset allocation," Journal of Economic Dynamics and Control, Elsevier, vol. 27(6), pages 987-1011, April.
    5. Gaivoronski, Alexei A. & Krylov, Sergiy & van der Wijst, Nico, 2005. "Optimal portfolio selection and dynamic benchmark tracking," European Journal of Operational Research, Elsevier, vol. 163(1), pages 115-131, May.
    6. Hiroshi Konno & Hiroaki Yamazaki, 1991. "Mean-Absolute Deviation Portfolio Optimization Model and Its Applications to Tokyo Stock Market," Management Science, INFORMS, vol. 37(5), pages 519-531, May.
    7. Giovanni Barone‐Adesi & Kostas Giannopoulos & Les Vosper, 1999. "VaR without correlations for portfolios of derivative securities," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 19(5), pages 583-602, August.
    8. Bawa, Vijay S., 1978. "Safety-First, Stochastic Dominance, and Optimal Portfolio Choice," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 13(2), pages 255-271, June.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Libo Yin & Liyan Han, 2013. "Options strategies for international portfolios with overall risk management via multi-stage stochastic programming," Annals of Operations Research, Springer, vol. 206(1), pages 557-576, July.
    2. Diana Barro & Elio Canestrelli, 2008. "Tracking error with minimum guarantee constraints," Working Papers 172, Department of Applied Mathematics, Università Ca' Foscari Venezia.
    3. Diana Barro & Elio Canestrelli, 2014. "Downside risk in multiperiod tracking error models," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 22(2), pages 263-283, June.
    4. Zhang, Tao & Zhou, Hongfeng & Li, Larry & Gu, Feng, 2015. "Optimal rebalance rules for the constant proportion portfolio insurance strategy – Evidence from China," Economic Systems, Elsevier, vol. 39(3), pages 413-422.
    5. 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).
    6. Andrea Scozzari & Fabio Tardella & Sandra Paterlini & Thiemo Krink, 2013. "Exact and heuristic approaches for the index tracking problem with UCITS constraints," Annals of Operations Research, Springer, vol. 205(1), pages 235-250, May.
    7. Aleksandr G. Alekseev & Mikhail V. Sokolov, 2016. "Benchmark-based evaluation of portfolio performance: a characterization," Annals of Finance, Springer, vol. 12(3), pages 409-440, December.
    8. Diana Barro & Elio Canestrelli, 2005. "Time and nodal decomposition with implicit non-anticipativity constraints in dynamic portfolio optimization," GE, Growth, Math methods 0510011, University Library of Munich, Germany.
    9. Diana Barro & Elio Canestrelli, 2011. "Combining stochastic programming and optimal control to solve multistage stochastic optimization problems," Working Papers 2011_24, Department of Economics, University of Venice "Ca' Foscari", revised 2011.
    10. Alexander Alekseev & Mikhail Sokolov, 2016. "Portfolio Return Relative to a Benchmark," EUSP Department of Economics Working Paper Series Ec-04/16, European University at St. Petersburg, Department of Economics.
    11. Jun Nakayama & Daisuke Yokouchi, 2018. "Applying Time Series Decomposition to Construct Index-Tracking Portfolio," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 25(4), pages 341-352, December.
    12. 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.
    13. Leonardo Riegel Sant’Anna & Tiago Pascoal Filomena & Pablo Cristini Guedes & Denis Borenstein, 2017. "Index tracking with controlled number of assets using a hybrid heuristic combining genetic algorithm and non-linear programming," Annals of Operations Research, Springer, vol. 258(2), pages 849-867, November.
    14. Diana Barro & Elio Canestrelli, 2012. "Dynamic tracking error with shortfall control using stochastic programming," Working Papers 2012_18, Department of Economics, University of Venice "Ca' Foscari", revised 2012.
    15. Aleksandr Alekseev & Mikhail Sokolov, 2016. "Portfolio Return Relative to a Benchmark," EUSP Department of Economics Working Paper Series 2016/04, European University at St. Petersburg, Department of Economics.
    16. Diana Barro & Elio Canestrelli & Giorgio Consigli, 2019. "Volatility versus downside risk: performance protection in dynamic portfolio strategies," Computational Management Science, Springer, vol. 16(3), pages 433-479, July.
    17. Emilio Ricardo Carvalhais & Antonio Marcos Duarte Júnior, 2015. "Indexation of Fixed-Income Portfolios to the IMA-B," Brazilian Business Review, Fucape Business School, vol. 12(3), pages 116-142, May.
    18. Diana Barro & Elio Canestrelli, 2016. "Combining stochastic programming and optimal control to decompose multistage stochastic optimization problems," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 38(3), pages 711-742, July.

    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. ManMohan S. Sodhi, 2005. "LP Modeling for Asset-Liability Management: A Survey of Choices and Simplifications," Operations Research, INFORMS, vol. 53(2), pages 181-196, April.
    2. Diana Barro & Elio Canestrelli & Giorgio Consigli, 2019. "Volatility versus downside risk: performance protection in dynamic portfolio strategies," Computational Management Science, Springer, vol. 16(3), pages 433-479, July.
    3. Leitner Johannes, 2005. "Optimal portfolios with expected loss constraints and shortfall risk optimal martingale measures," Statistics & Risk Modeling, De Gruyter, vol. 23(1/2005), pages 49-66, January.
    4. Rockafellar, R. Tyrrell & Uryasev, Stanislav, 2002. "Conditional value-at-risk for general loss distributions," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1443-1471, July.
    5. Schuhmacher, Frank & Auer, Benjamin R., 2014. "Sufficient conditions under which SSD- and MR-efficient sets are identical," European Journal of Operational Research, Elsevier, vol. 239(3), pages 756-763.
    6. 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.
    7. Akhter Mohiuddin Rather & V. N. Sastry & Arun Agarwal, 2017. "Stock market prediction and Portfolio selection models: a survey," OPSEARCH, Springer;Operational Research Society of India, vol. 54(3), pages 558-579, September.
    8. Salo, Ahti & Doumpos, Michalis & Liesiö, Juuso & Zopounidis, Constantin, 2024. "Fifty years of portfolio optimization," European Journal of Operational Research, Elsevier, vol. 318(1), pages 1-18.
    9. Wong, Wing-Keung, 2007. "Stochastic dominance and mean-variance measures of profit and loss for business planning and investment," European Journal of Operational Research, Elsevier, vol. 182(2), pages 829-843, October.
    10. Diana Barro & Elio Canestrelli & Fabio Lanza, 2014. "Volatility vs. downside risk: optimally protecting against drawdowns and maintaining portfolio performance," Working Papers 2014:18, Department of Economics, University of Venice "Ca' Foscari".
    11. Kaplanski, Guy & Kroll, Yoram, 2002. "VaR Risk Measures versus Traditional Risk Measures: an Analysis and Survey," MPRA Paper 80070, University Library of Munich, Germany.
    12. N. Edirisinghe & E. Patterson, 2007. "Multi-period stochastic portfolio optimization: Block-separable decomposition," Annals of Operations Research, Springer, vol. 152(1), pages 367-394, July.
    13. Diana Barro & Elio Canestrelli, 2016. "Combining stochastic programming and optimal control to decompose multistage stochastic optimization problems," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 38(3), pages 711-742, July.
    14. Serhat Gul & Brian T. Denton & John W. Fowler, 2015. "A Progressive Hedging Approach for Surgery Planning Under Uncertainty," INFORMS Journal on Computing, INFORMS, vol. 27(4), pages 755-772, November.
    15. Diana Barro & Elio Canestrelli, 2014. "Downside risk in multiperiod tracking error models," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 22(2), pages 263-283, June.
    16. Yu, Bosco Wing-Tong & Pang, Wan Kai & Troutt, Marvin D. & Hou, Shui Hung, 2009. "Objective comparisons of the optimal portfolios corresponding to different utility functions," European Journal of Operational Research, Elsevier, vol. 199(2), pages 604-610, December.
    17. Miguel A. Lejeune, 2012. "Game Theoretical Approach for Reliable Enhanced Indexation," Decision Analysis, INFORMS, vol. 9(2), pages 146-155, June.
    18. Giuseppe Galloppo, 2010. "A Comparison Of Pre And Post Modern Portfolio Theory Using Resampling," Global Journal of Business Research, The Institute for Business and Finance Research, vol. 4(1), pages 1-16.
    19. Fima Klebaner & Zinoviy Landsman & Udi Makov & Jing Yao, 2017. "Optimal portfolios with downside risk," Quantitative Finance, Taylor & Francis Journals, vol. 17(3), pages 315-325, March.
    20. de Lange, Petter E. & Fleten, Stein-Erik & Gaivoronski, Alexei A., 2004. "Modeling financial reinsurance in the casualty insurance business via stochastic programming," Journal of Economic Dynamics and Control, Elsevier, vol. 28(5), pages 991-1012, February.

    More about this item

    JEL classification:

    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • D5 - Microeconomics - - General Equilibrium and Disequilibrium
    • D9 - Microeconomics - - Micro-Based Behavioral Economics

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:wpa:wuwpge:0510012. 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: EconWPA (email available below). General contact details of provider: https://econwpa.ub.uni-muenchen.de .

    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.