Fear of financial contagion was a major motivation behind the bailouts and other interventions provided during the recent sovereign debt crisis in Europe. Given the interconnected network of financial relationships among European nations, the potential for contagion seemed self-evident. But what really was – and is – the magnitude of the risk of sovereign contagion in Europe?

While the direct losses to creditors from a sovereign default can generally be observed, quantifying the spillover losses that would result from such a default is less straightforward. Understanding the potential magnitude of these spillovers is essential for evaluating the net benefits (or costs) of bailouts and other interventions designed to prevent or mitigate the impact of a default.

## Modelling contagion

Measuring the potential spillovers from a sovereign default requires a modelling framework that can distinguish the effect of a default (or risk of default) on the credit risk of other sovereigns, separately from comovement in country-specific factors. Moreover, one must account for the fact that credit risk is jointly determined among financially interconnected sovereigns – as it would be in any network of financial entities.

Recently, a number of economists have developed theoretical models of contagion in financial networks (see Acemoglu et al. 2014, Elliott et al. 2014, and Glasserman and Young 2014). These models define contagion based on the direct financial losses that occur when an entity defaults, or more generally loses value. Contagion emerges if any creditors to the defaulting entity experience large enough losses so that they in turn become insolvent. These models show how, in an interconnected network, the default of one entity can cause increased borrowing costs and even trigger a cascade of defaults among the other entities.

In recent work, we have applied such a network model to evaluate credit market perceptions of the potential spillovers from a sovereign default in Europe (Glover and Richards-Shubik 2014). Data from the Bank for International Settlements (BIS) and International Monetary Fund (IMF) can be used to construct a network of sovereign debt holdings among European countries.^{1} Credit default swap (CDS) spreads on sovereign debt provide a measure of credit market expectations about the risk of default.^{2} The model of contagion then determines the extent to which this risk should correlate among countries, based on the cross-holdings of sovereign debt.

## Default simulations – the example of Greece

The estimated model can be used to simulate the impact of the default of one sovereign on the credit risk of other sovereigns in the network. Figure 1 presents the results of these simulations for a Greek default. For each quarter, it shows the increase in risk-neutral default probabilities for other selected sovereigns, given a hypothetical Greek default in that quarter. (These are the short-run impacts, as each quarter is considered separately.) We see that the predicted spillovers onto the default risk of other sovereigns are quite minimal, less than 10 basis points, except for Ireland and Portugal.

For Portugal, the predicted impact of a Greek default rises to 60 basis points by 2011-Q1. This is the simulated increase in the risk-neutral probability of default per quarter. However, the baseline quarterly default probability inferred from the CDS spreads on Portugal’s debt was 7.5% (750 basis points) at that time. Thus, the potential spillover from Greece was not large, relative to the overall risk of a Portugal default. Similarly, the baseline quarterly default probability for Ireland was 5.3% in 2010-Q3, and so the potential spillover from Greece accounted for less than 8% of the total risk of an Ireland’s default.^{3}

**Figure 1**. Simulated change in credit risk from Greece default

## Potential spillovers account for small portion of overall risk

A measure of the expected losses due to this channel for contagion can be constructed by combining the results from the default simulations for each sovereign, weighted by their baseline probabilities of default.^{4} For comparison, we can also consider the total expected losses that are implied by the CDS spreads on sovereign debt.^{5}

Figure 2 shows the results of these calculations. The total expected losses and the expected spillover losses are negligible for the first three years in our data, then rise with the 2009 recession and the emergence and escalation of the sovereign debt crisis. The expected spillover losses due to possible contagion of defaults reaches over $4 billion by 2011-Q3. At the same time, however, the total expected losses from sovereign defaults reaches $400 billion. Thus, the predicted losses due to contagion account for only 1% of the total losses that were implied by sovereign CDS spreads at that time. This indicates the spillovers from this channel for contagion accounted for a relatively negligible portion of total sovereign credit risk during the recent crisis.

**Figure 2**. Expected losses from contagion and total expected losses

Similar calculations indicate there was very little impact on the cost of borrowing for European sovereigns, at least from this channel for contagion. The most affected country, according to our estimates, was Portugal. The potential for contagion from Greece and other sovereigns could account for only 2% (not two percentage points) of the total interest rate spread on Portugal’s sovereign bonds, at most.

## Measuring the contagion risk from each sovereign

In addition to quantifying the aggregate potential for losses, this analysis provides some insight into how the network of sovereign debt holdings distributes risk throughout Europe. In particular, the model can be used to quantify the contagion risk associated with each sovereign’s debt. The measure expresses the expected spillover losses following the default of a sovereign, per dollar of its debt. This could be understood as the per-dollar ‘contagiousness’ of each sovereign’s debt, in the event of its default.

A surprising result from this analysis is that Austria has the most potentially ‘contagious’ debt. This reflects its position in the network, not its aggregate amount of external debt or probability of default. Much of Austria’s debt is held by Italy, a financially vulnerable sovereign with a large debt load. Triggering the default of Italy would greatly multiply any direct losses from Austria. Thus, while Austria’s probability of default is low, the model predicts higher than average spillovers in the event of an Austrian default. Still, however, the absolute magnitude of the expected spillovers is small. At most, each dollar lost directly from a default of the Austrian sovereign is predicted to generate an additional 2.5 cents in spillover losses.

## Conclusion

Politicians and policymakers have invoked the possibility of financial contagion as a central motivation for providing bailouts. Understanding the probability and magnitude of these spillover effects is therefore essential for economic policymaking. We apply a recently developed framework for modelling contagion in financial networks to data on the cross-holdings and credit risk of sovereign debt in Europe. Our analysis indicates that credit markets perceived little risk of contagion from these spillovers following a sovereign default.

It is important to note that the economics literature has suggested other possible channels for contagion that could generate additional, and perhaps more substantial, losses. Changes in risk aversion, or an updating of creditors’ beliefs about the likelihood of a sovereign default, are such factors that could lead to further spillovers across sovereigns in their cost of borrowing.^{6} It will be important to assess these other channels so that policymakers are fully informed about the potential externalities from a sovereign default.^{7}

## References

Acemoglu, D, A Ozdaglar, and A Tahbaz-Salehi (2014), “Systemic Risk and Stability in Financial networks”, *American Economic Review*, forthcoming.

Aizenman, J, M Binici, and M M Hutchison (2013), “Credit Ratings and the Pricing of Sovereign Debt during the Euro Crisis”, National Bureau of Economic Research Working Paper 19125.

Arellano, C, and Y Bai (2013), “Linkages Across Sovereign Debt Markets”, National Bureau of Economic Research Working Paper 19548.

Benzoni, L, P Collin-Dufresne, R S Goldstein, and J Helwege (2012), “Modeling Credit Contagion via the Updating of Fragile Beliefs”, Federal Reserve Bank of Chicago Working Paper 2012-04.

Elliott, M, B Golub, and M O Jackson (2014), “Financial Networks and Contagion”, *American Economic Review*, 104(10): 3115-53.

Gande, A, and D C Parsley (2005), “News Spillovers in the Sovereign Debt Market”, *Journal of Financial Economics*, 75(3): 691-734.

Glasserman, P, and H P Young (2014), “How Likely is Contagion in Financial Networks?” *Journal of Banking & Finance*, forthcoming.

Glover, B, and S Richards-Shubik (2014), “Contagion in the European Sovereign Debt Crisis”, National Bureau of Economic Research Working Paper 20567.

Kodres, L E, and M Pritsker (2002), “A Rational Expectations Model of Financial Contagion”, *Journal of Finance* 57(2): 769-799.

## Footnotes

1 Our analysis uses Austria, Belgium, Finland, France, Germany, Greece, Ireland, Italy, the Netherlands, Portugal, Spain, Sweden, and the UK. Other countries are omitted due to the lack of complete data on foreign financial claims from the BIS or on CDS spreads over our study period, 2005-2011.

2 The relationship between the quarterly default probability and the five-year CDS spread is constructed assuming a risk-free discount factor and a constant hazard rate for default.

3 The potential spillover to Ireland drops in the last two quarters because our data indicate the exposure of Irish banks to Greek debt decreased substantially at that time.

4 More precisely, the formula is as follows. Let *D _{jt}* be the total external debt of sovereign

*j*in period

*t*. Let

*p̂*be the baseline solvency probability for sovereign

_{jt}*j*from the estimated model. Let

*p̃*(

_{jt }*i*) be the simulated solvency probability if sovereign

*i*defaults. The expected spillovers from the default of

*i*are Ʃ

_{j≠i }(

*p̂*–

_{jt}*p̃*(

_{jt}*i*)). Then, the total expected spillovers from all possible sovereign defaults in period

*t*, weighted by their baseline probabilities of default, is Ʃ

_{i}(1 –

*p̂*) Ʃ

_{it}_{j≠i }

*(p̂*

_{jt}– p̃_{jt}(i))D_{jt}.5 Using the same notation, this is simply Ʃ_{i}(1 – *p̂ _{it}*)

*D*.

_{it}6 See for example Kodres and Pritsker (2002), Benzoni et al. (2012), and Arellano and Bai (2013).

7 One line of research considers the informational impact of changes in credit ratings. See, for example, Gande and Parsley (2005) and Aizenman et al. (2013).