Sovereign Risk in Macroprudential Solvency Stress Testing
  • 1, International Monetary Fund

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This paper explains the treatment of sovereign risk in macroprudential solvency stress testing, based on the experiences in the Financial Sector Assessment Program (FSAP). We discuss four essential steps in assessing the system-wide impact of sovereign risk: scope, loss estimation, shock calibration, and capital impact calculation. Most importantly, a market-consistent valuation approach lies at the heart of assessing the resilience of the financial sector in a tail risk scenario with sovereign distress. We present a flexible, closed-form approach to calibrating haircuts based on changes in expected sovereign defaults affecting bank solvency during adverse macroeconomic conditions. This paper demonstrates the effectiveness of using extreme value theory (EVT) in this context, with empirical examples from past FSAPs.


This paper explains the treatment of sovereign risk in macroprudential solvency stress testing, based on the experiences in the Financial Sector Assessment Program (FSAP). We discuss four essential steps in assessing the system-wide impact of sovereign risk: scope, loss estimation, shock calibration, and capital impact calculation. Most importantly, a market-consistent valuation approach lies at the heart of assessing the resilience of the financial sector in a tail risk scenario with sovereign distress. We present a flexible, closed-form approach to calibrating haircuts based on changes in expected sovereign defaults affecting bank solvency during adverse macroeconomic conditions. This paper demonstrates the effectiveness of using extreme value theory (EVT) in this context, with empirical examples from past FSAPs.

I. Introduction1

1. Sovereign distress has been a significant source of systemic financial risk in many countries where banks hold large exposures to the public sector. In advanced economies (AEs), bank claims on domestic government debt range from a few percents of bank assets (e.g., Sweden and Switzerland) to more than 10 percent of assets (e.g., Italy, Japan, and Spain; see Figure 1). In many emerging market and developing economies (EMDEs), sovereign exposures are twice as high as in advanced economies (AEs) on average and particularly large in Argentina, Brazil, China, Egypt, Hungary, India, and Mexico. A broader definition of sovereign exposures (see Box 1), which includes sub-national governments, lending (i.e., loans and receivables), and sovereign guarantees, more than doubles these amounts.2

Figure 1.
Figure 1.

Bank Sovereign Exposures

(Bank claims on domestic government debt in percent of total banking sector assets)

Citation: IMF Working Papers 2019, 266; 10.5089/9781513519968.001.A001

Sources: Authors’ calculations, Haver Analytics, IMF International Financial Statistics.Notes: The charts show sovereign exposures as bank claims on central, state, and local governments, except for China, Hong Kong SAR, India, Switzerland, and the United Kingdom, where data on claims on state and local governments are not available. Data for the United Kingdom are missing for the years 2001 and 2007. For Egypt and Turkey, missing data for 2001 were replaced with data for 2002 and 2004, respectively.

2. In addition to the sheer size of exposures, sovereign risk could affect banks’ solvency through a wide range of transmission channels with potentially complex feedback effects. Unlike private-sector debt, where individual default is frequent (but the effects are diversified among many counterparties), sovereign default occurs rarely but has wide-ranging consequences. Sovereign risk also results in many hard-to-assess spillover effects across sectors and countries, which can further amplify the bank-sovereign nexus. Sovereign distress can take many forms, including (i) outright default or restructuring, (ii) a technical default (e.g., missing payments if there is no fundamental debt sustainability problem), (iii) currency redenomination, (iv) hyperinflation (and currency crisis), and (v) default by quasi-sovereign entities (BCBS 2017a; Ams and others 2018). These severe forms of distress have been more frequently observed in EMDEs and affect banks through direct (e.g., losses from direct exposures) as well as indirect (e.g., the impact on economic growth, inflation, and exchange rates) transmission channels. The episode of such explicit sovereign distress is rare among AEs in the post-World War II period. During the European sovereign debt crisis, for instance, the key channels included valuation losses of sovereign securities and their impact on bank funding costs as well as the feedback effects to sovereigns through potential bank support measures (Enria and others 2016).

3. The paper shows how to assess banks’ vulnerability to sovereign risk in macroprudential stress testing. We discuss four aspects of the tests: scope of exposures and transmission channels, loss estimation methods, shock calibration, and calculation of capital impact. Our discussion is largely based on the experiences with stress testing of banks in the IMF’s Financial Sector Assessment Program (FSAP) over the past decade. The same loss-estimation and calibration approach is, in principle, applicable to not only banks but also other types of financial institutions, such as insurance companies, pension funds, and asset managers.

4. The potential scope for sovereign risk varies across countries. So far, FSAPs have focused on the direct impact through security holdings, but a more comprehensive coverage of exposures and channels seems appropriate in some cases (IMF 2015). This is partly because the European sovereign debt crisis, which motivated the integration of sovereign risk in stress tests, took place in countries where most sovereign exposures were securities (and, thus, banks’ solvency situation was significantly influenced by the market valuation of their security holdings). However, such an approach may miss essential transmission channels in other countries where the primary bank-sovereign direct linkages stem from loans to the general government and its deposits. If a country has a relatively frequent history of sovereign default— including payment delays, restructuring, hyperinflation—then the test may need to incorporate these channels explicitly. Indeed, the Basel III monitoring exercises (BCBS 2018a and 2018b) confirms that exposures other than securities (i.e., banking book exposures) are a large part of overall sovereign exposures.

Definition of Bank Sovereign Exposures: Basel III Monitoring Exercise

As part of the semi-annual Basel III Monitoring Exercise, the Basel Committee on Banking Supervision (BCBS, 2018a and 2018b) monitors the exposures of major banks across all member jurisdictions. Sovereign exposures1 are one of the key elements of this exercise and are defined as:

  • Direct sovereign exposures are exposures to sovereigns (as immediate counterparts). They include both banking book (e.g., loans and receivables) and trading book assets (securities and financial instruments, including derivatives assets and valuation margins). For the monitoring of Basel III liquidity ratios, liabilities from sovereigns are also monitored, including deposits, secured borrowings, derivatives liabilities, and valuation margins among others.

  • Indirect exposures are exposures to counterparties other than the sovereign itself, which are (i) protected (guaranteed) by a sovereign entity, and (ii) collateralized by instruments issued by sovereign entities and not subject to haircuts. An example of the latter is a reverse repo transaction, where a bank swaps an asset for government bond as collateral. Another example is a credit default swap (CDS) on sovereign securities.

Note: 1/ “Sovereign” includes a central bank, a central government, multilateral development banks and some international organizations, subnational governments, and public sector entities (PSEs).

5. The method to estimate potential losses from a sovereign distress scenario in FSAPs has been broadly following the Basel III framework with some modifications desirable for a macroprudential perspective. The outputs of FSAP stress tests are not expected to result in immediate supervisory actions—unlike those of microprudential stress tests—but may inform discussions on the robustness of systemic crisis preparedness and the use of possible macroprudential policy measures. As a result, they focus on assessing the potential capital impact of systemic risk as fully and transparently as possible, mainly by applying market-implied estimates of expected sovereign default to all types of sovereign exposures. In contrast, microprudential rules smooth out short-term cyclical volatility to avoid introducing excessive procyclicality to capital ratios.

6. The main FSAP approach for stress testing sovereign risk has been to measure valuation effects on traded government debt caused by changes in expected default rather than actual default during adverse macroeconomic conditions.3 A sovereign risk shock is calibrated as the market-consistent haircut implied by the estimated (and not realized) decline in the fair value of government bonds (“market valuation approach”) using their price or yield volatility (i.e., standard deviation). For each country, the haircut reflects the observable cost of protecting the value of government bond against rising default risk perceived in markets and is applied to most sovereign security holdings to determine the capital impact of the sovereign risk shock.

7. In this paper, we advance the existing approach towards a tractable method for the calibration of sovereign risk shocks as tail events. For instance, if a shock is defined relative to the historical average, the shape of the distribution function is fundamental the calibration process. For instance, a two-standard-deviation shock drawn from a standard normal distribution is much smaller than if the shock were drawn from a distribution with a fat tail. The size of the haircut could differ substantially depending on the method to account for tail risks. For instance, a one standard deviation valuation shock from a distribution with a fat tail is far more sizeable than the shock drawn from a standard normal distribution. Therefore, we fit a generalized extreme value (GEV) distribution to the historical spread dynamics of spot and forward sovereign credit default swaps (CDS). This approach allows us to derive the density forecast of severe, non-linear changes in the credit risk premium consistent with the tail risk nature of sovereign distress within a flexible functional form. Once a level of credit risk premium under stress is chosen, we can derive market-consistent valuation haircuts using standard bond pricing models. Compared to the approaches using changes in government bond yields, sovereign CDS spreads, when available, provide a “pure” measure of maturity-consistent default risk without potential contamination from varying security characteristics and policy measures influencing government bond prices (Box 2).

8. As part of this approach, the determination of a market-implied valuation haircut provides the conceptual foundation for incorporating broader bank-sovereign linkages. A higher sovereign risk may also imply a lower probability as well as diminished capacity of governments to bail out banks in a systemic event. These indirect effects may have additional costs ex-ante (e.g., higher funding costs, especially if the sovereign risk is originally triggered by deteriorating bank solvency) and ex-post (e.g., a higher probability of bank failure and lower recovery rates). The effects are usually covered as contingent liabilities in the public debt sustainability analysis of the IMF’s Article IV surveillance. When sovereign loan exposures are sizeable, credit risk parameters that are consistent with the market valuation haircut could be more useful to model tail risk when the actual history of the credit risk parameters do not include extreme events.

9. The paper is structured as follows. The next four sections describe the key steps of stress testing sovereign risk, which inform the specification of our approach, followed by its empirical application during the European sovereign debt crisis. The final section concludes the paper by summarizing the key aspects of measuring sovereign risk in bank stress tests and providing suggestions for incorporating sovereign risk within integrated stress testing frameworks that model dynamic and systemic effects from the interaction of credit, market and liquidity risks.

II. Scope of the Test

A. Exposures and Transmission Channels

10. The relevant forms of sovereign distress, types of exposures, and channels of transmission differ substantially across countries. For instance, AEs have rarely experienced “crude forms” of sovereign distress such as restructuring and (hyper) inflation in the post-World War II period, while such incidents have been more frequent among EMDEs (BCBS 2017a). Banks’ sovereign exposures are largely securities in countries with developed sovereign bond markets (AEs and major emerging market (EM) countries). When financial markets are underdeveloped (many EMDEs), loans and other types of exposures become more important. It is important to adjust the scope and the design of sovereign risk stress tests according to the ecosystem of each financial system.

Economies with Developed Financial Markets with Low Outright Sovereign Default Risk

11. In these systems, sovereign distress propagates through the valuation shock to sovereign bonds with significant indirect effects. Then, a test could focus on securities exposures and apply a valuation haircut to them. This approach implicitly defines sovereign default as a market risk, rather than a credit risk.

12. A severe indirect channel could stem from the interaction of bank solvency and liquidity. The resulting decline of bank solvency ratio could increase the counterparty risk of the affected banks, raising their funding costs, especially when they rely on wholesale funding that is more sensitive to counterparty risk than deposits. Banks could struggle to satisfy liquidity requirements, as the value of liquid asset buffer that includes sovereign securities diminishes. Such liquidity stress could eventually lead to higher overall funding costs.

Economies with Underdeveloped Financial Markets with Higher Outright Sovereign Default Risk

13. These economies face higher chances of sovereign distress with various forms of default. Delayed interest payments or unilateral debt restructuring—which often constitute “credit events” for CDS contracts (see Appendix II, Box A2)—could occur frequently. Such “defaults” could also manifest as the monetization of public deficits and lead to hyperinflation, which would reduce public debt in real terms and weaken the exchange rate (potentially resulting in a currency crisis).

14. Sovereign distress could be closely related to external vulnerabilities, raising the role of global investors and macro-financial conditions. Sovereign risk in many EMDEs tends to be more influenced by external factors than those of AEs. Especially small open economies are susceptible to global demand shocks. Also external and public sector balances of commodity exporters could experience large swings along the commodity price cycle. In countries where governments, banks, and non-financial corporates depend on external finance, global market sell-off events could reduce or reverse capital outflows, resulting in potentially extreme exchange rate and asset valuation shocks in line with a high “beta” of EMDE securities found in empirical studies (IMF 2014a).

15. Broader types of sovereign exposures become relevant, given the considerable role of the state. The prevalence of state-owned banks could create strong cyclical linkages between bank performance and public finance (as well as contingent liabilities). These linkages manifest in interest rate controls, directed credit, or financial repression, which may force banks to take on higher credit risk. They may also raise the resolution cost of failed banks

B. Determining the Scope

16. A comprehensive assessment includes all types of relevant sovereign exposures, beyond the valuation of traded exposures during times of stress (see Box 1).4 In most FSAPs for AEs, solvency stress was mostly driven by the market valuation losses from government debt securities, and cash balances at central banks as well as repurchase agreements (repos) or asset swaps were often excluded. Loan exposures are included, but they tend to be a small part of bank assets, and the estimated losses are usually negligible given the limited history of outright sovereign default in most AEs (see the following section on loss estimation for details). However, in macroprudential stress testing exercise for the economies with higher outright default risk and underdeveloped capital markets, it will be essential to think beyond the market risk aspect, securities exposures, and central government debt, since a larger share of losses are likely to come from loan or loan guarantee exposures to broader government (including state-owned enterprises). Where needed, a reliable test may require additional data collection to supplement standard reporting.

III. Method to Estimate Potential Losses A. Benchmark Approach

17. Like any other risk factors, sovereign risks generate both expected and unexpected losses impacting bank solvency (see Figure 2). Expected losses represent average losses that are likely to materialize in the future based on current information. These losses affect the capital adequacy ratio (CAR) (i.e., capital divided by risk-weighted-assets, RWA) through its numerator—either as a direct hit to capital or through profit and losses (P&L), depending on the types of exposures (e.g., securities held for trading, HfT, available for sale, AfS, and held to maturity, HtM). In contrast, unexpected losses are extreme losses that tend to occur with a very low probability—say once in 1,000 years shown as the Value-at-Risk (VaR) at 99.9th percentile in the figure. These tail risks affect the CAR though its denominator by increasing the capital intensity of assets (i.e., risk weights).

Figure 2.
Figure 2.

Conceptual Difference between Expected and Unexpected Losses

(Example for loan exposures)1

Citation: IMF Working Papers 2019, 266; 10.5089/9781513519968.001.A001

Source: adapted from Jobst, Ong, and Schmieder (2013).1 For loan exposures, Basel require banks to set aside loan-loss provisions equivalent to expected losses. Additional provisions (i.e., credit cost) in a given year will reduce bank profit and therefore the numerator of the solvency ratio.

18. Generally, the methods to estimate expected loss differ depending on whether the exposures are in the banking book or trading book (see Table 3):

  • Trading book exposures are mostly bonds and other market instruments; their expected losses stem from the securities’ market valuation changes.

  • Banking book exposures are mostly loans (see Appendix II). Therefore, their expected losses are estimated with credit risk approach that includes an empirical satellite model that forecasts credit risk parameters with macro-financial covariates. If banks use internal rating-based (IRB) approaches, expected losses are estimated as the product of the probability of default (PD) and loss given default (LGD). Under the standardized approach, the losses are estimated using loan classification (or non-performing loan information) or credit rating, assuming a certain level of required provision rate for each category/rating of loans.

Table 1.

Treatment of Sovereign Exposures in Mandatory FSAPs in European Union and European System-wide Stress Tests

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Sources: Authors, EBA (2010, 2011a, 2014, 2016 and 2018), ECB (2011), and IMF FSAP country reports.Notes: Y=yes, N=no; n.a.=not available.

The haircut model in this paper (Appendix II) was applied in the FSAPs for Belgium (2013), Germany (2011), Hong Kong SAR (2014), Spain (2012), Sweden (2011), and the United Kingdom (2011); other FSAPs followed similar approaches—with an empirically derived sovereign credit spread shock, using either (i) the historical volatility of CDS spreads, such as in the case of France (2013), Italy (2013), Netherlands (2011), Singapore (2013), and Sweden (2011), or (ii) the historical volatility of bond yields, such as in the case of Argentina (2016), Austria (2014), Denmark (2014), Indonesia (2017), Ireland (2016), Japan (2012), Mexico (2016), Norway (2015), South Africa (2015), and Korea (2015) as well as most European countries in the second FSAP.

In the FSAPs for Germany (2011), Japan (2012), and Italy (2013), MtM is applied to HtM securities only in separate sensitivity analysis (unlike UK FSAP’s bottom-up test in 2011); 3/ HtM exposures tend to be assessed using the credit risk approach; 4/ Haircuts are applied only to non-”AAA”-rated debt, and French sovereign exposures (“AAA”-rated) were not subject to a valuation haircut; 5/ Only domestic sovereign exposures were stressed; 6/ MtM is applied to HtM sovereign exposures, and the AfS filter was removed; 7/ Including only direct exposures (indirect exposures were covered in the market risk impact); 8/ A part of the overall sensitivity analysis of the capital impact of credit risk; 9/ Following Longstaff and others (2011).

Table 2.

Treatment of Sovereign Exposures in Mandatory FSAPs (Excluding European Union Countries)

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Sources: Authors and IMF FSAP country reports. Notes: Y=yes, N=no; n.a.=not available.

The haircut model in this paper (Appendix II) was applied in the FSAPs for Belgium (2013), Germany (2011), Hong Kong SAR (2014), Spain (2012), Sweden (2011), and the United Kingdom (2011); other FSAPs followed similar approaches—with an empirically derived sovereign credit spread shock, using either (i) the historical volatility of CDS spreads, such as in the case of France (2013), Italy (2013), Netherlands (2011), Singapore (2013), and Sweden (2011), or (ii) the historical volatility of bond yields, such as in the case of Argentina (2016), Austria (2014), Denmark (2014), Indonesia (2017), Ireland (2016), Japan (2012), Korea (2015), Mexico (2016), Norway (2015), and South Africa (2015), as well as most European countries in the second FSAP since it became mandatory for IMF member countries with systemically important financial systems, such as Belgium (2018), Germany (2016), Luxembourg (2017), Netherlands (2017), Spain (2017), Sweden (2017), and the United Kingdom (2016); 2/ Sovereign debt exposures were tested indirectly via market-implied distress dependence, limited to emerging market debt (so domestic sovereign debt was excluded); 3/ Market-based distress dependence between U.S. financial institutions and emerging market sovereigns measured using Segoviano (2006); 4/ Sovereign risk was not tested explicitly, but a general increase of credit risk from higher expected losses due to European sovereign debt exposures; 5/ Only domestic sovereign exposures were stressed; 6/ Credit risks from SOEs were considered more important than market risk.

Table 3.

Asset Valuation Rules and Regulatory Capital Impact*

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Source: Author categories based on Fuster and Vickery (2018), EBA (2011a, 2017a, 2017b), and BCBS (2015, 2017b, 2017c, 2018b).Notes: GFC = global financial crisis; IAS = international accounting standards; IFRS = international financial reporting standards; IRB = internal ratings-based approach; LGD = loss given default; MtM = mark-to-market; NPV = net present value; OCI = other comprehensive income; PD = probability of default; P&L = profit and loss statement; TTC = through-the-cycle. */ The same valuation rules apply to all securities (sovereign and others).1/ The exact category names may differ depending on the local accounting rules used in each jurisdiction. For instance, IFRS 9 does not use this nomenclature. Roughly speaking, HfT corresponds to “held with a trading intent,” AfS corresponds to “Fair Value Reported in Other Comprehensive Income,” and HtM corresponds to “Fair Value through Profit and Loss” at amortized cost (see Annex V of EBA (2017a)). However, U.S. GAAP continues using these categories (under Accounting Standard Codification (ASC) 320, see Deloitte). FSAP stress testing exercises have been (and are likely to continue) using these concepts for communication of stress testing method across broad jurisdictions.2/ The credit risk parameters (PD and LGD) for the calculation of regulatory capital requirements could differ from those applied in statutory reporting (i.e., financial statements) based on prevailing accounting standards.3/ These national authorities include regulators in Japan and the United States. For instance, the recently completed FSAP for Japan found that smaller regional banks that are allowed to apply the AfS filter hold substantially more sovereign securities than larger global banks. 4/ The market valuation approach is at the minimum applied to all (traded) government debt securities irrespective of their accounting classification.

19. Stress tests broadly follow the Basel regulatory capital rules to estimate expected losses but tend to widen the application of market-consistent valuation. The objective of capital rules is to provide a fair and timely measure of bank solvency without introducing short-term volatility. For instance, if banks hold substantial amounts of traded securities, mark-to-market (MtM) valuation changes could lead to frequent changes in regulatory capital, which complicates both lending and investment activities. Therefore, the regulatory framework (and underlying accounting standards) includes features to smooth out excessive volatility and cyclical effects. In contrast, the main objective of macroprudential stress tests is to examine banks’ resilience to tail events rather than normal cyclical downturns. For this purpose, it is critical to reflect all potential losses immediately and transparently using MtM valuation (i.e., the economic valuation approach).5

20. In doing so, all traded exposures are ideally valued using a market-consistent approach to make stress test results more comparable across banks. The same sovereign securities could be valued differently depending on their accounting treatment (and the way this informs the calculation of the CAR, see Table 3). If the market value of sovereign securities declines sharply, it is fully reflected in the valuation of HfT and AfS securities but not necessarily HtM securities, which are valued at amortized cost using historical estimates of credit risk parameters. Some jurisdictions, including Japan and the United States, allow some banks to continue applying the “AfS filter” that limits the impact of short-term volatility of the value of AfS securities on solvency ratio, though many (European) jurisdictions entirely removed the filter in the mid-2010s.6 Thus, banks with precisely the same portfolio and balance sheet may have different CARs depending on the share of AfS and HtM securities.

21. The market-consistent approach is also useful for determining expected losses from banking book exposures when a country’s history does not include any sovereign distress episode(s). No empirical satellite model can capture sovereign distress well without historical precedents. Market valuation, in contrast, is more sensitive to investors’ perception about the likelihood of sovereign distress.

22. The market-consistent approach is critical when potential regulatory arbitrage or forbearance is a concern. During the European sovereign debt crisis, banks received a one-time supervisory approval to re-classify sovereign HfT and AfS securities as HtM (Acharya 2018). While such a measure is vital as a crisis management measure that limits the undesirable amplification effects from the banking sector, it reduces transparency for stress testing. Moreover, there is evidence that banks optimize the accounting treatment of government debt securities to reduce their capital impact.7

23. This approach also helps assess the impact of sovereign-bank linkages on bank funding costs. As discussed in Section II, one of the sovereign-bank linkage channels is through bank (wholesale) funding costs.8 Investors are likely to pay attention to bank solvency based on a full market valuation in addition to regulatory ratios. Therefore, one approach is to use a sensitivity test that estimates the impact of sovereign distress on market-value based solvency ratio and then estimate its impact on bank funding. The resulting reduction of net interest income could be part of the broader scenario tests where valuation losses from HtM securities are excluded.

24. However, for unexpected losses from sovereign exposures, stress tests usually follow the regulatory practice, even though it is considered problematic in the financial stability community. Under Basel regulations, local currency-denominated sovereign debt preserves their nominal value during times of stress, and, thus, could be considered “safe assets.” In many cases, these sovereign exposures are assigned a zero percent credit risk weight (RW) under the standardized approach (SA) and very low RWs under the IRB approach if banks estimate PDs and LGDs for sovereigns with no (or limited) distress episodes in the past. While these practices underestimate sovereign risk (Hannoun 2011), recent BCBS regulatory reform efforts to change them have not concluded (BCBS 2017a). The challenge is that there are multiple reform approaches and different options, ranging from concentration-based measures to credit risk-based capital charges, but is not straightforward to see which one works the best. In the absence of any clear direction regarding potential changes in the regulatory treatment of sovereign risk, most FSAPs, for example, have not changed this practice. Introducing case-by-case adjustments would also reduce the comparability across different exercises.

B. FSAP Practice

25. Most FSAPs follow the above benchmark approach, with varying degree of valuation practices (see Tables 1 and 2). Many exercises during the European sovereign debt crisis for the EU Member States applied market-consistent valuations to all sovereign securities including AfS9 and HtM securities (except for France and Spain). For HtM securities, this meant applying valuation losses instead of provisions according to their credit risks. In the 2012 Italy FSAP, the valuation losses from HtM securities were excluded from a macro scenario test but included in a sensitivity test. For these cases, transparency was deemed most important, especially under various crisis management measures that mitigated valuation changes (e.g., the ECB’s quantitative easing) and the forbearance. More recent FSAPs have applied the market valuation approach to HtM securities less frequently unless banks reported a high share of HtM securities or the share rose noticeably. Most FSAPs applied the credit risk approach for assessing sovereign risks with loans and receivables using historical credit risk parameters. Some FSAP are attempting to incorporate the indirect effects through funding cost as a part of broader efforts to incorporate solvency-liquidity interactions.

26. For countries with elevated sovereign risk, FSAP exercises have also included valuation losses that were not fully reflected in prudential reporting. Since CARs do not fully reflect the short-term cyclical changes in asset valuation, there could be a gap between the current market valuation of sovereign debt securities and their valuation in the last reported statutory accounts. Thus, a test would overestimate CAR without adjusting for the valuation gap. Similar adjustments are critical when there is forbearance to manage a crisis or due to the general weakness of the supervisory framework to handle problem assets. However, if sovereign securities are already priced at historically low levels, it may make sense to apply a smaller-than-otherwise shock (in line with adjusting the adversity of macroeconomic scenarios for stress tests that occur when banks already experience some distress).

IV. Calibrating Shocks

27. Sovereign risk shocks are difficult to calibrate with standard macroeconomic models. The baseline scenario usually includes the entire yield curve of (own) government securities, with which the forward yield curve can be estimated. For adverse scenarios, the size of shocks may not be sufficiently severe in macroeconomic models, which tend to be focused on changes in the short-term (policy) rate (and a projected long-term yield if available). Standard empirical and dynamic stochastic general equilibrium models do not endogenously model shocks to financial risk. Also, most of these models do not integrate essential non-linear effects of financial risks.

28. Therefore, stress testers often use the market-implied valuation approach as an alternative, statistical method to calibrate sovereign shocks to sovereign securities. Many FSAPs have used the approach since the European sovereign debt crisis to estimate the haircut to sovereign securities (see Tables 1 and 2). The next section describes a specific modeling technique, which is well-suited for the estimation of valuation haircuts that capture the tail risk of sovereign exposures under this approach. The haircuts can be derived from the expected change in the price of government bonds in response to changes in default risk. The price of government bonds broadly reflects two components—the risk-free interest rate and the credit risk premium.10The risk-free rate represents the intertemporal cost of money in line with expected inflation expectations and the real interest rate. The credit risk component signifies sovereign default risk. In the absence of sovereign distress, government bonds are considered safe and yield a risk-free rate of return whose volatility determines any valuation changes. However, when investors recognize higher potential sovereign default risk (or their risk aversion increases),11 they demand a (higher) credit risk premium, which reduces the price of government bonds. Thus, haircuts reflect the differential price impact of higher sovereign risk, with general macro models providing the risk-free component.12 These valuation haircuts are applied to all sovereign exposures for a fully market-consistent capital assessment of sovereign risk; however, empirical constraints might preclude reasonable estimates for the valuation changes for all types of credit exposures under stress, limiting the market valuation approach to capital market instruments (in the trading book) only.

29. For sovereign exposures in the banking book, especially non-capital market instruments, the credit risk approach may substitute for the market valuation approach to determine sovereign default risk, particularly in absence of reliable market prices. All banks set aside reserves for expected losses from sovereign exposures in the same manner as commercial and consumer loans, consistent with applicable accounting standards. For credit-sensitive exposures, such as loans and receivables, these reserves are called loan loss provisions (LLP) and typically cover the non-accrual amount of outstanding balances (which can be proxied via changes in non-performing loans and write-downs). If banks use IRB approaches to determine their capital requirement for credit risk, provisions for expected losses are based on estimated through-the-cycle PDs (or better, point-in-time) and downturn LGDs (see Table 3).13Since PDs (and non-accruals) of sovereign exposures might change in ways that are quite different from that of commercial and retail exposures, a separate provisioning model for sovereign risk might be warranted.14 Otherwise, the sovereign risk shock is modelled as a downgrade scenario, which implies a significant deterioration of PDs and LGDs, resulting in additional provisions to be held for banking book exposures.

30. In some cases, sovereign risk shocks also include a “common” (global/regional) interest rate component. For stress tests covering a region (such as the EU system-wide stress test) and smaller, open EMDEs, the change in sovereign bond yields comprises country-specific and common global/regional components. Each component covers adverse changes in the risk-free rate and the sovereign credit risk premium at different points of the interest rate term structure of government bonds (see Box 1).

  • Common interest rate shock. The total change of sovereign yields reflects the changes of the regional risk-free rate and sovereign default risk across multiple countries if widespread concerns about public debt sustainability cause spillover effects within a region. For many smaller, open EMDEs, the interest rates in large advanced economies (especially the United States) have a substantial influence on domestic sovereign yields. If the common interest rate shock is uniform,15 and, thus, results in a parallel upward shift of the yield curve (i.e., it does not affect its curvature), the term structure remains unchanged.16

  • Country-specific interest rate shock. The primary driver of the sovereign risk shock is the country-specific credit risk component. The sovereign credit shock can be calibrated based on the historical volatility of sovereign credit spreads, which can be derived explicitly (via sovereign CDS) or implicitly (via excess spreads over a benchmark government bond yield, such as the J.P. Morgan Emerging Markets Bond Index (EMBI) spreads).17 The data can then be parametrically modeled to generate point estimates of expected default risk at different maturities for each year of the stress test horizon (after controlling for contemporaneous changes in the general level of interest rates, which may influence the pricing of default risk). For an adverse scenario, high sovereign credit spreads away from their historical median could be applied (i.e., choosing the spreads at the tail of the historical distribution).18

31. For loans and other non-capital market exposures in the banking book, the credit risk approach could be more suitable, particularly in the absence of reliable market prices. For loans, these reserves are called loan loss provisions and typically cover the potential losses from NPLs (that are not receiving interest payments). If banks use IRB approaches to determine their capital requirement for credit risk, provisions for expected losses are based on estimated through-the-cycle PDs (or better, point-in-time) and downturn LGDs (see Table 3). Since credit risk parameters for sovereign exposures are likely to behave distinctively from private loans, a separate credit risk model for sovereign risk, which predicts PDs and LGDs or NPLs of sovereign loans as a function of various macro-financial variables, might be warranted. However, when the country’s history does not include any sovereign distress episode, such a model may not pick a meaningful level of default risk. Under the credit risk approach, the sovereign risk shock is modelled as a downgrade scenario, which implies a significant and sudden jump of PDs and LGDs.

32. The sovereign risk shock would be less severe if countries were already in distress. During times of stress, the current sovereign yield curve already includes a level of default risk, which might already be high by historical standards. Further raising the default risk could lead to implausibly severe stress, especially compared to countries with stable interest rates.

V. Calculating the Capital Impact

33. The accounting classification of sovereign exposures determines how their expected losses impact bank’ capital adequacy under stress. As Table 3 shows, security exposures in HfT, AfS, HtM, and loan exposures affect bank capital differently. Trading losses from HfT securities are considered realized losses, become a part of net income and are subject to taxation and dividend payout. Assuming all the AfS filters are removed,19 all unrealized gains and losses from AfS securities also become part of net income. However, the unrealized valuation changes are not subject to taxation (and do are usually not included in dividend payments).20 Therefore, all the valuation changes will reduce capital one-to-one. Expected credit loss from loan exposures will require additional loan loss reserves (LLRs), which are a part of the (taxable) net income. Banks usually pay tax and dividend only when taxable net income is positive.

34. If the market valuation approach is used to value securities in HtM, the capital ratio under stress is calculated as follows.


where d is the dividend payout ratio, τ is the applicable tax rate, LLR denotes the amount of loan loss reserves, ∆MtM is mark-to-market valuation loss of securities (losses carry a positive sign), and ∆RWA defines the possible change in unexpected losses. Time t is the latest actual value before adding stress, and t+1 means after stress. Expected losses from HtM securities affects the capital ratio similarly as the AfS securities. One difference is that HtM securities are likely to have a valuation gap at time t, which represents the difference between the amortized cost applied to value HtM securities and their market values. The LLR earmarked for HtM securities can cover a part of the gap, but a positive gap is likely to remain. Then, the stressed capital ratio represents both existing and additional losses from stress by including the remaining gap to the equation.

35. Alternatively, if the credit risk approach is applied to HtM, their expected losses are treated in the same way as those from loans. Banks need to set aside additional loan loss provisions to cover the deterioration of credit quality in the HtM securities in the stress scenario.


VI. Empirical Application: Examples from Stress Tests in FSAPs for Selected European Countries

36. This section illustrates the empirical application of the market-consistent valuation approach for assessing sovereign risk consistent with current FSAP practices in macroprudential solvency stress tests. We present a flexible, closed-form approach to calibrating market-implied haircuts using extreme value theory (EVT) to capture the impact of significant shocks to sovereign risk on bank solvency.

A. Data Collection and Haircut Estimation

37. For estimating haircuts, we model the valuation change of government bonds using the credit risk premium implied in the cost of protecting against sovereign default risk— sovereign CDS spreads (see Appendix II). Since sovereign credit distress is a rare event, the historical CDS spread dynamics are fitted to a generalized extreme value (GEV) distribution to derive the density forecast of a large, non-linear change in default risk (see Box 2).21 The density forecast is then incorporated into the relevant bond pricing formula or proxies of price-yield sensitivity, such as duration and convexity of the bonds. The bond pricing formula combines the default risk premium at different maturities of selected government debt securities (“benchmark bonds”) with the applicable risk-free rate at the beginning of the estimation period.22 The haircuts for the market-consistent valuation of government bonds differ by the severity of sovereign risk shocks at different maturity tenors and macroeconomic scenarios. This approach was applied— with a full parametric modeling of the CDS spread dynamics—in the FSAPs for Belgium (2013), Germany (2011), Spain (2012), and the United Kingdom (2011).23 Other FSAPs followed similar approaches using either the historical volatility of CDS or bond yields.

38. This approach generalizes the treatment of sovereign risk when the system-wide stress test of the EU banking sector was introduced (EBA 2010, 2011a; see Table 4).24,25 We use the daily data from January 2009 to December 2010 for the empirical application of the model, so that we can easily compare our results to those used in the two European exercises. This cross-validation helps assess whether our methodology can be a viable alternative to those used by European authorities using greater model flexibility.

Table 4.

Comparison of Sovereign Valuation Haircut Methods in IMF FSAP and EU System-wide Stress Tests

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Sources: Authors’ research, EBA (2010, 2011a, 2014, 2016 and 2018b), ECB (2011), ESRB (2015), and IMF FSAP country reports. Notes: Y=yes, N=no; n.a.=not available. 1/ The haircut model in this paper (Appendix II) was applied in the FSAPs for Belgium (2013), Germany (2011), Hong Kong SAR (2014), Spain (2012), and the United Kingdom (2011); other FSAPs followed similar approaches using either the historical volatility of CDS or bond yields; 2/ Changes in country-specific default risk over a specific time horizon; 3/ Since the credit spread curve tends to flatten beyond the five-year maturity, the extension of default risk shocks over longer maturities produce similar results; 4/ This method was used only for cross-validation to replicate the EBA-ECB approach using forward CDS spreads; 5/ Changes in prices of benchmark sovereign bonds over a specific time horizon subject to estimated spread shocks to yield; 6/ The deviation of U.S. long-term bond yields from the baseline considered in the EBA/ECB Banking Supervision adverse scenario is broadly similar in magnitude and profile to what was used in the adverse scenario of the November 2013 Comprehensive Capital Analysis and Review stress test conducted by the U.S. Federal Reserve; 7/ In addition, banks were requested to compute (stressed) regulatory risk-weighted assets according to the applicable prudential framework; 8/ In most FSAP stress tests of major economies since 2011, the banking book has also been fully subjected the market-based valuation haircut with and without the “AfS filter” (see Tables 1, 3, and 4); 9/ Indirect exposures only for sovereign positions in the trading book; 10/ For sovereign positions in the banking book, banks were requested to estimate impairments/losses in line with sovereign downgrades.

39. More specifically, we followed four steps for deriving the valuation haircuts:26

  • Selecting liquid government bonds at different maturities. For each country, we selected the most liquid fixed-rate local-currency-denominated government debt securities (“benchmark bonds”)27 and create groups of bonds maturing within one year around the desired maturity tenor (“maturity buckets”). The sample of bonds was assumed to be representative of typical maturities of bank sovereign exposures (without knowing actual maturity information).

  • Estimating the sovereign credit risk shock. For each of the identified maturity, we obtained daily time series data of the spot and forward sovereign CDS spreads28 to estimate the historical spread dynamics and determine the market-implied default rate.29 The recovery rate is endogenized in the default rate implied by the observable spread. We then calibrated the variation of spread changes over a sufficiently long estimation period30 using the GEV distribution. The distribution is suited for modeling tail events and provides a closed-form expression of their asymptotic tail behavior.31 We then obtained point estimates of expected PD at certain levels of severity (i.e., percentiles) for each year of the five-year test horizon. For the baseline scenario, we chose the last observable current or forward CDS spread (whichever is larger) to reflect current market expectations. For adverse scenarios, we applied higher country-specific credit shocks at the 75th percentile (and higher) of the forecasted distribution.32 In all scenarios, we estimated the sovereign credit spread shock with and without a common interest rate shock of 50 basis points.33

  • Calculating individual valuation haircuts. The haircuts were set as the expected change in the prices of selected benchmark bonds vis-à-vis their market value as of the data cut-off date. The price change corresponds to the total yield changes, including the effects of the expected PDs and the risk-free rate, which varies across maturity tenors. Within each maturity group, individual bonds were priced over a five-year stress test horizon using both the adjusted zero-coupon bond and discounted cash flow methods, and considering the specific maturity dates, coupons, and coupon frequencies.34

  • Determining the aggregate valuation haircut. The haircuts for the individual bonds were then aggregated to country-specific haircuts for each maturity group by taking weighted averages using the outstanding amount of these bonds as weights.35Since the valuation haircut is specific to each benchmark bond, the aggregate valuation haircut for each country represents the weighted-average change in market valuation over the relevant stress test horizon. This implies that banks hold portfolios of sovereign debt securities similar to the portfolio of benchmark bonds used for deriving the aggregate valuation haircut when accurate portfolio data are not available (or cannot be accessed for estimation of the valuation haircuts).36 However, if complete portfolio data is indeed available, the valuation haircut can be more nuanced within each maturity bucket based on the term structure of credit risk premiums.37

Reasons for Choosing CDS Spread Dynamics for Estimating Valuation Haircuts

A closed-form pricing approach for estimating market-implied sovereign risk using CDS spread dynamics seems to be preferable to other methods that calibrate sovereign valuation haircuts based on the price volatility of government bonds:

  • Risk measurement—CDS spreads are relatively “pure” measures of default risk (IMF 2013), which might otherwise be “contaminated” by the price impact of security characteristics (such as coupon frequency, creditor rights, and redemption features) as well as inflation and term premia (and their volatility) if it were extracted from government bond prices. Using CDS spreads also avoids potential basis risk from the choice of the appropriate risk-free rate and its term structure impacting the extraction of the credit spread component of government bond yields. In the event of a default, the CDS contract payout usually recovers the par value, which means there is no need to determine the implied default probability (since the recovery rate is endogenized in the observed bond price). Moreover, CDS spreads represent sovereign risk more accurately than sovereign bond yields when yields are kept artificially low by central bank bond purchase programs. However, sovereign CDS spreads could also be influenced by price distortions. Since sovereign CDS contracts for most countries tend to be denominated in U.S. dollars, FX rate changes (which are often positively correlated with shocks to sovereign risk) could amplify the CDS spread dynamics and lead to a potential overestimation of sovereign risk during times of stress (relative to the dynamics of credit spreads implied by price changes of local currency-denominated government bonds). In addition, CDS contracts provide protection sellers with a “delivery option” (i.e., the cheapest-to-deliver government bond), which might raise the credit spread if it implies a relative reduction of the expected recovery rate (relative to that of cash instruments).1

  • Market expectations—In addition, our model specification incorporates market expectations of future changes in sovereign risk (as reflected in forward CDS contracts), and, therefore, ensures time-consistency between the market-based valuation haircut and the actual valuation change in each year of the stress test horizon. We can also examine the performance of using forward CDS contracts. Figure A2.2 (in Appendix II) shows the empirical distribution of spot and forward sovereign CDS spreads (with different starting times) for major AE and EMDE countries as of end-2010 (fitted to the GEV distribution specified in equation (8) in Appendix II). These data were used for the estimation of market-based valuation haircuts in Appendix V, Tables A5.1 and A5.2. We find that forward CDS contracts overstated sovereign default risk in the wake of the European sovereign debt crisis but adequately projected the potential escalation of sovereign risk in vulnerable countries.2

  • Model flexibility and price consistency of shocks—The functional form supports a more nuanced assessment of sovereign risk over the projection horizon and generates tractable estimates of tail events (outside the historical experience, which can be reconciled to the probabilistic severity of the overall scenario). This also offers the opportunity to cross-validate other approaches. Moreover, the estimated default risk is integrated into an asset pricing model, and, thus, controls for the marginal effect of changes in default risk on the convexity of government bond prices.

Note: 1/ All CDS spreads are derived from over-the-counter (OTC) markets and tend to be liquid only for a few maturities (compared to government bonds, which, at least in advanced economies, are traded in very liquid markets with a wide investor participation). The methodology in this paper is focused on 5-year sovereign CDS contracts, which is the most liquid maturity term (see Tables 4 and 5). 2/ For most countries, the estimated CDS spread under the two adverse scenarios (defined as the historical density forecast at the 75th and 90th percentiles) exceeded the realized CDS spread—measured at the end of each year (shown as grey dots in the boxplots on the left side of each country chart) and during each year (shown as boxplots on the right side of each country chart), except for the first year of the stress test horizon. Germany, Japan, and the United States notably benefitted from safe haven flows during the European sovereign debt crisis, which resulted in a gradual decline of sovereign CDS spreads. In contrast, for Italy and France, the actual sovereign CDS spreads during the first year of the risk horizon were higher than projected in the mild adverse scenario (75th percentile)—at the 86th and 81th percentiles of the empirical distribution of one-year forward CDS and the 89th and 87th percentiles of the empirical distribution of spot CDS.
Table 5.

Comparison of Sovereign Valuation Haircuts in European Stress Tests (2010–2011) and Results in IMF Stress Testing (Percent)

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Sources: Authors’ research, EBA, and ECB.Notes: Estimation based on the valuation haircuts of benchmark bonds at 5-year maturity. 1/ Valuation haircuts under both baseline and adverse scenarios (EBA 2010); 2/ Valuation haircuts under the adverse scenario (ECB 2011); 3/ FSAP haircuts using the zero-coupon pricing approach (as specified in Appendix II) based on current market expectations using end-year forward CDS prices (baseline scenario) as well as the 75th and the 90th percentiles of the empirically fitted density distribution of a country-specific credit spread shock (adverse scenario), with and without a common interest rate shock of 50 basis points for all countries; 4/ No availability of liquid benchmark bonds/CDS swaps for Norway.

B. Findings

40. Our estimated haircuts are broadly consistent with those in the European stress testing exercise but provide a more comprehensive and nuanced assessment. Table 5 provides the estimated valuation haircuts for sovereign exposures with an average maturity of five years in the baseline scenario and two adverse scenarios at end-2010 (see also Appendix V, Tables A5.1 and A5.2 for detailed results, including for non-European countries). The haircuts are broadly comparable to those used in the first European system-wide stress testing exercises (EBA 2010, 2011a; ECB 2011).38 However, the severity of haircuts seemed more plausible and differentiated across countries due to greater model flexibility regarding statistical confidence and configuration of interest rate shocks (see Box 2).39 Our distribution-based model specification also considers the market-implied assessment of future changes in sovereign risk, and, therefore, enhances the analysis of sovereign risk by anchoring the calibration of shocks in market expectations.

41. Under a severe adverse scenario, sovereign haircuts on stressed European countries average 15 percent during the first year of the stress test horizon. As of end-2010, forward CDS spreads indicate elevated expected default risk relative to the historical experience. Actual CDS-implied default risk of stressed European economies was already much higher than their historical average (and higher than the 75th percentile of the density distribution) at that time. In the case of Greece, forward prices on CDS imply near-default, which pushes the haircuts based on actual end-2010 data beyond the 99th percentile (not reported). The results for other European countries are relatively benign at an average haircut of about five percent during the first year of the test horizon. There are little (if any) additional haircuts beyond 2011, given the flattening of the CDS curve at longer maturities and heavy discounting of bonds issued by stressed countries during 2011.

VII. Conclusion

42. In this paper, we presented how to stress test for sovereign risk, largely based on FSAP experiences, with a particular focus on a novel approach for calibrating market-consistent valuation haircuts. Macroprudential solvency stress tests, such as those in FSAPs, share the following common characteristics in assessing the capital impact of sovereign distress:

  • Comprehensive scope—It is ideal for covering all sovereign exposures in both the trading and banking books, for instance, by following the BCBS’s semi-annual Basel III monitoring exercises (BCBS 2018a and 2018b), including indirect exposures that are either government-guaranteed or collateralized by instruments issued by sovereign entities. Nonetheless, the structure of sovereign exposures (and their materiality) or data constraints varying across countries and may require narrowing the scope to (i) market valuation losses from government securities (mostly for banks in AEs) and (ii) higher provisions for loan exposures to general government and SOEs, which often dominate sovereign exposures of banks in EMDEs.

  • Market-consistent valuation—The market valuation approach provides a transparent capital assessment of sovereign risk. Applying this approach to all securities, including HtM securities, allows the most transparent and comparable assessment across banks and jurisdictions. The treatment of HtM securities varied across FSAPs. In most cases, the credit risk approach was applied to loans and receivables (to capture the impact of impairments and downgrade risk); however, this approach might underestimate potential losses if there is no major distress event in the historical data. In these cases, using credit risk parameters consistent with the market valuation approach can generate sufficiently severe shocks.

  • Unchanged risk weights—Capital requirements for unexpected losses from local sovereign exposures are very low due to their status as “safe assets.” Stress tests typically maintain the prevailing capital intensity since the capital impact of revising the risk weights for sovereign exposures is likely to be very large, and policy discussions on reforming the current regulatory treatment are evolving.

  • Adjusting for existing losses for sovereigns with ongoing distress—When stress is already ongoing, the latest market valuation could be even lower than the value reflected in solvency ratio for some exposures. Then, it is more transparent to separate deterioration of solvency ratio due to already materialized stress from additional stress in the adverse scenario.

  • Integrating sovereign risk into the macroeconomic scenario—Where there are higher chances of outright sovereign default in economies where a large part of sovereign exposures are loans and guarantees (including state-owned enterprises), a more extensive range of macro-financial spillover effects become more important. Then, focusing on the valuation changes with sovereign securities may become too narrow. A more comprehensive approach, including an effort to embed them in a macro scenario—the monetization of fiscal deficits (or large fiscal deficits with loose monetary policy) and resulting hyperinflation and currency crises with capital outflows—is likely to be essential.

43. When calibrating the valuation haircuts for sovereign securities, our approach underscores the importance of accounting for the tail-risk nature of sovereign risk. The potential losses from sovereign risk are likely to have a long tail: there is a very small chance that could cause extreme losses. Without using an adequate method, a stress test is likely to underestimate the potential impact. The paper presented the method that fits a GEV distribution to the historical spread dynamics of spot and forward sovereign CDS. This approach allows us to derive the density forecast of severe, non-linear changes in the credit risk premium consistent with the tail risk nature of sovereign distress within a flexible functional form. CDS spreads, when available, tend to provide a “pure” measure of maturity-consistent default risk than bond yields.

44. An integrated sovereign risk assessment for macroprudential surveillance and financial stability analysis will require additional work. The market valuation approach focuses on the direct impact of sovereign distress on bank solvency but does not consider other transmission channels across sectors and countries. Such feedback effects can be assessed more comprehensively by either (i) interacting sovereign debt sustainability analysis and bank stress tests or (ii) estimating the effects in empirical multi-sector models (such as Global Vector Autoregressive (GVAR) approaches), co-dependence models for both banks and sovereigns, or general equilibrium models with bank and sovereign distress. In addition, the interaction between solvency and liquidity conditions under stress could be explicitly addressed as part of integrated stress testing frameworks that model dynamic and systemic effects from credit, market and liquidity risks. For example, the implications of higher sovereign risk on bank profitability and liquidity risk due to higher funding costs could be explored, as well as the implications of setting higher haircuts on government debt as a key component of bank liquidity buffers.40 While these models are being developed, it is still hard to assess their performance.

Sovereign Risk in Macroprudential Solvency Stress Testing
Author: Mr. Andreas A. Jobst and Ms. Hiroko Oura