Sheri Markose ( scher@essex.ac.uk ) Simone Giansante ( S.Giansante @ bath.ac.uk )

1. Multi-Agent Financial Network Models for Systemic Risk Monitoring and Design of Pigou Tax for SIFIs Sheri Markose (scher@essex.ac.uk) Simone Giansante (S.Giansante@bath.ac.uk) Ali RaisShaghaghi (araiss@essex.ac.uk) ESRC Conference – Diversity in Macroeconomics University of Essex 25th February 2014

2. Roadmap • Research Questions & Motivation • Eigen-Pair Analysis • Target SIFIs • Internalizing Systemic Risk • Conclusions

3. Three Main Questions of Macro-prudential Regulation Is financial system more or less stable? Who contributes to Systemic Risk? How to stabilize and internalizing Systemic Risk of Super-spreaders?

4. Multiple Determinant-based Measurement Model of SIFIs Source: BCBS, 2012; BCBS, 2013a; IMF/BIS/FSB, 2009 reports

5. Back to basis • Market signals can be misleading • We need to go back to Fundamentals

6. Banking Stability Index (Segoviano, Goodhart 09/04) vs Market VIX and V-FTSE Indexes : Sadly market data based indices spike contemporaneously with crisis ; devoid of requisite info for Early Warning System

7. “Paradox of Stability” : Stock Index and Volatility Index “Paradox of Volatility” (Borio and Drehman(2009); Minsky (1982))

8. RBI Project in mapping the Indian financial system shows the following networks structures(Sheri Markose & Simone Giansante) • Project: April 2011 – December 2013 • Collection of Bilateral Data of Interbank (Fund, Non-Fund), Derivatives, etc. as well as Global Flows • Stress Test Contagion Analysis on a Multi-layer Framework (Solvency & Liquidity) • Eigen Pair Analysis and Design of Pigou Tax for SIFIs.

9. FUNDED DERIVATIVES • Top RHS Derivatives Exposures : Shows highly tiered core-periphery structure with large numbers of participants in the periphery and a few in the core • Top LHS Interbank Exposures: Shows a more diffused core with more numbers of banks in the core • Bottom: network for Indian RTGS shows no marked tiering with few financial institutions in the periphery RTGS

10. Within A larger System with non bank FIs- Net Lenders to Banks Are Mutual Funds and Insurance Companies (Code G-H)

11. Banks and Non Banks • The analysis revealed that the largest net lenders in the system were theinsurance companies and the Asset Management Companies (AMCs), while the banks were the largest borrowers. • This renders the lenders vulnerable to the risk of contagion from the banking system. The random failure of a bank which has large borrowings from the insurance and mutual funds segments of the financial system may have significant implications for the entire system

12. Domestic Banks vs Foreign Borrowers Source : Data collected from a sample of 50 banks that form 90 per cent of banking sector assets – LHS by Foreign Banks, RHS by Countries

13. Multilayer Approach to Solvency & Liquidity Contagion

14. Contagion from Most EVC/ SI Banks

15. Three Main Questions of Macro-prudential Regulation Is financial system more or less stable? Who contributes to Systemic Risk? How to stabilize and internalizing Systemic Risk of Super-spreaders?

16. Eigen Pair Analysis Monitoring Systemic Risk : Is the financial system becoming more or less stable ? Monitor maximum Eigen-value of the ratio of net liabilities to Tier 1 capital matrix

17. Why Does Network Structure Matter to Stability ? s< 1. • My work influenced by Robert May (1972, 1974) • Stability of a network system based on the maximum eigenvalue lmax of an appropriate dynamical system • May gave a closed form solution for lmax in terms of 3 network parameters , C : Connectivity , number of nodes N and s Std Deviation of Node Strength : lmax= s A highly asymmetric network such as core periphery, its connectivity has to be very low for it to be stable

18. Eigen Pair ApproachEigen Pair analysis (Markose 2012, IMF; MarkoseGiansanteShaghaghi, 2012, JEBO) • Bilateral Gross Matrix X

19. 0 222.91 138.37 129.28 109.64 105.29 … 221.42 0 124.15 116.34 104.96 100.80 … 126.66 122.08 0 70.80 60.04 57.66 … 118.78 114.48 71.07 0 56.31 54.07 … 105.10 101.29 62.88 58.74 0 47.84 … 95.87 92.40 57.36 53.58 45.44 0 … … … … … … … … X = M = X – XT :antisymmetric matrix of payables mij > 0 is net payables by node i from node j mji = –mijis corresponding amount by j to i Considering only matrix of +ve values, i.e., m+ij = mij if mij >0, mij= 0 otherwise we obtain the weighted adjacency matrix for the directed network 0 1.49 11.71 10.49 4.54 9.42 … 0 0 2.08 1.86 3.67 8.40 … 0 0 0 0 0 0.30 … 0 0 0.27 0 0 0.49 … 0 0 2.84 2.44 0 2.40 … 0 0 0 0 0 0 … … … … … … … … links point from the net borrower or net protection seller in derivatives to the net buyer (the direction of contagion) M+ =

20. Stability Analysis – SolvencyEigen Pair analysis (Markose 2012, IMF; Markose et al 2012, JEBO) • Stability of Matrix Θ

21. Eigenvector Centrality A variant is used in the Page Ranking algorithm used by Google Centrality: a measure of the relative importance of a node within a network Eigenvector centrality Based on the idea that the centrality vi of a node should be proportional to the sum of the centralities of the neighbors  is maximum eigenvalue of Θ The vector v, containing centrality values of all nodes is obtained by solving the eigenvalue equation Θ = λmax. λmaxis a real positive number and the eigenvector associated with the largest eigenvalue has non-negative components by the Perron-Frobenius theorem (see Meyer (2000)) Right Eigenvector Centrality : Systemic Risk Index Θ Left Eigenvector centrality Leads to vulnerability

22. Stability of the dynamical network system : Eigen Pair (λmax, v) In matrix algebra dynamics of bank failures given Ut+1 = [´ + (1- )I] Ut = Q Ut I is identity matrix and  is the % buffer • U0 with elements (u1t , u2t, ..... unt) = (1,0,......0) to indicate the trigger bank that fails at initial date, t=0, is bank 1 and the non-failed banks assume 0’s STABILITY: λmax(Q) < 1; λmax(´) < 

23. Stability Condition: lmax(Q´) < r •  is the % capital buffer • The criteria of failure of a bank in the contagion analysis is based on the Basel rule that • (Tier 1 Capital – Loss)/ RWA < 0.06 = TRWA • Equivalence of the above Basel rule with a Absolute Tier 1 capital threshold criteria (Tc) for failure • TC = 1 - TRWA(RWA/Tier 1 Capital) = 

24. How Useful is the Eigen Vector Centrality Rank Order As a Proxy for Furfine Losses of Capital ? Table 5 : Pearson Correlation in the Rank Order of EVC and that of Furfine Losses Figure 3 Scatter Plot of Pearson Correlation of 0.98993 in the Rank Order of Eigenvector centrality (EVC) and that of Furfine Losses (1 being the highest and 76 is lowest) Q3 2011

25. Application to Macro-Networks Source Castren and Racan, 2013 (BIS data)

26. Application to Macro-Networks The high EVC of the French and Italian Non Bank Sector and that of French Public Sector signalling their foreign indebtedness is worrying In turn Spanish and Turkish banking systems are most vulnerable to global exposures

27. Loss Multiplier vsEigenPair Loss multiplier (BLUE) is very low in the run up to the crisis in 2007-2009 and peaks well after the crisis (Paradox of Volatility) vsEigePair (GREEN).

28. Questions n.3 How to stabilize and internalizing Systemic Risk of Super-spreaders?

29. There are 5 ways in which stability of the financial network can be achieved

30. Design of Pigou Tax To Internalize Systemic Risk Costs: Proportional to Damage

31. How to stabilize ? Superspreader tax escrow fund: tax using EV centrality of each bank vito reduce max eigenvalue of matrix from .91 to closer to threshold0.25

32. Super Spreader PigouTax: To Mitigate Socialized Losses

33. Contagion from Most EVC/ SI Banks : (LHS before Stabilization; RHS after Stabilization)

34. Concluding Remarks • Changes in eigenvector centrality of FIs can give early warning of instability • These banks will, like Northern Rock, be winning bank of the year awards ; however potentially destabilizing from macro-prudential perspective • Capital for CCPs to secure system stability can use same calculations • Insights and how to quantify systemic risk from multiple clearing platforms for derivatives products (point made by Manmohan Singh, IMF)

35. THANK YOU!