A New Formulation of Maximum Diversification Indexation Using Rao's Quadratic Entropy

This paper proposes a new formulation of the Maximum Diversification indexation strategy based on Rao’s Quadratic Entropy (RQE). It clarifies the investment problem underlying the Most Diversified Portfolio (MDP) formed with this strategy, identifies the source of the MDP’s out-of-sample performance, and suggests dimensions along which this performance can be improved. We show that these potential improvements are quantitatively important and are robust to portfolio turnover, portfolio risk, estimation window, and covariance matrix estimation

L’immigration en question dans "Et Dieu seul sait comment je dors" d’ Alain Mabanckou

INTRODUCTION I- POURQUOI L’IMMIGRATION ? 1°) La quête du mieux-être 2°) La quête de l’exutoi re 3°) La quête de la personnalité II- QUE DIRE DE L’IMMIGRATION ? 1°) L’immigration comme avatar 2°) L’immigration co mme perte de repères 3°) L’immigration comme échec III- QUE FAIRE DE L’IMMIGRATION ? 1°) La Prise de conscience 2°) La création de condit ions optimales de vie 3°) Le retour aux sources ------------------------------------------------------------------------------------------- CRELAF (Cercle de Reflexion des Etudiants en Littératures Africaines), Département de Littératures Africaines, Université Omar Bongo, Gabo

Unifying Portfolio Diversification Measures Using Rao's Quadratic Entropy

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

Coherent Diversification Measures in Portfolio Theory: An Axiomatic Foundation

We provide an axiomatic foundation for the measurement of correlation diversification in a one-period portfolio model. We propose a set of eight desirable axioms for this class of diversification measures. We name the measures satisfying these axioms coherent correlation diversification measures. We study the compatibility of our axioms with rank-dependent expected utility theory. We also test them against the two most frequently used methods for measuring correlation diversification in portfolio theory: portfolio variance and the diversification ratio. Lastly, we provide an example of a functional representation of a coherent correlation diversification measure

Rao's Quadratic Entropy, Risk Management and Portfolio Theory

Cette thèse porte sur le concept de la diversification et sa mesure en théorie des choix de portefeuille. La diversification est un concept clé en finance et en économique, et est au coeur de la théorie des choix de portefeuille. Elle représente l’un des plus importants outils de gestion du risque. Ainsi, plusieurs mesures de diversification de portefeuille ont été proposées, mais aucune ne s’est révélée totalement satisfaisante et la discipline recherche toujours une approche unifiée et cohérente de mesure et gestion de la diversification. Cette thèse répond à ce besoin et développe une nouvelle classe de mesures de diversification de portefeuille en adaptant à l’économie financière l’entropie quadratique de Rao, une mesure de diversité proposée par Rao et utilisée en statistique, en biodiversité, en écologie et dans plusieurs autres domaines. La thèse démontre que si l’entropie quadratique de Rao est bien calibrée, elle devient une classe valide de mesures de diversification de portefeuille résumant, de manière simple, les caractéristiques complexes de la diversification de portefeuille, et offrant en même temps une théorie unifiée qui englobe de nombreuses contributions antérieures. Ensuite, la thèse présente deux applications de la classe de mesures proposée. La première application s’est intéressée à la stratégie de diversification de portefeuille maximum diversification (MD) développée par Choueifaty and Coignard (2008). Elle propose de nouvelles formulations de cette dernière en se basant sur la classe de mesures proposée. Ces nouvelles formulations permettent de donner un fondement théorique à la stratégie MD et d’améliorer ses performances. La deuxième application s’est intéressée au modèle moyenne-variance de Markowitz (1952). Elle propose une nouvelle formulation de ce dernier en se basant sur la classe de mesures proposée. Cette nouvelle formulation améliore significativement la compréhension du modèle, en particulier le processus de rémunération des actifs. Elle offre également de nouvelles possibilités d’amélioration des performances de ce dernier sans coûts d’implementation supplémentaires.This thesis is about the concept of diversification and its measurement in portfolio theory. Diversification is one of the major components of portfolio theory. It helps to reduce or ultimately to eliminate portfolio risk. Thus, its measurement and management is of fundamental importance in finance and insurance domains as risk measurement and management. Consequently, several measures of portfolio diversification were proposed, each based on a different criterion . Unfortunately, none of them has proven totally satisfactory. All have drawbacks and limited applications. Developing a coherent measure of portfolio diversification is therefore an active research area in investment management. In this thesis, a novel, coherent, general and rigorous theoretical framework to manage and quantify portfolio diversification inspiring from Rao (1982a)’s Quadratic Entropy (RQE), a general approach to measuring diversity, is proposed. More precisely, this thesis demonstrates that when RQE is judiciously calibrated it becomes a valid class of portfolio diversification measures summarizing complex features of portfolio diversification in a simple manner and provides at the same time a unified theory that includes many previous contributions. Next, this thesis presents two applications of the proposed class of portfolio diversification measures. In the first application, new formulations of maximum diversification strategy of Choueifaty and Coignard (2008) is provided based on the proposed class of measures. These new formalizations clarify the investment problem behind the MD strategy, help identify the source of its strong out-of-sample performance relative to other diversified portfolios, and suggest new directions along which its out-of-sample performance can be improved. In the second application, a novel and useful formulation of the mean-variance utility function is provided based on the proposed class of measures. This new formulation significantly improves the mean-variance model understanding, in particular in terms of asset pricing. It also offers new directions along which the mean-variance model can be improved without additional computational costs

Coherent Diversification Measures in Portfolio Theory: An Axiomatic Foundation

We provide an axiomatic foundation for the measurement of correlation diversification in a one-period portfolio model. We propose a set of eight desirable axioms for this class of diversification measures. We name the measures satisfying these axioms coherent correlation diversification measures. We study the compatibility of our axioms with rank-dependent expected utility theory. We also test them against the two most frequently used methods for measuring correlation diversification in portfolio theory: portfolio variance and the diversification ratio. Lastly, we provide an example of a functional representation of a coherent correlation diversification measure