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
|Date of creation:||Feb 2009|
|Date of revision:||Nov 2009|
|Contact details of provider:|| Postal: 106-112 boulevard de l'Hôpital 75 647 PARIS CEDEX 13|
Phone: + 33 44 07 81 00
Fax: + 33 1 44 07 83 01
Web page: http://centredeconomiesorbonne.univ-paris1.fr/
More information through EDIRC
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- repec:hrv:faseco:30747159 is not listed on IDEAS
- K. Geert Rouwenhorst, 1998.
"International Momentum Strategies,"
Journal of Finance,
American Finance Association, vol. 53(1), pages 267-284, 02.
- K. Rouwenhorst, 1996. "International Momentum Strategies," Yale School of Management Working Papers ysm36, Yale School of Management, revised 01 Feb 2008.
- 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.
- Barberis, Nicholas & Shleifer, Andrei & Vishny, Robert, 1998. "A model of investor sentiment," Journal of Financial Economics, Elsevier, vol. 49(3), pages 307-343, September.
- Nicholas Barberis & Andrei Shleifer & Robert W. Vishny, 1997. "A Model of Investor Sentiment," NBER Working Papers 5926, National Bureau of Economic Research, Inc.
- 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. Full references (including those not matched with items on IDEAS)
When requesting a correction, please mention this item's handle: RePEc:mse:cesdoc:09003. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Lucie Label)
If references are entirely missing, you can add them using this form.