Assessing Banks’ Systemic Risk Contribution: A Leave-One-Out Approach

Stefano Zedda

Universita di Cagliari

Giuseppina Cannas

European Commission Joint Research Center

November 2, 2015

Abstract:

The last financial crisis has shown that large banking crises not only pose a highly dangerous risk to financial systems, but also to both the real economy and public finances. Reducing that risk has become a priority for regulators and governments.

In this paper we propose an alternative approach for measuring risk contributions, based on the idea that the contribution of each bank to the system can be obtained comparing the banking system performances (in terms of expected shortfall), to the performances of the same banking system when excluding the considered bank. We thus refer to it as the Leave-One-Out contribution to systemic risk.

In an unprecedented insight, that can result of great relevance for banking supervision, we split the Leave-One-Out contribution as the sum of two components, namely the idiosyncratic bank risk (the value of expected losses of the bank when not linked to the system), and the systemic component, defined as the system expected loss variation due to the bank linkages to the system. For testing the method we compared the Leave-One-Out outcome to the Shapley values on a sample of nine French banks, then applied it to the list of financial institutions included in the last EU-wide stress testing conducted by the European Banking Authority.

Results show that Leave-One-Out contributions are highly correlated with the Shapley values. More, we proof that thresholds set for computing the ES relevantly affect results, so that some banks can have a barrier effect in small crises while having a positive contribution in larger crises. Finally the distinction in idiosyncratic and systemic contribution allows assessing how the two components are affecting the bank riskiness and which balance sheet variables are related to. This consciousness of how linkages affect the system riskiness can relevantly contribute to macroprudential regulation.

Assessing Banks’ Systemic Risk Contribution: A Leave-One-Out Approach – Introduction

As witnessed by the ruinous outcomes of many financial intuitions’ defaults during the last financial crisis, the default of a single bank may produce effects that extend far beyond the institution itself, possibly hitting large shares of banking systems and of the real economy. In this context, the scientific debate has focused its attention on what systemic risk is and how to measure it.

Systemic crises can be the effect of a single important default, but also of more smaller defaults, and contagion effects. While the first case is evidently driven by dimension, in the second case, and anyway when contagion spreads out, it is not simple to assess each single contribution to the crisis. It is evident that the same initial default (or defaults) can turn on, or not, a systemic crisis depending on the importance of financial linkages, on the strength/weakness of the other banks, on the strength/weakness of the real economy, etc.

As suggested by Brunnermeier et al (2009), a systemic risk measure should identify both the risk by individually systemic institutions, so large that they can cause negative risk spillover effects on others via their linkages, and by smaller institutions which are systemic as part of a herd. This complexity is still not solved, so the debate is open on how to charge each of the participants to their responsibility share (risk contribution) to the crisis (or to a possible crisis).

This turned out to be a question of fundamental importance for determining how the macroprudential approach to banking regulation (such as the one proposed by the Basel Committee on Banking Supervision) should be pursued.

This paper aims at contributing to this stream of literature by proposing an original approach for determining the risk contribution of each bank to the system.

We argue that the contribution of each bank to the system can be obtained comparing the banking system performances as it is, to the performances of the same banking system when excluding the considered bank.

In an unprecedented insight, we split this difference as the sum of two components, namely the idiosyncratic risk contribution of the bank, i.e. the loss of the considered bank as single, not connected to the system (as in the Basel II approach), plus the “systemic contribution” of the bank to the system, which accounts for the losses transmission role of the bank.

While the idiosyncratic contribution is always positive, as the risk of a single bank default is always present, the systemic contribution is generally positive, indeed cases where the systemic contribution is negative exist, signaling a barrier effect to defaults propagation.

Considering the relevance of large crises we experienced (the small ones can be managed with the standard resolution tools) we focus our analysis on large crises, where the system stability is actually threatened.

As our approach is in someway related to the Shapley value, we considered worth benchmarking our model results with the Shapley value, so we compared the two measures on a small sample of nine French banks. We also tested, on a larger sample of 116 European banks included in the EBA panel, whether different crises dimension relevantly affect results, and if the idiosyncratic systemic contribution have different roles in different crises dimension, and which input variables are related to each of the two components.

The rest of the paper is organized as follows. In Section 2 we revise the recent literature on risk contribution, Section 3 defines the LOO contribution to systemic risk. Section 4 presents the model implementation and the simulation model used for deriving the individual and joint distribution of losses. Section 5 presents and discusses results of the model empirical application to a set of nine French banks and for the EBA panel. Section 6 concludes.

Systemic Risk

Systemic Risk

Systemic Risk

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