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Portfolio Symmetry and Momentum

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.

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File URL: ftp://mse.univ-paris1.fr/pub/mse/CES2009/09003.pdf
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Paper provided by Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne in its series Documents de travail du Centre d'Economie de la Sorbonne with number 09003.

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Length: 23 pages
Date of creation: Feb 2009
Date of revision: Nov 2009
Handle: RePEc:mse:cesdoc:09003
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  1. K. Geert Rouwenhorst, 1998. "International Momentum Strategies," Journal of Finance, American Finance Association, vol. 53(1), pages 267-284, 02.
  2. Barberis, Nicholas & Shleifer, Andrei & Vishny, Robert, 1998. "A model of investor sentiment," Journal of Financial Economics, Elsevier, vol. 49(3), pages 307-343, September.
  3. 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(02), pages 425-447, June.
  4. 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.
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