## Introduction

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---

### Purpose and scope
- SDRs are international reserve assets created by the IMF to supplement its member countries’ official reserves.
- Most recently, a general allocation of SDR 456.5 billion (equivalent to about US$650 billion) was implemented on August 23, 2021.
- Paper objectives:
  - Estimate the expected cost of using SDRs for countries with negative SDR Department positions.
  - Assess implications of expected SDR Department payments for IMF members’ capacity to pay charges to the SDR Department.

### Operations of the SDR Department and operational mechanics
- In the SDR Department, members receive interest on cumulative SDR holdings and are assessed charges against cumulative SDR allocations; both are assessed at the SDR interest rate.
- A negative net SDR Department position (holdings < allocations) generates net interest expense (“charges”) to the SDR Department at the SDR interest rate.
- The SDR interest rate:
  - Is a floating rate determined weekly by a formula based on the weighted average of interest rates of SDR basket currencies with a floor set at 5 basis points.
- Uses of SDRs: retain as reserves; (i) transactions to get freely usable currencies; (ii) Fund-related operations; or (iii) IMF‑authorized operations with SDR Department participants or prescribed holders.

### Recent evolution of the SDR interest rate and forward curves
- SDR interest rate has risen from 5 basis points in August 2021 to 395 basis points as of end-June 2023.
- Implied SDR forward curves indicate the SDR forward rate curve over the 30-year horizon rose about 230 basis points on average from August 2021 to June 2023.
- The June 2023 SDR forward curve is inverted in the 0–5-year time horizon.

### Main findings on expected cost and concessionality (selected statistics)
- Median expected present value (PV) cost among IMF members with negative net SDR Department positions of converting SDRs:
  - Increased from $37 million in August 2021 to $134 million in June 2023 — an increase of 262 percent.
- Median one-year-ahead annual expected cost:
  - Increased from $0.1 million in August 2021 to $7.8 million in June 2023 — a nearly eighty-fold increase.
- Higher-exposure members:
  - Top quartile one-year-ahead cost: $19 million; PV cost: $333 million.
  - Largest nominal negative SDR Department position: one-year-ahead $259 million; PV $4,471 million.
- Grant element (concessionality) of SDRs:
  - Declined from about 80 percent in August 2021 to 34 percent at end-June 2023 (concessionality threshold convention: greater than 35 percent).
  - If SDRs were cancelled or the interest rate rises further, the grant element would fall further.
- Overall assessment: members’ exposure to upcoming SDR Department charges is generally manageable under baseline and stress scenarios, although for some members increased financial cost can be material.

### Methodology overview and key assumptions
- Expected cost definition: PV of all future net interest payments and face value payments of SDRs for the projection period.
- Key modelling assumptions and parameter choices:
  - IMF Board of Governors will not decide to cancel SDRs nor request member states to reconstitute them in the baseline scenario.
  - Basket weights fixed at the initial 2015 weights through July 2022, then follow August–2022 basket weights for the rest of the projection period.
  - SDR basket instruments are fixed for the projection period.
  - SDR Department charges are assessed on a quarterly basis at a constant, imputed interest rate for that quarter (quarterly average of weekly SDR interest rate).
  - Discount rate (r) is assumed to be 5 percent for all IMF members.
  - Members’ SDR holdings are assumed converted in period 0 and unchanged thereafter; interest expense begins in period 1 (q=1) into perpetuity under the baseline.
  - Market data are used for the first thirty years (120 quarters) of the projection horizon; the expected SDR interest rate in quarter 120 is assumed constant for quarters 121 into perpetuity (terminal rate).

### Forward-curve construction and data sources
- Implied SDR forward rates derived from market-determined interest rates of SDR basket currencies: US dollar, Japanese yen, euro, U.K. pound sterling, Chinese renminbi.
- Forward curves derived at multiple vintages: August 23, 2021; January 1, 2022; end-June, 2023.
- Two-step approach for each SDR basket currency:
  - Step 1: Estimate zero-coupon bond yield curves using regression-based (Nelson-Siegel-Svensson (NSS)) or interpolation techniques depending on currency.
  - Step 2: Derive implied three-month forward rates from zero-coupon curves using no-arbitrage conditions.
- Implied SDR forward curve computed by weighting currency forward rates by SDR basket currency amounts (weights fixed per valuation reviews).
- Data sources: central bank websites (Fed, ECB, BoE), Bloomberg, CEIC; forward-curve robustness checked with WEO projections.

### SDR basket composition (valuation review weights and currency amounts)
- Oct. 2016–Jul. 2022 (2015 Valuation Review):
  - USD US dollar: 41.7% — currency amount fixed 0.58252
  - EUR Euro: 30.9% — currency amount fixed 0.38671
  - RMB Chinese yuan: 10.9% — currency amount fixed 1.0174
  - JPY Japanese yen: 8.3% — currency amount fixed 11.900
  - GBP Pound sterling: 8.1% — currency amount fixed 0.085946
- Aug. 2022–Jul. 2027 (2022 Valuation Review):
  - USD US dollar: 43.4% — currency amount fixed 0.57813
  - EUR Euro: 29.3% — currency amount fixed 0.37379
  - RMB Chinese yuan: 12.3% — currency amount fixed 1.0993
  - JPY Japanese yen: 7.6% — currency amount fixed 13.452
  - GBP Pound sterling: 7.4% — currency amount fixed 0.080870

### Assessing members’ capacity to service SDR Department obligations — key results
- Sample: 59 LIC and 62 EM IMF members with negative net SDR Department positions.
- PV of SDR Department payments greater than 1 percent of GDP:
  - August 2021 forward curve: five countries.
  - June 2023 forward curve: 36 countries (about 31 percent of all members).
- Reserve-based metrics:
  - August 2021: 14 countries had PV greater than 5 percent of gross foreign exchange reserves.
  - June 2023: 45 countries had PV greater than 5 percent of reserves, with 9 countries having a ratio greater than 20 percent.
- Flow indicators:
  - SDR Department payments as percent of GDP are less than 0.1 percent for 90 percent of members with negative net SDR positions.
  - Payments as a percentage of fiscal revenues are less than 0.5 percent for 90 percent of the sample.
- Heterogeneity and vulnerabilities:
  - LICs show greater increases in expected cost over time relative to EMs, especially on flow measures.
  - Combined exposure and reserve adequacy:
    - 5 EMs and 9 LICs have PV > 1 percent of GDP while having reserves < 100 percent of the IMF’s ARA metric.
    - Among LICs with reserves < 100 percent of ARA, South Sudan and Zimbabwe have PV above 3 percent of GDP.
    - Among EMs, Jamaica has PV at about 3 percent of GDP with reserves < 100 percent of ARA.
  - Debt-vulnerability intersections:
    - EMs: Jamaica and Suriname have PV > 2 percent of GDP and total public debt > 60 percent of GDP.
    - EMs: Jamaica, Suriname, and Venezuela have PV > 2 percent of GDP and external debt > 60 percent of GDP.
    - LICs: Burundi, Central African Republic, South Sudan, São Tomé and Principe, Yemen, and Zimbabwe have PV > 2 percent of GDP and total public debt > 40 percent of GDP.
    - LICs: São Tomé and Principe, Yemen, and Zimbabwe have PV > 2 percent of GDP and external debt > 40 percent of GDP.
  - Some countries have large credit outstanding to the IMF’s PRGT and General Resources Account that may compound capacity weaknesses.

### Stress test scenario and sensitivity analysis — design and outcomes
- Stress scenario design:
  - Forward rates at year 30 onward assumed higher than baseline by one standard deviation of the historical SDR interest rate (2.9 percentage points).
  - From years 0 to 30, SDR forward rates rise linearly from the baseline projection in quarter 0 to the new higher steady-state interest rate in year 30 onward (a “higher-for-longer” scenario).
- Stress scenario outcomes:
  - Median converter’s PV cost increases from $134 million to $196 million.
  - Average PV of SDR Department obligations:
    - LICs: 1.60 percent of GDP.
    - EMs: 0.89 percent of GDP.
  - Members with PV > 2 percent of GDP:
    - Baseline: 9 members.
    - Stress scenario: 21 members.
  - Members with PV > 20 percent of reserves:
    - Baseline: 9 members.
    - Stress scenario: 17 members.
  - Despite deterioration in indicators, no country is expected not to be able to service SDR Department obligations currently.
- Concessionality impacts under stress:
  - Under a 5 percent discount rate and no cancellation, stress scenario reduces the grant element from about thirty-four percent to about three percent.
- Sensitivity to SDR cancellation:
  - SDR cancellation at twenty years would reduce the grant element from 34 to 21 percent for the June 2023 forward curve vintage (assuming no cancellation in baseline).
- Sensitivity to discount-rate choice:
  - Baseline uses uniform 5 percent discount rate.
  - Increasing the discount rate from 5 percent to 8 percent (no cancellation) raises the grant element from 34 percent to 58 percent using the end-June 2023 SDR forward curve.
  - Using an 8 percent discount rate in the stress scenario yields a grant element of 44 percent, compared to 3 percent under a 5 percent discount rate.
  - Country-specific discount rates could reflect issuer-specific sovereign risk; riskier debtors may warrant higher discount rates.

### Table 3 (selected grant element entries — June 2023 forward curve)
- Baseline concessionality (June 2023 forward curve):
  - Discount rate None / Cancellation horizon 1Y 2Y 5Y 10Y 20Y 30Y: 1% -3% -6% -12% -22% -40% -58% -225%
  - Discount rate 3%: -1% -2% -3% -3% -4% -5% -9%
  - Discount rate 5%: 1% 2% 6% 12% 21% 26% 34%
  - Discount rate 8%: 4% 7% 17% 30% 45% 52% 58%
  - Discount rate 10%: 5% 10% 24% 40% 56% 62% 66%
- Stress test concessionality (June 2023 SDRi forward curve vintage stress scenario):
  - Discount rate None / Cancellation horizon 1Y 2Y 5Y 10Y 20Y 30Y: 1% -3% -6% -13% -26% -57% -93% -474%
  - Discount rate 3%: -1% -2% -4% -7% -17% -29% -73%
  - Discount rate 5%: 1% 2% 5% 9% 11% 9% 3%
  - Discount rate 8%: 4% 7% 16% 28% 38% 41% 44%
  - Discount rate 10%: 5% 10% 23% 37% 50% 54% 56%
- Change in grant element due to stress (June 2023 vintage, baseline vs stress):
  - Discount rate None / Cancellation horizon 1Y 2Y 5Y 10Y 20Y 30Y: 1% 0% 0% -1% -4% -17% -35% -249%
  - Discount rate 3%: 0% 0% -1% -4% -13% -24% -64%
  - Discount rate 5%: 0% 0% -1% -3% -10% -17% -31%
  - Discount rate 8%: 0% 0% -1% -3% -7% -11% -14%
  - Discount rate 10%: 0% 0% -1% -2% -6% -8% -10%

### Policy-relevant implications and recommendations
- The rise in SDR interest costs has materially reduced the grant element of SDRs as a financing instrument; financing terms of SDRs moved to just below the IMF’s concessionality threshold of 35 percent as of end-June 2023.
- Recommendations and operational uses:
  - Consider SDR Department obligations when determining macroeconomic and financial policy settings for members with sizeable SDR obligations to ensure adequate capacity to service them over time.
  - Use additional interest rate projection methodologies (for example, surveys) and more granular projections (including potential changes to the foreign exchange composition and currency weights of the SDR basket).
  - Conduct different types of stress tests, including attenuated and near-term shocks to the SDR interest rate, and sensitivity analysis related to reconstitution of SDRs.
  - Operational applications:
    - SDR forward curves from this exercise can be used in IMF staff tools such as debt sustainability analyses and assessments of aggregate negative SDR Department balances.
    - Methodology and results can inform capacity assessments for countries with large credit outstanding to the IMF.
    - Findings can inform members’ decisions to convert SDR holdings, incorporating interest-rate risks.
    - Forward curve methodology can be used by foreign exchange reserve managers to forecast expected cost of a negative net SDR Department position.

### Annex and robustness notes
- Robustness check: forward curves derived using WEO data yield results consistent with the market-implied primary method.
- WEO-based method advantages: consistency, stability, less subject to market volatility, replicable by country authorities and IMF country teams.
- WEO data gaps noted (e.g., China short-term deposit rates for certain months) were filled with reasonable assumptions; WEO projection periods are five years with final year value treated as the terminal rate.
- Primary method: market-determined data, reflects market’s “best guess” but may incorporate risk- and term-premia.

*Source: IMF Working Paper — The Financial Cost of Using Special Drawing Rights: Implications of Higher Interest Rates (Working Paper No. WP/23/193) — Introduction.*

### Introduction ...........................................................................................................

### Introduction

### Operations of the SDR Department
- Section present in the content unit; details likely cover institutional operations and mechanics of the SDR Department.

### The expected cost of SDR conversion
- Section present in the content unit; addresses expected financial cost of converting SDRs.

### Deriving forward rates using zero coupon curves
- Section present in the content unit; outlines methodology for deriving forward rates from zero-coupon yield curves.
- Related table: Table 1. Composition and Weights of the SDR Basket.

### Results and sensitivity analysis
- Section present in the content unit; presents empirical results and sensitivity checks.
- Related table: Table 2. Illustrative Nelson-Siegel-Svensson Estimates for Zero-Coupon Yield Curves in August 2021.
- Related figure: Figure 4. 3-Month SDR Interest Rate Forward Curves Based on Market-Implied Estimates.

### SDR forward curves for different vintages and expected costs for IMF members
- Section present in the content unit; compares forward curves across vintages and reports expected costs for IMF members.
- Related figures: Figure 4. 3-Month SDR Interest Rate Forward Curves Based on Market-Implied Estimates; Figure 5. PV of SDR Department Obligations and Expected 2023 Payments for IMF Members; Figure 6. Expected Grant Element of SDRs and Other Facilities at Different Forward Curve Vintages.

### Assessing IMF members’ capacity to service SDR Department obligations
- Section present in the content unit; assesses members’ capacity through metrics such as reserves and debt.
- Related figures: Figure 7. Distribution of Expected Cost of SDRs Over Time and for LICs vs EMs; Figure 8. Members’ Capacity to Service SDR Department Obligations—Reserves; Figure 9. Members’ Capacity to Service SDR Department Obligations—Debt.

### Stress test scenario and sensitivity analysis
- Section present in the content unit; applies stress testing and additional sensitivity analyses.
- Related figure: Figure 10. Stress Rest Results.

### Concluding remarks
- Section present in the content unit; synthesizes findings and implications.

### Annex. SDR interest rate forward curves
- Annex present; contains SDR interest rate forward curves.
- Related table: Table 3. Grant Element of SDRs with Cancellation and with Variable Discount Rates.

Figures and tables included in the content unit (selection)
- Figures: 1. SDR Allocations; 2. SDR Interest Rate Since the 2021 General Allocation; 3. Stylized Central Bank Balance Sheet; 4. 3-Month SDR Interest Rate Forward Curves Based on Market-Implied Estimates; 5. PV of SDR Department Obligations and Expected 2023 Payments for IMF Members; 6. Expected Grant Element of SDRs and Other Facilities at Different Forward Curve Vintages; 7. Distribution of Expected Cost of SDRs Over Time and for LICs vs EMs; 8. Members’ Capacity to Service SDR Department Obligations—Reserves; 9. Members’ Capacity to Service SDR Department Obligations—Debt; 10. Stress Rest Results.
- Tables: 1. Composition and Weights of the SDR Basket; 2. Illustrative Nelson-Siegel-Svensson Estimates for Zero-Coupon Yield Curves in August 2021; 3. Grant Element of SDRs with Cancellation and with Variable Discount Rates.

Glossary (selected acronyms appearing in the content unit)
- BoE, DLP, ECB, ECF, EMDC, EUR, FIN, FV, GAS, GBP, IDA, IMF, JPY, LIC, LIC-DSF, NIR, NPV, NSS, PRGT, PV, RMB, SDR, USD, VTAs, WEO.

*Source: wpiea2023193-print-pdf - Introduction*

### Introduction

### Introduction

### Purpose and scope
- Special Drawing Rights (SDRs) are international reserve assets created by the IMF to supplement its member countries’ official reserves.
- Most recently, a general allocation of SDR 456.5 billion (equivalent to about US$650 billion) was implemented on August 23, 2021.
- The paper has two objectives:
  - Estimate the expected cost of using SDRs for countries with negative SDR Department positions.
  - Assess implications of expected SDR Department payments for IMF members’ capacity to pay charges to the SDR Department.

### Operational context and mechanics
- In the SDR Department, IMF members receive interest on cumulative SDR holdings and are assessed charges against cumulative SDR allocations; both are assessed at the SDR interest rate.
- A negative net SDR Department position (holdings < allocations) generates net interest expense (“charges”) to the SDR Department at the SDR interest rate.
- The SDR interest rate is a floating rate determined weekly by a formula based on the weighted average of interest rates of SDR basket currencies with a floor set at 5 basis points.
- SDR uses: retain as reserves; (i) transactions to get freely usable currencies; (ii) Fund-related operations; or (iii) IMF‑authorized operations with SDR Department participants or prescribed holders.

### Recent evolution of the SDR interest rate
- SDR interest rate has risen from 5 basis points in August 2021 to 395 basis points as of end-June 2023.
- Implied SDR forward curves indicate the SDR forward rate curve over the 30-year horizon rose about 230 basis points on average from August 2021 to June 2023.
- The June 2023 SDR forward curve is inverted in the 0–5-year time horizon.

### Main findings on expected cost and concessionality
- The median expected present value (PV) cost among IMF members with negative net SDR Department positions of converting SDRs:
  - Increased from $37 million in August 2021 to $134 million in June 2023 — an increase of 262 percent.
- The median one-year-ahead annual expected cost:
  - Increased from $0.1 million in August 2021 to $7.8 million in June 2023 — a nearly eighty-fold increase.
- For higher-exposure members:
  - Top quartile one-year-ahead cost: $19 million; PV cost: $333 million.
  - Largest nominal negative SDR Department position: one-year-ahead $259 million; PV $4,471 million.
- The grant element (concessionality) of SDRs:
  - Declined from about 80 percent in August 2021 to 34 percent at end-June 2023 (concessionality threshold convention: greater than 35 percent).
  - If SDRs were cancelled or the interest rate rises further, the grant element would fall further.
- Overall assessment: IMF members’ exposure to upcoming SDR Department charges is generally manageable under baseline and stress scenarios, although for some members increased financial cost can be material.

### Methodology overview
- Expected cost definition: PV of all future net interest payments and face value payments of SDRs for the projection period.
- Key modelling assumptions and parameter choices:
  - IMF Board of Governors will not decide to cancel SDRs nor request member states to reconstitute them in the baseline scenario.
  - Basket weights fixed at the initial 2015 weights through July 2022, then follow August–2022 basket weights for the rest of the projection period.
  - SDR basket instruments are fixed for the projection period.
  - SDR Department charges are assessed on a quarterly basis at a constant, imputed interest rate for that quarter (quarterly average of weekly SDR interest rate).
  - Discount rate (r) is assumed to be 5 percent for all IMF members.
  - Members’ SDR holdings are assumed converted in period 0 and unchanged thereafter; interest expense begins in period 1 (q=1) into perpetuity under the baseline.
  - Market data are used for the first thirty years (120 quarters) of the projection horizon; the expected SDR interest rate in quarter 120 is assumed constant for quarters 121 into perpetuity (terminal rate).
- Forward-curve construction:
  - Implied SDR forward rates derived from market-determined interest rates of SDR basket currencies (US dollar, Japanese yen, euro, U.K. pound sterling, Chinese renminbi).
  - Forward curves derived at multiple vintages: August 23, 2021; January 1, 2022; end-June, 2023.
  - Two-step approach to derive forward curves for each SDR basket currency:
    - Step 1: Estimate zero-coupon bond yield curves using regression-based (Nelson-Siegel-Svensson (NSS)) or interpolation techniques depending on currency.
    - Step 2: Derive implied three-month forward rates from zero-coupon curves using no-arbitrage conditions.
  - Implied SDR forward curve computed by weighting currency forward rates by SDR basket currency amounts (weights fixed per valuation reviews).
- Data and robustness:
  - Zero-coupon yield curve data sourced from central bank websites (Fed, ECB, BoE), Bloomberg, CEIC.
  - Forward-curve results complemented and assessed for robustness using WEO projections (Annex).

### SDR basket composition (valuation review weights and currency amounts)
- Oct. 2016–Jul. 2022 (2015 Valuation Review):
  - USD US dollar: 41.7% — currency amount fixed 0.58252
  - EUR Euro: 30.9% — currency amount fixed 0.38671
  - RMB Chinese yuan: 10.9% — currency amount fixed 1.0174
  - JPY Japanese yen: 8.3% — currency amount fixed 11.900
  - GBP Pound sterling: 8.1% — currency amount fixed 0.085946
- Aug. 2022–Jul. 2027 (2022 Valuation Review):
  - USD US dollar: 43.4% — currency amount fixed 0.57813
  - EUR Euro: 29.3% — currency amount fixed 0.37379
  - RMB Chinese yuan: 12.3% — currency amount fixed 1.0993
  - JPY Japanese yen: 7.6% — currency amount fixed 13.452
  - GBP Pound sterling: 7.4% — currency amount fixed 0.080870

### Policy-relevant implications highlighted
- The rise in SDR interest costs has materially reduced the grant element of SDRs as a financing instrument; financing terms of SDRs moved to just below the IMF’s concessionality threshold of 35 percent as of end-June 2023.
- Higher and sustained SDR interest rates increase the financial cost of using SDRs, potentially affecting some members’ capacity to service obligations to the SDR Department—particularly LICs and credit-constrained EMDEs facing rising debt vulnerabilities and tighter financing conditions.
- The expected cost estimates are intended as input into country-specific cost-benefit analyses of SDR conversion decisions, recognizing that conversions may be offset by returns on proceeds or may affect external sustainability.

*Source: IMF Working Paper — Introduction (wpiea2023193-print-pdf - Introduction)*

### 2023. The numbers for IDA and the ECF are based on illustrative estimates discussed in International Monetary Fund (2023

### The Financial Cost of Using Special Drawing Rights: Implications of Higher Interest Rates (2023)

### Assessing IMF members’ capacity to service SDR Department obligations
- Analysis uses public information on IMF members with negative net open positions vis-à-vis the SDR Department (i.e., SDR holdings less SDR allocations).
- Two SDR interest-rate forward curve vintages are used for baseline comparisons: August 2021 and end-June 2023.
- Calculations use SDR forward curves at a 5 percent discount rate, assume no SDR cancellation, and use net short positions as of end-June 2023 to isolate interest-rate expectation effects across vintages.
- Outlier observations (values exceeding 1.5 times the interquartile range) are not shown in some figures but are included in histograms when discussing manageability on an individual-country basis.
- Data sources: Bloomberg, WEO, IMF (2023a), and authors’ calculations.

### Key findings on exposure and manageability
- Sample: 59 LIC and 62 EM IMF members with negative net SDR Department positions.
- Expected cost of SDRs has risen between vintages:
  - Using August 2021 forward curve: five countries had a PV of SDR Department payments greater than 1 percent of GDP.
  - Using June 2023 forward curve vintage: 36 countries had a PV of SDR Department payments greater than 1 percent of GDP (about 31 percent of all members).
- Reserve-based metrics:
  - August 2021: 14 countries had PV of SDR Department payments greater than 5 percent of gross foreign exchange reserves.
  - June 2023: 45 countries had PV greater than 5 percent of reserves, with 9 countries having a ratio greater than 20 percent.
- Flow indicators of manageability:
  - SDR Department payments as a percent of GDP are less than 0.1 percent for 90 percent of members with negative net SDR positions.
  - Payments as a percentage of fiscal revenues are less than 0.5 percent for 90 percent of the sample.

### Heterogeneity and identified vulnerabilities
- LICs show greater increases in expected cost over time relative to EMs, particularly on flow measures (SDR Department payments to GDP and fiscal revenues).
- Combined exposure and reserve adequacy:
  - 5 EMs and 9 LICs have a PV of SDR Department obligations greater than 1 percent of GDP while having reserves less than 100 percent of the IMF’s ARA metric.
  - Among LICs with reserves less than 100 percent of the IMF’s ARA metric, South Sudan and Zimbabwe have PV of SDR Department obligations above 3 percent of GDP.
  - Among EMs, Jamaica has a PV of SDR Department obligations at about three percent of GDP with reserves less than 100 percent of the IMF’s ARA metric.
- Debt-vulnerability intersections:
  - Out of 62 EMs, two countries (Jamaica and Suriname) have PV of SDR Department obligations greater than 2 percent of GDP and total public debt greater than 60 percent of GDP.
  - Three EMs with PV of SDR Department exposures greater than 2 percent of GDP also have external debt levels greater than 60 percent of GDP: Jamaica, Suriname, and Venezuela.
  - Out of 59 LICs, six countries (Burundi, Central African Republic, South Sudan, São Tomé and Principe, Yemen, and Zimbabwe) have PV of SDR Department obligations greater than 2 percent of GDP and total public debt greater than 40 percent of GDP.
  - Three LICs (São Tomé and Principe, Yemen, and Zimbabwe) have PV of SDR obligations greater than 2 percent of GDP and external debt greater than 40 percent.
- Additional vulnerability note: Some of these countries also have large credit outstanding to the IMF’s PRGT and General Resources Account that may contribute to weakness in capacity to service SDR Department obligations.

### Policy implications and recommendations
- Countries should take SDR Department obligations into account when determining macroeconomic and financial policies to ensure adequate capacity to service obligations over time.
- For IMF members with low levels of SDR holdings, early purchases of SDRs to meet payments of charges to the SDR Department and the GRA would be beneficial to reduce the risk of arrears, recognizing this may increase operational costs by requiring additional transactions.
- IMF staff can assist members through policy advice and technical assistance on broader external debt management issues.

### Stress test scenario and sensitivity analysis
- Stress scenario design:
  - Forward rates at year 30 onward are assumed higher than baseline by one standard deviation of the historical SDR interest rate (2.9 percentage points).
  - From years 0 to 30, SDR forward rates rise linearly from the baseline projection in quarter 0 to the new higher steady-state interest rate in year 30 onward to represent a “higher-for-longer” scenario.
- Stress scenario outcomes:
  - Median converter’s cost (present value of expected payments) increases from $134 million to $196 million.
  - Average PV of SDR Department obligations:
    - LICs: 1.60 percent of GDP.
    - EMs: 0.89 percent of GDP.
  - Number of members with PV of SDR Department obligations greater than 2 percent of GDP increases to 21 in the stress scenario compared to 9 in the baseline.
  - Number of members with PV greater than 20 percent of reserves increases to 17 in the stress scenario compared to 9 in the baseline.
  - Despite weakening indicators, no country is expected not to be able to service SDR Department obligations currently.
- Concessionality impacts under stress:
  - Under a 5 percent discount rate and assumptions of no cancellation, the stress scenario reduces the grant element of the SDR by 31 percentage points—from about thirty-four percent to about three percent.
- Sensitivity to SDR cancellation:
  - SDR cancellation at twenty years would reduce the grant element of SDRs from 34 to 21 percent for the June 2023 forward curve vintage (assuming no cancellation in baseline).
- Sensitivity to discount-rate choice:
  - Analysis uses a uniform 5 percent discount rate per convention.
  - Increasing the discount rate from 5 percent to 8 percent (assuming no cancellation) raises the grant element from 34 percent to 58 percent using the end-June 2023 SDR forward curve.
  - Using an 8 percent discount rate in the stress scenario yields a grant element of 44 percent, compared to 3 percent under a 5 percent discount rate.
  - Country-specific discount rates could be used to reflect issuer-specific sovereign risk; riskier debtors may warrant higher discount rates.

*Source: IMF Working Paper — The Financial Cost of Using Special Drawing Rights: Implications of Higher Interest Rates (figures and calculations based on IMF (2023a), Bloomberg, WEO, and authors’ calculations).*

### 6. SDR Department Payments (est.) / Fiscal

### 6. SDR Department Payments (est.) / Fiscal

### Key quantitative findings
- Since the August 2021 general allocation, the SDR interest rate has risen by over 390 basis points.
- Over the same period, the expected path of SDR interest rates has shifted upward by about 230 basis points on average across the forward curve.
- For the median country, the expected cost based on the present value of net SDR Department payments has increased almost threefold.
- The grant element of SDRs is 34 percent, or below the IMF’s concessionality threshold of 35 percent.
- Average present value (PV) of SDR Department obligations is less than 2 percent of GDP for 82 percent of countries.

### Table 3 (Grant Element of SDRs with Cancellation and with Variable Discount Rates)
- June 2023 SDR forward curve (baseline and stress scenarios) reporting grant element values across cancellation horizons and discount rates. Selected entries as reported:
  - Baseline concessionality (June 2023 forward curve):
    - Discount rate None / Cancellation horizon 1Y 2Y 5Y 10Y 20Y 30Y: 1% -3% -6% -12% -22% -40% -58% -225%
    - Discount rate 3%: -1% -2% -3% -3% -4% -5% -9%
    - Discount rate 5%: 1% 2% 6% 12% 21% 26% 34%
    - Discount rate 8%: 4% 7% 17% 30% 45% 52% 58%
    - Discount rate 10%: 5% 10% 24% 40% 56% 62% 66%
  - Stress test concessionality (June 2023 SDRi forward curve vintage stress scenario):
    - Discount rate None / Cancellation horizon 1Y 2Y 5Y 10Y 20Y 30Y: 1% -3% -6% -13% -26% -57% -93% -474%
    - Discount rate 3%: -1% -2% -4% -7% -17% -29% -73%
    - Discount rate 5%: 1% 2% 5% 9% 11% 9% 3%
    - Discount rate 8%: 4% 7% 16% 28% 38% 41% 44%
    - Discount rate 10%: 5% 10% 23% 37% 50% 54% 56%
  - Change in grant element due to stress test (June 2023 vintage, baseline vs stress scenario):
    - Discount rate None / Cancellation horizon 1Y 2Y 5Y 10Y 20Y 30Y: 1% 0% 0% -1% -4% -17% -35% -249%
    - Discount rate 3%: 0% 0% -1% -4% -13% -24% -64%
    - Discount rate 5%: 0% 0% -1% -3% -10% -17% -31%
    - Discount rate 8%: 0% 0% -1% -3% -7% -11% -14%
    - Discount rate 10%: 0% 0% -1% -2% -6% -8% -10%

### Interpretation and implications
- The financing terms of SDRs are substantially higher and now slightly below the IMF’s concessionality threshold.
- The grant element of SDR use would decline further if:
  - interest rates were to increase further;
  - a discount rate lower than 5 percent is used;
  - the SDR allocation were to be cancelled after 30 years or sooner.
- Most IMF members’ capacity to service SDR Department obligations remains broadly adequate, though there are some exceptions where SDR Department obligations are a significant part of external debt stock or occur alongside lower reserves coverage or higher debt levels.
- In a stress scenario, capacity-to-service indicators generally deteriorate, but SDR obligations would remain relatively manageable for most members.

### Policy-relevant recommendations and operational uses
- Consider SDR Department obligations when determining macroeconomic and financial policy settings for members with sizeable SDR obligations to ensure adequate capacity to service them over time.
- Use additional interest rate projection methodologies (for example, surveys) and more granular projections (including potential changes to the foreign exchange composition and currency weights of the SDR basket).
- Conduct different types of stress tests, including a more attenuated and near-term shock to the SDR interest rate, and sensitivity analysis related to reconstitution of SDRs.
- Operational applications:
  - SDR forward curves constructed in this exercise can be used as inputs in IMF staff tools, such as debt sustainability analyses and assessments of aggregate negative SDR Department balances.
  - Methodology and results could be used to assess capacity to service SDR Department obligations in countries with large credit outstanding to the IMF.
  - Findings can inform IMF members’ decisions to convert SDR holdings, incorporating interest rate risks.
  - Forward curve methodology can be used by foreign exchange reserve managers to forecast the expected cost of having a negative net SDR Department position.

### Annex — Forward curve robustness and primary method notes
- Robustness check: forward curves derived using WEO data (official forecasts) yield results consistent with the market-implied primary method.
- WEO-based method advantages: consistency, stability, less subject to market volatility, replicable by country authorities and IMF country teams.
- WEO data gaps: e.g., no January 2020 nor March 2020 short-term deposit rate information available for China; gaps filled by assuming rates equal to the December 2020 vintage.
- WEO projection periods are five years; final year value is assumed to be the terminal rate for the relevant basket currency.
- Differences between methods:
  - Primary method: market-determined data, reflects market’s “best guess” but may incorporate risk- and term-premia.
  - Robustness check: official forecasts, less noisy, may produce flatter outer-year forward curves due to five-year projection horizon.

*Source: IMF Working Paper — The Financial Cost of Using Special Drawing Rights: Implications of Higher Interest Rates (Working Paper No. WP/23/193).*

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_Source: https://www.imf.org/-/media/files/publications/wp/2023/english/wpiea2023193-print-pdf.pdf_