Systemic risk, here meant as the risk of default of a large portion of the financial system, depends on the network of financial exposures among institutions. However, there is no widely accepted methodology to determine the systemically important nodes in a network. To fill this gap, we introduce, DebtRank, a novel measure of systemic impact inspired by feedback-centrality. As an application, we analyse a new and unique dataset on the USD 1.2 trillion FED emergency loans program to global financial institutions during [2008][2009][2010]. We find that a group of 22 institutions, which received most of the funds, form a strongly connected graph where each of the nodes becomes systemically important at the peak of the crisis. Moreover, a systemic default could have been triggered even by small dispersed shocks. The results suggest that the debate on too-big-to-fail institutions should include the even more serious issue of too-central-to-fail. he characterization of the architecture of economic and financial networks is gaining increasing importance 1, 2 . Indeed, the recent economic turmoil has raised a broad awareness that the financial system should be regarded as a complex network whose nodes are financial institutions and links are financial dependencies 3 . In this perspective, systemic risk is meant here as the risk of a systemic default, i.e. the default of a large portion of the financial system. It can be quantified and measured from the analysis of the dynamical evolution of the nodes and from the structure of the network [4] [5] [6] [7] . The main open question regarding financial networks concerns the determination of the so-called ''systemically important'' financial institutions, namely, the ones that, if defaulting, can trigger a systemic default and are thus to be considered ''too-big-to-fail''. From a network science perspective, this question is related to the concept of recursive centrality measures such as eigenvector centrality and PageRank. It is also related to the more general issue of the controllability of a complex network 8 . However, the investigation of how financial networks function and how systemic risk emerges is only at the beginning. The scarcity of data, due to confidentiality constraints, has limited so far the study to few national datasets [9] [10] [11] [12] . The goal of this paper is to show how network science can contribute to a quantitative assessment of systemic risk. To this end, we analyse a unique and very relevant dataset by means of a novel indicator of systemic importance. In the US, the financial crisis reached a peak in the period March 2008 -March 2010. During this time, many US and international financial institutions received aid from the US Federal Reserve Bank (FED) through emergency loans programs, including the so-called ''FED Discount Window''. The amount and the recipients of these loans were not disclosed until very recently (see more details in Supplementary Information, SI, Section 1-2) . This data represents, to our knowledge, the first data set, publicly available, on the daily financial exposures between a central bank and a large set of institutions over several months. The data was previously analysed mainly from the point of view of accounting practice and conflicts of interests 13 . Here, we instead present an analysis from the perspective of complex financial networks and systemic risk. The contributions of this paper are the following. We first analyse the portfolio of loans granted by the FED over time, both in terms of concentration and fragility. We then investigate the distribution of outstanding debt across institutions and across time. We also combine the FED dataset with data on equity investment relations among these institutions and we analyse the structure of the network of dependencies among the institutions that received funding. Finally, in order to estimate the systemic importance of the various institutions, we introduce Debt Rank. This is a novel measure, akin to feedback centrality, that takes into account in a recursive way the impact of the distress of one or more institutions to their counterparties across the whole network. Credit concentration and fragility. We start our analysis of the dataset (see Methods) from the sum of the outstanding debt across institutions, which represents the total exposure of the FED, i.e. its total potential loss in case of default of the borrowers. This number rose very sharply in November of 2008, up to around USD 1.2
Contrary to the conventional stereotype that large institutions are "too big to fail", the truth is the position of the institution in the network is equally and sometimes more important than its size REF .
DebtRank: Too Central to Fail? Financial Networks, the FED and Systemic Risk
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