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.

Torrente, M., Uberti, P. (2021). Connectedness versus diversification: two sides of the same coin. MATHEMATICS AND FINANCIAL ECONOMICS, 15(3), 639-655 [10.1007/s11579-021-00291-4].

Connectedness versus diversification: two sides of the same coin

Pierpaolo Uberti
2021

Abstract

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.
Articolo in rivista - Articolo scientifico
C60; Connectedness; D81; Diversification; E30; G01; G10; G11; Portfolio risk; Systemic risk;
English
2021
15
3
639
655
open
Torrente, M., Uberti, P. (2021). Connectedness versus diversification: two sides of the same coin. MATHEMATICS AND FINANCIAL ECONOMICS, 15(3), 639-655 [10.1007/s11579-021-00291-4].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/394005
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