An Empirical Study of the Mexican Banking Systems Network and its Implications for Systemic Risk

Transcription

1 An Empirical Study of the Mexican Banking Systems Network and its Implications for Systemic Risk Martínez-Jaramillo, Alexandrova-Kabadjova, Bravo-Benítez & Solórzano-Margain

2 Outline Motivation Relevant concepts and literature Data Interbank exposures data Payment system s data Topological and other metrics Centrality An Empirical Study of the Mexican Banking Systems Network and its Implications for Systemic Risk 2 / 29

3 Motivation The most recent financial crisis once again put emphasis on the need of a broad comprehensive prespective of the financial systems The financial systems are among the most studied complex social structures Networks have become a widely used method to model social relationships The relationships between financial institutions can be modeled as a multidimensional network, in which participants form different kind of business relationships among each other An Empirical Study of the Mexican Banking Systems Network and its Implications for Systemic Risk 3 / 29

4 Interconnectedness Assessment methodology based on network topology approach: size interconnectedness lack of substitutability global (cross-jurisdictional) activity complexity The vertices represent the institutions, while edges model the relationships between them: In payment systems, represent transactions over a period of time (one day), which are normally expressed in aggregated level. In interbank markets, usually represent exposures between institutions. An Empirical Study of the Mexican Banking Systems Network and its Implications for Systemic Risk 4 / 29

5 Network models and payment systems. Studies describing payment systems around the world: Soramki et al. (2006) Bech & Atalay (2008) Becher et al. (2008) Rordam & Bech (2008) Propper et al. (2008) Wetherilt et al. (2010) An Empirical Study of the Mexican Banking Systems Network and its Implications for Systemic Risk 5 / 29

6 Other Related Works. Empirical analysis of the Italian interbank market, Iori et al. (2008) Simulation to model interbank lending and study contagion, Iori et al. (2006) Cascade processes on networks, Lorenz et al. (2009) Marquez-Diez-Canedo et al. (2009) Core-periphery model Craig and von Peter (2010) DebtRank, Battiston et al. (2012) Martinez-Jaramillo et al. (2010b & 2010b) An Empirical Study of the Mexican Banking Systems Network and its Implications for Systemic Risk 6 / 29

7 Interbank s data Time window contemplating data from the 3rd of January 2005 to 31st December 2010 Comprises deposits and loans, securities, and foreign exchange Three type of networks: Interbank Interbank - CLS Interbank - FX An Empirical Study of the Mexican Banking Systems Network and its Implications for Systemic Risk 7 / 29

8 SPEI s data Daily data from January 2005 onwards A time window contemplating data from the 3rd of January 2005 to 31st December 2010 Three types of networks: Low value Large value Total value Network built accumulating the daily payments sent and received. An Empirical Study of the Mexican Banking Systems Network and its Implications for Systemic Risk 8 / 29

9 Topological measures Topological measures Degree Clustering coefficient Reciprocity Affinity Completeness Index Other measures Strength Flow Herfindahl-Hirschman Index (HHI) Preference Index An Empirical Study of the Mexican Banking Systems Network and its Implications for Systemic Risk 9 / 29

10 SPEI Network Figure : January the 3rd 2005 Figure : July the 27th 2010 An Empirical Study of the Mexican Banking Systems Network and its Implications for Systemic Risk 10 / 29

11 SPEI Number of Arcs Number of arcs Time Average Degree Average degree Time An Empirical Study of the Mexican Banking Systems Network and its Implications for Systemic Risk 11 / 29

12 SPEI 0.7 Completeness index 0.65 Completeness Index Time An Empirical Study of the Mexican Banking Systems Network and its Implications for Systemic Risk 12 / 29

13 Interbank 5 Bank 13 s flow 45 LPI bank Flow 2 % LPI Time 0 A C D E F G H Bank An Empirical Study of the Mexican Banking Systems Network and its Implications for Systemic Risk 13 / 29

14 Interbank HHI L Time Figure : Lending HHI bank B An Empirical Study of the Mexican Banking Systems Network and its Implications for Systemic Risk 14 / 29

15 Tiering Craig and von Peter (2010) propose a methodology to fit a core-periphery model to empirical networks, in order to assess whether interbank markets have a tiered structure in which banks do not lend to each other directly but through banks which act as intermediaries. The methodology includes the calculation of an error score which aggregates the inconsistencies between the real network and the core-periphery model, normalized by the number of links. An Empirical Study of the Mexican Banking Systems Network and its Implications for Systemic Risk 15 / 29

16 Normalized error score (interbank exposures) Mexican Interbank Networks Scale Free Networks Erdös Rényi Random Graphs Mexican Interbank Networks Scale Free Networks Erdös Rényi Random Graphs Frequency 60 Frequency Normalized error score (in % of links) Normalized error score (in % of links) Figure : Jan 2005-Jun 2008 Figure : Jan 2009-Oct 2009 An Empirical Study of the Mexican Banking Systems Network and its Implications for Systemic Risk 16 / 29

17 Scale free networks The Mexican interbank market used to be tiered before Lehmann Brother s failure (consistent with Solis-Montes 2012), after that event the structure of the network changed, exhibiting errors similar for a scale free network with the same characteristics (consistent with Fricke and Lux and with van Lelyveld and In t Veld (2012)) SPEI networks did not reveal any structural change through time and display errors which are small enough to reject the hypothesis of a scale free topology An Empirical Study of the Mexican Banking Systems Network and its Implications for Systemic Risk 17 / 29

18 Centrality measures Concept commonly used in social network analysis Several important interpretations Power Influence Independence Control Characteristics of a relevant financial institution (Henggeler-Muller (2006)): Possesses many linkages to other members (Degree) Amount of assets, liabilities or flow is very large (Strength) Its failure could transmit contagion rapidly (Closeness) Its counterparties are also relevant (EEC & PageRank) There are many paths which passes through it (Betweenness) An Empirical Study of the Mexican Banking Systems Network and its Implications for Systemic Risk 18 / 29

19 Centrality measures Strength centrality The sum of its interbank assets and liabilities. Degree centrality A vertex is more important if it is connected to many other vertices. Betweenness centrality A vertex with high betweenness centrality can stop or distort the information that passes through it. Closeness centrality A node with high centrality would depend less on others. An Empirical Study of the Mexican Banking Systems Network and its Implications for Systemic Risk 19 / 29

20 Centrality measures Entropic Eigenvector Centrality (Bonacich (1972)) Based on Perron s eigenvector (e P F ) Considers the relevance of its neighbors. PageRank centrality (Page et al. (1999)) Based on the Google s algorithm Considers the centrality of its neighbors. A principal components unified measure of centrality Different measures are equally important Preserves most information provided by such measures From the policy making perspective, it is important to have only one measure of importance enabling to rank vertices An Empirical Study of the Mexican Banking Systems Network and its Implications for Systemic Risk 20 / 29

21 Interbank s centrality Ranking PC Strength Closeness Degree PageRank EEC Betweenness Time Figure : Principal components centrality An Empirical Study of the Mexican Banking Systems Network and its Implications for Systemic Risk 21 / 29

22 SPEI s centrality Total Low value Large value Total Low value Large value Ranking Ranking Time Time Figure : Low vs large centrality bank C Figure : Low vs large centrality bank D An Empirical Study of the Mexican Banking Systems Network and its Implications for Systemic Risk 22 / 29

23 Robustness of the centrality measures Interbank Exposures Network SPEI Total Top 3 Correlation Overlap 10 Top 3 Correlation Overlap 10 C B (17%, 20%) (0.29, 0.31) (0.36, 0.37) (32%, 36%) (0.47, 0.49) (0.45, 0.46) C C (43%, 48%) (0.93, 0.93) (0.52, 0.53) (93%, 95%) (0.84, 0.85) (0.74, 0.75) C D (43%, 48%) (0.895, 0.898) (0.537, 0.549) (93%, 95%) (0.89, 0.9) (0.74, 0.75) EEC (41%, 45%) (0.47, 0.49) (0.4, 0.42) (64%, 69%) (0.61, 0.62) (0.34, 0.35) PR (46%, 51%) (0.67, 0.68) (0.5, 0.51) (92%, 94%) (0.845, 0.85) (0.48, 0.49) PC (3) (26%, 30%) (0.72, 0.73) (0.44, 0.45) (79%, 83%) (0.83, 0.84) (0.63, 0.64) PC (6) (40%, 43%) (0.74, 0.75) (0.49, 0.5) (91%, 94%) (0.877, 0.88) (0.62, 0.63) C S (46%, 51%) (0.62, 0.63) (0.49, 0.5) (88%, 91%) (0.816, 0.82) (0.43, 0.44) Table : 95% confidence intervals for the congruence measures in the interbank exposures and total SPEI networks An Empirical Study of the Mexican Banking Systems Network and its Implications for Systemic Risk 23 / 29

24 PC centrality ranking vs. Asset size ranking Figure : PC vs assets ranking Figure : PC vs contagion ranking An Empirical Study of the Mexican Banking Systems Network and its Implications for Systemic Risk 24 / 29

25 Congruence Low vs. large value Exposures vs. SPEI Number Average Average Top 1 Top 3 Top 1 Top 3 of banks Overlapping Overlapping Table : Congruence: Low value vs. Large value network and Exposures vs. SPEI. An Empirical Study of the Mexican Banking Systems Network and its Implications for Systemic Risk 25 / 29

26 Summary The payments system network is more connected than the interbank exposures network. Bank importance in the payments network is different than in the exposures network. Bank s importance changes depending on the type of payment and depending if they are acting as lenders of borrowers. Bank s behavior can change over time. Determining systemic importance based only on asset s size could be misleading. Topology of the network is also relevant to characterize systemic importance. Most of the centrality measures are robust. An Empirical Study of the Mexican Banking Systems Network and its Implications for Systemic Risk 26 / 29

27 Future work: Network formation models Studying other financial networks, like the securities settlement network Bank s behavior in distress Centrality in payment systems Link to economic variables An Empirical Study of the Mexican Banking Systems Network and its Implications for Systemic Risk 27 / 29

28 Thanks Thank you! An Empirical Study of the Mexican Banking Systems Network and its Implications for Systemic Risk 28 / 29

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