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Portfolio Symmetry and Momentum

Author

Listed:
  • Monica Billio

    (Dipartimento di Scienze Economiche - Universit Ca' Foscari di Venezia)

  • Ludovic Cal s

    (Dipartimento di Scienze Economiche - Universit Ca' Foscari di Venezia et Centre d'Economie de la Sorbonne)

  • Dominique Guegan

    (Centre d'Economie de la Sorbonne - Paris School of Economics)

Abstract

This paper presents a theorical framework to model the evolution of a portfolio whose weights vary over time. Such a portfolio is called a dynamic portfolio. In a first step, considering a given investment policy, we define the set of the investable portfolios. Then, considering portfolio vicinity in terms of turnover, we represent the investment policy as a graph. It permits us to model the evolution of a dynamic portfolio as a stochastic process in the set of the investable portfolios. Our first model for the evolution of a dynamic portfolio is a random walk on the graph corresponding to the investment policy chosen. Next, using graph theory and quantum probability, we compute the probabilities for a dynamic portfolio to be in the different regions of the graph. The resulting distribution is called spectral distribution. It depends on the geometrical properties of the graph and thus in those of the investment policy. The framework is next applied to an investment policy similar to the Jeegadeesh and Titman's momentum strategy [JT1993]. We define the optimal dynamic portfolio as the sequence of portfolios, from the set of the investable portfolios, which gives the best returns over a respective sequence of time periods. Under the assumption that the optimal dynamic portfolio follows a random walk, we can compute its spectral distribution. We found then that the strategy symmetry is a source of momentum

Suggested Citation

  • Monica Billio & Ludovic Cal s & Dominique Guegan, 2009. "Portfolio Symmetry and Momentum," Documents de travail du Centre d'Economie de la Sorbonne 09003, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne, revised Nov 2009.
    • Handle: RePEc:mse:cesdoc:09003
    DOI: 10.1016/j.ejor.2011.05.012
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    File URL: https://doi.org/10.1016/j.ejor.2011.05.012
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    Cited by:

    1. is not listed on IDEAS
    2. Monica Billio & Ludovic Calès & Dominique Guegan, 2012. "Cross-Sectional Analysis through Rank-based Dynamic Portfolios," Post-Print halshs-00707430, HAL.
    3. Pätäri, Eero & Karell, Ville & Luukka, Pasi & Yeomans, Julian S, 2018. "Comparison of the multicriteria decision-making methods for equity portfolio selection: The U.S. evidence," European Journal of Operational Research, Elsevier, vol. 265(2), pages 655-672.
    4. Cai, Xing & Xia, Wei & Huang, Weihua & Yang, Haijun, 2024. "Dynamics of momentum in financial markets based on the information diffusion in complex social networks," Journal of Behavioral and Experimental Finance, Elsevier, vol. 41(C).
    5. Monica Billio & Ludovic Calès & Dominique Guegan, 2012. "Cross-Sectional Analysis through Rank-based Dynamic," Documents de travail du Centre d'Economie de la Sorbonne 12036, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    6. Timo H. Leivo, 2012. "Combining value and momentum indicators in varying stock market conditions," Review of Accounting and Finance, Emerald Group Publishing Limited, vol. 11(4), pages 400-447, October.
    7. López-García, M.N. & Trinidad-Segovia, J.E. & Sánchez-Granero, M.A. & Pouchkarev, I., 2021. "Extending the Fama and French model with a long term memory factor," European Journal of Operational Research, Elsevier, vol. 291(2), pages 421-426.
    8. Pätäri, Eero & Leivo, Timo & Honkapuro, Samuli, 2012. "Enhancement of equity portfolio performance using data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 220(3), pages 786-797.

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    Keywords

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    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory

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