How do balance sheets and network effects shape systemic risk in interbank networks?

Separating balance sheets from network wiring

The paper asks a narrow but consequential question: how much of the systemic risk seen in a real interbank network is already implied by the balance sheets of the banks in it, and how much comes from the specific pattern of who lends to whom? To answer it, the authors compare risk measured on the actual network with risk generated by a counterfactual in which each bank keeps its balance-sheet totals and number of counterparties, but the bilateral links are placed randomly.

That counterfactual is the key device. If the random-link benchmark reproduces the observed risk, then knowing balance sheets is enough for the purpose at hand. If it does not, the particular configuration of exposures carries information that balance sheets miss. The paper treats this as a statistical test rather than a single forecast, so the comparison is between an observed value and a distribution of expected values, not between two point estimates.

A maximum-entropy benchmark that keeps diversification

The benchmark is built with the Separable Directed Enhanced Configuration Model, a maximum-entropy approach. In plain terms, the model searches for the least structured set of networks consistent with fixed constraints taken from the data: each bank keeps the same number of borrowing and lending counterparties and the same total interbank assets and liabilities. Everything else about which bank trades with which is randomized. For each year the authors generate an ensemble of 1,000 such networks, so expected risk comes with a standard deviation rather than as a single number.

This matters because a simpler random benchmark would spread exposures too evenly and make banks look more diversified than they are. By preserving each bank's diversification pattern, the null model isolates the contribution of the actual bilateral configuration. The authors describe the benchmark as analogous to a policy counterfactual: it is the outcome expected if only balance-sheet variables mattered and link patterns were random.

Overnight Italian data with equity inferred from BankFocus

Observed risk is measured on the electronic Market of Interbank Deposits, a trading platform for unsecured money-market loans that covers the entire domestic overnight deposit market in Italy and is also open to foreign banks. The sample runs from the first quarter of 2005 to the third quarter of 2012, restricted to overnight loans, which account for roughly 90% of total volume, and aggregated to the yearly level. Each loan becomes a directed weighted link from lender to borrower.

The platform data do not contain bank equity, and banks are anonymized, so the authors infer equity from BankFocus balance-sheet data for euro-area institutions. Across 2,366 financial institutions between 2005 and 2012, the logarithm of equity and the logarithm of average interbank assets and liabilities show a strong linear relationship, with an average Pearson correlation of 0.94 and an R² of 0.88. The fitted relationship is then used to assign a simulated equity value to each e-MID bank. This is an inference step, not a direct measurement, and it conditions how the contagion simulations should be read.

Aggregate risk matches until 2009 and 2012

For the aggregate experiment, a small shock reduces every bank's net external assets in proportion to its equity, and the authors track the resulting relative equity loss H through repeated rounds of DebtRank contagion. H runs from 0, when shocks do not propagate, toward 1 − λ, when all banks have defaulted. Early in the dynamics, observed H usually falls within one standard deviation of the expected value, and after about 10 rounds the system has nearly converged.

The converged values are where the interesting splits appear. In the 2009 network, observed systemic risk is 14.8% (3.3σ) and 12.7% (3σ) lower than expected for initial shocks of 0.5% and 1%, though the gap shrinks to 3% (0.8σ) at a 5% shock. The 2012 network moves the other way: observed H is 50%, 25% and 13% higher than expected for shocks of 0.5%, 1% and 5%. Averaged across propagation rounds, 2009 shows observed risk 15.3% (2.54σ) below expectation, while 2012 shows a relative equity loss 47.2% higher (1.28σ). The negative gaps tend to vanish for large shocks, but the 2012 excess remains, at about 12% (1.73σ) on average.

The nonlinear DebtRank variant, which lets the probability of default rise as equity falls, tells a consistent story: significantly negative deviations in 2007, 2008 and especially 2009 for shocks up to 0.25, and large positive deviations in 2012 across nonlinearity and shock parameters. The authors read the two episodes through the events around them: the Lehman default appears to have reduced connectivity and raised counterparty caution, while the three-year ECB refinancing operations appear to have changed trading behavior and possibly lowered risk aversion. They explicitly note that their model can detect deviations but cannot test causality.

Individual banks deviate from their balance-sheet risk

The aggregate agreement does not carry over to individual institutions. The authors measure each bank's impact, the relative equity the system loses if that bank defaults first, and its vulnerability, the average equity loss it suffers when another bank defaults. Plotting observed values against the benchmark shows meaningful deviations in both directions, and averaging banks into equity deciles shrinks but does not remove them. In 2009 the deviations cluster above the diagonal, meaning banks are less risky than their balance sheets would suggest; in 2012 they turn positive.

The pattern depends on the contagion model. Deviations are largest when the valuation function is highly nonlinear, so that even small equity losses raise default probabilities and change the value of exposures. When the model approaches contagion at default, the exact network structure matters much less: with the Furfine valuation function, deviations are nearly non-existent in all years. The authors connect this to the idea that distress contagion, not default contagion, is where network position earns its keep.

What the 2005–2012 window supports

Several boundaries qualify the result. The e-MID data are a proxy for direct interbank exposures, and the authors note that by the mid-2010s unsecured overnight lending had nearly disappeared in favor of secured transactions, so the findings characterize the interbank market in the 2005–2012 period rather than the market today. Equity is simulated from a cross-sectional regression rather than observed bank by bank. The null model assumes a matching process driven by pure randomness, which is a deliberately agnostic choice but also a substantive one: if banks choose counterparties based on default risk, the benchmark will miss that channel, as the authors suggest happened after the Lehman disruption.

The paper also cannot establish causality for the 2009 and 2012 episodes. Its contribution is a statistical decomposition, not an identification of the events' effects on network formation.

Use balance sheets for aggregates, networks for banks

The paper's most useful distinction is between two levels of analysis. For aggregate systemic risk, a maximum-entropy framework built on balance-sheet variables and diversification patterns gives estimates consistent with observed risk in normal years, which supports using such benchmarks when detailed bilateral data are unavailable. For stress testing an individual bank, especially after a systemic event, the balance sheet is not enough: the bank's position in the network can make it materially more or less risky than its own totals imply.

The clearest contrast is between the modelled risks in 2009 and 2012. In 2009 the observed network produced less risk than the balance-sheet benchmark; in 2012 it produced more, with the excess persisting under large simulated shocks. Within this comparison, balance-sheet information alone does not reveal which direction the actual network deviates from the benchmark.

Sources used in this answer