By Amanah Ramadiah, Fabio Caccioli, Daniel Fricke

Financial networks are an essential source of systemic risk. Unfortunately, detailed data on (direct and indirect) interactions between individual financial institutions is often unavailable, and the only the total aggregate position is known.

To conduct a stress test, one must resort to network reconstruction methods to infer the network from partial information. However, given the number of proposed financial reconstruction methods, the remaining question is, which is the best method? In ‘Reconstructing and Stress Testing Credit Networks, Ramadiah, Caccioli and Fricke (2021) answer this question by performing a horse race between different reconstruction methods. They conduct the analysis using data on bank-firm credit relationships i Japan from 1980 to 2010.

As shown in Figutre 1, the network is bipartite as links can only arise between banks and firms. Moreover, a connection between a bank and a firm implies a credit relationship between the two.

The paper considers four essential reconstruction methods:

  • CM1 (Squartini and Garlacheilli, 2o11)
  • CM2 (Squartini et al., 2017)
  • Max Entropy
  • MinDensity (Anand et al., 2015)

The comparison between each method is listed in Table 1. Ramadiah, Caccioli and Fricke (2021) examine the performance of these methods along two different dimensions. First, is the capability of reconstruction methods to reproduce the actual level of systemic risk.

Ramadiah, Caccioli and Fricke (2021) show that the ‘best’ construction method depends on the assumed criterion of interest. Nevertheless, they find that the ways that succeed in reproducing the topological structure (related to heterogeneity) observed in the existing network (i.e. CM1 and CM2) consistently perform best. They first found a significantly negative time trend for a significantly negative time trend for the actual systemic risk level of the Japanese banking system, which suggests that the system has become more robust over time.


Secondly, Ramadiah, Caccioli and Fricke find that the actual level of systemic risk in most instances which suggests that many reconstruction methods tend to underestimate the systemic risk (see Figure 2).

This paper also explores different policies (such as merging or breaking up banks or leverage caps) which make the financial system less vulnerable. Leverage caps and bank mergers can improve robustness of the network (see figure 3), even though it is unable to reach the systemic risk level shown by the most stable reconstruction method.


Overall, the paper studies a critical topic on systemic risk. It providers supervisors with the techniques to understand the consequences of taking a particular setup when conducting a stress test. It also gives an insight into how to conduct more accurate stress tests, particularly, when detailed interactions are not available. It also recommends to Central Banks and regulators which is the best network reconstruction method to use.


Read the full paper here


Ramadiah, T., Caccioli, F., Fricke, D., 2020. Reconstructing and stress testing credit networks. Journal of Economic Dynamics and Control, 111. doi:

Squartini, T., Almog, A., Caldarelli, G., Van Lelyveld, I., Garlaschelli, D., Cimini, G., 2017. Enhanced capital-asset pricing model for the reconstruction of bipartite financial networks. Phys. Rev. E 96. doi: 10.1103/PhysRevE.96.032315 . 

Squartini, T., Garlaschelli, D., 2011. Analytical maximum-likelihood method to detect patterns in real networks. New J. Phys. 13, 1–47. doi: 10.1088/ 1367-2630/13/8/083001 . 

Anand, K., Craig, B., von Peter, G., Von Peter, G., 2015. Filling in the blanks: network structure and interbank contagion. Quant. Finance 15 (4), 625–636. doi: 10.1080/14697688.2014.968195 .


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