Connectedness versus diversification: two sides of the same coin (Q2037770)

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 the authors propose a theoretical approach which sheds light on the relation between connectedness and 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. More precisely, in order to highlight the similarities between connectedness and diversification, the authors explicitly introduce the weights in the computation of connectedness, generalizing its definition and showing that standard measures of connectedness can be related to the special case of the equally weighted portfolios. Further, they effectively analyze this correspondence by comparing the axiomatic frameworks of the proper measures of connectedness (PMCs) and the coherent portfolio diversification measures (CPDMs). It is noted that, due to the peculiarities of the two settings, the requirements for PMCs are less restrictive than the ones for CPDMs. As a consequence, a specific PMC needs to verify some additional properties to be properly related to a CPDM. To summarize briefly, 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, is constructed, the general properties of the proposed transformation function are pointed out and are applied to a selection of measures of connectedness, such as the well-known variance inflation factor.