IDEAS home Printed from https://ideas.repec.org/a/kap/compec/v64y2024i5d10.1007_s10614-024-10555-y.html
   My bibliography  Save this article

Constructing Optimal Portfolio Rebalancing Strategies with a Two-Stage Multiresolution-Grid Model

Author

Listed:
  • Tian-Shyr Dai

    (National Yang Ming Chiao Tung University
    National Chengchi University)

  • Bo-Jen Chen

    (National Yang Ming Chiao Tung University)

  • You-Jia Sun

    (National Yang Ming Chiao Tung University)

  • Dong-Yuh Yang

    (National Taipei University of Business)

  • Mu-En Wu

    (National Taipei University of Technology)

Abstract

Sophisticated predetermined ratios are used to allocate portfolio asset weights to strike a good trade-off between profitability and risk in trading. Rebalancing these weights due to market fluctuations without incurring excessive transaction costs and tracking errors is a vital financial engineering problem. Rebalancing strategies can be modeled by discretely enumerating portfolio weights to form a grid space and then optimized via the Bellman equation. Discretization errors are reduced by increasing the grid resolution at the cost of increased computational time. To minimize errors with constrained computational resources (e.g., grid nodes), we vary the grid resolution according to the probability distribution of asset weights. Specifically, a grid space is first divided into several areas, and each area’s probability is estimated. Then, the discretization error’s upper bound is minimized by inserting an adequate number of grid nodes determined by Lagrange multipliers in a non-uniform fashion. In experiments, the proposed multiresolution rebalancing outperforms traditional uniform-resolution rebalancing and popular benchmark strategies such as the periodic, tolerance-band, and buy-and-hold strategies.

Suggested Citation

  • Tian-Shyr Dai & Bo-Jen Chen & You-Jia Sun & Dong-Yuh Yang & Mu-En Wu, 2024. "Constructing Optimal Portfolio Rebalancing Strategies with a Two-Stage Multiresolution-Grid Model," Computational Economics, Springer;Society for Computational Economics, vol. 64(5), pages 3117-3142, November.
    • Handle: RePEc:kap:compec:v:64:y:2024:i:5:d:10.1007_s10614-024-10555-y
    DOI: 10.1007/s10614-024-10555-y
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10614-024-10555-y
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10614-024-10555-y?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. Alfonsi Aurélien & Alexander Schied & Alla Slynko, 2012. "Order Book Resilience, Price Manipulation, and the Positive Portfolio Problem," Post-Print hal-00941333, HAL.
    2. Hubert Dichtl & Wolfgang Drobetz & Martin Wambach, 2014. "Where is the value added of rebalancing? A systematic comparison of alternative rebalancing strategies," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 28(3), pages 209-231, August.
    3. Brennan, Michael J. & Schwartz, Eduardo S. & Lagnado, Ronald, 1997. "Strategic asset allocation," Journal of Economic Dynamics and Control, Elsevier, vol. 21(8-9), pages 1377-1403, June.
    4. Nicole Branger & Beate Breuer & Christian Schlag, 2010. "Discrete-time implementation of continuous-time portfolio strategies," The European Journal of Finance, Taylor & Francis Journals, vol. 16(2), pages 137-152.
    5. repec:dau:papers:123456789/9561 is not listed on IDEAS
    6. David B. Brown & James E. Smith, 2011. "Dynamic Portfolio Optimization with Transaction Costs: Heuristics and Dual Bounds," Management Science, INFORMS, vol. 57(10), pages 1752-1770, October.
    7. Gallmeyer, Michael F. & Kaniel, Ron & Tompaidis, Stathis, 2006. "Tax management strategies with multiple risky assets," Journal of Financial Economics, Elsevier, vol. 80(2), pages 243-291, May.
    8. Prayut Jain & Shashi Jain, 2019. "Can Machine Learning-Based Portfolios Outperform Traditional Risk-Based Portfolios? The Need to Account for Covariance Misspecification," Risks, MDPI, vol. 7(3), pages 1-27, July.
    9. Imen Ben Tahar & Nizar Touzi & Mete H. Soner, 2007. "The Dynamic Programming Equation for the Problem of Optimal Investment Under Capital Gains Taxes," Post-Print hal-00703103, HAL.
    10. Obizhaeva, Anna A. & Wang, Jiang, 2013. "Optimal trading strategy and supply/demand dynamics," Journal of Financial Markets, Elsevier, vol. 16(1), pages 1-32.
    11. Carroll, Rachael & Conlon, Thomas & Cotter, John & Salvador, Enrique, 2017. "Asset allocation with correlation: A composite trade-off," European Journal of Operational Research, Elsevier, vol. 262(3), pages 1164-1180.
    12. Bregu, Klajdi, 2020. "Overconfidence and (Over)Trading: The Effect of Feedback on Trading Behavior," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 88(C).
    13. Martin L. Puterman & Moon Chirl Shin, 1978. "Modified Policy Iteration Algorithms for Discounted Markov Decision Problems," Management Science, INFORMS, vol. 24(11), pages 1127-1137, July.
    14. Figlewski, Stephen & Gao, Bin, 1999. "The adaptive mesh model: a new approach to efficient option pricing," Journal of Financial Economics, Elsevier, vol. 53(3), pages 313-351, September.
    15. Kumar Muthuraman & Sunil Kumar, 2006. "Multidimensional Portfolio Optimization With Proportional Transaction Costs," Mathematical Finance, Wiley Blackwell, vol. 16(2), pages 301-335, April.
    16. Roni Israelov & Michael Katz, 2011. "To Trade or Not to Trade? Informed Trading with Short-Term Signals for Long-Term Investors," Financial Analysts Journal, Taylor & Francis Journals, vol. 67(5), pages 23-36, September.
    17. Robert Almgren, 2003. "Optimal execution with nonlinear impact functions and trading-enhanced risk," Applied Mathematical Finance, Taylor & Francis Journals, vol. 10(1), pages 1-18.
    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. Olivier Guéant, 2016. "The Financial Mathematics of Market Liquidity: From Optimal Execution to Market Making," Post-Print hal-01393136, HAL.
    2. Phillip Monin, 2014. "Hedging Market Risk in Optimal Liquidation," Working Papers 14-08, Office of Financial Research, US Department of the Treasury.
    3. Najafi, Amir Abbas & Pourahmadi, Zahra, 2016. "An efficient heuristic method for dynamic portfolio selection problem under transaction costs and uncertain conditions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 448(C), pages 154-162.
    4. Dirk Becherer & Todor Bilarev & Peter Frentrup, 2015. "Optimal Asset Liquidation with Multiplicative Transient Price Impact," Papers 1501.01892, arXiv.org, revised Apr 2017.
    5. Arne Lokka & Junwei Xu, 2020. "Optimal liquidation trajectories for the Almgren-Chriss model with Levy processes," Papers 2002.03376, arXiv.org, revised Sep 2020.
    6. Qinghua Li, 2014. "Facilitation and Internalization Optimal Strategy in a Multilateral Trading Context," Papers 1404.7320, arXiv.org, revised Jan 2015.
    7. Nico Achtsis & Dirk Nuyens, 2013. "A Monte Carlo method for optimal portfolio executions," Papers 1312.5919, arXiv.org.
    8. Lokka, A. & Xu, Junwei, 2020. "Optimal liquidation trajectories for the Almgren-Chriss model," LSE Research Online Documents on Economics 106977, London School of Economics and Political Science, LSE Library.
    9. Gianbiagio Curato & Jim Gatheral & Fabrizio Lillo, 2017. "Optimal execution with non-linear transient market impact," Quantitative Finance, Taylor & Francis Journals, vol. 17(1), pages 41-54, January.
    10. Igor Skachkov, 2013. "Market Impact Paradoxes," Papers 1312.3349, arXiv.org.
    11. Gianbiagio Curato & Jim Gatheral & Fabrizio Lillo, 2014. "Optimal execution with nonlinear transient market impact," Papers 1412.4839, arXiv.org.
    12. Daniel Hern'andez-Hern'andez & Harold A. Moreno-Franco & Jos'e Luis P'erez, 2017. "Periodic strategies in optimal execution with multiplicative price impact," Papers 1705.00284, arXiv.org, revised May 2018.
    13. Olivier Guéant & Charles-Albert Lehalle, 2015. "General Intensity Shapes In Optimal Liquidation," Mathematical Finance, Wiley Blackwell, vol. 25(3), pages 457-495, July.
    14. Samuel N. Cohen & Lukasz Szpruch, 2011. "A limit order book model for latency arbitrage," Papers 1110.4811, arXiv.org.
    15. Christopher Lorenz & Alexander Schied, 2013. "Drift dependence of optimal trade execution strategies under transient price impact," Finance and Stochastics, Springer, vol. 17(4), pages 743-770, October.
    16. Aur'elien Alfonsi & Alexander Schied & Florian Klock, 2013. "Multivariate transient price impact and matrix-valued positive definite functions," Papers 1310.4471, arXiv.org, revised Sep 2015.
    17. Saif Benjaafar & Daniel Jiang & Xiang Li & Xiaobo Li, 2022. "Dynamic Inventory Repositioning in On-Demand Rental Networks," Management Science, INFORMS, vol. 68(11), pages 7861-7878, November.
    18. Aur'elien Alfonsi & Antje Fruth & Alexander Schied, 2007. "Optimal execution strategies in limit order books with general shape functions," Papers 0708.1756, arXiv.org, revised Feb 2010.
    19. Wei Cui & Anthony Brabazon & Michael O'Neill, 2011. "Dynamic trade execution: a grammatical evolution approach," International Journal of Financial Markets and Derivatives, Inderscience Enterprises Ltd, vol. 2(1/2), pages 4-31.
    20. Guanxing Fu & Ulrich Horst & Xiaonyu Xia, 2022. "Portfolio liquidation games with self‐exciting order flow," Mathematical Finance, Wiley Blackwell, vol. 32(4), pages 1020-1065, October.

    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:kap:compec:v:64:y:2024:i:5:d:10.1007_s10614-024-10555-y. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.