Financial risk distribution in European Union

Highlights

• A methodology to forecast the inequality of financial risk in the EU.

• Markov chains and dynamic entropy measures applied to credit ratings and spread.

• The financial inequality is different depending on the rating agency.

• The Brexit should not change the inequality within European Union.

• Development of an open source software to apply the methodology.

Abstract

A methodology based on Markov chains and dynamic entropy measures is proposed for measuring and forecasting the evolution of the inequality of financial risks in the European Union (EU). The proposed methodology requires knowledge of the past evolution of sovereign credit rating for the EU member states and historical data concerning harmonized interest rates of government bonds. The methodology is applied to real data from European countries for the three rating agencies Fitch, Moody’s and Standard & Poor’s. Obtained results show that, although these rating agencies share similar view on the rating assignment process, they have a different perception of the risk when expressed in terms of basis points and this fact determines divergences on the forecasted financial inequality in the EU. The development of an open source and user friendly (i.e. we implemented also a Graphical User Interface) software (https://github.com/lstorchi/markovctheil) will permit the replication of all the results both for the actual scenario in the EU and for possible future scenarios as the Brexit.

Introduction

Changes of European Union’s structure is of wide interest considering the economic and financial consequences for both the member states and the rest of the world. An important aspect, that should be deepened, is the financial risks related to each member state and to the EU as a whole. The aim of this work is the assessment of the inequality of the financial risk distribution among European countries in order to understand criticisms, if there exist, in the financial structure and to forecast future developments.

With the term financial risk we refer to the credit spread of government bonds paid by each country, whose evolution is influenced by credit rating events. This relationship has been studied for corporate bonds see, e.g. Ref. [1]. In their work the authors proposed a model for the mean evolution of the yield spread, considering the rating evaluation as the determinant of it. Rating migration has been widely studied. In particular, sovereign credit migration risk has become a major research topic in finance. In Ref. [2], the author investigated sovereign credit ratings, developing a multi-factor Markov chain model for rating migrations that is applicable both to sovereign and corporate debts. Fuertes et al. [3] compared three estimators within a discrete and continuous time framework applied to a sample of sovereign credit rating data of $72$ countries. More recently, Perilioglu and Tuysuz [4] proposed a factor model to estimate sovereign conditional transition probability matrices, extending the existing models on corporate debts. Emphasis has also been placed on the importance of rating assignment and on the differences among rating agencies. In their work, Alsakka and Gwilym [5] and Hill et al. [6] described the disagreement about credit quality assignment among the major credit rating agencies.

Information theory has been applied to economic and financial issues: as an example in Refs. [[7], [8]] the regional wealth inequality in computed by comparing Theil’s, Gini and Herndahl–Hirschman indices for the Italian case. Zunino et al. [9] and Bariviera et al. [10] proposed an information theory approach in order to assess risk linked to market informational efficiency applied both to sovereign and corporate bond markets. Furthermore, Oh et al. [11] analysed the uncertainty in the financial market using Shannon entropy, and Jizba et al. [12] investigated financial time series by means of Rényi’s entropy. Income inequality is investigated in Refs. [[13], [14]] where Theil’s index is modified to face with stochastic processes.

Interestingly, the study of the financial risk inequality within a group of countries over a horizon time it has been never faced in the financial literature. In this paper we fill this gap with the main new contribution represented by the construction of a methodology for the assessment and forecasting of inequality distribution of financial risk in the EU. The methodology is based on the population dynamic Theil’s entropy proposed by D’Amico et al. [14] as a measure of inequality given the credit rating migration historical data and the harmonized interest rates of government bonds. We notice that: the outputs are different depending on the rating agency and this is mainly due to the evolution of credit spreads which are significantly different among rating agencies; the historical entropy has decreased since $1998$ as the risk has become gradually more equi-distributed; the known Brexit should not change dramatically the inequality within European Union, while removing the newest members (i.e. Bulgaria, Romania and Croatia) the dissimilarities are more pronounced.

Moreover, we develop an open source software (implemented in Python) to apply the methodology, and a GUI (graphical user interface) to make it easy to use for the reader (see Appendix).

The paper is organized as follow: Section 2 describes the data collected; Section 3 shows the methodology applied to the datasets, the results are instead shown in Section 4. The work ends with some conclusions and future developments. Finally some computational details illustrating the developed software are reported in the Appendix.