## Sovereign Risk in Bank Stress Testing (WP/19/266 extract) ## Source details **Canonical URL:** [Sovereign Risk in Bank Stress Testing (WP/19/266 extract)](https://www.imf.org/-/media/files/publications/wp/2019/wpiea2019266-print-pdf.pdf) ## Other formats - [Markdown version](/-/media/files/publications/wp/2019/wpiea2019266-print-pdf.pdf.md) - [Structured JSON version](/-/media/files/publications/wp/2019/wpiea2019266-print-pdf.pdf.json) --- ### Key findings on sovereign exposures and systemic risk - 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). - 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 (including sub-national governments, lending, and sovereign guarantees) more than doubles the amounts measured by claims on government debt. - Forms of sovereign distress include: - (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), - (v) default by quasi-sovereign entities (BCBS 2017a; Ams and others 2018). - Transmission channels from sovereign distress to banks include valuation losses on sovereign securities, higher bank funding costs, feedback effects to sovereigns through potential bank support measures, and macroeconomic channels (growth, inflation, exchange rates). ### Scope of stress tests: heterogeneity across countries - Economies with developed financial markets and low outright sovereign default risk: - Sovereign distress propagates primarily through valuation shocks to sovereign bonds with significant indirect effects. - Tests can focus on securities exposures and apply valuation haircuts, effectively treating sovereign default as a market risk. - Economies with underdeveloped financial markets and higher outright sovereign default risk: - Higher chances of sovereign distress in “crude forms” (delayed interest payments, unilateral restructuring, monetization leading to hyperinflation). - Broader types of sovereign exposures (loans, deposits, guarantees) and state-owned banks raise cyclical linkages and contingent liabilities. - Sovereign risk often linked to external vulnerabilities; global investor behavior and commodity price cycles can amplify stress. ### Methodology and advances in FSAP sovereign stress testing - FSAPs follow a market-consistent valuation approach broadly aligned with Basel III, with macroprudential modifications: - Apply market-implied estimates of expected sovereign default to all types of sovereign exposures. - Main FSAP approach measures valuation effects on traded government debt caused by changes in expected default rather than realized default. - Sovereign risk shock is calibrated as the market-consistent haircut implied by the estimated decline in fair value of government bonds using price or yield volatility (standard deviation). - Advances toward tail-event consistent shocks: - Fit a generalized extreme value (GEV) distribution to historical spread dynamics of spot and forward sovereign credit default swaps (CDS) to capture fat tails. - Once a stressed level of credit risk premium is chosen, derive market-consistent valuation haircuts using standard bond pricing models. - Sovereign CDS spreads (when available) provide a maturity-consistent measure of default risk less contaminated by changing security characteristics or policy measures. - Rationale for market-consistent haircuts: - Provide foundation for incorporating broader bank-sovereign linkages, including reduced likelihood or capacity of sovereign bank bailouts and associated ex-ante and ex-post costs (higher funding costs, higher bank failure probability, lower recovery rates). - When sovereign loan exposures are sizeable, credit risk parameters consistent with market valuation haircuts are useful to model tail risk where historical credit parameters lack extreme events. ### Practical considerations for test design and loss estimation - Important dimensions: - Scope of exposures and transmission channels (securities vs. banking book exposures, guarantees, subnational exposures). - Loss estimation methods (market valuation haircuts, credit risk calibration for loans). - Shock calibration (distributional assumptions, tail risk modeling via GEV). - Calculation of capital impact (apply haircuts to holdings and estimate solvency/liquidity feedbacks). - FSAP outputs aim to inform macroprudential preparedness rather than trigger immediate supervisory action; emphasize transparency and market-consistent measures rather than microprudential smoothing. ### Transmission channels and feedbacks emphasized - Direct channels: - Losses from direct exposures to sovereign debt (securities and loans). - Indirect channels: - Valuation losses reduce liquid asset buffers and can cause liquidity stress and higher funding costs. - Bank solvency deterioration can raise counterparty and funding risk, amplifying stress. - Sovereign distress can reduce the probability or capacity of government bailouts, increasing systemic outcomes and contingent liability concerns covered in public debt sustainability analysis. - Integrated stress testing recommended to model dynamic feedback among credit, market, and liquidity risks. ### Supporting definitions and data notes - Basel III Monitoring Exercise definition of sovereign exposures: - Direct sovereign exposures: exposures to sovereigns (immediate counterparts), including banking book (loans and receivables) and trading book assets (securities and financial instruments, including derivatives assets and valuation margins). Liabilities from sovereigns are also monitored for liquidity ratios. - Indirect exposures: exposures to counterparties other than the sovereign that are (i) protected (guaranteed) by a sovereign entity, and (ii) collateralized by instruments issued by sovereign entities and not subject to haircuts (examples: reverse repo transactions, CDS on sovereign securities). - “Sovereign” includes a central bank, a central government, multilateral development banks and some international organizations, subnational governments, and public sector entities (PSEs). - Data sources used: authors’ calculations, Haver Analytics, IMF International Financial Statistics. Note: charts show claims on central, state, and local governments except where state/local data are not available (China, Hong Kong SAR, India, Switzerland, United Kingdom). Data gaps: UK missing 2001 and 2007; Egypt and Turkey 2001 values replaced with 2002 and 2004 respectively. ### Coverage and key findings on sovereign exposures in FSAPs - In most FSAPs for AEs, solvency stress was mostly driven by the market valuation losses from government debt securities. - Cash balances at central banks as well as repurchase agreements (repos) or asset swaps were often excluded. - Loan exposures are included but tend to be a small part of bank assets; estimated losses usually negligible given limited history of outright sovereign default in most AEs. - For economies with higher outright default risk and underdeveloped capital markets, losses are likely to come from loan or loan guarantee exposures to broader government (including state-owned enterprises); in these cases, tests should go beyond market risk, securities exposures, and central government debt. - Where needed, reliable tests may require additional data collection to supplement standard reporting. ### Empirical practice across jurisdictions - European FSAPs and EU-wide exercises typically covered direct and indirect exposures similar to the BCBS definition; examples include exercises in 2010–2019 across many jurisdictions. - Valuation approaches used in FSAPs included: - Zero coupon pricing with cash/forward CDS spreads for country-specific shock. - Discounted cash flow pricing with cash CDS spreads or with country-specific shock to bond yield. - Haircut model applied in selected FSAPs. - Expected losses based on a three-notch downgrade using historical PD and LGD (Finland 2016 example). - Distress dependence with emerging market sovereigns (United States 2010). - Treatment differences: - Some FSAPs applied MtM to HtM securities only in separate sensitivity analysis. - Haircuts sometimes applied only to non-"AAA"-rated debt. - Some jurisdictions stressed only domestic sovereign exposures. - Data constraints sometimes prevented full analysis or made credit risks from SOEs more important than market risk. ### Conceptual framework: expected vs unexpected losses - Expected losses: - Represent average losses likely to materialize based on current information. - Affect the capital adequacy ratio (CAR) through its numerator—either as a direct hit to capital or through profit and losses (P&L), depending on exposure type (HfT, AfS, HtM). - Unexpected losses: - Extreme losses with very low probability (illustrated as Value-at-Risk (VaR) at the 99.9th percentile). - These tail risks affect the CAR through its denominator by increasing the capital intensity of assets. - Metrics referenced: - Value-at-Risk (VaR) 99.9th percentile. - Conditional Tail Expectation (CTE). ### Valuation rules and regulatory capital impact - Trading book (HfT): - Accounting: Fair value: MtM (or model-based) gains/losses reported in P&L and taxed. - Economic valuation (FSAP Principle): Fair value: MtM (or NPV) gains/losses for all assets (“market valuation approach”). - Impact: P&L and economic capital reflect these changes immediately. - Securities available-for-sale (AfS): - Accounting: Fair value; after post-GFC reforms gains/losses reported in P&L as OCI (but not taxed). - Economic/regulatory: Basel III generally removed the AfS filter (but some national authorities still permit it). - Impact: P&L and regulatory capital affected; national discretion matters. - Banking book (HtM and Loans): - Accounting: HtM—book value (amortized cost): expected loss provision reduces taxable net income. - IFRS differences: IAS 39 used backward-looking PD and LGD for incurred losses; IFRS 9 uses forward-looking PD and LGD for expected losses. - Regulatory capital: IRB credit risk weights determined using forward-looking (12-month ahead) TTC PD and downturn LGD. - Application notes: - Market valuation approach is at minimum applied to all traded government debt securities irrespective of accounting classification. - FSAP stress testing uses these valuation concepts for cross-jurisdictional communication. ### Estimating expected loss by exposure type - Trading book exposures: - Mostly bonds and other market instruments. - Expected losses stem from market valuation changes (market valuation approach). - Banking book exposures: - Mostly loans. - Expected losses estimated with a credit risk approach that includes an empirical satellite model forecasting credit risk parameters with macro-financial covariates. - If banks use IRB approaches, expected losses are estimated as PD × LGD. - Under standardized approach, losses estimated using loan classification or credit rating with assumed provision rates for each category/rating. - Stress tests vs regulatory capital rules: - Stress tests broaden application of market-consistent valuation and apply point-in-time parameters; regulatory frameworks include features to smooth volatility. ### Jurisdictional exceptions and timing - AfS filter: - Many European jurisdictions removed the AfS filter in the mid-2010s. - Some jurisdictions (e.g., Japan and the United States) allow some banks to continue applying the AfS filter. - Impact on CAR: - Banks with identical portfolios may show different CARs depending on the share of AfS and HtM securities. - Timing of shock: - Tests varied in timing: all front-loaded (F) or over time (T); scenarios considered baseline (B) and adverse (A) depending on country exercises. ### Market-consistent approach: uses and advantages - Useful for determining expected losses from banking book exposures when a country’s history does not include any sovereign distress episode(s). - Market valuation is more sensitive to investors’ perception about the likelihood of sovereign distress, whereas empirical satellite models may fail without historical precedents. - Helps assess impacts where regulatory arbitrage or forbearance is a concern (example: reclassification to HtM during European sovereign debt crisis). ### Sovereign-bank linkages and funding cost channel - A practical sensitivity test: estimate impact of sovereign distress on market-value based solvency ratio and then estimate its impact on bank funding; resulting reduction of net interest income could be included in broader scenario tests where valuation losses from HtM securities are excluded. ### Regulatory practice vs market valuation for unexpected losses - Under Basel regulations: - Local currency-denominated sovereign debt often assigned a zero percent credit risk weight (SA) and very low RWs under IRB if PDs and LGDs show little past sovereign distress. - These practices can underestimate sovereign risk (Hannoun 2011). Recent BCBS reform efforts have not concluded (BCBS 2017a). - In absence of clear reform, most FSAPs retain existing practice to preserve comparability. ### FSAP practice and valuation choices - Many EU Member State exercises during the European sovereign debt crisis applied market-consistent valuations to all sovereign securities including AfS and HtM (except France and Spain). - More recent FSAPs apply market valuation to HtM less frequently unless HtM share is high or rising noticeably. - Most FSAPs applied a credit risk approach for sovereign risks with loans and receivables using historical credit risk parameters. - For countries with elevated sovereign risk, FSAPs adjusted CARs to reflect valuation gaps between market valuation and last statutory accounts. - If sovereign securities are already priced at historically low levels, applying a smaller-than-otherwise shock may be appropriate. ### Calibrating sovereign shocks - Market-implied valuation approach used to estimate haircuts from expected change in government bond prices due to changes in default risk. - Haircuts derive from bond price components: risk-free interest rate and credit risk premium. - Sovereign risk shocks may include: - Common interest rate component: reflects changes in regional risk-free rate; example common shock considered: 50 basis points. - Country-specific component: calibrated based on historical volatility of sovereign credit spreads (via sovereign CDS or excess spreads). - CDS spreads often represent a “purer” measure of credit risk than government bond yields; useful when yields are kept artificially low by central bank bond purchase programs. - Example: European system-wide stress testing applied a 75-basis-point shock (40 percent increase compared to the latest actual yield) to all euro area government bonds and CDS spreads with 10-year maturities, then assumed CDS spreads with other maturities increase by 40 percent. ### Calculating capital impact and accounting classification effects - Accounting classification determines how expected losses affect bank capital: - Trading losses from HfT are realized, part of net income, and subject to taxation and dividend payout. - Assuming AfS filters are removed, unrealized gains and losses from AfS become part of net income; they reduce capital one-to-one. - Expected credit loss from loan exposures requires additional loan loss reserves (LLRs), which are part of taxable net income. - If market valuation is used for HtM securities, stressed capital ratio formula is provided in the source text (formula fragment preserved in source). Key parameters: - d = dividend payout ratio. - τ = applicable tax rate. - LLR denotes loan loss reserves. - ∆MMMV denotes mark-to-market valuation loss of securities (losses carry a positive sign). - HtM securities likely have a valuation gap at time t; LLR earmarked for HtM can cover part of the gap; remaining positive gap reduces stressed CET1. ### Treatment of HtM under the credit risk approach - Expected losses on HtM securities are treated like those from loans. - Banks set aside additional loan loss provisions to cover deterioration of credit quality in HtM securities in the stress scenario. - CET1 and RWA implication preserved as formula fragments in source. ### Empirical application: market-consistent valuation using EVT/GEV - Purpose: illustrate empirical application of market-consistent valuation approach consistent with FSAP practice. - Key features: - Use sovereign CDS spreads to model credit risk premium. - Fit GEV distribution to historical CDS spread dynamics to derive density forecast of large, non-linear changes in default risk. - Incorporate density forecast into bond pricing or duration/convexity proxies. - Data example: daily data from January 2009 to December 2010 used for comparison with European exercises. - Steps for deriving valuation haircuts: 1. Select liquid government bonds at different maturities and create maturity buckets (1, 3, 5, 7, 10 years; discretionary margin ±0.5 years). 2. Estimate sovereign credit risk shock from daily spot and forward CDS spreads; calibrate spread variation using GEV; obtain point estimates of expected PD at percentiles for each year of five-year test horizon. - Baseline: last observable current or forward CDS spread (whichever is larger). - Adverse: apply higher country-specific credit shocks at the 75th percentile (and higher). - In all scenarios, estimate sovereign credit spread shock with and without a common interest rate shock of 50 basis points. - Example estimation period: January 1, 2009 through December 30, 2010. 3. Calculate individual valuation haircuts as expected change in benchmark bond prices over stress horizon using zero-coupon and discounted cash flow methods; focus on five-year maturity tenor because CDS curve flattens beyond five years. 4. Determine aggregate valuation haircut as weighted averages using outstanding amounts of benchmark bonds as weights; adjust if portfolio maturity profile differs from benchmark. - Key parameter choices in empirical application: - Maturity buckets: 1, 3, 5, 7, 10 years. - Forecast horizon: 5 years. - Adverse scenario percentile: 75th percentile (consistent with EU guidance). - Common interest rate shock: 50 basis points. - Estimation window: January 1, 2009 to December 30, 2010. - Bond valuation methods: zero-coupon and discounted cash flow. - Use cases: applied in FSAPs for Belgium (2013), Germany (2011), Spain (2012), United Kingdom (2011), and Hong Kong SAR (2014). ### Reasons for choosing CDS spread dynamics (Box 2) - CDS spreads are relatively “pure” measures of default risk and avoid contamination from security characteristics, inflation and term premia, and risk-free rate choice. - CDS contracts typically recover par value in default, endogenizing recovery rate in observed prices. - CDS spreads represent sovereign risk more accurately than bond yields when yields are artificially low (e.g., central bank purchase programs). - Caveats: - CDS denominated in U.S. dollars: FX changes can amplify CDS spread dynamics and potentially overestimate sovereign risk relative to local-currency spreads. - CDS delivery option (cheapest-to-deliver) can raise spreads by implying reduced expected recovery relative to cash instruments. - Model advantages: - Incorporates market expectations via forward CDS contracts ensuring time-consistency across projection horizon. - Flexibility supports tractable estimates of tail events and integration into asset pricing models with duration/convexity control. - Empirical notes: - Focus on 5-year sovereign CDS as most liquid maturity. - In most countries, estimated CDS under adverse scenarios (75th and 90th percentiles) exceeded realized CDS spread except in the first year of the horizon. - Key empirical findings on haircuts: - 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 indicated elevated expected default risk; for other European countries average haircut about five percent during the first year. - For Greece, forward CDS implied near-default, pushing haircuts beyond the 99th percentile (not reported). - Little additional haircut beyond 2011 given CDS curve flattening and heavy discounting in 2011. - Greece example aligned with average 21 percent mark-down of private creditors. ### Policy implications and further work (from Box 2 conclusions) - Sovereign risk has long-tail distribution; accounting for tail risk via GEV fitting to CDS spread dynamics improves stress-test calibration. - Integration and further work: - Interact sovereign debt sustainability analysis and bank stress tests. - Use empirical multi-sector models (e.g., GVAR), co-dependence models, or general equilibrium models with bank and sovereign distress. - Explicitly model solvency–liquidity interactions in integrated stress testing. - Same haircut estimation approach could be used for liquidity stress tests; haircuts for liquidity tests should be higher and use shorter time horizons (monthly yield-change distributions wider than annual). ### APPENDIX I — Contingent Claims Analysis (CCA) of sovereign–bank interaction - CCA generalizes option pricing theory (Merton-type) to model sovereign expected losses and banking-sector contingent liabilities. - Sovereign expected losses expressed as a European put option with underlying government asset A, strike debt amount D, and maturity T; sovereign spreads defined in basis points with exact formula preserved in source. - Implied sovereign asset value R̃ is defined as sum of: - foreign currency reserves R, - present value of primary fiscal surplus, - implicit/explicit contingent liabilities from banking sector α P_bvab(R,D,H,T) where α is share of expected banking losses borne by sovereign, - Other (public sector assets and unrealized liabilities). - Banking-sector contingent liabilities analogously defined as a put option. - Bank credit spread includes sovereign spillover premium δ in exact formulation preserved in source. - Channels through which higher sovereign spreads increase bank spreads: - (i) decline in value of implicit bank put option for sovereign guarantees (α declines), - (ii) decline in value of bank holdings of government debt, - (iii) increase in bank default barrier due to higher borrowing costs as premium δ increases. - Applications: - Use term structure of sovereign spreads to estimate implied sovereign asset value and asset volatility. - Calibrate market-implied sovereign risk when sovereign equity/volatility unobservable. - Systemic CCA framework applied in FSAPs for Germany, Hong Kong SAR, Spain, Sweden, the United Kingdom, and the United States. ### APPENDIX II — Estimating valuation haircuts for sovereign risk (methodology) - Valuation haircuts derived from expected change in government bond prices consistent with market-implied sovereign default risk. - Procedure highlights: - Select benchmark local-currency fixed-rate bonds up to 10 years; group into maturity buckets k ∈ {1,3,5,7,10} years (±0.5 years). - Convert coupon bonds to zero-coupon equivalents (ZCE) and apply duration/convexity adjustments (φ_p). - Express ZCE using sovereign CDS to infer PD via CDS spreads: s_ZCDC_j[k],t definition preserved. - Future pricing includes allowance for a positive common shock to risk-free rate ∆f̂_p_j[k],t and country-specific risk changes. - EVT/GEV approach for adverse scenarios: - Fit GEV to historical forward CDS spread extremes. - Use density forecasts at high percentiles (CTE) for stressed country-specific risk components replacing min(...) term in pricing equations. - Calibration choices in application: - Test horizon maturities i ∈ I = {0.5,1,3,5,7,10} years. - GEV shape parameter calibrated uniformly to ξ = 0.33 in the application. - Density forecast percentiles for adverse scenarios: 75th percentile (adverse 1) and 90th percentile (adverse 2). - Scenario implementation and haircut construction: - For each year v obtain bond prices under baseline (forward CDS) and two adverse density forecasts (m ∈ {0.75; 0.90}). - Bond-level haircuts computed as percent change relative to base year t using ∆Π formulas preserved. - Aggregate country haircut h_j is issuance-size weighted average across q outstanding bonds; h set to zero when bond prices rise. - Apply country haircuts to firms’ total exposures to country j across banking and trading books; sovereign bond losses in year v = Σ_j (h_b1,j[b],v, h_b2,j[b],v) × exposure_e_v,j. - Practical notes and limitations: - Use local-currency debt only. - When bond-by-bond data unavailable, approximate using average duration and volume-weighted yield changes. - Duration valid for small yield changes (< 100 bps); include convexity for larger shocks. - Forward CDS-based estimates in outer years biased downward; percentile choice should match probabilistic severity of macro scenario. - Example: ξ uniformly set to 0.33 when generating reported results. ### APPENDIX III — GEV moments and LRS estimation of shape parameter - LRS estimator for shape parameter ξ̂ derived from linear combination of log-ratio spacings; formula and notations preserved in source. - Moments existence conditions: - Mean finite if ξ < 1. - Variance finite if ξ < 1/2. - Skewness finite if ξ < 1/3 (special-case formulas for ξ ≤ 0 and ξ = 0). - Kurtosis finite if ξ < 1/4 (special-case behavior for ξ = 0 and ξ ≥ 1/4). - Practical implication: existence of moments depends critically on ξ; LRS provides practical estimation method via log-ratio spacings and inverse GEV transforms. *Source: wpiea2019266-print-pdf — IMF working paper extract* ### References ............................................................................................................. ### Sovereign Risk in Bank Stress Testing (WP/19/266 extract) ### Key findings on sovereign exposures and systemic risk - 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). - 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 (including sub-national governments, lending, and sovereign guarantees) more than doubles the amounts measured by claims on government debt. - Sovereign distress can take many forms: (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). - Sovereign distress has wide-ranging direct and indirect transmission channels to banks, including valuation losses on sovereign securities, higher bank funding costs, feedback effects to sovereigns through potential bank support measures, and macroeconomic channels (growth, inflation, exchange rates). ### Scope of stress tests: heterogeneity across countries - Economies with developed financial markets and low outright sovereign default risk: - Sovereign distress propagates primarily through valuation shocks to sovereign bonds with significant indirect effects. - Tests can focus on securities exposures and apply valuation haircuts, effectively treating sovereign default as a market risk. - Economies with underdeveloped financial markets and higher outright sovereign default risk: - Higher chances of sovereign distress in “crude forms” (delayed interest payments, unilateral restructuring, monetization leading to hyperinflation). - Broader types of sovereign exposures (loans, deposits, guarantees) and state-owned banks raise cyclical linkages and contingent liabilities. - Sovereign risk often linked to external vulnerabilities; global investor behavior and commodity price cycles can amplify stress. ### Methodology and advances in FSAP sovereign stress testing - FSAPs have followed a market-consistent valuation approach broadly aligned with Basel III, with macroprudential modifications: - Apply market-implied estimates of expected sovereign default to all types of sovereign exposures. - Main FSAP approach measures valuation effects on traded government debt caused by changes in expected default rather than realized default. - Sovereign risk shock is calibrated as the market-consistent haircut implied by the estimated decline in fair value of government bonds using price or yield volatility (standard deviation). - The paper advances calibration toward tail-event consistent shocks: - Fit a generalized extreme value (GEV) distribution to historical spread dynamics of spot and forward sovereign credit default swaps (CDS) to capture fat tails. - Once a stressed level of credit risk premium is chosen, derive market-consistent valuation haircuts using standard bond pricing models. - Sovereign CDS spreads (when available) provide a maturity-consistent measure of default risk less contaminated by changing security characteristics or policy measures. - Rationale for using market-consistent haircuts: - Market-implied valuation haircut provides a foundation for incorporating broader bank-sovereign linkages, including reduced likelihood or capacity of sovereign bank bailouts and associated ex-ante and ex-post costs (higher funding costs, higher bank failure probability, lower recovery rates). - When sovereign loan exposures are sizeable, credit risk parameters consistent with market valuation haircuts are useful to model tail risk where historical credit parameters lack extreme events. ### Practical considerations for test design and loss estimation - Important dimensions for stress tests: - Scope of exposures and transmission channels (securities vs. banking book exposures, guarantees, subnational exposures). - Loss estimation methods (market valuation haircuts, credit risk calibration for loans). - Shock calibration (distributional assumptions, tail risk modeling via GEV). - Calculation of capital impact (apply haircuts to holdings and estimate solvency/liquidity feedbacks). - FSAP outputs aim to inform macroprudential preparedness rather than trigger immediate supervisory action; they emphasize transparency and market-consistent measures rather than microprudential smoothing of cyclical volatility. ### Transmission channels and feedbacks emphasized - Direct channels: losses from direct exposures to sovereign debt (securities and loans). - Indirect channels: - Valuation losses reduce liquid asset buffers and can cause liquidity stress and higher funding costs. - Bank solvency deterioration can raise counterparty and funding risk, amplifying stress. - Sovereign distress can reduce the probability or capacity of government bailouts, increasing systemic outcomes and contingent liability concerns covered in public debt sustainability analysis. - Interaction of sovereign and financial sectors may require integrated stress testing that models dynamic feedback among credit, market, and liquidity risks. ### Supporting definitions and data notes - Basel III Monitoring Exercise definition of sovereign exposures: - Direct sovereign exposures: exposures to sovereigns (immediate counterparts), including banking book (loans and receivables) and trading book assets (securities and financial instruments, including derivatives assets and valuation margins). Liabilities from sovereigns are also monitored for liquidity ratios. - Indirect exposures: exposures to counterparties other than the sovereign that are (i) protected (guaranteed) by a sovereign entity, and (ii) collateralized by instruments issued by sovereign entities and not subject to haircuts (examples: reverse repo transactions, CDS on sovereign securities). - Note: “Sovereign” includes a central bank, a central government, multilateral development banks and some international organizations, subnational governments, and public sector entities (PSEs). - Data sources and figure notes (Figure 1): authors’ calculations, Haver Analytics, IMF International Financial Statistics. Charts show claims on central, state, and local governments except where state/local data are not available (China, Hong Kong SAR, India, Switzerland, United Kingdom). Data gaps: UK missing 2001 and 2007; Egypt and Turkey 2001 values replaced with 2002 and 2004 respectively. *Source: wpiea2019266-print-pdf - References* ### 16. A comprehensive assessment includes all types of relevant sovereign exposures, ### 16. A comprehensive assessment includes all types of relevant sovereign exposures, beyond the valuation of traded exposures during times of stress (see Box 1). ### Coverage and key findings on sovereign exposures in FSAPs - In most FSAPs for AEs, solvency stress was mostly driven by the market valuation losses from government debt securities. - Cash balances at central banks as well as repurchase agreements (repos) or asset swaps were often excluded. - Loan exposures are included but tend to be a small part of bank assets; the estimated losses are usually negligible given the limited history of outright sovereign default in most AEs. - For economies with higher outright default risk and underdeveloped capital markets, losses are likely to come from loan or loan guarantee exposures to broader government (including state-owned enterprises). In these cases, tests should go beyond market risk, securities exposures, and central government debt. - Where needed, reliable tests may require additional data collection to supplement standard reporting. ### Empirical practice across jurisdictions (summary from Tables 1 and 2) - European FSAPs and EU-wide exercises typically covered direct and indirect exposures similar to the BCBS definition; exercises include the 2011 capital exercise and subsequent tests. - Treatment of domestic debt, valuation timing, and valuation method varied across jurisdictions (examples from Tables 1 and 2 include UK 2011, Germany 2011, France 2013, Italy 2013, Spain 2012, United States 2010, Japan 2012, Canada 2014, Hong Kong SAR 2014, Brazil 2012, Korea 2015, Singapore 2013, Turkey 2012, Argentina 2016, Norway 2015, Sweden 2011/2017, Poland 2019, Euro Area Policies 2018, and others). - Valuation approaches used in FSAPs included: - Zero coupon pricing with cash/forward CDS spreads for country-specific shock. - Discounted cash flow pricing with cash CDS spreads or with country-specific shock to bond yield. - Haircut model applied in selected FSAPs (Appendix II). - Expected losses based on a three-notch downgrade using historical PD and LGD (Finland 2016 example). - Distress dependence with emerging market sovereigns (United States 2010). - Treatment differences noted: - Some FSAPs applied MtM to HtM securities only in separate sensitivity analysis. - Haircuts sometimes applied only to non-"AAA"-rated debt. - Some jurisdictions stressed only domestic sovereign exposures. - In some cases (data constraints), full analysis was prevented or credit risks from SOEs were considered more important than market risk. ### Method to estimate potential losses — conceptual framework - Sovereign risks generate both expected and unexpected losses impacting bank solvency. - Expected losses: - Represent average losses likely to materialize based on current information. - Affect the capital adequacy ratio (CAR) through its numerator—either as a direct hit to capital or through profit and losses (P&L), depending on exposure type (HfT, AfS, HtM). - Unexpected losses: - Are extreme losses with very low probability (illustrated as Value-at-Risk (VaR) at the 99.9th percentile). - These tail risks affect the CAR through its denominator by increasing the capital intensity of assets. - Figure elements and metrics referenced: - Value-at-Risk (VaR) 99.9th percentile. - Conditional Tail Expectation (CTE). ### Valuation rules and regulatory capital impact (Table 3 summary) - Trading book (Securities held-for-trading, HfT): - Accounting: Fair value: MtM (or model-based) gains/losses reported in P&L and taxed. - Economic valuation (FSAP Principle): Fair value: MtM (or NPV) gains/losses for all assets (“market valuation approach”). - Impact: P&L: impact of gains/losses on net operating income; Regulatory capital: non-taxable gains/losses not distributed as dividends are fully reflected in economic capital. - Securities available-for-sale (AfS): - Accounting: Fair value; before post-GFC reforms gains/losses accounted only as part of equity in financial statements (and not taxed); after post-GFC reforms gains/losses are reported in P&L as OCI (but not taxed). - Economic/regulatory: Basel I and II allowed an “AfS filter”; Basel III generally removed the AfS filter (but some national authorities still permit it). - Impact: P&L and regulatory capital affected; national discretion matters. - Banking book (Securities held-to-maturity, HtM and Loans): - Accounting: HtM—book value (amortized cost): expected loss (based on estimated PD and LGD) is provisioned and reduces (taxable) net income. - IFRS differences: IAS 39 used backward-looking PD and LGD for incurred losses; IFRS 9 uses forward-looking PD and LGD for expected losses. - Impact: P&L: provisioning for expected losses based on accounting rules (“credit risk approach”); Regulatory capital: IRB credit risk weights determined using forward-looking (12-month ahead) TTC PD and downturn LGD. - Notes on application: - The same valuation rules apply to all securities (sovereign and others). - The market valuation approach is at minimum applied to all (traded) government debt securities irrespective of accounting classification. - Exact category names differ across jurisdictions; FSAP stress testing exercises use these concepts for cross-jurisdictional communication. ### Estimating expected loss by exposure type - Trading book exposures: - Mostly bonds and other market instruments. - Expected losses stem from market valuation changes (market valuation approach). - Banking book exposures: - Mostly loans. - Expected losses estimated with a credit risk approach that includes an empirical satellite model forecasting credit risk parameters with macro-financial covariates. - If banks use IRB approaches, expected losses are estimated as PD × LGD. - Under standardized approach, losses estimated using loan classification or credit rating with assumed provision rates for each category/rating. - Stress tests vs. regulatory capital rules: - Stress tests broadly follow Basel regulatory capital rules but tend to widen the application of market-consistent valuation. - Regulatory frameworks include features to smooth volatility (to avoid frequent changes in regulatory capital), while macroprudential stress tests aim to reflect potential losses immediately and transparently using MtM valuation (economic valuation approach). - For banking book, Basel uses through-the-cycle (TTC) PDs and LGD for capital; stress tests usually apply point-in-time (PiT) PDs and downturn LGD as “raw parameters.” ### Jurisdictional exceptions and timing - AfS filter: - Many European jurisdictions removed the AfS filter in the mid-2010s. - Some jurisdictions (e.g., Japan and the United States) allow some banks to continue applying the AfS filter. - Impact on CAR: - Banks with identical portfolios may show different CARs depending on the share of AfS and HtM securities because HfT and AfS reflect market declines immediately while HtM may not. - Timing of shock in exercises: - Tests varied in timing of shock: all front-loaded (F) or over time (T), and in scenarios considered baseline (B) and adverse (A) depending on country exercises. *Source: IMF FSAP chapter content provided.* ### 21. The market-consistent approach is also useful for determining expected losses from ### wpiea2019266-print-pdf - 21. The market-consistent approach is also useful for determining expected losses from ### Market-consistent approach: uses and advantages - Useful for determining expected losses from banking book exposures when a country’s history does not include any sovereign distress episode(s). - Market valuation is more sensitive to investors’ perception about the likelihood of sovereign distress, whereas no empirical satellite model can capture sovereign distress well without historical precedents. - Helps assess impacts where regulatory arbitrage or forbearance is a concern: - Example: 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). Such measures can limit amplification effects but reduce transparency for stress testing. - Evidence that banks optimize accounting treatment of government debt securities to reduce their capital impact (Fuster and Vickery (2018) noted reclassification to HtM instead of reducing trading book risk when AfS filter was removed). ### Sovereign-bank linkages and funding cost channel - One sovereign-bank linkage channel operates through bank (wholesale) funding costs; investors pay attention to market-value based solvency in addition to regulatory ratios. - Practical approach: sensitivity test that estimates the impact of sovereign distress on market-value based solvency ratio and then estimates its impact on bank funding; resulting reduction of net interest income could be included in broader scenario tests where valuation losses from HtM securities are excluded. ### Regulatory practice vs market valuation for unexpected losses - Stress tests usually follow regulatory practice for unexpected losses from sovereign exposures, even if considered problematic in the financial stability community. - Under Basel regulations: - Local currency-denominated sovereign debt preserves their nominal value during times of stress and could be considered “safe assets.” - Often 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 with little past sovereign distress. - These practices can underestimate sovereign risk (Hannoun 2011). Recent BCBS reform efforts to change them have not concluded (BCBS 2017a). - Multiple reform options exist (concentration-based measures to credit risk-based capital charges), but no clear superior option; absence of clear direction leads most FSAPs to retain existing practice to preserve comparability. ### FSAP practice and valuation choices - Most FSAPs follow benchmark approach with varying valuation practices; many EU Member State exercises during the European sovereign debt crisis applied market-consistent valuations to all sovereign securities including AfS and HtM (except for France and Spain). - For HtM securities this meant applying valuation losses instead of provisions according to their credit risks. - Example: 2012 Italy FSAP excluded valuation losses from HtM securities from a macro scenario test but included them in a sensitivity test. - More recent FSAPs apply market valuation to HtM less frequently unless HtM share is high or rising noticeably. - Most FSAPs applied a credit risk approach for sovereign risks with loans and receivables using historical credit risk parameters. - Some FSAPs are attempting to incorporate indirect effects through funding cost as part of solvency-liquidity interaction modeling. - For countries with elevated sovereign risk, FSAPs included valuation losses not fully reflected in prudential reporting because CARs may not reflect short-term cyclical valuation changes; tests should adjust for valuation gaps between market valuation and last statutory accounts. - If sovereign securities are already priced at historically low levels, applying a smaller-than-otherwise shock may be appropriate. ### Calibrating sovereign shocks - Sovereign risk shocks are difficult to calibrate with standard macroeconomic models: - Baseline includes entire yield curve of (own) government securities to estimate forward yield curve. - Macroeconomic models often focus on short-term policy rate and do not endogenously model shocks to financial risk or integrate essential non-linear financial risk effects. - Market-implied valuation approach used as alternative statistical method to calibrate sovereign shocks (used by many FSAPs since the European sovereign debt crisis) to estimate haircuts to sovereign securities. - Haircuts derived from expected change in government bond prices in response to changes in default risk. - Bond price components: risk-free interest rate and credit risk premium. - Haircuts reflect differential price impact of higher sovereign risk; general macro models provide the risk-free component. - Valuation haircuts are applied to all sovereign exposures for a fully market-consistent capital assessment; empirical constraints may limit market valuation to capital market instruments only. - For banking book sovereign exposures (non-capital market instruments), credit risk approach may substitute when reliable market prices are absent: - Banks set aside reserves for expected losses (LLP for loans and receivables), covering non-accrual amounts (proxied via NPLs and write-downs). - If banks use IRB, provisions for expected losses based on through-the-cycle PDs (or preferably point-in-time) and downturn LGDs. - A separate provisioning model for sovereign risk might be warranted because PDs (and non-accruals) of sovereign exposures can behave differently from commercial/retail exposures. - Under the credit risk approach, sovereign shock is modelled as a downgrade scenario implying a significant deterioration of PDs and LGDs. - Sovereign risk shocks may include common (global/regional) interest rate component and country-specific component: - Common interest rate shock: reflects changes in regional risk-free rate and sovereign default risk across multiple countries; for many smaller, open EMDEs, interest rates in large advanced economies (especially the United States) influence domestic yields. - If the common interest rate shock is uniform, it results in a parallel upward shift of the yield curve and term structure remains unchanged. - Country-specific interest rate shock: primary driver is country-specific credit risk component; can be calibrated based on historical volatility of sovereign credit spreads (via sovereign CDS or excess spreads over benchmark, e.g., J.P. Morgan EMBI). - Data can be parametrically modeled to generate point estimates of expected default risk at different maturities for each year of the stress horizon. - For adverse scenarios, high sovereign credit spreads away from historical median (i.e., spreads at the tail of the historical distribution) can be applied. - Example calibration practice: European system-wide stress testing applied a 75-basis-point shock (40 percent increase compared to the latest actual yield) to all euro area government bonds and CDS spreads with 10-year maturities, then CDS spreads with other maturities assumed to increase by 40 percent. - CDS spreads often represent a “purer” measure of credit risk than government bond yields; useful when yields are kept artificially low by central bank bond purchase programs. - For loans and other non-capital market exposures, credit risk approach may be more suitable; a separate credit risk model predicting PDs and LGDs or NPLs of sovereign loans as function of macro-financial variables might be warranted. - Sovereign risk shock should be less severe if countries are already in distress because current sovereign yield curve already embeds a level of default risk; further raising default risk may lead to implausibly severe stress compared to stable-interest-rate countries. ### Calculating capital impact and accounting classification effects - Accounting classification (HfT, AfS, HtM, loans) determines how expected losses affect bank capital under stress: - Trading losses from HfT are realized, part of net income, and subject to taxation and dividend payout. - Assuming AfS filters are removed, all unrealized gains and losses from AfS become part of net income; unrealized valuation changes are not subject to taxation and are usually not included in dividend payments, so valuation changes reduce capital one-to-one. - Expected credit loss from loan exposures requires additional loan loss reserves (LLRs), which are part of taxable net income; banks usually pay tax and dividend only when taxable net income is positive. - If market valuation is used for HtM securities, stressed capital ratio formula provided in text: CET1_stress_{t+1} / RWA_stress_{t+1} = ( CET1_t + [ Net income before sovereign losses − ∆MMMV × HHHHHH − ∆LLR for sovereign loans ] (1−d)(1−τ) — valuation placeholder — − [ ∆MMMV × (AH A + H HMM) + max[ valuation gap_p − LLR_p, 0 ] HHHHHH ] vvv cv pvvpl ) / RWA_t (1 + ∆RWA / RWA_t) - Definitions and notes from text: - d is the dividend payout ratio. - τ is the applicable tax rate. - LLR denotes the amount of loan loss reserves. - ∆HHHHHH is mark-to-market valuation loss of securities (losses carry a positive sign). - ∆RRRRRR defines the possible change in unexpected losses. - Time t is the latest actual value before adding stress; t+1 means after stress. - Expected losses from HtM securities affect the capital ratio similarly to AfS securities. - HtM securities are likely to have a valuation gap at time t (difference between amortized cost used for HtM valuation and market values). LLR earmarked for HtM can cover part of the gap, but a positive gap is likely to remain; the stressed capital ratio thus represents both existing and additional losses by including the remaining gap. *Source: wpiea2019266-print-pdf (excerpt: market-consistent approach, FSAP practice, shock calibration, capital impact).* ### 35. Alternatively, if the credit risk approach is applied to HtM, their expected losses are ### 35. Alternatively, if the credit risk approach is applied to HtM, their expected losses are ### Treatment of HtM under the credit risk approach - Expected losses on held-to-maturity (HtM) securities 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. ### CET1 and RWA implication (formula fragment preserved) - CET1 stress t+1 RWA stress t+1 = CET1 t + � Net income before sovereign losses −∆퐌퐌퐌퐌퐌퐌×퐇퐇퐇퐇퐇퐇 −∆LLR for sovereign loans and HtM � ( 1−d )( 1−τ ) ��������������������������������� 푣푣푣푣푣푣 푝푝푝푝푝푝푝푝 푣푣푝푝 푣푣푎푎푎푎 푙푙푝푝푙푙푙푙 −∆퐌퐌퐌퐌퐌퐌×퐀퐀퐇퐇 퐀퐀��������� 푣푣푣푣푣푣 푐푐푣푣푝푝푣푣푝푝푣푣푙푙 RWA t �1+ ∆RWA RWA t � ### VI. EMPIRICAL APPLICATION: Examples from stress tests in FSAPs for selected European countries - Purpose: Illustrate empirical application of the market-consistent valuation approach for assessing sovereign risk consistent with current FSAP practices in macroprudential solvency stress tests. - Key methodological feature: 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 — overview - Valuation change of government bonds modeled using the credit risk premium implied in sovereign CDS spreads. - Historical CDS spread dynamics fitted to a generalized extreme value (GEV) distribution to derive the density forecast of a large, non-linear change in default risk. - Density forecast incorporated into bond pricing formula or proxies of price-yield sensitivity (duration and convexity). - Bond pricing combines 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. - Haircuts differ by severity of sovereign risk shocks, maturity tenors, and macroeconomic scenarios. - Daily data from January 2009 to December 2010 used for empirical application to compare with European exercises. ### Steps for deriving valuation haircuts (four steps) - Selecting liquid government bonds at different maturities: - Select most liquid fixed-rate local-currency-denominated government debt securities (“benchmark bonds”). - Create maturity buckets around desired maturity tenor. - Sample assumed representative of typical maturities of bank sovereign exposures when actual portfolio data not available. - Estimating the sovereign credit risk shock: - Obtain daily time series of spot and forward sovereign CDS spreads to estimate historical spread dynamics and determine market-implied default rate. - Recovery rate endogenized in default rate implied by observable spread. - Calibrate variation of spread changes using the GEV distribution. - Obtain point estimates of expected PD at percentiles for each year of the five-year test horizon. - Baseline scenario: last observable current or forward CDS spread (whichever is larger). - Adverse scenarios: apply higher country-specific credit shocks at the 75th percentile (and higher) of the forecasted distribution. - In all scenarios, estimate sovereign credit spread shock with and without a common interest rate shock of 50 basis points. - Estimation example: estimation period limited to two years (January 1, 2009 through December 30, 2010). - Rationale: GEV distribution suited for modeling tail events and provides closed-form expression of asymptotic tail behavior. - Calculating individual valuation haircuts: - Haircuts set as expected change in prices of selected benchmark bonds vis-à-vis their market value as of data cut-off date. - Price change corresponds to total yield changes, including expected PDs and risk-free rate, varying across maturity tenors. - Within each maturity group, individual bonds priced over a five-year stress test horizon using both adjusted zero-coupon bond and discounted cash flow methods, considering maturity dates, coupons, and coupon frequencies. - Focus on five-year maturity tenor of credit spreads because CDS spread curve flattens beyond five years. - Determining the aggregate valuation haircut: - Aggregate haircuts for each maturity group obtained as weighted averages using outstanding amounts of benchmark bonds as weights. - Aggregate valuation haircut represents weighted-average change in market valuation over stress test horizon. - If complete portfolio data are available, valuation haircut can be more nuanced within each maturity bucket based on term structure of credit risk premiums. - If size-weighted maturity profile of sovereign portfolios differs significantly from benchmark maturity terms, haircuts may be adjusted to match actual key rate durations. ### Key parameters, choices, and references used in empirical application - Maturity buckets: 1, 3, 5, 7, and 10 years (with discretionary margin of +/- 0.5 years in bond selection example). - Forecast (stress) time horizon: multiple periods (5 years) in the IMF FSAP approach. - Adverse scenario percentile: 75th percentile for country-specific credit shocks (selection consistent with EU-wide stress test guidance). - Common interest rate shock considered: 50 basis points. - Estimation window used in example: January 1, 2009 to December 30, 2010. - Bond valuation methods: zero-coupon bond pricing and discounted cash flow method. - Scope of application in IMF FSAP approach: sovereign exposures (direct and indirect) in both trading and banking books assessed under market valuation approach; possible exception of loans and receivables under credit risk approach. - Use cases: Approach applied in FSAPs for Belgium (2013), Germany (2011), Spain (2012), United Kingdom (2011), and Hong Kong SAR (2014). *Source: IMF working paper content (excerpt).* ### Box 2. Reasons for Choosing CDS Spread Dynamics for Estimating Valuation Haircuts ### Box 2. Reasons for Choosing CDS Spread Dynamics for Estimating Valuation Haircuts ### Rationale for using CDS spread dynamics - Risk measurement - CDS spreads are relatively “pure” measures of default risk (IMF 2013) and avoid contamination from security characteristics (coupon frequency, creditor rights, redemption features), inflation and term premia (and their volatility) that affect government bond prices. - Using CDS spreads avoids potential basis risk from the choice of the appropriate risk-free rate and its term structure when extracting credit spread components from bond yields. - In the event of a default, the CDS contract payout usually recovers the par value, obviating the need to determine the implied default probability (since the recovery rate is endogenized in the observed bond price). - CDS spreads represent sovereign risk more accurately than sovereign bond yields when yields are kept artificially low by central bank bond purchase programs. - Caveats: sovereign CDS spreads can be influenced by price distortions: - CDS contracts are often denominated in U.S. dollars; FX rate changes (often positively correlated with shocks to sovereign risk) can amplify CDS spread dynamics and potentially overestimate sovereign risk during stress relative to local-currency bond-implied credit spreads. - CDS contracts provide protection sellers with a “delivery option” (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). - Market expectations - The model incorporates market expectations of future changes in sovereign risk (as reflected in forward CDS contracts), ensuring time-consistency between the market-based valuation haircut and the actual valuation change in each year of the stress test horizon. - Empirical evidence (Figure A2.2 in Appendix II) using end-2010 spot and forward sovereign CDS spreads (fitted to the GEV distribution) informed estimation in Appendix V, Tables A5.1 and A5.2. - Forward CDS contracts overstated sovereign default risk in the wake of the European sovereign debt crisis but adequately projected potential escalation of sovereign risk in vulnerable countries. - Model flexibility and price consistency of shocks - The functional form supports a nuanced assessment of sovereign risk over the projection horizon and generates tractable estimates of tail events (outside historical experience) that can be reconciled to the probabilistic severity of the overall scenario. - The estimated default risk is integrated into an asset pricing model, controlling for the marginal effect of changes in default risk on the convexity of government bond prices. - The approach allows cross-validation of other methods. ### Notes and methodological specifics - 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. The methodology focuses on 5-year sovereign CDS contracts, identified as the most liquid maturity term. - 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 and during each year—except for the first year of the stress test horizon. - Germany, Japan, and the United States benefitted from safe haven flows during the European sovereign debt crisis, resulting in a gradual decline of sovereign CDS spreads. - For Italy and France, 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 81st percentiles of the empirical distribution of one-year forward CDS and the 89th and 87th percentiles of the empirical distribution of spot CDS. ### Key findings on valuation haircuts and stress tests - Comparison and consistency - The estimated haircuts are broadly consistent with those in the European stress testing exercise but provide a more comprehensive and nuanced assessment. - Table 5 provides estimated valuation haircuts for sovereign exposures with an average maturity of five years in the baseline scenario and two adverse scenarios at end-2010; results are broadly comparable to those used in the first European system-wide stress testing exercises (EBA 2010, 2011a; ECB 2011). - The severity of haircuts appeared more plausible and differentiated across countries due to greater model flexibility regarding statistical confidence and configuration of interest rate shocks. - The distribution-based model anchors calibration of shocks in market expectations by considering market-implied assessments of future sovereign risk. - Magnitude and timing - 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 indicated elevated expected default risk relative to 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). - For Greece, forward CDS prices implied near-default, pushing haircuts based on end-2010 data beyond the 99th percentile (not reported). - For other European countries, results were relatively benign with an average haircut of about five percent during the first year of the test horizon. - There were little (if any) additional haircuts beyond 2011, given flattening of the CDS curve at longer maturities and heavy discounting of bonds issued by stressed countries during 2011. - In the case of Greece, estimated haircuts are close to those used in the European system-wide stress testing exercise (EBA, 2011a) and align with the average 21 percent mark-down of private creditors (Boone and Ardanga 2011). - Liquidity considerations - The approach does not seem to be influenced by liquidity concerns in the sovereign CDS market. Historical data (since January 2011) suggest pricing and trading volume of sovereign CDS spreads in major sample countries are only weakly correlated. ### Conclusions and policy implications - Accounting for tail risk - Sovereign risk exhibits a long-tail distribution: very small chances of extreme losses can occur. Failure to account for tail risk can lead to underestimation of potential impact in stress tests. - The paper fits a GEV distribution to historical spread dynamics of spot and forward sovereign CDS to derive a density forecast of severe, non-linear changes in the credit risk premium consistent with sovereign-tail risk within a flexible functional form. - CDS spreads, when available, tend to provide a “pure” measure of maturity-consistent default risk compared with bond yields. - Integration and further work - An integrated sovereign risk assessment for macroprudential surveillance and financial stability analysis requires additional work to capture transmission channels across sectors and countries. - Possible approaches for comprehensive assessment: - Interacting sovereign debt sustainability analysis and bank stress tests. - Estimating effects in empirical multi-sector models (such as Global Vector Autoregressive (GVAR) approaches), co-dependence models for banks and sovereigns, or general equilibrium models with bank and sovereign distress. - The interaction between solvency and liquidity conditions under stress should be explicitly addressed in integrated stress testing frameworks that model dynamic and systemic effects from credit, market and liquidity risks. - The same haircut estimation approach could be used for gauging haircuts to liquid assets in liquidity stress tests; haircuts for liquidity stress tests should be higher than those used for solvency tests (e.g., by taking shocks from tails of the distribution). The time horizon for a liquidity stress test is much shorter, and the distribution of yield changes within a month is much wider than the distribution of annual yield changes. *Source: Box 2, wpiea2019266-print-pdf.* ### 2. Washington, DC: International Monetary Fund. ### APPENDIX I. INTERACTION AND FEEDBACK BETWEEN THE SOVEREIGN AND FINANCIAL SECTOR BALANCE SHEETS USING CONTINGENT CLAIMS ANALYSIS (CCA) ### Overview - The appendix uses contingent claims analysis (CCA) to illustrate the interaction between the sovereign and financial sector balance sheets and the potential rise of their respective credit spreads during stress episodes. - Banks are assumed to be the only relevant financial institutions for the assessment of contingent liabilities from this interaction. - The CCA generalizes option pricing theory (Black and Scholes 1973; Merton 1973, 1974), modeling equity as an implicit call option and risky debt as the default-free value of debt less an implicit put option capturing expected losses. ### Sovereign expected losses and implied asset valuation - Expected losses from total sovereign debt are expressed as a European put option where: - underlying asset = government asset A, - strike price = debt amount D, - maturity = sovereign debt maturity T. - The sovereign put valuation appears as 풫풫푙푙푝푝푣푣(푅푅,퐷퐷,퐻퐻,푇푇) with cumulative normal 풩풩(⋅) and terms 푥푥± defined using asset volatility 휎휎퐴퐴푠푠푠푠푠푠 and time horizons (e.g., √푇푇−푝푝 and (푇푇−퐻퐻)). - Sovereign spreads (in basis points) are defined exactly as: - 푠푠푙푙푝푝푣푣푡푡 = − 1/(푇푇−퐻퐻) ln�1 − 풫풫푙푙푝푝푣푣(푅푅,퐷퐷,퐻퐻,푇푇)퐷퐷푙푙푝푝푣푣푝푝,푇푇 e−푝푝(푇푇−푝푝)� × 10,000 - Rearranged expression for sovereign spread used to estimate implied sovereign asset value and asset volatility: - 푠푠푙푙푝푝푣푣푡푡 = − 1/(푇푇−푝푝) ln�1 − 풩풩(−푥푥−) − 퐴퐴�푠푠푠푠푠푠푡푡/퐷퐷푠푠푠푠푠푠푡푡,푇푇 e−푟푟(푇푇−푡푡) 풩풩(−푥푥+)� × 10,000 ### Sovereign asset composition (implied sovereign asset value) - Implied sovereign asset value is defined exactly as: - 푅푅푙푙푝푝푣푣푝푝 = 푅푅푝푝 + 푃푃푃푃푃푃푆푆푝푝 + 훼훼풫풫푏푏푣푣푎푎푏푏(푅푅,퐷퐷,퐻퐻,푇푇) + 푂푂퐻퐻ℎ푒푒푓푓 - Components explicitly listed: - (i) foreign currency reserves, 푅푅, - (ii) present value of the primary fiscal surplus (or net fiscal assets), 푃푃푃푃푃푃푆푆, - (iii) implicit and explicit contingent liabilities from the aggregate banking sector risk, 훼훼풫풫푏푏푣푣푎푎푏푏(푅푅,퐷퐷,퐻퐻,푇푇) where 훼훼 is the share of expected banking-sector losses borne by the sovereign, - (iv) remainder items labeled “Other” (public sector assets and unrealized liabilities). - The banking-sector contingent liabilities are analogously defined as a put option: - 풫풫푏푏푣푣푎푎푏푏(푅푅,퐷퐷,퐻퐻,푇푇) = 풩풩(−푥푥−)퐷퐷푏푏푣푣푎푎푏푏푝푝,푇푇 e−푝푝(푇푇−푝푝) − 풩풩(−푥푥+)푅푅̃푏푏푣푣푎푎푏푏푝푝 - “Other” is solved residually given observable reserves and primary fiscal balance; it includes pension and healthcare obligations, contingent support to non-bank financial institutions, guarantees, and backstop assets. ### Feedback mechanism between sovereign and bank spreads - Bank credit spread formulation (including sovereign spillover premium δ) is given exactly as: - 푠푠푏푏푣푣푎푎푏푏푡푡 = − 1/(푇푇−퐻퐻) ln�1 − (1 − 훼훼) 풫풫푏푏푣푣푎푎푏푏(푅푅,퐷퐷,퐻퐻,푇푇)퐷퐷푏푏푣푣푎푎푏푏푝푝,푇푇 e−푝푝(푇푇−푝푝) + 훿훿� × 10,000 - Channels through which higher sovereign spreads increase bank spreads: - (i) the value of the implicit bank put option for sovereign guarantees decreases (i.e., 훼훼 declines), - (ii) the value of the bank’s holdings of government debt decreases, - (iii) the bank default barrier may increase due to higher borrowing costs as the premium (훿훿) increases. - The model demonstrates a potential destabilization process via sovereign–bank spread interaction. ### Applications, estimation, and stress-testing implications - The term structure of sovereign credit spreads can be used to: - estimate implied sovereign asset value 푅푅̃푙푙푝푝푣푣푝푝 and asset volatility 휎휎퐴퐴푠푠푠푠푠푠, - calibrate a risk-adjusted market-implied sovereign risk measure when sovereign equity and equity volatility are unobservable. - The valuation approach enables sensitivity analysis and stress testing of sovereign default risk by varying reserves, primary fiscal balance, and the implicit banking-sector guarantee. - The contingent liabilities can be estimated using the Systemic CCA framework; this framework has been applied in macroprudential stress tests of banking sectors as part of IMF FSAPs for Germany, Hong Kong SAR, Spain, Sweden, the United Kingdom, and the United States. *Source: APPENDIX I, wpiea2019266-print-pdf — International Monetary Fund.* ### APPENDIX II. ESTIMATING VALUATION HAIRCUTS FOR SOVEREIGN RISK ### APPENDIX II. ESTIMATING VALUATION HAIRCUTS FOR SOVEREIGN RISK ### Methodology overview - Valuation haircuts are derived from the expected change in government bond prices consistent with estimated changes in market-implied sovereign default risk. - Haircuts vary by shock severity, maturity tenor, and macroeconomic scenario, and are modeled using forward-looking information from past changes in the cost of sovereign default risk protection (sovereign CDS). - For each country, select the most liquid fixed-rate local-currency-denominated government debt securities (“benchmark bonds”) with residual maturity up to 10 years and group bonds into maturity buckets of 푘 ∈ {1,3,5,7,10} years (with discretionary margin ±0.5 years). - Bond valuation changes under a scenario combine: - The default risk premium at different maturities (inferred from CDS spread dynamics); and - The applicable risk-free rate at the beginning of the estimation period. - When detailed bond-by-bond data are available, use the standard bond valuation (discounted coupon and principal) to compute bond values and valuation haircuts; alternatively approximate using average duration of a portfolio if individual bond data are not available. - Aggregate country haircuts are issuance-size weighted averages of individual bond haircuts; banks are assumed to hold sovereign portfolios similar to their supply when portfolio data are unavailable. ### Specification of the risk-free rate and conversion to zero-coupon equivalents - Observed coupon bond price P_b1,j[b],p conforms to a discounted cash flow pricing formula with yield-to-maturity f_b1,j[b],p observed at time H over remaining life T−H. - Convert coupon bond prices into zero-coupon equivalents (ZCE) P_b1,j[b],p_ZCE by stripping coupon payments and applying adjustment factor 휑_p to account for first- and second-order pricing effects of removed coupons (duration and convexity adjustments). - Zero-coupon bond pricing formula used: - P_b2,j[b],p = exp( − f_j[b],p × (1 − LLGD_j[b] × PD_j[b],T−p) ) - Cumulative PD used: PD_j[b],T−p = 1 − (1 − PD_j[b],p)^(T−p). - Use sovereign CDS to measure country-specific default risk and express ZCE as: - P_b1,j[b],p_ZCE = p × (1 + p_b1,j[k],t)^(T−t) + φ_p = exp( − f̂_p_j[k],t × (1 − LLGD_j[k] × PD_j[b],T−p) ) - Cash k-year sovereign CDS spread is s_ZCDC_j[k],t = −(1/(T−H)) ln(1 − PD_j[b],T−p) × LLGD_j[b] × 10,000 (basis points). - Solve for time-varying country-specific risk-free rate f̂_p_j[k],t from the ZCE expression after smoothing market-implied credit risk. Default risk used is min(last observable cash CDS spread s_ZCDC_j[k],t, 12-month average s̄_ZCDC_j[k],t). - Introduce market value adjustment for potential mismatch in data cut-off timing by decreasing the yield by ∆f_b2,j[b] = f_b2,j[b],p+τ − f_b2,j[b],p to reflect shortening residual maturity via a τ ∈ ]0,1[ year fraction. Generalized expression for f̂_p_j[k],t+τ provided (equation (4)) allowing τ≥0. ### Calculation of the credit risk premium under baseline conditions - Future zero-coupon price of bond b at time H+τ+i (over horizon T−H−τ−i) is: - P_b2,j[b],v = exp( − ( f̂_p_j[k],t+τ + ∆f̂_p_j[k],t + mvm_min(...) / 10,000 ) × (T−H−τ) ) (equation (5) structure retained) - The haircut is informed by P_b2,j[b],v − P_b2,j[b],p+τ relative to current valuation. - Implied default risk PD_j[b],v derived from continuous-time expression using the hazard rate PD_j[b],v × LLGD_j[b]; the k-year CDS spread at the ith period is defined as the greater of: - (i) the minimum of last observable cash CDS spread and the 12-month average cash CDS spread; and - (ii) the minimum of the last observable forward CDS spread and the 12-month average forward CDS spread (forward CDS interpreted as price effect of uncertainty around expected default risk). - Allow for a positive common shock to the risk-free rate ∆f̂_p_j[k],t > 0, maturity-specific to allow a parallel shift or slope change in the term structure. - Parallel computation applied to DCF pricing (coupon-bearing bonds) with pricing expression (equation (6)) and with θ_j[k],t defined to include ∆f̂_p_j[k],t, market value adjustment ∆f_b1,j[b] and the marginal increase of country-specific risk (equation (7)). ### Estimation of credit risk premium under adverse scenarios (EVT / GEV approach) - Adverse scenario specification derives changes in sovereign risk from historical dynamics of forward CDS spreads using extreme value theory (EVT) to model tail behavior. - Historical series of forward CDS spreads assumed to be in the domain of attraction of a generalized extreme value (GEV) distribution; fit GEV parametrically to forward CDS spread extremes to estimate limiting tail behavior. - Use density forecasts at high percentile levels (conditional tail expectation, CTE) as stressed country-specific risk components to replace the min(...) term in future pricing equations (5) and (6). - Notable numeric and calibration choices: - Test horizon maturities i ∈ I = {0.5,1,3,5,7,10} years are used for forward CDS matrix construction (example context provided). - The GEV shape parameter is calibrated uniformly to 휉 = 0.33 in the application generating results described in Appendix V. - Density forecast percentiles for adverse scenarios: 75th percentile (mild adverse, “adverse 1”) and 90th percentile (severe adverse, “adverse 2”). - EVT fitting details: - Define vector of forward CDS spreads f_ZCDC_j[k],i and construct sample maxima over z observations; normalize and fit GEV via scale (σ̂_j[..] > 0), location (μ̂_j[..] > 0), and shape (ξ̂_j[..]) parameters. - Use the linear combinations of ratios of spacings (LRS) method for moment estimation and maximum likelihood (ML) for parameter estimation (ML may fail for ξ ≤ −1). - Quantile function for GEV used to obtain percentile shocks: - L_p_CDC_j[k],i^−1(m) = μ̂_j[b],v + σ̂_j[k],i / ξ̂_j[k],i × ( − ln(m) )^(−ξ̂_j[k],i) − 1 (equation (10) representation preserved). - Compute CTE (conditional VaR) at confidence level a via the standard CTE definition (equation (9) structure retained). ### Scenario implementation and haircut construction - For each year i over the test horizon obtain vectors of bond prices under: - Baseline (market expectations via forward sovereign CDS spreads f_ZCDC_j[k],i), and - Two adverse density forecasts at statistical confidence levels m ∈ {0.75; 0.90} derived from historical forward CDS dynamics (GEV-based CTE). - Compute bond-level haircuts as percent change relative to base year t: - ∆Π_b1,j[b],v = ( Π_b1,j[b],v / P_b1,j[b],p_ZZ − 1 ) × 100 - ∆Π_b2,j[b],v = ( Π_b2,j[b],v / P_b2,j[b],p − 1 ) × 100 - (Π variables denote bond prices under each pricing method and scenario; formula forms preserved as presented.) - Aggregate to country haircut h_j as issuance-size-weighted average across q outstanding bonds: - h = max( ( Σ_b ∆Π_b1,j[b],v + Σ_b ∆Π_b2,j[b],v ) × Amp_b,j / Σ_b Amp_b,j , 0 ) - Haircuts set to zero when bond prices rise (e.g., safe-haven sovereigns). - Apply country haircuts to firms’ total exposures to country j across banking and trading books; sovereign bond losses/value changes in year v calculated as Σ_j (h_b1,j[b],v, h_b2,j[b],v) × exposure_e_v,j. ### Practical notes, limitations, and implementation choices - Use local-currency debt only because credit and interest rate assumptions refer to domestic currency yield curves. - When bond-by-bond data are available, a standard bond valuation formula (MS Excel “IMF Sovereign Risk Stress Testing Tool.xls”) can be used; when not available, approximate using average duration and volume-weighted sovereign yield changes. - Duration is a first-order approximation valid for small yield changes (less than 100 bps); convexity adjustments may be added for larger shocks. - The forward CDS spread matrix (for illustrative extraction via Bloomberg commands) and forward CDS interpretation are discussed; forward CDS reflects price effect of uncertainty around expected default risk. - The forward CDS-based estimates in outer years are biased downward due to simplifying assumptions in forward CDS term structure pricing. - The percentile choice for density forecasts should match the probabilistic severity of the macroeconomic scenario; due to higher frequency of CDS data, percentile levels for CDS-based shocks tend to be lower than those implied by low-frequency macro variables. - Calibration example: shape parameter uniformly set to 휉 = 0.33 in generating reported results; EVT estimation over rolling windows using LRS and ML methods (practical templates provided in data input Excel). *Source: APPENDIX II. ESTIMATING VALUATION HAIRCUTS FOR SOVEREIGN RISK (wpiea2019266-print-pdf)* ### APPENDIX III. MOMENTS OF THE GEV DISTRIBUTION AND ESTIMATION OF THE SHAPE ### APPENDIX III. MOMENTS OF THE GEV DISTRIBUTION AND ESTIMATION OF THE SHAPE PARAMETER USING THE LINEAR COMBINATION OF RATIOS OF SPACINGS (LRS) METHOD ### Estimator of the shape parameter (LRS) - The natural estimator of 휉̂ is derived by means of the Linear Combination of Ratios of Spacings (LRS) method using the linear combination - 휉̂ = (n/4)^{-1} ∑_{v=1}^{4} [ ln(υ̃_v) − ln(c) ] for n observations. - Definitions used in the LRS construction: - υ̃_v = m_n(1−a):n − m_n a c:n m_n a c:n − m_n a:n (as given in source notation) - c = [ ln(a(1−v)) / ln(a(v)) ] (for quantile m = i/n) - x_a:v:a = L^{-1}(m) - Approximation: υ̃_v ≈ [ L^{-1}(1−v) − L^{-1}(v c) ] / [ L^{-1}(v c) − L^{-1}(v) ] = c^{−1} + ξ̂ ### Moments of the GEV distribution (raw moments and conditions) - Simple statistics (expressions and existence conditions are given as follows): - Mean: me_n: - = μ + σ (l_1 − 1)/ξ if ξ ≠ 0, ξ < 1 - = μ + σ l_1 if ξ = 0 - = ∞ if ξ ≥ 1 - Variance: vmfmin_n:ce: - = σ^2 (l_2 − l_1^2)/ξ^2 if ξ ≠ 0, ξ < 1/2 - = σ^2 π^2 / 6 if ξ = 0 - = ∞ if ξ ≥ 1/2 - Skewness: sske_sne_sss: - = [ −(l_3 − 3 l_1 l_2 + 2 l_1^3) / (l_2 − l_1^2)^{3/2} ] if 0 < ξ < 1/3 - = [ (l_3 − 3 l_1 l_2 + 2 l_1^3) / (l_2 − l_1^2)^{3/2} ] if ξ < 0 - = ∞ if ξ = 0 - = 12 √6 ζ(3)/π^3 if ξ ≥ 1/3 - Kurtosis: kssfHfssis: - = [ (l_4 − 4 l_1 l_3 − 3 l_2^2 + 12 l_2 l_1^2 − 6 l_1^4) / (l_2 − l_1^2)^2 ] if ξ ≠ 0, ξ < 1/4 - = ∞ if ξ = 0 - = 12^5 if ξ ≥ 1/4 - Notation and special functions appearing in moment expressions: - l_p are constants arising from the GEV moments expressions (as in source notation). - g_p = Γ(1 − p ξ) for p ∈ [1, ...,4] - Euler’s constant σ (Sondow 1998) - Riemann zeta function ζ(⋅) (Borwein, Bradley, and Crandall 2000) - Γ(⋅) denotes the gamma probability density/function. ### Practical implications for estimation and inference - Existence of moments depends critically on the value of the shape parameter ξ: - Mean finite only if ξ < 1. - Variance finite only if ξ < 1/2. - Skewness finite only if ξ < 1/3 (with special-case formulas for ξ ≤ 0 and ξ = 0). - Kurtosis finite only if ξ < 1/4 (with special-case behavior noted for ξ = 0 and ξ ≥ 1/4). - The LRS estimator provides a way to estimate ξ̂ via linear combinations of log-ratio spacings and approximations involving inverse GEV transforms L^{-1}(·). *Source: APPENDIX III. MOMENTS OF THE GEV DISTRIBUTION AND ESTIMATION OF THE SHAPE PARAMETER USING THE LINEAR COMBINATION OF RATIOS OF SPACINGS (LRS) METHOD (from supplied PDF content)* --- _Source: https://www.imf.org/-/media/files/publications/wp/2019/wpiea2019266-print-pdf.pdf_