Unifying Portfolio Diversification Measures Using Raoʼs Quadratic Entropy

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01 Mai 2015
Types de publication: 
Cahier de recherche
Auteur(s): 
Gilles Boevi Koumou
Kevin Moran
Axe de recherche: 
Enjeux économiques et financiers
Mots-clés: 
Portfolio Diversification
Rao’s Quadratic Entropy
Diversification Return
Portfolio Variance Normalized
Gini-Simpson Index
Markowitz’s Utility Function
Bouchaud’s General Free Utility
Classification JEL: 
G11

This paper extends the use of Rao(1982b)’s Quadratic Entropy (RQE) to modern portfolio theory. It argues that the RQE of a portfolio is a valid, flexible and unifying approach to measuring portfolio diversification. The paper demonstrates that portfolio’s RQE can encompass most existing measures, such as the portfolio variance, the diversification ratio, the normalized portfolio variance, the diversification return or excess growth rates, the Gini-Simpson indices, the return gaps, Markowitz’s utility function and Bouchaud’s general free utility. The paper also shows that assets selected under RQE can protect portfolios from mass destruction (systemic risk) and an empirical illustration suggests that this protection is substantial.

Contact: 

Carmichael: CIRPÉE et Département d’économique, Université Laval benoit.carmichael@ecn.ulaval.ca
Koumou: Corresponding author. CIRPÉE et Département d’économique nettey-boevi-gilles-b.koumou.1@ulaval.ca
Moran: CIRPÉE et Département d’économique, Université Laval Canada kevin.moran@ecn.ulaval.ca