DebtRank: too central to fail? Financial networks, the FED and systemic risk

Abstract

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 2008-2010. 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.

Figure 1. Exposure, concentration and fragility of the FED.

(a) Plot over time of the total exposure of the FED (blue) and of Herfindhal index H of the FED credit portfolio (in red). The effective number of borrowers is given by the reciprocal of H, which varies between 10 and 30. (b) Plot over time of the total exposure of the FED (blue) and of fragility the FED credit portfolio (in red). The peaks correspond to major distress events. E.g., the rescue of Bear Sterns in March of 2008, the Citigroup big losses (USD 2.8 billions) in October of 2008 and the market drop of March, 2009. Note that in this picture we removed big peak in fragility caused by the shock of the Lehman and Brothers default (for more details see SI).

Figure 2. Distribution and temporal patterns of debt.

(a) We split data into three phases: (1) Beginning of the crisis (from August, 2007 until April, 2008), where the FED's exposure is below USD 20 billion; (2) Plateau (April, 2008 till October 2008), where the exposure raises and stays around 380 billion for 3 months; (3) Peak and decline (October, 2008 until April, 2010), where the exposure peaks in a short span of time and starts to decline at a slower rate, due to a parallel toxic asset purchasing program (see SI, Section 3) We have chosen ten representative periods of 30 days, as shown in the inset. For each period, debt values across days were pooled together in order to increase the statistics (under the assumption that such data are generated by the same stochastic process). The main plot shows the empirical complementary cumulative distributions of outstanding debt, computed in each of the 10 periods. For each distribution, the values of debt are rescaled by the total debt across institutions in that period. Note that distributions within the same phase look similar. (b) The debt of the top 100 institutions (by average debt) is represented as a topographic map where the color indicates the debt of each institution as a percentage of its own maximum debt: from green to yellow, to red (respectively, 0-30%, 30-70%, 70-100%). The institutions are sorted by their peak date, from upper left to bottom: institutions having an earlier peak are in the upper left corner of the plot. The inset figure shows an histogram counting how many institutions were in their peak of debt during each month. Note that in the worst case almost 30 institutions where in their maximum level of debt at the same time, thus indicating a high degree of synchronicity.

Figure 3. The network of the top borrowers.

Nodes represent financial institutions (selected as explained in the text). Outgoing links represent the estimated potential impact of an institution to another one (see Methods). The nodes are positioned within a circle of radius 1, centred in 0. The distance of each node from the center is , while the angle increases linearly with R^(D) from 0 to 10π. Thus, the closer a node is to the center the higher is its DebtRank (the intuition here is its centrality). A node in the center (DebtRank = 1) is able to put under distress the entire economic value of the network. DebtRank decreases by moving outwards and leftwards along the spiral. The diagram allows at the same time to visualise the structure of the network and to compare the importance of any two given nodes. The size and the color of the node reflects the DebtRank value (larger and red nodes have higher DebtRank). The color of a link reflects the DebtRank of the node from which it originates (red links originate from node with high DebtRank and make high impact to the destination nodes). (a) Period one, at the beginning of the crisis (see also inset of Fig. 2a). Most of the nodes have low levels of DebtRank, i.e., they are located close to the border. (b) Period four (peak of the crisis). Nodes have comparable levels of Debt Rank. However, they are also much more central, i.e., they can impact a large fraction of the total economic value. A single default is likely to trigger a systemic failure.

Figure 4. Debt Rank, asset size and fragility.

Scatter plot of DebtRank versus asset size, measured as a fraction (in %) of the total of the asset size in the network. For sake of simplicity, in the experiment, asset size was assumed constant during the time span of the data. Notice that institutions such as UBS, or CITIGROUP alone account for almost 10% of the total assets. The size of each bubble is proportional to the outstanding debt of the institution while the color reflects its fragility, defined as the ratio of debt over market capitalization in the given period, as in the previous section. (a) Period one. Since the outstanding debt was very low or zero, most nodes appear small and have levels of DebtRank below 0.3, but comparable among each other. (b) Period four. Many institutions have a Debt Rank larger then 0.5, i.e. each can impact, alone, the majority of the economic value in the network. The outstanding debt in this period is close to the peak for all the institutions, as reflected by the size of the bubbles. Notice, also a higher fragility, most bubbles are red, although with some heterogeneity.