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Portfolio Symmetry and Momentum

Author

Listed:
  • Monica Billio

    (University of Ca’ Foscari [Venice, Italy])

  • Ludovic Calès

    (University of Ca’ Foscari [Venice, Italy], CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

  • Dominique Guegan

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris sciences et lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement)

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 Calès & Dominique Guegan, 2011. "Portfolio Symmetry and Momentum," Post-Print halshs-00645814, HAL.
    • Handle: RePEc:hal:journl:halshs-00645814
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00645814
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    References listed on IDEAS

    as
    1. Barberis, Nicholas & Shleifer, Andrei & Vishny, Robert, 1998. "A model of investor sentiment," Journal of Financial Economics, Elsevier, vol. 49(3), pages 307-343, September.
    2. K. Geert Rouwenhorst, 1998. "International Momentum Strategies," Journal of Finance, American Finance Association, vol. 53(1), pages 267-284, February.
    3. Jegadeesh, Narasimhan & Titman, Sheridan, 1993. "Returns to Buying Winners and Selling Losers: Implications for Stock Market Efficiency," Journal of Finance, American Finance Association, vol. 48(1), pages 65-91, March.
    4. Okunev, John & White, Derek, 2003. "Do Momentum-Based Strategies Still Work in Foreign Currency Markets?," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 38(2), pages 425-447, June.
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    Cited by:

    1. 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.
    2. Monica Billio & Ludovic Calès & Dominique Guegan, 2012. "Cross-Sectional Analysis through Rank-based Dynamic Portfolios," Post-Print halshs-00707430, HAL.
    3. 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.
    4. 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.
    5. 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.
    6. 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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    More about this item

    Keywords

    Finance; Graph theory; momentum; quantum probability; spectral analysis.; spectral analysis;
    All these keywords.

    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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