Portfolio Symmetry and Momentum
AbstractThis 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.
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Date of creation: Oct 2009
Date of revision:
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Finance; Graph theory; momentum; quantum probability; spectral analysis.;
Other versions of this item:
- Monica Billio & Ludovic Calès & 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.
- Monica Billio & Ludovic Calès & Dominique Guegan, 2011. "Portfolio Symmetry and Momentum," UniversitÃ© Paris1 PanthÃ©on-Sorbonne (Post-Print and Working Papers) halshs-00645814, HAL.
- Monica Billio & Ludovic Calès & Dominique Guégan, 2009. "Portfolio Symmetry and Momentum," Working Papers 2009_05, Department of Economics, University of Venice "Ca' Foscari".
- 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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- Monica Billio & Ludovic Calès & Dominique Guegan, 2012. "Cross-Sectional Analysis through Rank-based Dynamic Portfolios," UniversitÃ© Paris1 PanthÃ©on-Sorbonne (Post-Print and Working Papers) halshs-00707430, HAL.
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- 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.
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