Systemic risk in financial networks: Quantification and control

Transcription

1 Systemic risk in financial networks: Quantification and control Stefan Thurner wien, apr 20, 2013

2 with Sebastian Poledna, Doyne Farmer, Peter Klimek, John Geanakoplos supported by EC FP7 project CRISIS, agreement no wien, apr 20,

3 Risk is a multiplex layer I: lending borrowing network layer II: insurance (derivative) network layer III: network of collateral layer IV: network of overlapping portfolios layer V: network of cross-holdings layer VI: liquidity networks wien, apr 20,

4 Difficulty of multiplex networks links in the multiplex influence each other network data of different layers at the same time wien, apr 20,

5 Part I: Systemic risk from lending borrowing networks wien, apr 20,

6 Credit default risk principle if I lend something there is risk that I will not get it back risk premium is decreasing function of your creditworthiness estimate for creditworthiness: assets - liabilities if this happens on NW, borrower is node in lending-borrowing network its creditworthiness depends on its financial conditions and on those of its neighbors (who have lending-borrowing relations with it) riskiness of neighbors depends on conditions of their neighbors, etc. no rational risk premium computable unless access to system-wide information on assets and liabilities of all nodes transparency wien, apr 20,

7 Systemic risk risk that significant fraction of financial NW defaults or stops functioning systemic risk credit default risk banks care about credit default risk banks do not care about systemic risk role of regulator: make them care wien, apr 20,

8 Measures of systemic risk? systemic risk: how to measure it? DebtRank! how does it propagate? Observation by borrowing! (note derivatives!) why: if you borrow from a s.r. bank and should you default this will hit the system through your effect on the s.r. bank you won t repay measure for these effects: centrality measures on IB exposure networks L ij, IB liability network at a given moment (loans of bank j to bank i) L i = j L ji, outstanding loans of i; economic value is v i = L i / j L j C i, capital of bank i wien, apr 20,

9 Exposure networks do exist 200 contagion [# banks] Pajek betweenness [%] Springer LNCS 2004 wien, apr 20,

10 DebtRank eigenvalue centrality: disconnected components Katz centrality: OK for NW without cycles DebtRank Katz centrality K i = α j L ij K j + β α = 1/κ 1, where κ 1 is largest eigenvalue of L ij, β = 1 Katz rank most risky bank i (highest Katz centrality) gets Katz rank R katz i (t) = 1 least risky bank j (lowest Katz centrality) gets Rj katz (t) = N B Note (i) nodes that only borrow (in-links only) may cause contagion and have non-zero Katz centrality (ii) banks that only provide loans (out-links) have zero Katz centrality wien, apr 20,

11 DebtRank recursive method to determine systemic relevance of node in fin. NW takes capital (equity) of banks into account corrects Katz rank for loops in the exposure network wien, apr 20,

12 Basic idea systemic risk spreads by borrowing from systemically risky agents how do we know how risky an agent is? debtrank, Katz-rank,... forbid borrowing with those with a high debtrank not full transparency is needed just the part that is systemically relevant self-organized critical way of spreading systemic risk evenly across the NW: those who can not lend become safer, those who are safe can lend and become unsafer equilibrium of evenly spread risk level Test: need a model wien, apr 20,

13 Model Households profits/losses wages/investments Firms Firms Firms Banks Banks Banks IB loans wien, apr 20,

14 F7 B7 F6 B6 B5 F5 F1 B1 B4 F4 F2 B2 B3 F3 HH firms approach their banks for firm-loans these are transferred to households, where they are redistributed to other firms or deposited in banks if bank can not service a firm-loan, tries to get IB loan if it can get IB loan firm-loan is payed out, if not, firm gets no loan closed system of banks, firms and households: no in- or out-flows of cash wien, apr 20,

15 The modes of regulation normal mode: not regulated. Banks don t know about their systemic impact on others. IB loans are traded around the inter bank offer rate, r ib. If they need an IB loan, they ask one of their neighbors randomly transparent mode: Banks know DebtRank-ranking of their neighbor banks in A ij. If they need IB loan, they start asking the safest of their neighbors (loses DR), then next safest, etc. DR computed once every timestep fast mode: same as transparent mode, DR computed after every IB transaction wien, apr 20,

16 Normal vs. transparent: distribution of losses normal mode transparent mode fast mode frequency total losses to banks (L) (a) E 1, irrespective of mode, except in the last timesteps A fully connected graph wien, apr 20,

17 Normal vs. transparent: cascades and trading volume frequency (b) cascade sizes of defaulting banks (C) frequency (c) transaction volume IB market (V) wien, apr 20,

18 Normal vs. transparent: DebtRank distribution transparent mode normal mode 0.03 ˆRi Banks ordered in DebtRank, most risky left, safest right. t = 100 i wien, apr 20,

19 DebtRank versus Katz rank DebtRank Katz rank frequency Tfd normal total losses to banks (L) = ± 33.8, and T transp. fd = ± 33.7 Both: kurtosis 3.3, skewness 0.4 wien, apr 20,

20 Dependence on network topology Normal mode ER IB network SF IB network Transparent mode frequency frequency total losses to banks (L) (a) total losses to banks (L) (b) ER and SF network: same average connectivity k = 11.5 wien, apr 20,

21 The curse of the multiplex derivatives derivatives effectively re-arrange exposure risk NWs risk is a multiplex given exposure data only: are SR rankings of banks sensible? are derivative NWs unavoidable? wien, apr 20,

22 Part II: Systemic risk from leverage and overlapping portfolios wien, apr 20,

23 The leverage cycle Basic idea agents take leverage to make speculative investments credit provider takes these investments as collateral if collateral declines in value, credit is called back, i.e. assets must be sold selling pushes prices down and collateral loses more value wien, apr 20,

24 An agent based model for the leverage cycle in FM 2 types of agents investing in a market of financial assets informed investors = hedge funds : have good concept on the true value of a financial asset poorly informed investors = noise traders: only rough picture of true value wien, apr 20,

25 The agents Hedge funds invest in e.g. stocks long only. Value investors. Hedge funds leverage their investments through loans from banks Banks extend credit to funds take stocks as collateral. Set a maximum leverage λ MAX. Can recall loans within one timestep Investors invest in hedge funds if they perform well, otherwise they redeem. Demand: mean-reverting random walk in log-coordinates How does the asset price form? funds and noise traders submit demand functions which depend on price and market clears D nt (p) + h D h (p) = N wien, apr 20,

26 Consequences of leverage on loss distributions and clustered volatility 10 0 (b) P(r>R m>0) " max =1 " max =10!= R 0.2! max =1 (a) 0.2! max =10 (b) r 0 r t t wien, apr 20,

27 Regulation schemes No regulation: λ MAX Limit maximum leverage by fixed upper bound: λ MAX Require capital cushions (Basle I + II + III +...) Hypothetical: impose hedges (options) for collateral of leverage wien, apr 20,

28 Regulation schemes and its limits <Probability of default> unreg. basel p. h. (a) λ max < D h (t) D h (t 1) > 1.8 x (b) unreg. basel p. h λ max unreg. basel p. h. (a) σ σ(t) λ max t x 10 4 wien, apr 20,

29 Part III: Cleaning up wien, apr 20,

30 Cleaning up imagine a closed economy (financial and real): no sources or sinks of money Households profits/losses wages/investments Firms Firms Firms imagine a bank collapses (negative capital). Who pays the loss? Banks Banks Banks IB loans Bailout modes no bailouts: defaulting banks are not bailed out or replaced other banks pay: each defaulting bank is bailed out, the required fund are collected pro rata from the other banks equities taxpayer pays: as above, the required money is collected pro rata from the household (and firm owner) deposits print money: bailouts are financed by newly printed money (central bank) wien, apr 20,

31 Cost of bailout modes (preliminary) 1500 no bailouts no bailouts 1500 no bailouts banks pay banks pay banks pay hist 500 hist 500 hist taxpayer pays taxpayer pays 1500 taxpayer pays print money print money print money Production Credit volume Unemployment wien, apr 20,

32 Conclusion risk requires a multiplex framework layer 1: asset-liability networks: (i) systemic risk spreads through borrowing from SR nodes (ii) measure for systemic risk: DebtRank, Katz rank,... (iii) regulation: eliminate SR by minimum level of transparency: don t allow borrowing from SR banks DebtRank transparency (iv) no loss of efficiency or volume (re-ordering of transactions) layer 2: overlapping portfolio / collateral networks: (i) understand leverage cycle, fat tailed loss distributions & vola clustering (ii) regulation: low leverage: Basle regulation works, but fails in high leverage scenario (when most needed) testing ways to deal with bank defaults (preliminary) taxpayer option seems unfavorable for: production and unemployment wien, apr 20,