How Much Can You Earn in the Stock Market ? Answers from the Algorithmic Graph Theory

22 Pages Posted: 14 Jul 2009 Last revised: 6 Jul 2012

See all articles by Olivier Brandouy

Olivier Brandouy

University of Angers - Groupe de Recherche en Économie Théorique et Appliquée (GREThA)

Philippe Mathieu

University of Lille I

Iryna Veryzhenko

University of Lille I

Date Written: July 6, 2012

Abstract

This paper proposes a new method for determining the upper bound of any investment strategy's maximum profit, applied in a given time window [0, T]. This upper bound is defined once all the prices are known at time T and therefore represents the ex-post maximum efficiency of any investment strategy determined during the relevant time interval. This approach allows us to gauge in absolute terms those behaviors defined through atomic "buy" and "sell" actions, and can be extended to more complex strategies. We show that, even in the ex-post framework, establishing this upper bound when transaction costs are implemented is extremely complex. We first describe this problem using a linear programming framework. Thereafter, we propose to embed this question in a graph theory framework and to show that determining the best investment behavior is equivalent to identifying an optimal path in an oriented, weighted, bipartite network or a weighted, directed, acyclic graph. We illustrate this method using real world data and introduce a new theory about absolute optimal behavior in the financial world.

Keywords: market timing, optimal strategy, finance, network, algorithm, computational method

JEL Classification: C63, G19, C61

Suggested Citation

Brandouy, Olivier and Mathieu, Philippe and Veryzhenko, Iryna, How Much Can You Earn in the Stock Market ? Answers from the Algorithmic Graph Theory (July 6, 2012). Available at SSRN: https://ssrn.com/abstract=1432988 or http://dx.doi.org/10.2139/ssrn.1432988

Olivier Brandouy (Contact Author)

University of Angers - Groupe de Recherche en Économie Théorique et Appliquée (GREThA) ( email )

Avenue Léon Duguit
Aveneu Duguit
Pessac, 33 608
France

Philippe Mathieu

University of Lille I ( email )

104, avenue du peuple Belge
Villeneuve d'Ascq Cedex, 59655
France

HOME PAGE: http://lifl.fr/~mathieu

Iryna Veryzhenko

University of Lille I ( email )

104, avenue du peuple Belge
Villeneuve d'Ascq Cedex, 59655
France

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