Multi-class predictive models are generally evaluated averaging binary classification indicators without a distinction between nominal and ordinal dependent variables. This paper introduces a novel approach to assess performances of predictive models characterized by an ordinal target variable and a new index for model evaluation is proposed. The new index satisfies mathematical properties and it can be applied to the evaluation of parametric and non parametric models. In order to show how our performance indicator works, empirical evidences obtained on toy examples and simulated data are provided. On the basis of the results achieved, we underline that our approach can be a more suitable criterion for model selection than the performance indexes currently suggested in the literature.

In the financial framework, the concepts of connectedness and diversification have been introduced and developed respectively in the context of systemic risk and portfolio theory. In this paper we propose a theoretical approach to bring to light the relation between connectedness and diversification. Starting from the respective axiomatic definitions, we prove that a class of proper measures of connectedness verifies, after a suitable functional transformation, the axiomatic requirements for a measure of diversification. The core idea of the paper is that connectedness and diversification are so deeply related that it is possible to pass from one concept to the other. In order to exploit such correspondence, we introduce a function, depending on the classical notion of rank of a matrix, that transforms a suitable proper measure of connectedness in a measure of diversification. We point out general properties of the proposed transformation function and apply it to a selection of measures of connectedness, such as the well-known Variance Inflation Factor.

This paper proposes a generalization of Markowitz model that incorporates skewness and kurtosis into the classical mean–variance allocation framework. The principal appeal of the present approach is that it provides the closed-form solution of the optimization problem. The four moments optimal portfolio is then decomposed into the sum of three portfolios: the mean–variance optimal portfolio plus two self-financing portfolios, respectively, accounting for skewness and kurtosis. Theoretical properties of the optimal solution are discussed together with the economic interpretation. Finally, an empirical exercise on real financial data shows the contribution of the two portfolios accounting for skewness and kurtosis when financial returns depart from Normal distribution.