Concentration des portefeuilles boursiers et asymétrie des distributions de rentabilités d’actifs

Le Courtois, Olivier; Walter, Christian

Journal de la société française de statistique, Tome 153 (2012) no. 2, pp. 1-20.

Cet article porte sur le lien existant entre l’asymétrie des distributions de rentabilités d’actifs et la concentration des portefeuilles. Nous commençons par rappeler la logique à l’œuvre dans la théorie de la diversification dans le but de faire apparaître qu’elle repose sur une réduction du risque au seul moment d’ordre 2 et à l’application corrélative de la théorie des erreurs du XVIII^e siècle. Nous exposons notamment la controverse ouverte par E. Fama en 1965 sur cette théorie des erreurs, pour faire apparaître qu’un changement dans le type d’aléa peut conduire à concentrer et non à diversifier. Ensuite, nous examinons comment l’inclusion dans le programme d’optimisation de la dissymétrie entre les gains et les pertes peut induire une propension à concentrer les portefeuilles. Nous présentons alors le modèle de Mitton et Vorkink [ 19 ], puis nous proposons ensuite une nouvelle approche dans l’esprit de ce modèle. Nous terminons par une application du modèle que nous proposons au marché américain, qui fait apparaître la grande différence de performance obtenue par un portefeuille classiquement diversifié, concentré selon les modèles existants, et concentré selon le modèle que nous proposons.

This article develops on the link between the asymmetry of asset return distributions and the concentration of portfolios. We start by recalling the rationale behind the theory of diversification, in order to let appear that this theory relies on a reduction of risk viewed only at order 2 and on the related application of the theory of errors, as developed during the ${\text{XVIII}}^{\text{th}}$ century. We also expose the controversy opened by E. Fama in 1965 on this theory of errors, in order to let appear that a change in the type of underlying randomness can lead to the concentration and not the diversification of portfolios. Then, we examine how the inclusion in the optimization program of the asymmetry between gains and losses can lead to a propensity to concentrate. We recall the main aspects of the Mitton and Vorkink [ 19 ] model, and then we propose a new approach in the spirit of this model. We end up with an illustration of the latter framework on American data, letting appear important differences between the performance obtained with a classically diversified portfolio, a portfolio concentrated along existing models, and a portfolio concentrated along the model that we propose.

Mot clés : Concentration, Asymétrie, Portefeuille, Co-asymétrie
Keywords: Concentration, Asymmetry, Portfolio, Co-asymmetry

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