Portfolio Symmetry and Momentum

Monica Billio, Ludovic Cal�s and Dominique Gu�gan
Additional contact information
Ludovic Cal�s: Department of Economics, University Of Venice C� Foscari and Universit� Paris-1 Panth�on-La Sorbone
Dominique Gu�gan: Universit� Paris-1 Panth�on-La Sorbone
Authors registered in the RePEc Author Service: Ludovic Calès

No 2009_05, Working Papers from Department of Economics, University of Venice "Ca' Foscari"

Abstract: This paper presents a theoretical 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. 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: Graph Theory; Momentum; Dynamic Portfolio; Quantum Probability; Spectral Analysis (search for similar items in EconPapers)
JEL-codes: C14 C44 (search for similar items in EconPapers)
Pages: 13
Date: 2009
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)

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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 (2011)
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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Persistent link: https://EconPapers.repec.org/RePEc:ven:wpaper:2009_05

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