Portfolio Symmetry and Momentum
Ca Foscari University of Venice - Department of Economics
Paris School of Economics - Université Paris-1 Panthéon-La Sorbonne; University of Lausanne - Institute of Banking and Finance (IBF); University of Venice - Department of Economics
Ecole Normale Superieure de Cachan
October 30, 2009
University Ca' Foscari of Venice, Dept. of Economics Research Paper No. 05/WP/2009
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.
Number of Pages in PDF File: 23
Keywords: Graph Theory, Momentum, Dynamic Portfolio, Quantum Probability, Spectral Analysis
JEL Classification: C14, C44working papers series
Date posted: March 1, 2009 ; Last revised: April 25, 2012
© 2013 Social Science Electronic Publishing, Inc. All Rights Reserved.
This page was processed by apollo5 in 0.453 seconds