Measuring the default risk of sovereign debt from the perspective of network
MMeasuring the default risk of sovereign debt from theperspective of network
Hongwei Chuang a, ∗ , Hwai-Chung Ho a,b a Institute of Statistical Science, Academia Sinica, Taiwan 11529 b Department of Finance, National Taiwan University, Taiwan 10617
Abstract
Recently, there has been a growing interest in network research, especiallyin these fields of biology, computer science, and sociology. It is natural toaddress complex financial issues such as the European sovereign debt crisisfrom the perspective of network. In this article, we construct a networkmodel according to the debt–credit relations instead of using the conventionalmethodology to measure the default risk. Based on the model, a risk indexis examined using the quarterly report of consolidated foreign claims fromthe Bank for International Settlements (BIS) and debt/GDP ratios amongthese reporting countries. The empirical results show that this index canhelp the regulators and practitioners not only to determine the status ofinterconnectivity but also to point out the degree of the sovereign debt defaultrisk. Our approach sheds new light on the investigation of quantifying thesystemic risk.
Keywords:
Default risk, Sovereign debt, Systemic risk, Financial networks ∗ Corresponding author
Email address: [email protected] (Hongwei Chuang)
Preprint submitted to Physica A November 8, 2018 a r X i v : . [ q -f i n . R M ] A p r . Introduction The stability of the financial system and the potential of systemic risksto alter the functioning of this system have long been important for centralbanks and related research communities. Thus, guarding against systemicrisk in the financial system is an emergent issue. However, specifically defin-ing this type of risk and managing it is difficult. Therefore, the FederalReserve Bank of New York and the National Research Council’s Board onMathematical Sciences and Their Applications held a conference to stimulatefresh ideas on systemic risk in May 2006 [ ? ]. The conference attracted morethan 100 experts from 22 countries, representing banks, regulators, invest-ment firms, US national laboratories, government agencies, and universities.This conference proposed the new directions for understanding systemic risk.A comprehensive survey of understanding systemic risk can be referred to [ ? ] and [ ? ].Some external events, such as recessions, wars, civil unrest, environmentalcatastrophes or financial crisis, have the potential to depress the value of abanks’ assets so severely that the system fails. In the wake of the globalfinancial crisis that began in 2007, there is increasing recognition of the needto address risk at the systemic level, as distinct from focusing on individualbanks [ ? ] [ ? ] [ ? ] [ ? ]. Sovereign debt defaults often make the financialsystem unstable, causing further systemic risk. A number of studies havebeen conducted on sovereign debt crises and the policy responses to thesesovereign defaults [ ? ] following the sovereign debt crises in the 1980s.However, a little comparative empirical work has been done on the sovereigndebt crises based on the macroeconomic and systemic perspectives. In this2rticle, we provide an another view to analyze this kind of issue on sovereigndebts from the network prospective.Currently, the increasingly complicated and globally interlinked financialmarkets are not immune to such systemic threats. Three questions immedi-ately arise: (i) Does globalization make the world too interconnected? (ii) Isthere a way to be immunized from the systemic threats? (iii) How can wefind a proper index to measure systemic risk? In the following, we first fo-cus on the role of growth in generating sovereign debt failure and instability.Second, we provide a systemic risk index to measure sovereign debt from theperspective of financial networks. Finally, we implement the empirical studythrough the quarterly data of consolidated foreign claims from the Bank forInternational Settlements (BIS) and debt/GDP ratios among the reportingcountries. This index not only can provide the regulators and practitionerswith the status of interconnectivity but also can point out the degree of thedefault risk. Moreover, it shields light on quantifying the systemic risk of theworld.
2. Connectivity of the sovereign debt
To answer the question “Does the globalization make the world too inter-connected?,” we use the quarterly report of consolidated foreign claims fromBIS. The foreign claims by nationality of the reporting banks are the ulti-mate risk basis consisting of 20 countries from 2005 Q1 to 2011 Q1. The con-solidated banking statistics reports banks’ on-balance sheet financial claimson the rest of the world, thus providing a measure of the risk exposuresof lenders’ national banking systems. The quarterly data cover contractual3ending by the head office and all its branches and subsidiaries on a worldwideconsolidated basis.We plot the debt–credit relations among these countries through FNA ,as shown in Figures 1 and 2. FNA is an analytics platform that can helpfinancial institutions and regulators better manage and understand financialdata with network analysis and visualization. The nodes are represented asthese 20 countries. The ties denote the debt–credit relations between any twoof them. Thickness and thinness represent the debt–credit amount. Figure1 shows the network structure of sovereign debts in 2005 Q1. < Insert Fig. 1 here > Figure 2 shows that for 2009 Q4. < Insert Fig. 2 here > These countries became more inter-connective from 2005 Q1 to 2009 Q4.The connectivity of the world has indeed intensified during these past years’globalization.
3. Network structure of sovereign debts
The inability of previous approaches to reproduce statistical regularitiesobserved empirically in network structures justifies our pursuit of a complexsystems approach that may provide predictions for large-scale networks. Sim-ple amplification mechanisms can dominate the network dynamics at large,despite the best intentions of the agents. Economic networks are subject to V , in which N countries belong, and the other part is thesovereign debt–credit relationship among these countries, E . The networkstructure of these sovereign debts is formed and denoted by G ≡ ( V, E ) . (1)We further assume the following: Assumption 1.
For an arbitrary node i ∈ V , the default probability of node i is defined as p i . Assumption 2.
Let q ij be the probability that node i defaults such that itslinkage node j defaults where j (cid:54) = i and q ii = 1 , i = 1 , , ..., N . Assumption 3.
The loss of the node i is l i . According to these assumptions, the following properties can be immedi-ately obtained:1. The default transition matrix (DTM) of the network system isDTM = q . . . q N q . . . q N ... ... ... ... q N . . . . . . ∗ Adj. ( E ) , where Adj. ( E ) represents the adjacency matrix of E .5. The network default probability (NDP) isNDP = DP ∗ DTM , where DP = (cid:16) p , . . . , p N (cid:17) .
3. The network expected loss (NEL) isNEL = NDP ∗ L , where L = (cid:16) l , . . . , l N (cid:17) (cid:48) .
4. Sovereign debts and systemic risk
Although systemic risk is a difficult concept to define precisely, a betterunderstanding of systemic risk is given by [ ? ]: “If a single node fails, itmay force other nodes to fail as well, which may eventually lead to failurecascades and the breakdown of the system, denoted as systemic risk.”According to the Property Casualty Insurers Association of America(PCIAA), there are two key assessments for measuring systemic risk: the “toobig to fail” (TBTF) and the “too interconnected to fail” (TICTF) tests . TheTBTF test is the traditional analysis for assessing the risk of required gov-ernment intervention. TBTF can be measured in terms of an institution’ssize relative to the national and international marketplaces, market shareconcentration, and competitive barriers to entry or how easily a product can
6e substituted. The TICTF test is a measure of the likelihood and amountof medium-term net negative effect on the larger economy of an institution’sfailure to conduct its ongoing business. The effect is measured beyond theinstitution’s products and activities to include the economic multiplier of allother commercial activities dependent specifically on that institution. Theeffect is also dependent on how correlated an institution’s business is withother systemic risks.Based on the two principles of PCIAA, finding such few economic vari-ables to describe DP , DT M and L are difficult. We adopt two economicvariables which can be observed to proxy them and also determine the sys-temic risk of these sovereign debts. We define systemic risk index (SRI)as SRI ≡ N (cid:88) i =1 d i · V ( k i ) , (2)where d i and V ( k i ) represent the debt/GDP ratio and the functions of thetopological importance of node i , respectively. To describe the topologicalimportance of node i , the network centrality is proper. There are two kinds ofcentrality measurements commonly be used in network theory: local measureand non-local measure. The local measure indicates the degree centralityor closeness centrality while the non-local measure denotes the betweennesscentrality or eigenvector centrality. Here, we use betweenness centrality tomeasure the topological importance of node i . The betweenness centrality ofa node i , g ( i ), is given by the following expression: g ( i ) = (cid:88) s (cid:54) = v (cid:54) = t σ st ( i ) σ st , (3)where σ st is the total number of shortest paths from node s to node t , and7 st ( i ) is the number of the paths that pass through i . We plot the time seriesof SRI from 2005 Q1 to 2011 Q1 as shown in Figure 3. < Insert Fig. 3 here > Figure 3 indicates that there is a peak around 2010 Q2. Beginning late2009, fears of a sovereign debt crisis developed among investors as a resultof the rising government debt levels around the world along with a waveof downgrading of government debts in some European states. Concernsintensified in early 2010 and thereafter, causing Europe’s finance ministerson May 9, 2010 to approve a rescue package worth 750 billion euros aimed atensuring financial stability across Europe by creating the European FinancialStability Facility.
5. Conclusions [ ? ] argues the argument that the recent financial crisis has significant ex-ternalities and systemic risks arising from the interconnectedness of financialintermediary risk portfolios. The negative externality arises because interme-diaries’ actions to diversify that are optimal for individual intermediary mayprove to be suboptimal for the society. This externality depends critically onthe distributional properties of the risks. The optimal social outcome involvesless risk–sharing, but also a lower probability for the massive collapse of inter-mediaries. Furthermore, [ ? ] and [ ? ] study the time-lag cross-correlationsin multiple time series by using time-lag random matrix theory. The increasein the level of globalization is related with the increase in cross-correlationsbetween different financial indices. The magnitude of the cross-correlations8onstitute “bad news” for the international investment managers who maybelieve the risk is reduced by diversifying across countries.In this paper, we propose a new index to measure the systemic risk infinancial systems. We use the quarterly report of consolidated foreign claimsfrom the BIS and debt/GDP ratios among these reporting countries. Ourresult indicate that the index can really help to quantify the level of systemicrisk. The index could further be considered in a wide range of global marketor other network-typed financial systems. Acknowledgements
This research is supported by the National Science Council (NSC-100-2118-M-001-007-MY2) in Taiwan. We are grateful to the seminar partici-pants at Institute of Sociology, Academia Sinica for their helpful commentsand suggestions. We also thank Kimmo Soramaki and the team of FNA fortheir software support. We thank the anonymous referees for their valuablecomments. All errors are our own. 9 igure 1: Network Structure of Sovereign Debt in 2009 Q4 igure 2: Network Structure of Sovereign Debt in 2009 Q4 igure 3: Systemic Risk Indexigure 3: Systemic Risk Index