Systemic Risk. The idea. The model. The simulations. The results. Conclusions 3 The simulations. Systemic Risk. The idea. The model.

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1 Interbank Lending and the Spread of Bank Failures: A Network Model of idea 1 idea 2 Andreas Krause University of Bath Simone Giansante University of Essex 3 [email protected] 4 5 issue literature on systemic risk idea One failing bank can lead to failures spreading Systemic risk idea Losses for other banks due to reduced asset values fire sales arising from sales of other failing banks (liquidity effects) Interbank lending as a tool to reduce the risk of systemic risk (monitoring, less susceptible to shocks) Interbank lending as a mechanism for the transmission of liquidity effects Interbank lending transmits failures directly as loans might not be repaid (restrictive assumptions: all banks identical, interbank loans of same size, Erdös-Renyi network,...)

2 Our contribution idea idea 1 idea Use a network of heterogenous banks 2 Different sizes, different interbank loans, different networks,... 3 Explore what determines the spread of failures 4 5 Balance sheet of banks banking system idea idea Assets (A i ) Cash (R i = ρ i A i ) Loans (C i = β i A i ) Liabilities Deposits (D i = γ i A i ) Banks are connected via interbank loans Bank sizes have a power-law distribution Scale-free network of interbank loans (number of links proportional to size) Bank loans (L i ) Bank loans (B i ) Equity (E i = α i A i )

3 Contagion mechanism Trigger mechanism If a bank fails it is liquidated idea It calls in all interbank loans given to other banks, called in loans are repaid not in full To repay those called in loans, these banks need cash y raise cash by calling in interbank loans themselves (if cash reserves are not sufficient) If calling in loans does not raise enough cash, they default (and are liquidated) idea We exogenously select one bank who we assume makes losses equal to its equity and liquidate it Banks selected are biggest, second biggest and one from each size decile beyond that If losses made from calling in loans exceeds equity, banks fail (and are liquidated) This process continues until all no banks are failing anymore Parameters used idea 1 idea 2 3 idea Banking system: [13; 1, 000] banks Asset value: [100; 100, 000, 000, 000] Tail index of size distribution: [1.5; 5] Recovery rate of loans: [0; 1] Fraction equity: α = [0; 0.25] 4 Fraction deposits: [0; 1 α] Fraction cash: [0; 0.25] 5 Fraction loans to public [0; 1]

4 Cumulative distribution function of the fraction of banks failing in the banking system Variables considered idea idea Principal components analysis Interpretation of factors idea idea TOPOLOGY measures the interconnectedness of the interbank loan network TIERING provides a measure for the degree of tiering in the network of interbank loans BALANCE SHEET provides a measure for the reliance of the bank on interbank loans LOAN STRUCTURE measures whether banks provide loans to banks of a similar size to their own RECOVERY is representing the recovery rate in case of bank failures TRIGGER measures the size of the initially failing bank

5 Regressions idea 1 idea 2 3 idea 4 5 Existence of contagion Extent of contagion idea idea Largest impact from the size of the trigger bank Interconnectedness (TOPOLOGY) is second most important factor Other factors of much less significance are the tiering and reliance on interbank loans (BALANCE SHEET) Most important factors are the tiring of the network (TIERING) and the interconnectedness (TOPOLOGY) Also important is whether banks provide loans to similar sized banks (LOAN STRUCTURE) Other factors have a low impact

6 Some observations Policy implications idea idea Balance sheet structure not relevant factor Influence of interconnectedness (TOPOLOGY) has different signs on likelihood of contagion and its extend same is true for tiering Analyzing banking systems with different tail indices strengthens the importance of tiering network of interbank loans matters Reliance on balance sheet structure alone is misleading Using random networks gives a quite different picture Summary idea 1 idea idea 2 3 network structure of interbank loans is an important determinant of the occurrence and extent of contagion Regulation should take these effects into account to effectively address systemic risk 4 5