How to Measure Interconnectedness between Banks, Insurers and Financial Conglomerates?

Transcription

1 How to Measure Interconnectedness between Banks, Insurers and Financial Conglomerates? G. Hauton 1 JC. Héam 2 1 ACPR 2 ACPR, CREST 3 rd EBA Policy Research Workshop, November 2014, London. The views expressed in this paper are those of the authors and do not necessarily reflect those of the Autorité de Contrôle Prudentiel et de Résolution (ACPR). contact: jean-cyprien[dot]heam[at]acpr[dot]banque-france[dot]fr JC. Héam (ACPR) Measuring Interconnectedness EBA Workshop, / 39

2 Outline Motivation 1 Motivation 2 Data 3 Network Integration and Network substitutability 4 Core-Periphery Structure Identification 5 Measures based on network stress-test 6 Comparisons 7 Concluding remarks JC. Héam (ACPR) Measuring Interconnectedness EBA Workshop, / 39

3 Motivation Motivation In 2009, Financial Stability Board proposed a general framework to identify Systematically Important Financial Institutions: size, substitutability and interconnectedness. Considering interconnectedness is motivated by the concern about contagion risk. Interconnectedness is defined as "linkage with other components of the system". Intuitively, contagion risk depends on size of bilateral exposures (larger or lower than equity), on the shape of the network (diversified or concentrated) and on the possible shock (individual/common, small/large...). Measuring interconnectedness is to summarize all these aspects. For insurers (FSII), interconnectedness is measured by "intra-financial system assets" and "intra-financial system liability". JC. Héam (ACPR) Measuring Interconnectedness EBA Workshop, / 39

4 Motivation Motivation A growing number of interconnectedness measures are proposed by central bankers or academia: centrality measures, core-periphery... However, there is still no consensus on the measure(s) to pick. Our methodological goal is to present few interconnectedness metrics in order to spot how they can/should be used: Descriptive statistics Network-integration and network-substitutability Core-periphery structure Measures based on network stress-test Our empirical contribution is to analyze a unique dataset of bilateral exposures between 21 French financial institutions encompassing financial conglomerates, banks and insurers. JC. Héam (ACPR) Measuring Interconnectedness EBA Workshop, / 39

5 Motivation 1 Motivation 2 Data 3 Network Integration and Network substitutability 4 Core-Periphery Structure Identification 5 Measures based on network stress-test 6 Comparisons 7 Concluding remarks JC. Héam (ACPR) Measuring Interconnectedness EBA Workshop, / 39

6 Outline Data 1 Motivation 2 Data 3 Network Integration and Network substitutability 4 Core-Periphery Structure Identification 5 Measures based on network stress-test 6 Comparisons 7 Concluding remarks JC. Héam (ACPR) Measuring Interconnectedness EBA Workshop, / 39

7 Perimeter Data The perimeter consists in: 6 Conglomerates (CG): BNP, Crédit Agricole, Société Générale, BPCE, Crédit Mutuel and La Banque Postale. 4 Pure banks (PB): HSBC, Crédit Logement, CRH, Oseo. 11 Pure Insurers (PI): Axa, Allianz, CNP, Generali, Covea, Maif, Macif, Scor. Date: 31/12/2011. Consolidated basis. Instruments: debt instruments: debt securities, deposits, subordinated debt... equity instruments: shares, equity securities, capital investment... In terms of equity, conglomerates accounts for about half, pure banks about a quarter and pure insurers about a quarter. In terms of total assets, we cover about 85% of the French financial sector. JC. Héam (ACPR) Measuring Interconnectedness EBA Workshop, / 39

8 Visualization Data Legend: Node color indicates legal status (red for conglomerates, blue for pure insurers and yellow for pure banks), edge width is proportional to exposure. JC. Héam (ACPR) Measuring Interconnectedness EBA Workshop, / 39

9 Data Overall distribution of exposures The financial institutions report a total of 227GEuros. 62% of potential exposures are non-zero. 38% of exposures are zeros. Most non-zero exposures are very small but there are few large exposures. JC. Héam (ACPR) Measuring Interconnectedness EBA Workshop, / 39

10 Summary Data Four stylized facts describe the considered network: Exposures are generally modest: 38% of exposures are zeros, the remaining are mostly small exposures. Large exposures exist but are not numerous. Conglomerates appear to be most important players in terms of links and volume. Pure insurers are mostly net fund providers. Debt instrument is the most common instrument used. JC. Héam (ACPR) Measuring Interconnectedness EBA Workshop, / 39

11 Network Integration and Network substitutability Outline 1 Motivation 2 Data 3 Network Integration and Network substitutability 4 Core-Periphery Structure Identification 5 Measures based on network stress-test 6 Comparisons 7 Concluding remarks JC. Héam (ACPR) Measuring Interconnectedness EBA Workshop, / 39

12 Network Integration and Network substitutability Notations Let us consider n financial institutions. Bilateral exposures are stacked into matrix E such that E(i, j) is the exposure of financial institution i to financial institution j. We denote K i the equity of institution i. Example with n = 6: 1) 2) 3) 4) 5) 6) 1) ) ) ) ) ) K = (3 ; 10 ; 9 ; 11 ; 10 ; 12 ; 7) JC. Héam (ACPR) Measuring Interconnectedness EBA Workshop, / 39

13 Network Integration and Network substitutability Comparing instead of giving scores One strategy is not to give to each institution a score of interconnectedness but to compare institutions. If two institutions are close, the same concerns should apply to both. Two institutions are close with respect to interconnectedness... when they are exposed similarly to their counterparts. integration when they are exposed similarly to the same counterparts. substitutability JC. Héam (ACPR) Measuring Interconnectedness EBA Workshop, / 39

14 Network Integration and Network substitutability Example Institutions 1 and 3 are close in terms of integration but not in terms of substitutability: 1) 2) 3) 4) 5) 6) 1) X 2.7 X ) X 2.9 X Institutions 1 and 2 are close in terms of integration and substitutability: 1) 2) 3) 4) 5) 6) 1) X X ) X X JC. Héam (ACPR) Measuring Interconnectedness EBA Workshop, / 39

15 Network Integration and Network substitutability Methodology Let us compare for instance institution i 0 and institution i 1. We analyze the closeness of I 0 = (E(i 0, 1),... E(i 0, i 1 1), E(i 0, i 1 + 1),... E(i 0, n)) and I 1 = (E(i 1, 1),... E(i 1, i 0 1), E(i 1, i 0 + 1),... E(i 1, n)). Institution i 0 is more integrated than institution i 1 if I 0 is stochastically greater than I 1. 1 We use the statistic of Mann-Whitney test as a distance. Institution i 0 is substitute to institution i 1 if I 0 and I 1 are drawn from the same distribution. We use the statistic of Wilcoxon s signed rank test as a distance. From the analysis of distances, one can form groups of close institutions (hierarchical clustering). = Should exposition be understood as volume or risk taking? To adopt a risk perspective, we need to control the size. We propose to derive two additional exposures matrices by dividing exposures by the equity of lender (credit risk) and the equity of the borrower (funding risk). 1 X is stochastically greater at first order than Y iff for any increasing f, E(f (X )) E(f (Y )). JC. Héam (ACPR) Measuring Interconnectedness EBA Workshop, / 39

16 Network Integration and Network substitutability Results These pair-wise comparisons draw the following stylized facts: Conglomerates form a typical group that tends to be exposed similarly both on their asset sides and on their liability sides. This similarity appears only when combining a size analysis (integration) and an allocation analysis (substitutability). Pure insurers and pure banks appear to invest in the similar amount (integration) but may differ in the allocation of these exposures (substitutability). Insurers are characterized from their relying on the network to get funding even if some of them can have funding mixes similar to other financial institutions. JC. Héam (ACPR) Measuring Interconnectedness EBA Workshop, / 39

17 Outline Core-Periphery Structure Identification 1 Motivation 2 Data 3 Network Integration and Network substitutability 4 Core-Periphery Structure Identification 5 Measures based on network stress-test 6 Comparisons 7 Concluding remarks JC. Héam (ACPR) Measuring Interconnectedness EBA Workshop, / 39

18 Core-Periphery Structure Identification Economists in game theory have pointed out different stylized network structures with associated narratives: The objective of network structure identification techniques is to find the underlying composition of the network to highlight specific roles. In interbank network, the core-periphery structure is the usual suspect. JC. Héam (ACPR) Measuring Interconnectedness EBA Workshop, / 39

19 Core-Periphery Structure Identification We inherit massively from Craig and von Peter (2014) in JFI. Stylized networks are described with an adjacency matrix, that is a binary exposure matrix. The first step is to transform an exposure matrix into an adjacency matrix. Considering a threshold level θ, we define A(θ) by { 1, if E(i, j) > θ, A(i, j; θ) = 0, otherwise. Adjacency matrix A(θ) is not corrupted by noise. JC. Héam (ACPR) Measuring Interconnectedness EBA Workshop, / 39

20 Core-Periphery Structure Identification The second step is to detect core nodes and peripheral nodes. For a given partition c of the set of institution, one can rearrange the adjacency matrix such that all core institutions are in the first rows (and lines) to get A(θ; c). Then we compute a (matrix) distance between A(θ; c) and the adjacency matrix corresponding to a perfect core-periphery structure A th. Identifying the core-periphery structure is minimizing this distance over c (best partition) and θ (avoiding noise). The last step is to interpret the partition. Loosely speaking, core institutions have high interconnectedness scores while peripheral institutions do not. JC. Héam (ACPR) Measuring Interconnectedness EBA Workshop, / 39

21 Results Core-Periphery Structure Identification Volume Credit Risk Funding Risk CG CG CG CG CG CG PB PB PB PB PI PI PI PI PI PI PI PI PI PI PI Distance (%) #Core JC. Héam (ACPR) Measuring Interconnectedness EBA Workshop, / 39

22 Summary Core-Periphery Structure Identification The core-periphery structure, usually applied to banking networks in volume, is also relevant when including insurance companies. However, when size is controlled for, this structure is not unveiled. For credit risk, the core is large. For funding risk, the adjustment is very poor. The core-periphery identification strategy seems to be corrupted by size effect. JC. Héam (ACPR) Measuring Interconnectedness EBA Workshop, / 39

23 Outline Measures based on network stress-test 1 Motivation 2 Data 3 Network Integration and Network substitutability 4 Core-Periphery Structure Identification 5 Measures based on network stress-test 6 Comparisons 7 Concluding remarks JC. Héam (ACPR) Measuring Interconnectedness EBA Workshop, / 39

24 Measures based on network stress-test Network stress-test methodology Results of a network stress-test can be interpreted as interconnected measures since they explicitly consider contagion risk. In that sense, they are the best candidate to provide interconnected measures in line with FSB perspectives. Network stress-test are composed of two main parts: An external shock that affects the financial institutions in the system. A contagion mechanism that models the propagation of the external shock through the financial system. The contagion channels are direct (solvency) or indirect (fire-sales, funding trouble, informative cascade...). Results should be interpreted in line with these two components. JC. Héam (ACPR) Measuring Interconnectedness EBA Workshop, / 39

25 Measures based on network stress-test Systemic importance and systemic fragility We use the contagion model proposed in Gourieroux et al. (2012) for solvency contagion. This methodology is relevant to analyze long-term investments, but does not model (re-)insurance contracts. The model distinguishes contagion through debt instruments from contagion through equity instruments. This contagion model can be plugged to any shocks design. For interconnectedness concern, the 21 scenarios where one institution is initially into default lead us to two dimensions of interconnectedness: The systemic importance is the impact of the default of institution X s default on other institutions. It is measured as the number of institutions whose losses exceed 10% of initial equity. The systemic fragility is the exposure of institution X to the default of other institutions. It is measured as the number of institutions whose defaults generate a losses larger than 10% of initial equity % is arbitrary. JC. Héam (ACPR) Measuring Interconnectedness EBA Workshop, / 39

26 Measures based on network stress-test JC. Héam (ACPR) Measuring Interconnectedness EBA Workshop, / 39

27 Outline Comparisons 1 Motivation 2 Data 3 Network Integration and Network substitutability 4 Core-Periphery Structure Identification 5 Measures based on network stress-test 6 Comparisons 7 Concluding remarks JC. Héam (ACPR) Measuring Interconnectedness EBA Workshop, / 39

28 Comparisons Comparisons We have presently three main strategies to measure interconnectedness: integration/substitutability, core-periphery identification, network stress-test results. Considering that FSB motivation to measure interconnectedness is based on contagion risk, let us take the results of network stress-test as benchmark. Can groups identified by other methods be good proxies to network stress-test results? JC. Héam (ACPR) Measuring Interconnectedness EBA Workshop, / 39

29 Comparisons Comparisons Importance Fragility Neither Volume Substitutability Integration Core Periphery Credit Risk Substitutability... Integration Core +.. Periphery... Funding Risk Substitutability Integration... Core... Periphery... Legend: "+++" indicates a p-value lower than 1% for the exact Fisher test between at least one group of the method in line and the group identified in column. Similarly, "++" for a p-value lower than 5%, "+" lower than 10%. JC. Héam (ACPR) Measuring Interconnectedness EBA Workshop, / 39

30 Outline Concluding remarks 1 Motivation 2 Data 3 Network Integration and Network substitutability 4 Core-Periphery Structure Identification 5 Measures based on network stress-test 6 Comparisons 7 Concluding remarks JC. Héam (ACPR) Measuring Interconnectedness EBA Workshop, / 39

31 Concluding remarks Concluding remarks Interconnectedness measures are derived from various strategies. Each strategy tackles the issue from a different point of view and provides more than one figure. Even if interconnectedness is a multidimensional concept, we should select parsimoniously the measures relevant from the objective. For contagion concern, network stress-test appear to provide results that are not proxied by other methods. Two main challenges are: 1) the measures are both individual and system-dependent and 2) size seems never far from interconnectedness measures. JC. Héam (ACPR) Measuring Interconnectedness EBA Workshop, / 39

32 Concluding remarks The right tool for the right job? Strategy Summary Integration & Core-Periphery Systemic importance Statistics Substitutability Identification Systemic fragility Design continuous continuous binary continuous individual pair-wise system-wide system-wide Measure quantitative none qualitative quantitative Complexity easy easy complex complex Potential?? size model bias effect dependence Policy concern usual cross-market SIFIs SIFIs monitoring comparison identification identification Thank you for your attention. JC. Héam (ACPR) Measuring Interconnectedness EBA Workshop, / 39

33 Concluding remarks The right tool for the right job? Strategy Summary Integration & Core-Periphery Systemic importance Statistics Substitutability Identification Systemic fragility Design continuous continuous binary continuous individual pair-wise system-wide system-wide Measure quantitative none qualitative quantitative Complexity easy easy complex complex Potential?? size model bias effect dependence Policy concern usual cross-market SIFIs SIFIs monitoring comparison identification identification Thank you for your attention. JC. Héam (ACPR) Measuring Interconnectedness EBA Workshop, / 39

34 Appendix Appendix JC. Héam (ACPR) Measuring Interconnectedness EBA Workshop, / 39

35 Appendix Contagion: Gouriéroux et al. (2012) model Asset Liability interbank { π i,1 K 1 cross. Lx i debt shareholding π i,n K n { γ i,1 Lx 1 interbank lending. K i equity γ i,n Lx n external asset Ax i ( K i = max 0 ; n π i,j K j + j=1 ( n Lx i = min π i,j K j + j=1 n ) γ i,j Lx j + Ax i Lxi j=1 n ) γ i,j Lx j + Ax i ; Lxi j=1 (1) (2) JC. Héam (ACPR) Measuring Interconnectedness EBA Workshop, / 39

36 Case of two banks Appendix Let us consider the basic network composed of two banks: bank 1 and bank 2. Bank 1 Bank 2 Asset Liability Asset Liability π 1,1 Y 1 L 1 π 2,1 Y 1 L 2 π 1,2 Y 2 π 2,2 Y 2 γ 1,1 L 1 γ 2,1 L 1 γ 1,2 L 2 γ 2,2 L 2 Ax 1 Ax 2 A 1 L 1 A 2 L 2 JC. Héam (ACPR) Measuring Interconnectedness EBA Workshop, / 39

37 Case of two banks Appendix Each bank can be either alive, or in default. Therefore, there are 2 2 = 4 possible regimes: Regime 1: both bank 1 and bank 2 are alive Regime 2: both bank 1 and bank 2 default Regime 3: bank 1 defaults while bank 2 is alive Regime 4: bank 1 is alive while bank 2 defaults The previous proposition states that, under portfolio crystallization, only one of the four previous regimes can arise. JC. Héam (ACPR) Measuring Interconnectedness EBA Workshop, / 39

38 Appendix Regimes of default without interconnections Ax 2 default of bank 1 only no default L 2 joint default default of bank 2 only L 1 Ax 1 JC. Héam (ACPR) Measuring Interconnectedness EBA Workshop, / 39

39 Appendix Regimes of default with interconnections Ax 2 default of bank 1 only no default Ax 2 joint default default of bank 2 only Ax 1 Ax 1 JC. Héam (ACPR) Measuring Interconnectedness EBA Workshop, / 39

40 Appendix Regimes of default with/out interconnections Ax 2 default of bank 1 only no default Ax 2 joint default default of bank 2 only Ax 1 Ax 1 JC. Héam (ACPR) Measuring Interconnectedness EBA Workshop, / 39