Liberty Street Economics

« | Main | »

June 26, 2019

How Large Are Default Spillovers in the U.S. Financial System?

Second of two posts

How Large Are Default Spillovers in the U.S. Financial System?

When a financial firm suffers sufficiently high losses, it might default on its counterparties, who may in turn become unable to pay their own creditors, and so on. This “domino” or “cascade” effect can quickly propagate through the financial system, creating undesirable spillovers and unnecessary defaults. In this post, we use the framework that we discussed in “Assessing Contagion Risk in a Financial Network,” the first part of this two-part series, to answer the question: How vulnerable is the U.S. financial system to default spillovers?

Detailed Network Data is Difficult to Obtain

The main challenge in estimating the expected value of default spillovers is that it requires knowledge of all the bilateral claims between each pair of nodes. Such granularity of data is not publicly available. Moreover, for some financial firms in less regulated parts of the financial system, such data may not even exist, except in fragmented form inside the firms themselves.

One way out of this limitation is to fill in the data gaps with artificial data simulated from a model. Another way is to construct top-down measures of interconnectedness that rely on more readily available data, such as stock market returns, instead of actual network-specific data. However, this also requires a model to tie the non-network specific data to the default spillovers we are trying to measure. A third strategy is to narrow down the network of interest enough—say, to a single asset or narrow subsector— so that all bilateral exposures can be obtained.

An Upper Bound on Network Default Spillovers

Our goal is to estimate expected default spillovers for the entire U.S. financial network, across all institutions and asset classes, with the fewest assumptions possible. To do so, we use a new way to deal with the problem of data deficiency proposed by Glasserman and Young. They show that for a very broad class of models, even though the actual expected spillover losses cannot be computed without knowledge of all bilateral exposures, an upper limit to these spillovers can be estimated using only node-specific information (that is, without a precise breakdown of the nodes’ counterparties or the magnitudes of obligations to them). In particular, the upper limit is based on each node’s probability of default, its total outside assets, and its ratio of inside liabilities to total liabilities. Thus, at the cost of estimating an upper bound on spillovers instead of their actual values, the data requirements are greatly reduced.

The upper bound shows how much larger expected losses in the connected network are, when compared to expected losses in an analogous disconnected network with its interconnections removed (see part 1 of this series for details). Estimating the upper bound in this way enables us to quantify the effects of the network structure, without needing additional assumptions about the initial shocks to each node’s outside assets.

Having an upper limit is very useful, especially if it turns out to be low. Indeed, if we know that the maximum possible expected default spillovers are negligible, then there is little gain in estimating the actual quantity.

Empirical Estimate

With this less stringent data requirement, in a New York Fed Staff Report, we study a network that captures around 85 percent of all assets of the U.S. financial system as reported in the Financial Accounts of the United States. We use publicly available data together with commercially available data from Moody’s. The chart below shows the upper limit on expected losses due to network default spillovers as a percentage of expected losses in the analogous disconnected network. In other words, the line in the chart shows an upper bound on the losses that can be attributed to the default spillovers as a fraction of the initial direct losses that do not stem from network effects.

How Large are Default Spillovers in the U.S. Financial System?t

The chart shows that between 2002 and 2007, the upper bound on default spillovers is rather small, which means that the financial network is robust to contagion arising from counterparty risk. However, between 2008 and 2011, the upper bound on spillovers is meaningfully above zero. Our results suggest that the financial network is most fragile in the first quarter of 2009, when we estimate that network default spillovers can amplify initial losses by up to 40 percent. After that quarter, the upper bound on default spillovers starts to decline and reverts to pre-crisis levels by 2015.

Individual Node Behavior

To understand how individual firms are influenced by and affect the network spillovers, we define the “financial connectivity” of a firm to be the fraction ratio of a firm’s inside liabilities to total liabilities. A firm specific “contagion index” can then be computed by multiplying the firm’s financial connectivity, its net worth, and the leverage of its outside assets (calculated as outside assets divided by net worth). The contagion index gives the worst-case payment shortfall that a firm can pass on to other nodes of the network. The table below shows the firms with the highest contagion index for the last quarter of 2016 together with their financial connectivity, outside assets and net worth.

How Large Are Default Spillovers in the U.S. Financial System?

The first notable feature of the table is that it is almost exclusively populated by bank holding companies, even though our sample contains insurance companies, asset managers, and many other types of financial institutions. In addition, the banks are fairly different with respect to why their contagion index is high. For example, the node with the largest connectivity is the one labeled “Top 10 Dealers,” which is a single node that aggregates the largest ten broker-dealers (we do not show individual results for broker-dealers for confidentiality reasons). Compared to the four nodes with the highest contagion index, the top 10 dealer node has a higher connectivity but lower outside assets.

Digging Deeper

Estimating an upper bound on spillovers is most useful when its value turns out to be low, since then we can then be more confident that actual spillovers are expected to be low. When the upper bound is high, as in 2008-09, actual expected spillovers can be as high as the bound or as low as zero. One way to obtain some further insight into situations in which the estimated upper bound is relatively high and uninformative is to look at all possible network topologies that are consistent with the observed data.

In the illustration below we show, for the third quarter of 2008, two possible network configurations for a subset of nodes. The size of the nodes represents their net worth, and the thickness of the connections represents the size of obligations between two nodes. The network on the left was constructed by looking at the set of all possible bilateral positions among nodes that yield the same node-specific numbers that we observe in the data, and then picking the bilateral positions that produce the largest expected default spillovers. The network on the right was found analogously by minimizing, rather than maximizing, the default spillovers. The most benign configuration has spillovers that are an order of magnitude lower than the “worst case” network, highlighting the importance of network topology.


Both worst-case and best-case networks show large bank holding companies, broker-dealers, and AIG being highly interconnected. However, the worst-case network has more connections, with AIG, JPMorgan Chase, and especially Lehman Brothers, having a large exposure to Citibank. The two networks thus illuminate how the failure of a single firm such as Lehman Brothers could have vastly different default spillover effects depending on the particular firms with which it is connected.

Fernando Duarte
Fernando M. Duarte is an economist in the Federal Reserve Bank of New York’s Research and Statistics Group.

Collin Jones is a former senior research analyst in the Bank’s Research and Statistics Group and a Ph.D. student in economics at University of California, Berkeley.

Francisco RuelaFrancisco Ruela is a senior research analyst in the Bank’s Research and Statistics Group.

How to cite this post:

Fernando M. Duarte, Collin Jones, and Francisco Ruela, “How Large are Default Spillovers in the U.S. Financial System?,” Federal Reserve Bank of New York Liberty Street Economics, June 26, 2019,


The views expressed in this post are those of the authors and do not necessarily reflect the position of the Federal Reserve Bank of New York or the Federal Reserve System. Any errors or omissions are the responsibility of the authors.


Feed You can follow this conversation by subscribing to the comment feed for this post.

I believe the Default Risk amongst US Financial Funds, Banks and etc. is larger than what is represented. They all have the same investments and many of these investments are Illiquid. Just like we are seeing in Europe, as the problems unfold with Illiquid Investments, Woodford, H20 Fund, GAM and etc. then we have Deutsche Bank, where there is serious Default Risk and I wonder how many US Firms are exposed to Deutsche Bank? The Default Risks and losses are in Credit, Debt, & Counterparty Risks. As an aside you noted AIG, AIG seeds of Failure began in the 1980’s where they made some large changes which lead to their failure in 2008.

The comments to this entry are closed.

About the Blog

Liberty Street Economics features insight and analysis from New York Fed economists working at the intersection of research and policy. Launched in 2011, the blog takes its name from the Bank’s headquarters at 33 Liberty Street in Manhattan’s Financial District.

The editors are Michael Fleming, Andrew Haughwout, Thomas Klitgaard, and Asani Sarkar, all economists in the Bank’s Research Group.

Liberty Street Economics does not publish new posts during the blackout periods surrounding Federal Open Market Committee meetings.

The views expressed are those of the authors, and do not necessarily reflect the position of the New York Fed or the Federal Reserve System.

Economic Research Tracker

Image of NYFED Economic Research Tracker Icon Liberty Street Economics is available on the iPhone® and iPad® and can be customized by economic research topic or economist.

Economic Inequality

image of inequality icons for the Economic Inequality: A Research Series

This ongoing Liberty Street Economics series analyzes disparities in economic and policy outcomes by race, gender, age, region, income, and other factors.

Most Read this Year

Comment Guidelines


We encourage your comments and queries on our posts and will publish them (below the post) subject to the following guidelines:

Please be brief: Comments are limited to 1,500 characters.

Please be aware: Comments submitted shortly before or during the FOMC blackout may not be published until after the blackout.

Please be relevant: Comments are moderated and will not appear until they have been reviewed to ensure that they are substantive and clearly related to the topic of the post.

Please be respectful: We reserve the right not to post any comment, and will not post comments that are abusive, harassing, obscene, or commercial in nature. No notice will be given regarding whether a submission will or will
not be posted.‎

Comments with links: Please do not include any links in your comment, even if you feel the links will contribute to the discussion. Comments with links will not be posted.

Send Us Feedback

Disclosure Policy

The LSE editors ask authors submitting a post to the blog to confirm that they have no conflicts of interest as defined by the American Economic Association in its Disclosure Policy. If an author has sources of financial support or other interests that could be perceived as influencing the research presented in the post, we disclose that fact in a statement prepared by the author and appended to the author information at the end of the post. If the author has no such interests to disclose, no statement is provided. Note, however, that we do indicate in all cases if a data vendor or other party has a right to review a post.