Data and calibration
(Extract from page 31 of BIS Quarterly Review, March 2011)
We analyse a system of 20 large banks on the basis of two sets of data.1 The first comprises estimated correlations of asset returns between 2006 and 2009. We use these estimates to generate correlated shocks to banks' claims on non-banks. The second dataset refers to banks' balance sheets at end-2009 (for our main analysis) and end-2006 (for a robustness check). We divide the assets side of each bank's balance sheet into interbank claims (precisely, loans and advances to banks) and claims on non-banks (total assets minus interbank claims). In turn, we divide the liabilities side into: interbank debt liabilities (deposits from banks), equity capital and debt liabilities to non-banks (total liabilities minus interbank debt liabilities minus equity capital).2
In order to simulate the probability distribution of losses in the system, we need information on each bank's probability of default (PD). We start with the premise that prudential authorities do not take a system-wide perspective. They set capital requirements based on bank-level information that does not reflect fully the complexity of counterparty exposures and system-level interbank linkages. In order to work in a straightforward setup, we then assume that each bank's probability of a first-round default is fixed at 0.1% but banks' different interbank exposures lead to different probabilities of second-round defaults and, thus, to different overall PDs.3 We implement this assumption by adjusting the marginal probability distribution of the exogenous shocks to each bank's claims on non-banks.
For second-round defaults, we need information on the bilateral linkages across the 20 banks in our sample.4 Since our data reveal only the total interbank positions on the balance sheet of each bank, we need to make certain assumptions. First, we assume that interbank linkages are fully captured by balance sheet data, thus excluding for instance securitised assets and derivative exposures. Second, we follow the literature in constructing a network of bilateral interbank linkages on the assumption that each bank in our sample spreads its entire interbank positions as evenly as possible across the other banks in the sample (Upper (2011)). Third, as in any empirical setting, our system is not truly closed in the sense that aggregate interbank assets are not exactly equal to aggregate interbank liabilities. Following the literature, we close the system by introducing a hypothetical "sink" bank.
The default of a bank, irrespective of whether it is first- or second-round, imposes losses on the bank's non-bank creditors. The magnitude of these losses depends on the level of the defaulted bank's assets and on bankruptcy costs. We assume that bankruptcy costs wipe out 20% of the bank's assets at default.
1 These banks are: Bank of America, Barclays, BNP Paribas, Citigroup, Commerzbank, Crédit Agricole, Credit Suisse, Deutsche Bank, HSBC, ING, JPMorgan, Lloyds, Mizuho, Royal Bank of Scotland, Santander, Société Générale, Sumitomo Mitsui, UBS, UniCredit and Wells Fargo.
2 Our data sources are Moody's KMV and Bankscope.
3 As a robustness check, we assess the empirical performance of the indicators under the assumption that supervisors can control a bank's overall PD, stemming from first- and second-round defaults. This setup leaves our conclusions broadly unchanged.
4 In principle, the correlations of banks' asset returns reflect both common exposures to non-banks and interbank linkages. Background analysis reveals, however, that interbank linkages affect the tail of the distribution of asset returns and, thus, have a negligible impact on asset return correlations, which are related mainly to the centre of this distribution. We abstract from this impact in our calibration of the banking system.