## pp032317state-contingent-debt-instruments-for-sovereigns-annexes

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---

### Annex I.A — Expanding Fiscal Space through Debt Management
- Core proposition:
  - Debt management policies can expand fiscal space for a given path of primary fiscal balances by reducing default risk through greater stability of the debt ratio.
  - Two policies examined: issuance of GDP-linked bonds (GLBs) and issuance of longer-maturity debt.

- Mechanisms:
  - Growth uncertainty raises stochastic variation in the debt ratio, increasing average interest rates because of convexity between default risk and debt ratio, which reduces the debt limit.
  - Fiscal fatigue: as debt rises, the primary balance response weakens and cannot indefinitely offset rising debt service, implying a finite debt limit and a notion of fiscal space (difference between current debt and debt limit).
  - GLBs link debt payments to issuing country growth, reducing debt service in bad times and increasing it in good times, stabilizing the debt ratio and lowering default risk.
  - Longer-maturity debt spreads debt service over time; market pricing tilts toward upside growth surprises, stabilizing bond prices and the debt ratio and conferring risk-sharing benefits.

- Quantitative potential:
  - Simulation results suggest substantial gains in fiscal space on the order of 20–70 percent of GDP are plausible from managing debt along maturity and state-contingency dimensions.

### Annex I.A — Numerical Illustration: GDP-linked Bonds
- Model setup and calibration:
  - Representative advanced economy using historical data per Ostry and others (2010).
  - Growth distribution from histograms for a sample of 23 advanced economies over 1980–2020 (projected data for 2016 onward from the IMF’s WEO).
  - Two uncertainty parametrizations with the same mean μ but different standard deviations σ:
    - low uncertainty (μ = 2.4 percent, σ = 1.4 percent)
    - high uncertainty (μ = 2.4 percent, σ = 2.5 percent)

- Simulation findings:
  - If debt is issued in GLBs, fiscal space can be increased by 15–25 percent of GDP under low growth uncertainty.
  - If uncertainty is high, fiscal space can be increased by some 30–60 percent of GDP (range reflects assumptions about cyclical fiscal response).
  - Partial adoption nonlinearities: increasing GLB share from 0 to 25 percent accounts for about 40 percent of the total gain from full replacement of nominal debt by GLBs.

### Annex I.A — Numerical Illustration: Longer-maturity Debt
- Model assumptions:
  - Long-duration bond with infinite maturity used in modeling; primary balance constant as share of GDP; growth outcomes follow truncated normal distribution.
  - Focus on lower bound of the debt limit.

- Simulation findings:
  - Fiscal space increases by 15–40 percent of GDP when duration increases from one year to 10 years.
  - If duration increases to 20 years, gains in fiscal space are on the order of 50–70 percent of GDP.

### Annex I.B — Debt Limits Model by Country Groups (Model Structure)
- Purpose:
  - Structural sovereign default model calibrated on country-group data, incorporating shocks to growth, exchange rates, primary balance; sovereign defaults if debt breaches endogenously determined debt limit.

- Core equations (preserved structure and notation):
  - ∆d_t = (r_t − g_t) / (1+g_t) . d_t − pb_t      (equation 1)
  - pb_t = min(α + β . d_t, γ) + ε_t^pb            (equation 2)
  - (1 + r_t) = (1 + r^*) . (1 − p_{t+1} . θ) / (1 − p_{t+1})      (equation 3)
  - ∆d_t = ( (1 + r^*) . (1 − p_{t+1} . θ) / (1 − p_{t+1}) − 1 − g^* + ε_t^g ) . d_t / (1 + g^* + ε_t^g) + d_t . F_t . (1 + ε_t^{er}) − ( min(α + β . d_t, γ) + ε_t^{pb} )      (equation 4)
  - p_{t+1} = Pr( d_{t+1} > d̄ )      (equation 5)
  - Debt limit d̄ defined as highest level sustainable at finite interest rates while satisfying fiscal constraint and equilibrium (numerically the highest debt with default probability below 1 and solvency inequality satisfied).

- Endogenous interaction:
  - Credit spread and debt limit interdependent: a lower debt limit raises default likelihood and spreads, worsening debt dynamics and lowering the debt limit further.

- Parameters with directional impact on debt limit:
  - steady-state real growth g*
  - default recovery rate θ
  - maximum primary balance γ
  - risk-free rate r*
  - share of foreign currency debt F_t
  - standard deviations std(ε_t^{pb}, ε_t^g, ε_t^{er})
  - growth and exchange rate premia r_gdp, r_er

- Instruments considered:
  - local currency bonds (insulating against exchange rate shocks)
  - GDP-linked bonds (insulating against GDP shocks)
  - Both instrument types bear a creditor premium; premium and insulation effect act in opposite directions on debt limit.

### Annex I.B — Calibration Inputs and Stylized Facts
- Representative country groups: All Countries (ACs), Advanced Economies (AEs), Emerging Markets (EMs), Low-Income Countries (LICs).
- Calibration inputs:
  - γ: 90th percentile of cyclically adjusted primary balances from consolidation episodes in Escolano et al. (2014).
  - Shocks ε_t^g, ε_t^{pb}, ε_t^{er}: IMF WEO data, demeaned, applied via bootstrap preserving contemporaneous correlations.
  - g*: WEO long-run growth (1960–2015) by country group.
  - F_t: group averages from WEO.
  - θ: assumed 80 percent if default occurs.

- Stylized facts (preserved numeric table entries):
  - Steady state real growth (percent): All countries 3.36, Advanced economies 2.9, Emerging markets 5.0, Low income countries 5.0.
  - Maximum primary balance (percent of GDP): All countries 6.0, Advanced economies 7.0, Emerging markets 5.5, Low income countries 4.0.
  - Share of foreign currency debt (percent): All countries 54.1, Advanced economies 3.0, Emerging markets 50.4, Low income countries 70.4.
  - StDev - real growth shock (percentage points): All countries 3.8, Advanced economies 2.3, Emerging markets 4.3, Low income countries 4.2.
  - StDev - primary balance shock (percentage points of GDP): All countries 1.0, Advanced economies n/a, Emerging markets 3.9, Low income countries 4.6.
  - StDev - exchange rate shock (percentage points): All countries 0.3, Advanced economies n/a, Emerging markets 0.9, Low income countries 0.2.
  - Exchange rate volatility risk premium (percentage points): All countries 2.3, Advanced economies n/a, Emerging markets 1.9, Low income countries 2.3.
  - Real GDP volatility risk premium (percentage points): All countries 2.0, Advanced economies 1.5, Emerging markets 2.1, Low income countries 2.0.

- Risk premia methodology:
  - Certainty-equivalent framework with CRRA utility U(c) = c^{1-δ}/(1−δ), δ = 2.
  - For each shock outturn, investor utility compared to guaranteed return; premium equates utilities.

### Annex I.B — Baseline Debt Limits and Instrument Scenarios (preserved numeric outcomes)
- Baseline debt limit (percent of GDP):
  - All countries: 52
  - Advanced economies: 137
  - Emerging markets: 58
  - Low income countries: 40

- Debt limit — 100% local currency (percent of GDP):
  - All countries: 78
  - Advanced economies: 137
  - Emerging markets: 98
  - Low income countries: 54

- Debt limit — 100% local currency; 20% GDP linked (percent of GDP):
  - All countries: 80
  - Advanced economies: 152
  - Emerging markets: 106
  - Low income countries: 54

- Debt limit — 100% local currency; 50% GDP linked (percent of GDP):
  - All countries: 84
  - Advanced economies: 175
  - Emerging markets: 120
  - Low income countries: 52

- Debt limit — 100% local currency; 100% GDP linked (percent of GDP):
  - All countries: 84
  - Advanced economies: 238
  - Emerging markets: 140
  - Low income countries: 50

### Annex I.B — Interpretation and Policy-relevant Findings
- Local currency shift:
  - Moving to full local currency debt raises debt limits across groups (AEs assumed already at full local currency).
  - EMs: debt limit increases by 40 percentage points (70 percent increase relative to baseline), indicating exchange rate shocks significantly threaten EM solvency.
  - LICs: fiscal space increases by 14 percentage points of GDP; less impact than EMs because growth and primary balance shocks remain important.

- GDP-linked bonds impact:
  - Modest issuance (20 percent of debt) materially raises debt limits:
    - AEs: rise by around 15 percentage points of GDP (sufficient to accommodate median fiscal costs of a systemic banking crisis).
    - EMs: increase fiscal space by 8 percentage points of GDP.
    - LICs: no change relative to 100% local currency scenario — higher GDP-volatility premium offsets lower GDP shock benefits.
  - Higher shares of GDP-linking continue to raise debt limits for AEs (maximized at 100% GDP-linked).
  - For EMs and LICs, marginal benefits can be diminishing or negative; LICs may see a modest decrease when moving to full GDP-linking.

- Marginal properties:
  - Aggregate (all economies) relationship between share of GDP-linked bonds and debt level appears quadratic; maximum debt limit at 80 percent GDP-linked.
  - Sovereigns may opt for lower shares for cost-benefit or risk-tolerance reasons; optimal welfare level not determined.

### Annex I.B — Sensitivity Analysis on Risk Premia (preserved numeric highlights)
- Exchange rate volatility risk premium sensitivity (relative to baseline debt level):
  - All countries: risk premium 2.1 percent; debt limit with 100% local currency 78 percent of GDP; risk premium range 0.1-4.1 percent; debt limit range 100-64 percent of GDP; 'Break-even' risk premium 5.5 percent.
  - Emerging markets: risk premium 1.9 percent; debt limit 98 percent of GDP; risk premium range 0.0-3.9 percent; debt limit range 138-78 percent of GDP; 'Break-even' risk premium 6.0 percent.
  - Low income countries: risk premium 3.0 percent; debt limit 54 percent of GDP; risk premium range 1.0-5.0 percent; debt limit range 82-42 percent of GDP; 'Break-even' risk premium 5.1 percent.

- GDP volatility risk premium sensitivity (relative to baseline debt level):
  - All countries: risk premium 2.0 percent; 100% GDP linked = 84 percent of GDP; risk premium range 0.0-4.0 percent; debt limit range 200-54 percent of GDP; 'Break-even' risk premium 4.0 percent.
  - Advanced economies: risk premium 2.2 percent; debt limit 238 percent of GDP; risk premium range 0.2-4.2 percent; debt limit range 280-108 percent of GDP; 'Break-even' risk premium 3.5 percent.
  - Emerging markets: risk premium 2.0 percent; debt limit 140 percent of GDP; risk premium range 0.0-4.0 percent; debt limit range 200-62 percent of GDP; 'Break-even' risk premium 4.2 percent.
  - Low income countries: risk premium 2.0 percent; debt limit 50 percent of GDP; risk premium range 0.0-4.0 percent; debt limit range 134-34 percent of GDP; 'Break-even' risk premium 3.0 percent.

- Key sensitivity insight:
  - Small changes (±2 percentage points) in risk premia produce large changes in debt limits (example: a 4 percentage point difference in GDP risk premium for AEs implies a 170 percentage point difference in the debt limit). Break-even risk premia reported are higher than most literature estimates.

### Annex I.B — Conclusions and Policy Implications
- The extended debt-limits framework with shocks and country differentiation offers a granular tool to explore debt contract design impacts on sovereign sustainability and issuance.
- No one-size-fits-all debt structure:
  - LICs: priority on reducing exchange rate risk via local currency issuance and building institutions to raise maximum sustainable primary balance.
  - EMs: after reducing exchange rate risk, GDP-linked bonds provide clear benefits.
  - AEs: largest benefits — debt limits nearly double if all bonds are GDP-linked.
- Marginal benefits of GDP-linked issuance decline as share rises; aggregate maximum at 80 percent GDP-linked but sovereigns may prefer lower shares.
- Results sensitive to parameter assumptions, especially risk premia; further research and market evidence important. Benefits in terms of higher debt limits are robust across a reasonable range of GDP-linked bond risk premia.

_*) STATE-CONTINGENT DEBT INSTRUMENTS FOR SOVEREIGNS—ANNEXES, INTERNATIONAL MONETARY FUND_

### Annex I. Potential Benefits from SCDIs: Analytics and Numerical

### Annex I. Potential Benefits from SCDIs: Analytics and Numerical Simulations

### A. Expanding Fiscal Space through Debt Management

- Core proposition:
  - Debt management policies can expand fiscal space for a given path of primary fiscal balances by reducing default risk through greater stability of the debt ratio.
  - Two policies examined: issuance of GDP-linked bonds (GLBs) and issuance of longer-maturity debt.

- Mechanism linking growth uncertainty to fiscal space:
  - Growth uncertainty raises stochastic variation in the debt ratio, increasing average interest rates because of convexity between default risk and debt ratio, which reduces the debt limit.
  - Fiscal fatigue: as debt rises, the primary balance response weakens and cannot indefinitely offset rising debt service, implying a finite debt limit and a notion of fiscal space (difference between current debt and debt limit).

- How GDP-linked bonds (GLBs) work:
  - GLBs link debt payments to the issuing country’s growth rate, providing reduced debt service in bad times and increased debt service in good times, keeping lender expected profit unchanged.
  - This state-contingent feature stabilizes the debt ratio by enabling risk sharing between sovereign and private investors, lowering default risk and raising the debt limit.
  - If the entire debt is issued in GLBs, debt dynamics may be fully insulated against growth uncertainty; fiscal space under growth uncertainty with GLBs can be identical to that with nominal debt absent growth uncertainty.

- How longer-maturity debt works:
  - Longer maturity spreads debt service over time, making debt service less sensitive to growth shocks.
  - Market pricing of long-maturity debt reflects expected future prices; upside growth surprises matter more than censored downside recovery values, which stabilizes bond prices and the debt ratio.
  - Pricing of longer-maturity debt confers a risk-sharing benefit that reduces default premia and raises the debt limit.

- Quantitative summary of potential magnitude:
  - Simulation results suggest substantial gains in fiscal space on the order of 20-70 percent of GDP are plausible from managing debt along these two dimensions.

### Numerical Illustration — GDP-linked Bonds

- Model setup and calibration:
  - Representative advanced economy parameterized using historical data for advanced economies per Ostry and others (2010).
  - Distribution of real GDP growth constructed from histograms for a sample of 23 advanced economies over 1980–2020 (projected data for 2016 onward from the IMF’s WEO).
  - Two uncertainty parametrizations with the same mean μ but different standard deviations σ:
    - low uncertainty (μ = 2.4 percent, σ = 1.4 percent)
    - high uncertainty (μ = 2.4 percent, σ = 2.5 percent)

- Simulation findings for GLBs:
  - If debt is issued in GLBs, fiscal space can be increased by 15–25 percent of GDP under low growth uncertainty.
  - If uncertainty is high, fiscal space can be increased by some 30–60 percent of GDP (the range reflects, inter alia, assumptions about the cyclical response of fiscal policy to output gap).
  - Partial adoption: initial gains are nonlinear—e.g., increasing the share of GLBs from 0 to 25 percent accounts for about 40 percent of the total gain from full replacement of nominal debt by GLBs.

### Numerical Illustration — Longer-maturity Debt

- Model assumptions:
  - Debt issued as a long-duration bond with infinite maturity (for the modeling exercise), primary balance constant as a share of GDP, growth outcomes follow a truncated normal distribution.
  - Simulation focuses on a lower bound of the debt limit.

- Simulation findings for maturity extension:
  - Fiscal space increases by 15–40 percent of GDP when duration increases from one year to 10 years.
  - If duration increases to 20 years, gains in fiscal space are on the order of 50–70 percent of GDP.

### B. Debt Limits Model by Country Groups

#### The Debt Limits Model: An Extension

- Purpose:
  - Structural model of sovereign default calibrated on data from country groups with differing fundamentals, incorporating shocks to growth, exchange rates, and the primary balance.
  - The sovereign defaults if debt breaches an endogenously determined debt limit.

- Core debt accumulation equation (all debt has one-year maturity in base model):
  - ∆d_t = (r_t − g_t) / (1+g_t) . d_t − pb_t      (equation 1)
    - where d_t is debt/GDP; r_t is real interest rate on debt; g_t is real GDP growth; pb_t is primary balance/GDP.

- Fiscal reaction function (primary balance response with a maximum):
  - pb_t = min(α + β . d_t, γ) + ε_t^pb      (equation 2)
    - primary balance is the minimum of (i) α + β·d_t and (ii) γ, plus shock ε_t^pb.

- Return on sovereign bond:
  - (1 + r_t) = (1 + r^*) . (1 − p_{t+1} . θ) / (1 − p_{t+1})      (equation 3)
    - p_{t+1} is next-period default probability; r^* is risk-free rate; θ is recovery value on default.

- Debt dynamics including growth and exchange rate shocks and foreign currency share F_t:
  - ∆d_t = ( (1 + r^*) . (1 − p_{t+1} . θ) / (1 − p_{t+1}) − 1 − g^* + ε_t^g ) . d_t / (1 + g^* + ε_t^g) + d_t . F_t . (1 + ε_t^{er}) − ( min(α + β . d_t, γ) + ε_t^{pb} )      (equation 4)

- Default probability and debt limit:
  - p_{t+1} = Pr( d_{t+1} > d̄ )      (equation 5)
  - Debt limit d̄ is defined as the highest level of debt that can be sustained at finite interest rates while satisfying fiscal constraint and interest rate equilibrium.
  - Numerical solution finds the highest debt level where default probability is below 1 and satisfies the inequality (expressed in equation 6 in the source), i.e., the probability that next-period debt dynamics yield nonnegative solvency condition is less than certain default.

- Endogenous interaction:
  - Credit spread and debt limit are interdependent: a lower debt limit raises default likelihood and spreads, which worsens debt dynamics and lowers the debt limit further.

#### Parameters and their directional impact on the debt limit (as identified in the model)

- Parameters affecting the debt limit (directional relationships are unambiguous though non-linear):
  - steady-state real growth g*
  - default recovery rate θ
  - maximum primary balance γ
  - risk-free rate r*
  - share of foreign currency debt F_t
  - standard deviations of shocks std(ε_t^{pb}, ε_t^g, ε_t^{er})
  - growth and exchange rate premia r_gdp, r_er

- Instruments considered to alter debt limit:
  - local currency bonds (insulating against exchange rate shocks)
  - GDP-linked bonds (insulating against GDP shocks)
  - Both instrument types have a price in the form of a premium required by creditors; the premium and the insulation effect act in opposite directions on the debt limit.

*Source: Annex I. Potential Benefits from SCDIs: Analytics and Numerical Simulations*

### 21.      In the case of GDP-linked bonds, the size of the GDP shock declines as the share of these

### pp032317state-contingent-debt-instruments-for-sovereigns-annexes - 21.

### Mechanics of GDP-linked bonds and local currency protection
- If interest rate and primary balance are zero, conventional bond debt-to-GDP follows: D_{t+1}/GDP_{t+1} = D_t/GDP_t .(1+g_{t+1}) — the debt-to-GDP ratio follows a random walk driven by past growth shocks.
- If debt level is linked to the level of GDP (U.K. CPI-linked bond design), a GDP shock affects numerator and denominator equally, so debt-to-GDP remains constant: D_{t+1}^{gdp}/GDP_{t+1} = D_t^{gdp}/GDP_t .(1+g_{t+1})/(1+g_{t+1}) = D_t^{gdp}/GDP_t — GDP shocks are eliminated.
- Local currency debt protection is modelled by adjusting the share of foreign currency debt F_t in equations 4 and 6, changing exposure to exchange rate shocks.
- Creditor premiums for exchange rate and GDP volatility (r_{er} and r_{gdp}) are assumed invariant through time and unrelated to debt level; they are added to the risk-free rate (r*) in equations 4 and 6.

### Model calibration and parameter choices
- Representative country groups: All Countries (ACs), Advanced Economies (AEs), Emerging Markets (EMs), Low-Income Countries (LICs).
- Calibration inputs:
  - Maximum primary balance (γ): 90th percentile of cyclically adjusted primary balances from fiscal consolidation episodes in Escolano et al. (2014).
  - Shocks to real GDP growth (ε_t^g), primary balance (ε_t^{pb}), nominal exchange rate (ε_t^{er}): data from IMF WEO, demeaned, applied via bootstrap simulations preserving contemporaneous correlations (Table AI.1).
  - Steady-state growth rate (g*): WEO long-run growth (1960–2015) by country group.
  - Share of foreign currency debt (F_t): group averages from WEO.
  - Default recovery rate (θ): assumed 80 percent if a default occurs.
- Stylized facts from calibration (Table AI.2):
  - Steady state real growth (percent): All countries 3.36, Advanced economies 2.9, Emerging markets 5.0, Low income countries 5.0.
  - Maximum primary balance (percent of GDP): All countries 6.0, Advanced economies 7.0, Emerging markets 5.5, Low income countries 4.0.
  - Share of foreign currency debt (percent): All countries 54.1, Advanced economies 3.0, Emerging markets 50.4, Low income countries 70.4.
  - StDev - real growth shock (percentage points): All countries 3.8, Advanced economies 2.3, Emerging markets 4.3, Low income countries 4.2.
  - StDev - primary balance shock (percentage points of GDP): All countries 1.0, Advanced economies n/a, Emerging markets 3.9, Low income countries 4.6.
  - StDev - exchange rate shock (percentage points): All countries 0.3, Advanced economies n/a, Emerging markets 0.9, Low income countries 0.2.
  - Exchange rate volatility risk premium (percentage points): All countries 2.3, Advanced economies n/a, Emerging markets 1.9, Low income countries 2.3.
  - Real GDP volatility risk premium (percentage points): All countries 2.0, Advanced economies 1.5, Emerging markets 2.1, Low income countries 2.0.
- Risk premia methodology:
  - Certainty-equivalent framework with CRRA utility U(c) = c^{1-δ}/(1−δ), δ = 2.
  - For each shock outturn, investor utility is compared to guaranteed return; the premium equates utility between risky and safe bond.

### Results — baseline debt limits and instrument scenarios (Table AI.3)
- Baseline debt limit (percent of GDP) by country group:
  - All countries: 52
  - Advanced economies: 137
  - Emerging markets: 58
  - Low income countries: 40
- Debt limit — 100% local currency (percent of GDP):
  - All countries: 78
  - Advanced economies: 137
  - Emerging markets: 98
  - Low income countries: 54
- Debt limit — 100% local currency; 20% GDP linked (percent of GDP):
  - All countries: 80
  - Advanced economies: 152
  - Emerging markets: 106
  - Low income countries: 54
- Debt limit — 100% local currency; 50% GDP linked (percent of GDP):
  - All countries: 84
  - Advanced economies: 175
  - Emerging markets: 120
  - Low income countries: 52
- Debt limit — 100% local currency; 100% GDP linked (percent of GDP):
  - All countries: 84
  - Advanced economies: 238
  - Emerging markets: 140
  - Low income countries: 50

### Interpretation of results and policy-relevant findings
- Moving to full local currency debt raises debt limits across groups (AEs assumed already at full local currency).
  - EMs: debt limit increases by 40 percentage points (70 percent increase relative to baseline), indicating exchange rate shocks significantly threaten EM solvency.
  - LICs: fiscal space increases by 14 percentage points of GDP, less impact than EMs because growth and primary balance shocks remain important.
- GDP-linked bonds impact:
  - Modest issuance (20 percent of debt) materially raises debt limits:
    - AEs: rise by around 15 percentage points of GDP (sufficient to accommodate median fiscal costs of a systemic banking crisis).
    - EMs: increase fiscal space by 8 percentage points of GDP.
    - LICs: no change relative to 100% local currency scenario — higher GDP-volatility premium offsets lower GDP shock benefits.
  - Higher shares of GDP-linking continue to raise debt limits for AEs (maximized at 100% GDP-linked).
  - For EMs and LICs, marginal benefits can be diminishing or negative; LICs may see a modest decrease when moving to full GDP-linking.
- Marginal properties:
  - Aggregate (all economies) relationship between share of GDP-linked bonds and debt level appears quadratic; maximum debt limit at 80 percent GDP-linked.
  - Sovereigns may opt for lower shares for cost-benefit or risk-tolerance reasons; optimal welfare level not determined here.

### Sensitivity analysis on risk premia (Tables AI.4 and AI.5)
- Exchange rate volatility risk premium sensitivity (Table AI.4, relative to baseline debt level):
  - All countries: risk premium 2.1 percent; debt limit with 100% local currency 78 percent of GDP; risk premium range 0.1-4.1 percent; debt limit range 100-64 percent of GDP; 'Break-even' risk premium 5.5 percent.
  - Emerging markets: risk premium 1.9 percent; debt limit 98 percent of GDP; risk premium range 0.0-3.9 percent; debt limit range 138-78 percent of GDP; 'Break-even' risk premium 6.0 percent.
  - Low income countries: risk premium 3.0 percent; debt limit 54 percent of GDP; risk premium range 1.0-5.0 percent; debt limit range 82-42 percent of GDP; 'Break-even' risk premium 5.1 percent.
- GDP volatility risk premium sensitivity (Table AI.5, relative to baseline debt level):
  - All countries: risk premium 2.0 percent; debt limit with 100% local currency; 100% GDP linked = 84 percent of GDP; risk premium range 0.0-4.0 percent; debt limit range 200-54 percent of GDP; 'Break-even' risk premium 4.0 percent.
  - Advanced economies: risk premium 2.2 percent; debt limit 238 percent of GDP; risk premium range 0.2-4.2 percent; debt limit range 280-108 percent of GDP; 'Break-even' risk premium 3.5 percent.
  - Emerging markets: risk premium 2.0 percent; debt limit 140 percent of GDP; risk premium range 0.0-4.0 percent; debt limit range 200-62 percent of GDP; 'Break-even' risk premium 4.2 percent.
  - Low income countries: risk premium 2.0 percent; debt limit 50 percent of GDP; risk premium range 0.0-4.0 percent; debt limit range 134-34 percent of GDP; 'Break-even' risk premium 3.0 percent.
- Key sensitivity insight: small changes (±2 percentage points) in risk premia produce large changes in debt limits (example: a 4 percentage point difference in GDP risk premium for AEs implies a 170 percentage point difference in the debt limit). Break-even risk premia reported are higher than most literature estimates.

### Conclusions and policy implications
- The extended debt-limits framework incorporating additional shocks and country differentiation offers a granular tool to explore debt contract design impacts on sovereign sustainability and potential sovereign issuance.
- No one-size-fits-all debt structure:
  - LICs: priority on reducing exchange rate risk via local currency issuance and building institutions to raise maximum sustainable primary balance.
  - EMs: after reducing exchange rate risk, GDP-linked bonds provide clear benefits.
  - AEs: largest benefits — debt limits nearly double if all bonds are GDP-linked.
- Marginal benefits of GDP-linked issuance decline as share rises; aggregate maximum at 80 percent GDP-linked but sovereigns may prefer lower shares.
- Results are sensitive to parameter assumptions, especially risk premia for local currency and GDP-linked bonds; further research and market evidence are important. Benefits in terms of higher debt limits are robust across a reasonable range of GDP-linked bond risk premia.

*STATE-CONTINGENT DEBT INSTRUMENTS FOR SOVEREIGNS—ANNEXES, INTERNATIONAL MONETARY FUND*

### Annex II. Conditions for Mutually Beneficial Exchange in SCDIs

### Annex II. Conditions for Mutually Beneficial Exchange in SCDIs

### A. Sovereign Issuer’s Problem
- Objective: Maximize expected utility Max{E[U(c_g)] by choosing government expenditure c_g (percent of GDP), subject to the budget constraint and a binding debt limit.
- Budget constraint and debt limit:
  - B1 = ∑[(1+r_i)/(1+g) b_i,0] + c_g − t     (1)
  - B1 = B0                                     (2)
  - B0 = ∑ b_i,0                                 (3)
- Government expenditure implied by constraints:
  - c_g = t − ∑[( (1+r_i)/(1+g) − 1 ) b_i,0 ]_{i≠j} − ( (1+r_j)/(1+g) − 1 )( B0 − ∑ b_i,0_{i≠j} )     (4)
- First-order condition for choosing b_i,0 yields equality of adjusted expected returns weighted by marginal utility and covariances; rearranged result:
  - E{(1+r_j)/(1+g)} − E{(1+r_i)/(1+g)} = [Cov{U′(c_g), (1+r_i)/(1+g)} − Cov{U′(c_g), (1+r_j)/(1+g)}] / E{U′(c_g)}     (5)
- With quadratic utility U(c_g) = α1 c_g − β1 c_g^2 and U′(c_g) = α1 − 2β1 c_g (6), and approximation E{(1+r)/(1+g)} ≅ E{r}, the issuer’s maximum willing premium on bond j over i becomes:
  - E{r_j} − E{r_i} = 2β1 { Cov{c_g, (1+r_j)/(1+g)} − Cov{c_g, (1+r_i)/(1+g)} } / ( α1 − 2β1 E{c_g} )     (7)
- Determinants of issuer willingness to pay a premium for bond j:
  - Higher covariance between government expenditure c_g and bond j’s growth-adjusted return increases the premium.
  - Greater sovereign risk aversion (higher β1) raises the premium for a given covariance difference.
- Expanded expression for Cov{c_g, (1+r_j)/(1+g)}:
  - Cov{c_g, (1+r_j)/(1+g)} = Cov{t, (1+r_j)/(1+g)} − ∑_{i≠j} b_i · Cov{ (1+r_i)/(1+g), (1+r_j)/(1+g) } − b_j · Var{ (1+r_j)/(1+g) }     (8)
- Implication: The sovereign is more willing to pay a premium for bond j when:
  - Covariance of return j with the tax ratio is higher;
  - Covariance between return j and returns of other bonds is lower;
  - Variance of the growth-adjusted return on bond j is lower.
- Special case: For a GDP-linked bond “a la Bank of England,” growth-adjusted real return would be constant and the covariance term would be zero.

### B. Investor’s Problem
- Objective: Investor maximizes expected utility Max{E[U(c_I)]} subject to wealth dynamics and a non-declining wealth floor.
- Budget and wealth constraints:
  - W1 = (1+r_w) b_w,0 + ∑(1+r_i) b_i,0 + y − c_I     (9)
  - W0 = b_w,0 + ∑ b_i,0                              (10)
  - W1 ≥ W0 = W                                      (11)
- Consumption implied:
  - c_I = (1+r_w)( W − ∑ b_i,0 ) + ∑(1+r_i) b_i,0 + y − W     (12)
- First-order conditions (for choices of b_i,0) imply equalities of expected returns weighted by marginal utility:
  - E{U′(c_I) · r_i} = E{U′(c_I) · r_w}     (13)
  - E{U′(c_I) · r_j} = E{U′(c_I) · r_w}     (14)
- Solving for minimum premium investor requires for bond j over i:
  - E{r_j} − E{r_i} = [ Cov{U′(c_I), r_i} − Cov{U′(c_I), r_j} ] / E{U′(c_I)}     (15)
- With quadratic utility U(c_I) = α2 c_I − β2 c_I^2 and U′(c_I) = α2 − 2β2 c_I (16), this yields:
  - E{r_j} − E{r_i} = 2β2 ( Cov{c_I, r_j} − Cov{c_I, r_i} ) / ( α2 − 2β2 E{c_I} )     (17)
- Expanded covariance between investor consumption and return on bond j:
  - Cov{c_I, r_j} = Cov{y, r_j} + b_w · Cov{r_w, r_j} + ∑_{i≠j} [ b_i · Cov{r_i, r_j} ] + b_j · Var{r_j}     (18)
- Implications for investor required risk premium:
  - Minimum premium is lower when bond j has low covariance with the investor’s income and assets (y, r_w, other r_i) and low variance Var{r_j}.
  - If b_w is negative (investor has liabilities), a higher covariance between r_j and the liability return r_w lowers the covariance term and thus the required premium.
  - Greater investor risk aversion (higher β2) raises the required premium for a given covariance difference.

### C. Conditions for a market in GDP-linked bonds (mutually beneficial exchange)
- Issuer’s ceiling and investor’s floor for premium, allowing differing expectations E_g and E_I:
  - Issuer (7’) : E_g{r_j} − E_g{r_i} ≤ 2β1 { Cov{c_g, (1+r_j)/(1+g)} − Cov{c_g, (1+r_i)/(1+g)} } / ( α1 − 2β1 E_g{c_g} )
  - Investor (17’): E_I{r_j} − E_I{r_i} ≥ 2β2 ( Cov{c_I, r_j} − Cov{c_I, r_i} ) / ( α2 − 2β2 E_I{c_I} )
- Interpretation of expectations:
  - Divergent expectations about r_j (often due to differing views on the underlying state variable) affect feasibility: lower E_g{r_j} and higher E_I{r_j} increase the chance both conditions hold.
- Conditions that increase likelihood of mutually beneficial exchange (synthesis from (7’), (17’), (8), and (18)):
  - Diversification scope for both sovereign and investor:
    - For investor: SCDI is beneficial if real return on SCDI has (i) high correlation with investor’s liabilities; and/or (ii) low correlation with investor’s assets (and income); and (iii) low variance (relevant if SCDI is a significant share of the portfolio).
    - For sovereign: SCDI is beneficial if (growth-adjusted) real return on the bond has (i) low correlation with returns of other sovereign debt instruments; (ii) high correlation with the sovereign’s tax revenues; and (iii) low variance (low variance in growth-adjusted return implies a high correlation between the real rate on the SCDI and real GDP growth).
  - Divergent expectations about expected return of the SCDI:
    - If the sovereign expects lower average payouts on the SCDI than investors expect (e.g., because the state variable will perform worse), the sovereign will be willing to offer more generous bond characteristics, facilitating trade.
  - Differential tolerance of risk:
    - If investors are less risk averse than the sovereign (β2 low and β1 high), investors may accept risk transfers at prices acceptable to the sovereign.
- If issuer and investor expectations coincide, the mutually beneficial condition reduces to:
  - 2β2 ( Cov{c_I, r_j} − Cov{c_I, r_i} ) / ( α2 − 2β2 E_I{c_I} ) ≤ E{r_j} − E{r_i} ≤ 2β1 ( Cov{c_g, (1+r_j)/(1+g)} − Cov{c_g, (1+r_i)/(1+g)} ) / ( α1 − 2β1 E_g{c_g} )

*Source: Annex II. Conditions for Mutually Beneficial Exchange in SCDIs*

### 3.      More recently, countercyclical official loans have provided state contingent financing terms

### 3.      More recently, countercyclical official loans have provided state contingent financing terms

### Countercyclical official loans — overview
- These instruments adjust debt service and maturity in line with economic conditions, providing state-contingent financing terms to debtor countries.

### Multilateral example: Agence Française de Développement (AFD)
- Since 2007, AFD has offered 16 countercyclical concessional loans amounting to €344m to five low-income countries that have benefitted from debt relief through the HIPC initiative; the loans are directed toward project finance.
- The Prêt Très Concessionnel Contracyclique (PTCC):
  - Thirty-year loan facility with a five-year grace period at the beginning of the loan.
  - Includes a five-year floating grace period for principal payments.
  - Debtor can exercise the floating grace period if export earnings fall below a predefined threshold.
- A nonconcessional version exists but has had little demand.

### Bilateral example: Petrocaribe
- Structure:
  - Bilateral loans extended by Venezuela to countries to purchase oil produced by PDVSA on predetermined flexible financing terms.
  - Specified amount paid at market prices up front; balance paid over about 25 years.
  - Down payment share, interest rate, and grace period are based on the prevailing price of oil.
  - Payment terms negotiated bilaterally; debtors can offer goods and services in lieu of currency.
- Timeline and scale:
  - First issued in 2005; Jamaica was the first recipient.
  - Approximately US$28 billion has been extended via Petrocaribe loans as of end-2015.
- Performance:
  - As oil prices began to decline in 2014, many threshold prices triggering nonconcessional terms were breached.
  - Some countries (e.g., Jamaica, and the Dominican Republic) bought back their Petrocaribe debt.

### Corporate example: Sonatrach (Algeria)
- In 1989 Sonatrach contracted a US$100 million oil-linked loan with a syndicate of international banks (led by Chase Investment Bank).
- Instrument components:
  - Conventional floating rate loan: seven-year maturity, four-year grace period.
  - Oil options: four call options on oil held by Chase and sold by Sonatrach (maturities between 6 and 24 months).
- Pricing outcome:
  - With options, financing cost estimated at 1pp above LIBOR relative to 3-4pp above LIBOR without the options.

### Commodity-linked instruments — overview and examples
- Sovereign commodity price hedging has been more prevalent than bonded instruments.
- Market characteristics:
  - Well-developed with sufficient counterparties.
  - Cost of acquiring hedges is relatively low.
  - Maturities of available hedges are relatively short; sovereigns may prefer shorter-term hedges under certain volatility conditions.

- Mexico petrobonds (April 1977–April 1980):
  - Three-year bonds issued by NAFINSA; each 1,000-peso unit backed by 2.149 barrels of oil.
  - First issue (April 1977) amounted to 2 billion pesos (about US$90 million) at 7 percent; the return on the 1979 bond was 12.658 percent.
  - Total of five issuances of about 50 billion pesos in total.
  - Investors made a loss despite oil price increase (from $22.60 to $32.50) due to unfavorable exchange rate used (4,553 pesos for a 1,000-peso bond).
  - Mexico did not issue a commodity-linked bond thereafter.

- India Sovereign (SGB) Gold Bonds (since November 2015):
  - Four tranches issued, amounting to about 4.908 tons of physical gold.
  - Objective: contain import of physical gold bullion.
  - Features:
    - Fixed interest rate of 2.75 percent per annum, paid semiannually.
    - Principal at maturity based on prevailing reference rate of gold.
    - Denominated in Indian rupees; issued in multiples of one gram (from 2 grams at launch).
    - Maturity of eight years with option to redeem from the fifth year.
    - Issued by the Reserve Bank of India on behalf of the Government of India; guaranteed by the government on both interest and redemption amount.
    - Can be used as collateral, sold, and traded on the National Stock Exchange as of June 2016.
    - For banks, SGBs are eligible for the Statutory Liquidity Ratio.
    - Only residents of India are eligible.
  - Uptake has been muted, partly due to low rate of return relative to cash bank balances (e.g., cash bank balances offer 8 percent) and cultural preference to hold physical gold.

- Confederate Erlanger (Cotton Loan), 1863:
  - £100 bonds redeemable for 8 bales of cotton; 7 percent interest; 20-year maturity.
  - Issued in five European cities; issuance raised about £1.76 million.
  - Price declined due to low confidence in the Confederacy.

### Catastrophe insurance — sovereign practice and examples
- Approach:
  - Sovereigns typically adopt a multilayered, complimentary approach to catastrophe insurance.
  - Private market insurance alone can be prohibitively expensive for sovereigns.
  - Some developed markets require private catastrophe insurance by law (e.g., New Zealand, California).

- Mexico CatMex (2006):
  - Only standalone sovereign catastrophe-linked bond to date.
  - US$160 million 3-year cat bond designed to provide FONDEN financing in the event of an earthquake.
  - Coupon was LIBOR-based.
  - Parametric trigger: earthquake with certain magnitude and depth in one of three predefined geographical zones.
  - Structured in two tranches for different regions; both rated BB+ by S&P.
  - Bond matured without being triggered.

B. During Restructurings

### Hurricane clause in Grenada’s debt restructurings
- Purpose:
  - Allows postponement of scheduled debt service payments upon realization of an exogenous natural disaster event.
  - Provides cash flow relief immediately after a natural disaster when financing needs are greatest, enabling redirection of funds intended for debt service to immediate needs.
  - Pre-defined contractual changes do not themselves constitute a ‘credit event’ and reduce the probability of another ad hoc debt restructuring.

- Key features:
  - Verifiable trigger event measured by an independent entity:
    - Grenada is a member of the Caribbean Catastrophic Risk Insurance Facility (CCRIF) SPC and has purchased insurance on its 2030 and Exim Bank of Taiwan bonds against risks of tropical cyclone, earthquake, and excess rainfall.
    - Event is triggered based on parametric measures; if CCRIF is triggered, the hurricane clause in the bond contract is also triggered.
  - Changes to cash flow:
    - Provides for deferred payments for up to two payment periods; no nominal principal or interest rate reduction.
    - Deferred interest payment is capitalized and deferred principal payment is distributed equally on top of scheduled payments until final maturity.
  - Maximum number of triggers: contract allows up to three triggers.

- Quantitative impacts and comparisons:
  - One-off trigger of the hurricane clause could provide a cash flow relief of up to 2.6 percent of GDP.
  - This compares with about 1.5 percent of GDP for the probable maximum loss from an event that occurs once in every 25 years in Grenada.
  - The average annual loss experienced in Grenada is 9.87 percent of GDP.
  - The clause provides liquidity relief but does not reduce the stock of debt or generate additional financing; for catastrophic events (e.g., Hurricane Ivan, damage estimated at 200 percent of GDP) a catastrophe bond or insurance would be more appropriate.

- Legal and market considerations:
  - The clause defines a “Caribbean Tropical Cyclone Event” distinct from an “event of default”; this distinction is important to avoid triggering an event of default and potential downgrade to Selected Default.
  - The clause was introduced in the context of a debt restructuring where existing creditors had vested interest in recovery; issuance under normal market conditions may face investor demand for additional risk premium.
  - Current market valuation suggests the clause is valued little, but pricing could be volatile.

### Details of hurricane clauses (summary of negotiated conditions)
- Private bondholders vs. Taiwan vs. Paris Club (selected elements preserved as in source table):
  - Event:
    - Private bondholders: Hurricane insured under CCRIF Parametric Insurance Contract dated June 1, 2015.
    - Taiwan: Hurricane, earthquake, excess rainfall insured under CCRIF Parametric Insurance Contract dated June 1, 2012.
    - Paris Club: Exogenous shocks, including natural catastrophes such as hurricanes and tsunamis.
  - Trigger:
    - Private bondholders & Taiwan: CCRIF SPC modelled losses exceeding US$15 million.
    - Paris Club: Assessment case-by-case with no pre-defined set of indicators.
  - Independent Body:
    - Private bondholders & Taiwan: CCRIF SPC.
    - Paris Club: Assessment by IFIs, regional institutions or any organization that the PC Creditors will judge relevant, including the IMF, World Bank, CCRIF SPC, the CDB and the National Hurricane Center.
  - Debts Affected:
    - Private bondholders & Taiwan: Principal and accrued interest due on the deferral dates.
    - Paris Club: Principal and/or accrued interest; creditors choose bilaterally whether to participate in debt relief.
  - Deferral Dates:
    - Private bondholders: Up to 6 months or one payment date (if CCRIF SPC payout > US$15 million and < US$30 million); up to 12 months or two payment dates (if CCRIF SPC payout > US$30 million).
    - Taiwan: 12 months (two payment dates).
    - Paris Club: Unspecified.
  - Repayment Terms:
    - Private bondholders & Taiwan: Principal deferred and accrued interest deferred and capitalized; both repayable in equal semi-annual installments over remaining term.
    - Paris Club: Unspecified.
  - Conditions:
    - Private bondholders & Taiwan: Policy payout by CCRIF SPC and submission of the deferral claim.
    - Paris Club: Unspecified, but past cases typically involved considerable damage and formal request.
  - Maximum number of triggers:
    - Private bondholders & Taiwan: Three.
    - Paris Club: Not stated.
  - Reporting:
    - Private bondholders & Taiwan: Progress reports on post-event relief, recovery and reconstruction programs.
    - Paris Club: Not stated.

### Interpretation
- Hurricane clause is a liquidity relief instrument, not a debt stock reduction tool.
- Practical effectiveness depends on event severity, timing, and complementary instruments (e.g., catastrophe bonds, insurance).

### Annex V — Evolution of government debt structures in Emerging Markets (lessons for SCDIs)
- Long-term trend:
  - Past three decades: seismic shift in composition of government debt in EM countries toward higher share of domestic debt.
  - The share of domestic debt in total debt has risen significantly in most EM countries in the sample.
- Drivers:
  - Investors are more willing to bear currency and credit risks.
  - Sovereigns’ increasing ability to borrow domestically.
- Composition shift:
  - Domestic debt instrument mix has increasingly shifted toward domestic long-term local currency-denominated fixed-rate debt (DLTF).
  - DLTF: domestic local currency non-indexed fixed-rate debt with original maturity over 1 year.
- Benefits and limits:
  - DLTF considered among the safest forms of debt for the debtor because creditors bear currency depreciation or inflation costs.
  - Some EM and LIC countries still find DLTF prohibitively costly.
  - SCDIs that offer upside risk to investors and can be priced cheaper than DLTF may be an attractive alternative or complement.
- Historical context:
  - Shift to local currency long-term debt reflects graduation from “domestic original sin” (inability to borrow domestically long-term in own currency).
  - “International original sin” and “domestic original sin” stem from different causes: global financial market structure vs. domestic macroeconomic and institutional factors.

- Data and coverage:
  - Figures and data referenced use the Jeanne-Guscina EM Debt Database 2014 and staff calculations.
  - Coverage notes:
    - Jeanne-Guscina EM Database covers 19 EM sovereigns.
    - Latin America sample: Argentina, Brazil, Chile, Colombia, Mexico, and Venezuela.
    - EMEA sample: Czech Republic, Hungary, Poland, Russia, Israel and Turkey.
    - Asia sample: China, India, Indonesia, Korea, Malaysia, Philippines, and Thailand.

*Prepared by IMF staff as presented in the source document.*

### 5.      The experience of EMs in trying to promote DLTF debt may offer valuable lessons relevant to

### 5.      The experience of EMs in trying to promote DLTF debt may offer valuable lessons relevant to

### Lessons from emerging market (EM) experience
- The composition of the debt portfolio, the level of debt market development, and the structure of the investor base have important implications for the attractiveness of DLTF instruments for sovereigns and investors.
- Macroeconomic policies and conditions affect the chances of success in expanding the investor base and the range of available instruments.
- Typical process of redemption from “domestic original sin” involves:
  - Better macroeconomic policies which have kept inflation in check. (Note: domestic original sin has not been a severe problem for most Asian economies.)
  - Use of inflation-linked and/or variable rate debt as an intermediary step in the transition from FX-denominated debt to DLTF debt. Even after successful disinflation and fiscal adjustment programs, foreign-currency and indexed debt can remain dominant because it often takes a long time to gain anti-inflationary credibility.
  - Active debt management decision to minimize FX-risk in sovereign debt portfolios.
  - Institutional reforms and technical and legal development of local bond markets.
  - Opportune external conditions—many EM sovereigns capitalized on increased interest of nonresident investors in domestic bond markets, driving down yields on local currency instruments. Foreign investors’ participation in local currency bond markets has risen sharply since the Global Financial Crisis, attributed to unconventional monetary policies in advanced economies, search for yield, and greater confidence in EM fundamentals.

### Country examples and evolution of domestic debt structures
- Brazil:
  - Share of FX denominated/indexed debt reduced from almost 60 percent in 1993 to less than 1 percent twenty years later.
  - Transition path: first toward floating rate local currency debt (short-term/variable rate), then toward CPI-indexed debt.
  - CPI-indexed debt now accounts for about a third of the debt portfolio.
  - Remaining two-thirds split evenly between DLTF, short-term and variable rate instruments.
- Turkey:
  - Phased out FX-denominated debt altogether after the depreciation shock around the 2001 crisis.
  - Transition path similar to Brazil: shifted toward floating rate local currency debt and then toward CPI-indexed debt.
  - At end-2013, about 55 percent of outstanding debt stock was composed of DLTF instruments, with the rest split evenly between variable rate and CPI-indexed instruments.
- Chile:
  - CPI-indexed debt prominent over the past three decades.
  - FX-denominated or indexed debt is no longer part of the domestic debt structure.
  - Floating-rate debt has never taken off in Chile.
  - The share of DLTF debt increased over the last decade to about 20 percent of the general government domestic debt outstanding.
  - CPI-indexed debt accounts for over 60 percent of domestic debt outstanding.

### Foreign ownership and investor base
- Foreign investors’ participation in local currency bond markets rose sharply since the Global Financial Crisis, contributing to lower yields on local currency instruments.
- (Sources cited in the source content for foreign ownership figures: Arslanalp and Tsuda (2014) and staff calculations. Coverage of debt is central government.)

### Groupings of potential issuers by characteristics (summary of proposed eight groups)
- Countries organized into eight broad groups: three Advanced Economy (AEs) groups and five Emerging Markets and Developing Countries (EMDCs) groups.
  - AE groups: Reserve currency issuers; Euro-area members; Small open economies.
  - EMDC groups: Commodity exporters; Small states; Local Currency issuers; Other EMs; Other LICs.
- Group-defining notes:
  - Reserve currency issuers: issue reserve currencies, have very liquid domestic debt markets, tend to experience ‘flight to quality’ inflows in distressed states.
  - Euro-area members: share a common monetary policy, somewhat constrained policy space for idiosyncratic shocks.
  - Small-open advanced economies: exposed to external shocks but generally face fewer constraints on monetary policy.
  - Local Currency issuers: issue more than 65% of debt in their own currency (group properties similar if threshold set at 75% or 50%, although composition would change).
- Key cross-group implications: reserve currency issuers experience relatively low real GDP and interest rate volatility though high debt levels; commodity exporters have much higher volatility along most dimensions; small states face high probability and vulnerability to natural disasters.

### Selected numeric averages and statistics by country group (stock variables, averages 2000–2015, selected columns preserved exactly)
- AEs (group averages):
  - Debt-to-GDP ratio (%): 72
  - Foreign currency debt share (%): 6
  - Annual real GDP growth: 2.3
  - Effective real interest rate (%): 2.3
  - Annual exchange rate depreciation (%, vs USD): 0.2
  - Primary Balance (% of GDP): -0.2
  - Change in debt-to-GDP ratio (pp): 4.5
- Reserve Currency Issuers:
  - Debt-to-GDP ratio (%): 116
  - Foreign currency debt share (%): 2
  - Annual real GDP growth: 1.7
  - Effective real interest rate (%): 2.3
  - Annual exchange rate depreciation (%, vs USD): 0.0
  - Primary Balance (% of GDP): -2.2
  - Change in debt-to-GDP ratio (pp): 4.3
- Euro area members:
  - Debt-to-GDP ratio (%): 81
  - Foreign currency debt share (%): 5
  - Annual real GDP growth: 2.1
  - Effective real interest rate (%): 2.1
  - Annual exchange rate depreciation (%, vs USD): 0.0
  - Primary Balance (% of GDP): -0.7
  - Change in debt-to-GDP ratio (pp): 5.0
- Small open economies:
  - Debt-to-GDP ratio (%): 42
  - Foreign currency debt share (%): 11
  - Annual real GDP growth: 2.8
  - Effective real interest rate (%): 2.6
  - Annual exchange rate depreciation (%, vs USD): 0.6
  - Primary Balance (% of GDP): 1.5
  - Change in debt-to-GDP ratio (pp): 3.8
- EMDCs (group averages):
  - Debt-to-GDP ratio (%): 50
  - Foreign currency debt share (%): 55
  - Annual real GDP growth: 4.4
  - Effective real interest rate (%): -2.0
  - Annual exchange rate depreciation (%, vs USD): 4.7
  - Primary Balance (% of GDP): -0.1
  - Change in debt-to-GDP ratio (pp): 10.2
- Commodity exporters:
  - Debt-to-GDP ratio (%): 35
  - Foreign currency debt share (%): 35
  - Annual real GDP growth: 5.5
  - Effective real interest rate (%): -1.8
  - Annual exchange rate depreciation (%, vs USD): 3.6
  - Primary Balance (% of GDP): 3.8
  - Change in debt-to-GDP ratio (pp): 9.8
- Small States:
  - Debt-to-GDP ratio (%): 61
  - Foreign currency debt share (%): 63
  - Annual real GDP growth: 2.9
  - Effective real interest rate (%): -0.1
  - Annual exchange rate depreciation (%, vs USD): 1.3
  - Primary Balance (% of GDP): -1.0
  - Change in debt-to-GDP ratio (pp): 8.9
- Local Currency issuers:
  - Debt-to-GDP ratio (%): 52
  - Foreign currency debt share (%): 16
  - Annual real GDP growth: 4.1
  - Effective real interest rate (%): 0.7
  - Annual exchange rate depreciation (%, vs USD): 5.0
  - Primary Balance (% of GDP): -0.7
  - Change in debt-to-GDP ratio (pp): 5.5
- Other EMs:
  - Debt-to-GDP ratio (%): 54
  - Foreign currency debt share (%): 60
  - Annual real GDP growth: 4.0
  - Effective real interest rate (%): -1.4
  - Annual exchange rate depreciation (%, vs USD): 6.8
  - Primary Balance (% of GDP): -0.4
  - Change in debt-to-GDP ratio (pp): 7.9
- Other LICs:
  - Debt-to-GDP ratio (%): 48
  - Foreign currency debt share (%): 71
  - Annual real GDP growth: 5.0
  - Effective real interest rate (%): -4.8
  - Annual exchange rate depreciation (%, vs USD): 6.1
  - Primary Balance (% of GDP): -1.2
  - Change in debt-to-GDP ratio (pp): 14.7

### State-contingent extendible bonds — rationale (Annex VII, opening)
- Rationale:
  - Extendible debt instruments that push out maturities (or impose debt service standstills) can generate “financing” for a country facing a liquidity shock, and thus prevent liquidity problems from translating into a full-blown/costly debt crisis in times of stress and low confidence.
  - Automatic provision of finance via maturity extension reduces the risk that temporary liquidity crises propagate into full-blown losses of confidence (through balance sheet effects, herd behavior, or confidence shocks), benefiting creditors, the debtor, and the system more widely.
  - If maturity extension stabilizes interest payments at pre-crisis levels, these instruments can prevent solvency of the sovereign from deteriorating.

*Italic: Prepared by Tom Best (SPR); material excerpted from STATE-CONTINGENT DEBT INSTRUMENTS FOR SOVEREIGNS—ANNEXES.*

### 2.      By ensuring automatic private sector involvement, extendible bonds could facilitate

### pp032317state-contingent-debt-instruments-for-sovereigns-annexes - 2.      By ensuring automatic private sector involvement, extendible bonds could facilitate

### Benefits and rationale for extendible bonds
- By ensuring automatic private sector involvement, extendible bonds could facilitate and potentially limit the need for official sector support.
- Maintaining private exposure:
  - Makes it politically easier for official creditors to provide financing, as it reduces the amount needed from official creditors.
  - Helps provide safeguards on debt sustainability.
  - Allows official sector resources to be used to allow for a more gradual policy adjustment by the sovereign to better support growth and reduce the risk of program failure.
- Extendible bonds can reduce the implicit anticipation of full official sector bail-out, so that sovereign bond yields would be more in line with perceived riskiness, as determined by fundamentals.
- Better risk differentiation by creditors can:
  - Incentivize debtors to improve fundamentals and reduce debt through the price mechanism.
  - Give policymakers time to assess debt sustainability and, if needed, undertake restructuring negotiations in an orderly way.
  - Maintain private sector exposure and thereby facilitate access to Fund financing (under its new lending rules), while reducing moral hazard in the system (Brooke and others, 2013).

### Potential complications and market challenges
- Extendible bonds could be hard to price because of the large one-off adjustment involved.
  - As mainly downside-protection instruments, investors may demand a high risk premia for holding them.
  - Issuers might not see benefits in paying such high premia in presence of other available debt instruments.
- Extension mechanics:
  - The extension could happen at the issuer’s discretion (perhaps with a penalty), or could be linked to a trigger.
- Market emergence conditions:
  - A market in extendible bonds is more likely if the sovereign attaches particularly high value to debt service relief in times of stress.
  - Sovereign subjective discount rates may increase by more than investors’ discount rate in stress, making extension options more valuable to sovereigns than investors.
  - Market participants may value extendible options if the alternative is debt restructuring (with corresponding deadweight costs) rather than an official sector bail-out.
- Data integrity, manipulation, and moral hazard concerns:
  - Triggers signaling liquidity pressures (such as CDS spreads, or bond yields) could be manipulated by investors.
  - Triggers linked to requests for IMF or ESM assistance could imply delays and get entangled with political economy difficulties associated with Fund programs.
  - Proposals include a 3-year standstill/extension in the event of request for IMF assistance or ESM program; others have argued for large increases in CDS spreads on bond yields.

### Design considerations for extendible bonds
- Issuer’s discretion extension:
  - The simplest form allows maturity extension at sovereign’s discretion but may be perceived as opportunistic behavior.
  - If cost of refinancing > perceived cost of extending, extension will be exercised; without high non-monetary costs, extensions could be exercised fairly regularly.
- Step-up (penalty) interest rate:
  - An option with a penalty interest rate (maturity extension accompanied by an increase in the coupon) may have greater market acceptability.
  - The step-up increases the cost of exercising extension relative to refinancing and limits use to larger interest rate hikes.
  - However, higher interest rates could worsen sovereign financing costs and debt sustainability.
- State-contingent automatic trigger:
  - An extendible bond with a state-contingent automatic trigger could address concerns about data manipulation and endogeneity to government policy.
  - Triggers can be calibrated to anticipate a very large adverse shock to reduce perverse incentives.
  - Externally verifiable triggers (international agency or international statistical agency) reduce scope for data manipulation (examples: commodity prices, hurricane intensity).
- Optimal length of maturity extension:
  - Depends on expected severity of the crisis defined by the trigger and the duration over which the sovereign is likely to need financing relief.
  - Real-life examples:
    - 6–9 months (municipal extendible bonds)
    - 1-year standstill (Grenada hurricane clause)
    - 5-years grace period extension for AFD’s countercyclical loans
  - If extension is too generous, some investors might be discouraged; the longer the extension, the higher the premia demanded by investors.
  - Grenada example: clause may provide a temporary cash flow relief of up to 2.6 percent of GDP over a 1-year period, although this gets reversed in the following year.

### Pricing extendible bonds — issuer’s discretion structures
- Compare an ‘issuer’s discretion’ extendible with two option-based replications so payoffs can be identical (no-counterparty-risk assumption):
  - (A) An ‘issuer’s discretion’ extendible bond: short initial maturity (m_S), coupon (c), embedded option to extend to long maturity (m_L > m_S) with step-up coupon (c+s) at issuer’s discretion.
  - (B) Short bond + (issuer’s) put option on long bond: short bond with coupon c and maturity m_S, plus a European put option with exercise date m_S and strike price equal to face value on a bond with maturity m_L and coupon c+s.
  - (C) Long bond + (issuer’s) call option on the long bond: when s = 0, sell a long bond with maturity m_L and coupon c, and buy a European call option on the same bond with exercise date m_S and price equal to face value.
- No-arbitrage pricing condition (identical payoffs) — preserve exact expression:
  - (1) Price of extendible = Price of long bond − Price of call option on long bond = Price of short bond − Price of put option on long bond
- Valuation methods:
  - Option values can be evaluated using standard approaches such as the Black-Scholes model or lattice-based methods (e.g., Black-Derman-Toy).
  - An extendible with a step-up coupon should have a lower expected yield than an extendible without a step-up (step-up reduces states in which option is exercised).
- Pricing dynamics after issuance:
  - As an issuer’s option extendible nears its initial maturity date, the time value of the embedded option would be expected to fall.
  - At unchanged yields, its price would move towards the lower of the long or short bond price.
  - The yield of an extendible would likely be more volatile than that of a conventional bond, and increase more under stress, since shifts in the yield curve affect both the value of the underlying bonds and the probability that the option to extend is exercised.

### Pricing extendible bonds with trigger conditions
- Option premium in issuer’s discretion extendibles could be expensive if issued ‘near the money’.
- Introduce a trigger condition linked to sovereign’s ‘need’ for liquidity relief to reduce the cost of the embedded option.
- Two broad trigger-based designs:
  - (i) ‘Automatic’ extendible: always extends in maturity if the trigger condition has been breached.
  - (ii) ‘Knock-in option’ structure: sovereign has the option (but not the obligation) to extend only after the trigger has been breached.
- Relative pricing logic (states of the world at initial maturity date):
  - Under issuer’s discretion, extend in all states where extension reduces sovereign expected interest cost (areas B and C in Figure AVII.2).
  - Under knock-in, extension only in states where sovereign prefers to extend AND trigger breached (area B); some opportunistic extensions are ruled out, so knock-in should be greater than or equal to issuer’s discretion extendible in price.
  - Under automatic extendible, extends in same states as knock-in (area B) and also extends in states where trigger is met but issuer would prefer not to extend (area A); thus automatic’s price should be greater than or equal to knock-in’s price.
- Relative pricing inequality (preserve exact expression):
  - (2) Price of "issuer’s option" extendible ≤ Price of "knock-in option" extendible ≤ Price of "automatic" extendible
- Pricing a knock-in extendible requires estimating joint distribution of interest rates and the trigger variable; Monte Carlo simulations based on that joint distribution can be used to determine the discounted expected value of the option to extend and the implied price of the extendible bond.

*Italic: Content based exclusively on the supplied IMF annex text.*

### 3. Key features in a sovereign guarantee product include:

### 3. Key features in a sovereign guarantee product include:

### Target countries
- For multilateral institutions, all member countries are eligible, but with different pricing structures conditional on income levels.
- Official bilateral creditors are politically motivated and may have a list of eligible countries based on geopolitical considerations, or key trading partners.

### Coverage
- The coverage ratio should provide incentives for creditors to properly assess and monitor the risks of the borrowers.
- Most guarantees have partial coverage, but some, for instance those given by the US AID, have 100 percent coverage.

### Fees
- Fees are typically charged to ensure that the guarantee program is self-sustaining.
- There are cases where fees are not charged, motivated by socio-political considerations.

### Cyclicality and types of guarantees
- Credit risk guarantees tend to be issued counter-cyclically.
  - They are issued when the sovereign requires external support while its credit standing is deteriorating, or when the market environment is not conducive to borrowing due to factors external to the sovereign’s credit outlook.
- Project risk guarantees are less sensitive to business cycles.
  - They tend to be associated with long term investments in infrastructure or new discoveries of commodities that could lead to future economic growth.

### Example: Ghana (World Bank partial credit risk guarantee)
- In October 2015, Ghana issued a US$1 billion Eurobond supported by a World Bank partial credit risk guarantee.
- Terms and market reaction:
  - Final maturity: 15-year final maturity
  - Coupon: 10.75 percent
  - Ratings: Moody’s and Fitch assigned a credit rating that is two notches above the regular sovereign ratings; Standard & Poor’s did not give any ratings uplift, per their policy for partial credit guarantee.
  - Market effect: The issuance spread compared to Ghana’s existing Eurobond suggested that the cost savings achieved by the guarantee was minimal, though the guarantee may have helped Ghana access the market at a time of heightened risk aversion.
  - Time-varying valuation: Post issuance secondary market spreads indicate the value of the guarantee diminishes in good times and increases in bad times.
- Chart context (labels preserved):
  - Ghana: 2023&2026 Spreads over PBG Eurobond
  - Spreads (In Basis Points)
  - Series: Ghana (2023 RegS), Ghana (2026 RegS)
  - X-axis dates shown: 10/12/2015 through 2/12/2017 (monthly markers as listed)

### Example: U.S. AID bilateral credit risk guarantees
- Recent beneficiaries: Jordan, Tunisia and Ukraine.
- Context: The three countries faced significant financing challenges and market access difficulties.
- Effect:
  - The guarantees significantly reduced the borrowing cost of the issuers.
  - The Ukrainian case was issued when market access on their own credit standing was closed; the guarantee helped access the market at significant cost advantage.
  - In Jordan and Tunisia the issuers could possibly have issued without a guarantee but at significantly higher costs.
- Coverage: All these credit risk guarantees covered 100 percent of the principal and interest payment obligations.
- Conditionality: The guarantees were issued in support of the governments’ commitment to implement macroeconomic adjustments.

### Recent Issuance under Bilateral Credit Guarantees (as listed)
- Ukraine | Date: 5/16/2014 | Issue size: US$ 1 billion | Maturity: 5 year | Interest rate: 1.844% | Spread to US Treasury at issuance: 28bp | Spread of existing instrument at issuance: (blank) | Sovereign Rating at issuance (S&P, Moody’s, Fitch): CCC/Caa3/CCC
- Ukraine | Date: 5/26/2015 | Issue size: US$ 1 billion | Maturity: 5 year | Interest rate: 1.847% | Spread to US Treasury at issuance: 32bp | Spread of existing instrument at issuance: (blank) | Sovereign Rating at issuance (S&P, Moody’s, Fitch): CC/Ca/CC
- Ukraine | Date: 9/29/2016 | Issue size: US$ 1 billion | Maturity: 5 year | Interest rate: 1.471% | Spread to US Treasury at issuance: 30bp | Spread of existing instrument at issuance: (blank) | Sovereign Rating at issuance (S&P, Moody’s, Fitch): B-/Caaa3/CCC
- Tunisia | Date: 8/5/2016 | Issue size: US$ 500 million | Maturity: 5 year | Interest rate: 1.416% | Spread to US Treasury at issuance: (blank) | Spread of existing instrument at issuance: (blank) | Sovereign Rating at issuance (S&P, Moody’s, Fitch): BB-/Ba3/BB-
- Jordan | Date: 6/30/2015 | Issue size: US$ 1 billion | Maturity: 7 year | Interest rate: 2.578% | Spread to US Treasury at issuance: (blank) | Spread of existing instrument at issuance: (blank) | Sovereign Rating at issuance (S&P, Moody’s, Fitch): BB-/B1/--
- Jordan | Date: 6/30/2015 | Issue size: US$ 500 million | Maturity: 10 year | Interest rate: 3.000% | Spread to US Treasury at issuance: (blank) | Spread of existing instrument at issuance: (blank) | Sovereign Rating at issuance (S&P, Moody’s, Fitch): BB-/B1/--

### Use of guarantees in debt restructurings
- Examples:
  - AfDB guarantee for Seychelles (2010) and CDB guarantee for St Kitts (2011) for new bonds offered in exchange for restructured debt.
- Effects:
  - Guarantee operations enhanced the value of the final package without significant additional fiscal drain to the debtor.
  - They were critical in providing comfort to creditors’ Boards and decision-making committees concerned about the impact of a large net present value reduction on their balance sheets.
  - This facilitated creditor participation in exchange offers that involved significant face value reduction.
- Counterexample:
  - A CDB guarantee was considered in the context of Grenada’s 2015 debt restructurings of the commercial bond; creditors rejected this, preferring to assume the risk themselves.

### Currency-swap guarantees
- Innovation example:
  - November 2015: Cameroon issued its debut Eurobond denominated in US$ for US$750 million.
  - AfDB provided a EUR500 million partial credit guarantee to cover Cameroon’s payment obligations related to a cross currency swap that converted Cameroon’s payment obligations from US$ to Euro, executed with commercial banks.
  - Transaction feature: Built-in payment moratorium in the event Cameroon has payment difficulties for up to two years, which will not trigger the guarantee or an event of default.

### Sovereign guarantees to subnational governments, SOEs, and private enterprises
- Purposes:
  - To facilitate borrowing by subnational governments, state owned enterprises, and private enterprises (from external sources or the domestic banking sector).
  - To support long-term investment projects implemented by other public sector borrowers, or private enterprises with critical public interests.
  - To support critical economic groups such as small enterprises that face asymmetric information, adverse selection, or first mover problems.
- Counter-cyclical role:
  - During financial crises, guarantee schemes have been used by sovereigns as a counter-cyclical instrument to soften private sector credit retrenchment.
  - They supported companies with existing bank relationships to maintain indebtedness levels during the financial crisis.
- Performance risk:
  - In the years 2010–12, guarantee schemes used in support of SMEs reported a considerable increase in bad debt (KPMG 2011).

*Prepared by Eriko Togo (MCM). STATE-CONTINGENT DEBT INSTRUMENTS FOR SOVEREIGNS—ANNEXES*

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_Source: https://www.imf.org/-/media/files/publications/pp/pp032317state-contingent-debt-instruments-for-sovereigns-annexes.pdf_