Portfolio Symmetry and Momentum

Monica Billio, Ludovic Calès and Dominique Guegan ()
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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 nationale des ponts et chaussées - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement

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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.

Keywords: Finance; Graph theory; momentum; quantum probability; spectral analysis.; spectral analysis (search for similar items in EconPapers)
Date: 2011
Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00645814v1
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Citations: View citations in EconPapers (7)

Published in European Journal of Operational Research, 2011, 214 (3), pp.759-767

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Related works:
Journal Article: Portfolio symmetry and momentum (2011)
Working Paper: Portfolio Symmetry and Momentum (2011)
Working Paper: Portfolio Symmetry and Momentum (2011)
Working Paper: Portfolio Symmetry and Momentum (2009)
Working Paper: Portfolio Symmetry and Momentum (2009)
Working Paper: Portfolio Symmetry and Momentum (2009)
Working Paper: Portfolio Symmetry and Momentum (2009)
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