## tarea2025051-print-pdf ## Source details **Canonical URL:** [tarea2025051-print-pdf](https://www.imf.org/-/media/files/publications/tar/2025/english/tarea2025051-print-pdf.pdf) ## Other formats - [Markdown version](/-/media/files/publications/tar/2025/english/tarea2025051-print-pdf.pdf.md) - [Structured JSON version](/-/media/files/publications/tar/2025/english/tarea2025051-print-pdf.pdf.json) --- ### Mission overview and participants - A Monetary and Capital Markets (MCM) Department mission visited Pretoria, South Africa, from July 17–26, 2024, at the request of the South African Reserve Bank (SARB). - Mission composition: Darryl King and Yuji Sakurai attended in person; Luyao Liu participated virtually. - Senior officials met: Deputy Governors Rashad Cassim and Mampho Modise; Advisor to the Governors David Fowkes; Chief Operating Officer Pradeep Maharaj. - Departments consulted: Financial Services, Legal, Economic Research, Financial Markets, and Financial Stability. - Purpose: Assist the SARB in stress testing its balance sheet and calibrating risk-based capital buffers, notably for the Gold and Foreign Exchange Contingency Reserve Account (GFECRA). - The mission demonstrated a Central Bank Stress Testing (CBST) model that produces total equity decomposed into realized earnings and the revaluation account and includes satellite models for items such as currency in circulation (CiC). ### Executive Summary — Major findings and framework outcomes - Prior recommendations (December 2023 mission): - Establish a high-level framework for distributing amounts accrued in GFECRA. - Establish a risk-based buffer for the contingency reserve (i.e., equity). - SARB and the National Treasury (NT) to publish a memorandum of understanding for transparency. - Principles agreed in February 2024 Budget: - SARB’s policy solvency should not be undermined by any GFECRA distribution. - No sales of foreign exchange (FX) to realize GFECRA gains if reserves are below estimated adequacy levels. - No distribution of unrealized GFECRA balances that could plausibly be unwound by future rand appreciations. - GFECRA distributions will be used to reduce government borrowing. - Any GFECRA distributions should be governed by a framework that rules out ad hoc decisions. - GFECRA settlement arrangements should be public to ensure transparency. - Waterfall distribution framework (high level): - First: GFECRA buffer calibrated to absorb large and plausible rand appreciations. - Second: Surplus transfers to the Contingency Reserve (equity buffer) calibrated to meet SARB losses including monetary operational costs (e.g., interest on excess reserves). - Third: Once contingency reserve buffer satisfied, surplus funds transferred to the National Treasury (NT). - February 2024 preliminary calibrations and transfers: - GFECRA buffer for the first year set at ZAR 250 billion, allowing for distribution of ZAR 250 billion. - Net transfer to NT agreed as ZAR 150 billion, implemented as: - ZAR 250 billion paid by SARB to NT and ZAR 100 billion transferred from NT to SARB (to reduce government borrowing). - ZAR 100 billion transferred to the SARB’s Contingency Reserve; no explicit target set for that buffer. - Institutional recommendations: - Institutionalize and publicly communicate methodologies for annual recalibration of GFECRA and contingency reserve buffers. - Assign ownership and dedicated staff to operate and run the CBST on a regular basis. - Ensure macroeconomic inputs to the CBST are consistent with internal macroeconomic projections used for policymaking. ### Key recommendations (summary) - 1. Assign responsibility, identify dedicated staff, and build relevant modeling capacity, including at-risk methodologies for inflation and FX. — Authority: SARB — Timeframe: Near-term - 2. Further develop satellite models (i.e., for CiC). — Authority: SARB — Timeframe: Medium-term - 3. Determine and agree with the NT on risk appetite appropriate for the calibration of GFECRA and Contingency Reserve buffers. — Authority: SARB/NT — Timeframe: Near-term - 4. Run the model at least annually using different macro scenarios to recalibrate the risk-based buffers. — Authority: SARB — Timeframe: Medium-term - Note: Near-term: < 12 months; Medium-term: 12 to 24 months. ### SARB financial structure, exposures, and objectives of the report - SARB is privately owned, with fixed statutory capital and no explicit recapitalization clause. - Government has a direct claim on revaluation gains that accumulate in GFECRA and is obligated to top up losses in that account (as occurred in 2003). - Foreign reserves represent 89 percent of assets (March 2024). - GFECRA represented 40 percent of the balance sheet (liabilities plus equity) (March 2024). - Prior to February 2024 budget, GFECRA was around ZAR 500 billion (7 percent of GDP). - Objectives of the report: - Quantitatively assess an appropriate GFECRA buffer. - Assess adequacy of the contingency reserve. - Help institutionalize a process to project SARB balance sheet under macro scenarios and to recalculate buffers annually using the CBST. ### Central Bank Stress Test (CBST) framework — policy solvency and model features - Policy solvency concept: - A central bank is “policy solvent” if, over time, it has realized earnings greater than its monetary policy and operating costs. - Financial arrangements and distributions should be grounded in the SARB’s legal framework and should not undermine policy solvency. - Model features: - Incorporates accounting rules and equations from macroeconomics and finance. - Generates total equity decomposed into realized earnings and the revaluation account. - Satellite models forecast key balance sheet items (e.g., CiC) conditional on macro scenarios. - Scenario design: - Base scenario: low but stable GDP growth with mild inflation. - Adverse scenario: external shocks induce temporary negative macro shock, recovery assumed after 2026. ### Core equations and satellite models (as specified) - Equity accounting identities: - (1) Equity_t = Total Assets_t − Total Liabilities_t - (2) Equity_t = Equity_{t−1} + Realized earnings_t + Reval Account_t - Excess reserves dynamic (ResEx paid at policy rate): - ResEx_t = ResEx_{t−1} + [ΔFXInt_t + ΔGovBond_t + ΔNT − ΔCiC_t − ΔResReq_t + IRExpense_t + Op_t] - Gross foreign reserves dynamic (simplest case): - FXRes_t = FXRes_{t−1} + FIRIncome_t + Revaluation^{FXRes}_t + ΔFXInt_t - CiC satellite specification: - CiC_t = η_{CiC} NGDP_t ⋅ (i0 / i_t)^{γ_{CiC}} - Required reserves in ZAR: - ResReq_t = η_{Req} NGDP_t + i_{req,t−1} ResReq_{t−1} - Two options for remuneration: zero interest or interest at policy rate; default used is zero. - Policy rate via simplified Taylor rule: - i_t = ρ_i i_{t−1} + (1−ρ_i) \bar{i}_t + σ_i ε_{i,t} - Target \bar{i}_t = \bar{π} + r^* + γ_π (π_t − \bar{π}) + γ_y (y_t − \bar{y}) ### GFECRA buffer calibration — VaR-based specification and findings - Two buffer specifications considered: - Prespecified deterministic function of time. - Value-at-Risk (VaR) for FX reserves aggregated across currencies: - GFECRA Buffer_t = ∑_{i=1}^N E_i ⋅ (1 − exp((μ_i − 0.5 σ_i^2) τ + √τ σ_i VaR(α))) - μ_i = average log return of exchange rate; σ_i = volatility of log return; τ = time horizon; α = percentile of VaR; VaR(α) is percentile of standard normal distribution. - Dependence between exchange rates is not modeled; specification assumes correlations equal to one for conservativeness. - Key quantitative result: - SARB’s current calibration of the GFECRA buffer (ZAR 250 billion) is close to the 5th percentile with 2-year time horizon (243 billion ZAR). - Recommendation: - SARB should employ a quantitative VaR-based approach for annual recalibrations reflecting: - (i) size of exposure for each currency; - (ii) exchange rate uncertainty (statistical moments such as volatility); - (iii) risk tolerance parameters (percentile and time horizon of VaR), which are policy decisions. ### Contingency reserve (equity) assessment and adequacy - Current equity buffer after the budgeted ZAR 100 billion transfer: ZAR 142 billion (42 billion ZAR + 100 billion ZAR). - Assessment approach: - Use combination of FX-at-Risk and Inflation-at-Risk scenarios to compute number of years to deplete equity. - For interpretability, additional distribution of GFECRA to equity beyond scheduled transfer is turned off in this exercise. - Illustrative VaR assumption: 1-percentile over a two-year horizon used for sensitivity (highly conservative). - Key findings: - Under the severest combination of FX-at-Risk and Inflation-at-Risk, equity (ZAR 142 billion) is forecasted to remain positive over the next 13 years. - Buffer estimates sensitive to assumptions: - If SARB purchases USD over next five years, cost of financing the USD purchase adds to excess reserves → larger interest expenses → buffer could decrease. - Potential credit risks from lender of last resort function are not captured; including them could lead to a higher buffer. - Changes in CiC dynamics would affect buffer estimates. ### Scenario results — Base, Adverse, and At-Risk highlights (selected quantitative outcomes) - Base scenario macro assumptions: - Real GDP growth expected to grow to 1 percent in 2024; projected to stabilize at 1.4 percent in the medium run absent accelerated structural reforms. - Base scenario results (no GFECRA distributions): - Equity reaches 1.3 percent of GDP by 2028Q4. - Base scenario with scheduled transfers (February 2024 budget): - Equity will reach 1.9 percent by 2028Q4. - Equity increases rapidly by around 100 billion during 2023–2024 due to transfer from GFECRA to the contingency reserve. - GFECRA declines by ZAR 250 billion because of its distribution, then starts to increase with continued ZAR depreciation. - Adverse scenario (external shocks, higher inflation, mild ZAR depreciation): - Equity increases more rapidly than in the base scenario, reaching 2.2 percent by 2028Q4. - Explanation: larger ZAR depreciation increases foreign interest income; net positive effect on equity outweighs higher interest expenses. - At-Risk scenarios (examples): - Growth-at-Risk example: Real GDP growth declines to −7 percent in 2024, then recovers; lower policy rate reduces interest expenses → equity increases faster than base. - Inflation-at-Risk (95th percentile): Inflation rises to 10 percent in 2024 then declines to base-case level; equity will reach 1.4 percent in 2028Q4. - FX-at-Risk (5th percentile): ZAR appreciates by 49 percent over five years; equity will reach 1.4 percent in 2028Q4. - Additional quantified outcomes (sensitivity checks): - Constant required reserves scenario: Equity will reach 1.8 percent in 2028Q4 (0.1 percent lower than base). - Foreign reserve accumulation scenario (20 percent increase in USD terms): Equity will start to decline in 2026Q1 and will reach 1.6 percent in 2028Q4 (0.3 percent lower than base). ### Historical context, plausible appreciation scenarios, and boxes summarized - Historical note: three-year historical log return example cited — three-year log return from 2001/12/31 to 2004/11/30 is −72.5 percent. - Box 1 — Combined Shocks of ZAR Appreciation and High Inflation: - Historical analysis 2000–2024 identifies three periods where ZAR appreciated while inflation exceeded 75 percent of recorded instances. - Box 2 — Possible Scenario of a Significant ZAR Appreciation: - Estimated USD/ZAR equation: FX_t = α0 + α1 I_t + α2 CDS_t (daily data 2014–2024). - Estimated coefficients and statistics (table): - α0 estimate: 0.0013; Standard Error 0.015; t-value 0.083; Pr(>|t|) 0.934. - α1 estimate: ***-1.1936; Standard Error 0.054; t-value -22.040; Pr(>|t|) 0.000. - α2 estimate: ***-0.1157; Standard Error 0.006; t-value -19.301; Pr(>|t|) 0.000. - Adjusted R-Square 0.385; Durbin-Watson Test Statistic = 2.286. - *** indicates statistical significance at the 99.9-percentile level. - Regression interpretation: implies ZAR expected to appreciate by approximately 29.73 percent assuming specified decreases in U.S. dollar index and CDS to 2014 levels; examples: 24 percent decrease in U.S. dollar index → 28.17 percent ZAR appreciation; 14 percent reduction in CDS → 1.57 percent ZAR appreciation. ### At-Risk methodology (Annex I) — overview and model construction - Four-step approach to forecast conditional distributions for real GDP growth, inflation, and ZAR/USD: - (i) Dimensionality reduction on explanatory variables via partial least squares regression (PLS). - (ii) Conditional average prediction using the Theil-Sen model (jackknife variant). - (iii) Skewness estimation using the Firth penalized-likelihood logistic regression. - (iv) Parameterize an asymmetrical Gaussian distribution assuming Theil-Sen variance. - At-risk percentiles used: - 95th percentile for adverse inflation. - 5th percentile for real GDP growth and FX appreciation as worst outcomes. - Synthetic regressor groupings (selected examples preserved exactly as in source): - Growth At-Risk model includes: Real GDP growth lag; Private consumption (percentage change); Central government deficit/surplus as percentage of GDP (first difference); Gross fixed capital formation (percentage change); Industrial production; Gold Index (percentage change); Crude Oil Index (percentage change); USA real GDP growth; China real GDP growth; REER (percentage change); Import (percentage change); Export (percentage change); Inflation (first difference); Policy rate (first difference); Predominant overdraft rate (first difference); Interbank rate (first difference); 3-month CD rate (first difference); FTSE/JSE all-share price index (percentage change). - Inflation-at-Risk model includes: Real GDP Growth; Import (percentage change); Export (percentage change); FTSE/JSE all-share price index (percentage change); USD/ZAR (first diff.); USD/EUR (first diff.); USD/SDR (first diff.); REER (percentage change); Policy rate (first diff.); Predominant overdraft rate (first diff.); Interbank rate (first diff.); 3-month CD rate (first diff.). - Exchange Rate-at-Risk model includes: Real GDP growth; FTSE/JSE all-share price index (percentage change); Inflation; Policy rate (first diff.); Predominant overdraft rate (first diff.); Interbank rate (first diff.); 3-month CD rate (first diff.); Current account balance to GDP (first diff.); Reserves and related items (first diff.); Financial account balance (first diff.). - Modeling choices and constraints: - Asymmetric Gaussian chosen for analytical tractability given three available moments (mean, variance, skewness). - Nonparametric or heavier-tailed asymmetric distributions not used due to limited sample size and requirement of additional moments (e.g., kurtosis). *Source: IMF staff, IMF Technical Assistance Report (Preface, Executive Summary, Introduction, I. Developments Since the 2023 Mission, and II. Central Bank Stress Test Framework sections).* ### Preface ................................................................................................................ ### Preface ### Mission overview and participants - A Monetary and Capital Markets (MCM) Department mission visited Pretoria, South Africa, from July 17–26, 2024, at the request of the South African Reserve Bank (SARB). - Mission composition: Darryl King and Yuji Sakurai attended in person; Luyao Liu participated virtually. - Senior officials met: Deputy Governors Rashad Cassim and Mampho Modise; Advisor to the Governors David Fowkes; Chief Operating Officer Pradeep Maharaj. - Departments consulted: Financial Services, Legal, Economic Research, Financial Markets, and Financial Stability. ### Purpose - Assist the SARB in stress testing its balance sheet and calibrating risk-based capital buffers, notably for the Gold and Foreign Exchange Contingency Reserve Account (GFECRA). ### Acknowledgements - The mission thanks staff, particularly David Fowkes, for cooperation and hospitality. ### Key factual items from the engagement - The mission demonstrated a Central Bank Stress Testing (CBST) model for institutionalizing balance-sheet forecasting under macro scenarios. - The model produces total equity decomposed into realized earnings and the revaluation account and includes satellite models for items such as currency in circulation (CiC). --- ### Executive Summary — Major findings and framework outcomes ### Background and prior recommendations - A December 2023 MCM mission assessed SARB’s financial arrangements with emphasis on GFECRA and recommended: - Establishing a high-level framework for distributing amounts accrued in GFECRA. - Establishing a risk-based buffer for the contingency reserve (i.e., equity). - SARB and the National Treasury (NT) to publish a memorandum of understanding for transparency. ### Principles agreed in February 2024 Budget - The SARB and NT announced principles underpinning a new financial framework: - The SARB’s policy solvency should not be undermined by any GFECRA distribution. - There should be no sales of foreign exchange (FX) to realize GFECRA gains if such reserves are below estimated adequacy levels. - There should be no distribution of unrealized GFECRA balances that could plausibly be unwound by future rand appreciations. - GFECRA distributions will be used to reduce government borrowing. - Any GFECRA distributions should be governed by a framework that rules out ad hoc decisions. - GFECRA settlement arrangements should be public to ensure transparency. ### Waterfall distribution framework and initial calibrations - The framework uses a “waterfall”: - First, a GFECRA buffer calibrated to absorb large and plausible rand appreciations. - Once met, surplus transfers to the Contingency Reserve (equity buffer) calibrated to meet SARB losses including monetary operational costs (e.g., interest on excess reserves). - Once that buffer is satisfied, surplus funds are transferred to the National Treasury (NT). - Preliminary agreement: GFECRA buffer for the first year set at ZAR 250 billion, allowing for distribution of ZAR 250 billion. - Net transfer to NT agreed as ZAR 150 billion, implemented as: - ZAR 250 billion paid by SARB to NT and ZAR 100 billion transferred from NT to SARB (to reduce government borrowing). - ZAR 100 billion transferred to the SARB’s Contingency Reserve; no explicit target set for that buffer. ### CBST modeling and scenarios - Two macro-scenarios used: - Base case: GDP growth low but stable with mild inflation. - Adverse case: external shocks cause temporary negative macro shock with assumed recovery after 2026. - SARB balance sheet characterized by relatively few interest-bearing liabilities, positive net foreign assets, and positive net claims on government. ### GFECRA buffer calibration - Mission recommended a value-at-risk (VaR) approach for FX revaluation losses. - Current calibration: ZAR 250 billion approximately corresponds to the 5th percentile with 2-year time horizon (243 billion ZAR). - This calibration is characterized as conservative and appropriate. ### Contingency reserve (equity) assessment - Current equity buffer after the budgeted ZAR 100 billion transfer: ZAR 142 billion. - The adequacy assessment uses a combination of FX-at-Risk and Inflation-at-Risk scenarios: - FX-at-Risk lowers foreign interest income (asset side). - Inflation-at-Risk raises domestic interest expenses on excess reserves (liability side). - Under the severest combination of FX-at-Risk and Inflation-at-Risk, equity (ZAR 142 billion) is forecasted to remain positive over the next 13 years. - Notes: - Required buffer increases for a given risk tolerance if foreign reserves are accumulated. - Potential credit risks from lender of last resort function are not accounted for in this assessment. ### Institutional recommendations and operationalization - SARB should institutionalize and publicly communicate methodologies for annual recalibration of GFECRA and contingency reserve buffers. - Assign ownership and dedicated staff to operate and run the CBST on a regular basis. - Ensure macroeconomic inputs to the CBST are consistent with internal macroeconomic projections used for policymaking. ### Key recommendations (Table 1) - 1. Assign responsibility, identify dedicated staff, and build relevant modeling capacity, including at-risk methodologies for inflation and FX. — Authority: SARB — Timeframe: Near-term - 2. Further develop satellite models (i.e., for CiC). — Authority: SARB — Timeframe: Medium-term - 3. Determine and agree with the NT on risk appetite appropriate for the calibration of GFECRA and Contingency Reserve buffers. — Authority: SARB/NT — Timeframe: Near-term - 4. Run the model at least annually using different macro scenarios to recalibrate the risk-based buffers. — Authority: SARB — Timeframe: Medium-term - Note: Near-term: < 12 months; Medium-term: 12 to 24 months. --- ### Introduction — Context and objectives ### SARB’s financial structure and risks - SARB is privately owned, with fixed statutory capital and no explicit recapitalization clause. - Government has a direct claim on revaluation gains that accumulate in GFECRA and is obligated to top up losses in that account (as occurred in 2003). - Foreign reserves are sizable: representing 89 percent of assets (March 2024). - GFECRA represented 40 percent of the balance sheet (liabilities plus equity) (March 2024). - Prior to February 2024 budget, GFECRA was around ZAR 500 billion (7 percent of GDP). - GFECRA contains both realized and unrealized gains, is a liability to the NT, and distributions require agreement of SARB and NT. ### Objectives of this report - Extend previous mission by: - Quantitatively assessing an appropriate GFECRA buffer. - Assessing adequacy of the contingency reserve. - Helping institutionalize a process to project SARB balance sheet under macro scenarios and to recalculate buffers annually. - Method: Apply Central Bank Stress Test (CBST) model with base and adverse scenarios using at-risk methodology to illustrate outcomes tied to identified risk tolerance levels. --- ### Developments Since the 2023 Mission — Implementation and remaining issues ### Implementation status - SARB implemented several December 2023 recommendations and developed a GFECRA distribution framework with NT. - SARB explicitly set a GFECRA buffer and implicitly set a contingency reserve buffer via the ZAR 100 billion transfer. - SARB publicly committed to annual recalibration of both buffers. ### Remaining methodological and operational issues - SARB did not differentiate between realized and unrealized gains in GFECRA distributions, contrary to earlier recommendation to distribute only realized gains. - Differentiation would require retrospective analysis complicated by the extended accrual period. - Instead, SARB’s approach aims to maintain a GFECRA buffer that would plausibly not be unwound by rand appreciations — effectively a risk-based approach consistent with policy solvency. ### February 2024 implementation specifics - GFECRA buffer set at ZAR 250 billion for first year, allowing distribution of ZAR 250 billion. - Transfer to NT of ZAR 150 billion over three years implemented as: - ZAR 250 billion paid by SARB to NT; ZAR 100 billion transferred from NT to SARB to reduce government borrowing. - ZAR 100 billion transferred to SARB’s Contingency Reserve (authorized by amendment to the Gold and Foreign Exchange Contingency Reserve Account Defrayal Act, 2003). - The transfer to contingency reserve intended to promote SARB policy solvency. --- ### Central Bank Stress Test Framework — Policy solvency and modeling notes ### Policy solvency concept - A central bank is considered “policy solvent” if, over time, it has realized earnings greater than its monetary policy and operating costs. - Financial arrangements and distributions should be grounded in the SARB’s legal framework and should not undermine policy solvency. ### Model features (high level) - CBST model incorporates accounting rules and equations from macroeconomics and finance. - Generates total equity decomposed into realized earnings and the revaluation account. - Satellite models forecast key balance sheet items (e.g., CiC) conditional on macro scenarios. ### Scenario design (summary) - Base scenario: low but stable GDP growth with mild inflation. - Adverse scenario: external shocks induce temporary negative macro shock, recovery assumed after 2026. --- *Source: IMF staff, IMF Technical Assistance Report (Preface, Executive Summary, Introduction, I. Developments Since the 2023 Mission, and II. Central Bank Stress Test Framework sections).* ### 8. A central bank is assessed to be policy solvent if it is on a sustainable path, which is a ### 8. A central bank is assessed to be policy solvent if it is on a sustainable path, which is a ### Policy solvency: definition and possible outcomes - Policy solvency requires positive realized earnings, on average, over time. - The absolute level of equity is less important; some central banks operate effectively with negative equity when they have: - strong institutional frameworks, - underlying (i.e., realized) profitability, - governments with strong fiscal positions. - If a central bank is not policy solvent, two possible outcomes: - Government has fiscal space: government should make a monetary transfer to the central bank’s reserves. - Government lacks fiscal space: outcomes limited to either financial repression (e.g., capital controls, negative real interest rates) or loss of control over financial conditions (e.g., the exchange rate), and consequently over inflation. ### Model overview: central bank stress test (CBST) framework - The model generates balance sheet projections from the initial balance sheet using macroeconomic scenarios. - Projections of real GDP, inflation, and the exchange rate are centered on area department assumptions; the policy rate follows a Taylor rule. - All material balance sheet items are modeled and total equity is split between retained earnings and the revaluation account. - Balance sheet items classification: - Exogenous or policy-determined items: net purchases of foreign currency and investments in domestic government bonds (derived from policy decisions, not estimated). - Autonomous items determined by macro variables: items outside immediate control of the central bank (e.g., CiC) forecasted using satellite models. - Endogenously determined items: excess reserves are key endogenous item, determined by CiC, required reserves, net USD purchases, and government bond investments; excess reserves affect interest expenses and operating costs. ### Core equations (accounting identities) - Equity can be obtained by: - (1) Equity_t = Total Assets_t − Total Liabilities_t - (2) Equity_t = Equity_{t−1} + Realized earnings_t + Reval Account_t - Clearing item (excess reserves or OMO) captures changes in assets/liabilities that affect realized earnings; revaluation gains/losses hit the revaluation account directly. - Excess reserves dynamic (as applied to SARB where clearing item is ResEx, paid at policy rate): - ResEx_t = ResEx_{t−1} + [ΔFXInt_t + ΔGovBond_t + ΔNT − ΔCiC_t − ΔResReq_t + IRExpense_t + Op_t] - Gross foreign reserves dynamic (simplest case): - FXRes_t = FXRes_{t−1} + FIRIncome_t + Revaluation^{FXRes}_t + ΔFXInt_t ### Satellite models (parsimonious specifications) - CiC specification (depends on nominal GDP and policy rate): - CiC_t = η_{CiC} NGDP_t ⋅ (i0 / i_t)^{γ_{CiC}} - Interest-sensitivity parameter η_{CiC} calibrated using historical data; parameter can change to capture structural breaks. - Required reserves in ZAR: - ResReq_t = η_{Req} NGDP_t + i_{req,t−1} ResReq_{t−1} - Two options for remuneration: zero interest or interest at policy rate; default used is zero consistent with institutional setting. - Policy rate via simplified Taylor rule: - i_t = ρ_i i_{t−1} + (1−ρ_i) \bar{i}_t + σ_i ε_{i,t} - Target \bar{i}_t = \bar{π} + r^* + γ_π (π_t − \bar{π}) + γ_y (y_t − \bar{y}) - ρ_i is autoregressive coefficient, σ_i volatility, ε_{i,t} ~ standard normal; r^* is constant real rate. ### Application to the SARB: institutional adaptations - GFECRA has FX revaluation accounts separated from equity; GFECRA incorporates revaluations from FX spot prices and gold. - Transfers from GFECRA to equity and transfers of equity to the National Treasury (NT) are modeled; excess of the equity buffer is added to excess reserves (transfer goes to commercial bank deposits). - Two GFECRA buffer specifications: - Prespecified deterministic function of time. - Value-at-Risk (VaR) for FX reserves: buffer computed per currency and summed across currencies. - GFECRA Buffer_t = ∑_{i=1}^N E_i ⋅ (1 − exp((μ_i − 0.5 σ_i^2) τ + √τ σ_i VaR(α))) - μ_i = average log return of exchange rate; σ_i = volatility of log return; τ = time horizon; α = percentile of VaR; VaR(α) is percentile of standard normal distribution. - Dependence between exchange rates is not modeled; specification assumes correlations equal to one for conservativeness. - Equity adequacy assessment: - Compute number of years to deplete equity under at-Risk scenarios. - Initial equity: 42 billion ZAR + 100 billion ZAR (announced in the 2024 budget) → ZAR 142 billion total contingency reserve included in equity. - When equity path does not reach zero within projection horizon (five years), equity path extrapolated linearly to compute depletion time. - Equity buffer calibration via Monte Carlo shocks: - Future equity E_{t+τ}^α = f_α(EquityBuffer_t, BS_t, Macro_t, Z_t, θ, τ) - Solve 0 = f_α(EquityBuffer_t^*, BS_t, Macro_t, Z_t, θ, τ) for target EquityBuffer_t^* given VaR percentile α. - Alternatively solve for time horizon τ^* such that E_{t+τ^*}^α = 0 under a prespecified at-Risk Macro_t^{VaR}. - Additional equity buffer specifications: - Prespecified deterministic path over time. - Function of policy rate and excess reserves: - EquityBuffer_t = γ ⋅ i_t ⋅ ExcessReserve_t - Parameter γ denotes how many years it takes to deplete the buffer; higher γ = more conservative. ### SARB balance sheet characteristics (as described) - Balance sheet mainly consists of foreign reserves; small interest-bearing liabilities. - Asset composition: 89 percent foreign assets, remaining domestic assets. - Liability side: excess reserves are 6 percent of total liabilities. - Aggregate balance sheet tables referenced for 2024Q1 (SARB data and IMF staff). ### Results: Base, Adverse, and At-Risk scenarios - Base scenario macro assumptions: - Real GDP growth expected to grow to 1 percent in 2024; projected to stabilize at 1.4 percent in the medium run absent accelerated structural reforms. - Base scenario results (absence of any distributions of GFECRA): - Equity reaches 1.3 percent of GDP by 2028Q4. - Observations: - Equity increases over time in absolute terms and per nominal GDP. - Accumulated FX revaluation gain included in equity does not change over time because almost all FX revaluation gains are included in GFECRA. - Net foreign reserves (NFR) and GFECRA increase over time due to ZAR depreciation against USD in base scenario. - Foreign interest income > domestic interest expenses + operational costs → accumulated realized earnings increase over time. - Base scenario with scheduled transfers of GFECRA (as announced in February 2024 budget): - Equity will reach 1.9 percent by 2028Q4. - Equity increases rapidly by around 100 billion during 2023–2024 due to transfer from GFECRA to the contingency reserve. - GFECRA declines by ZAR 250 billion because of its distribution to the contingency reserve and the excess reserves, then starts to increase with continued ZAR depreciation (FX revaluation gains). - Adverse scenario (higher inflation and mild ZAR depreciation shock): - Drivers: slowdown in China, escalation in Middle East conflict (oil and shipping costs), tighter U.S. monetary policy → higher premia and EM currency depreciation. - Result: lower private consumption and investment → decline in South Africa growth. - SARB equity outcome: - Equity increases more rapidly than in the base scenario, reaching 2.2 percent by 2028Q4. - Rationale: larger ZAR depreciation increases foreign interest income; higher inflation raises interest expenses via higher policy rate, but positive effect outweighs negative. - Implication: adverse macro scenario not necessarily adverse for SARB equity; stress scenarios should be designed specifically for SARB balance sheet risks. - At-Risk scenarios (three types used): Inflation-at-Risk, Growth-at-Risk, FX-at-Risk (primary risk is FX-at-Risk). - Growth-at-Risk example: - Real GDP growth declines to −7 percent in 2024, then recovers to base-case level. - Lower policy rate reduces interest expenses → equity increases faster than base. - Overall implication from scenarios: - SARB remains policy solvent under base and scheduled-transfer scenarios. - FX risk is the primary balance-sheet vulnerability and the main focus for at-Risk testing. *Source: IMF staff.* ### 2.6 percent in 2028Q4. ### 2.6 percent in 2028Q4. ### Equity dynamics under At-Risk scenarios - Growth-at-Risk (5th percentile) scenario: - Real GDP growth is modeled with a 5th-percentile adverse outcome (Figure 9). - Equity evolution under Growth-at-Risk is presented (Figure 9a, 9b). - Inflation-at-Risk (95th-percentile Inflation-at-Risk scenario described as adverse): - Inflation rises to 10 percent in 2024 and then declines to the same level as the base case. - Higher policy rate → larger interest expenses → equity decreases slowly over time. - The equity will reach 1.4 percent in 2028Q4. - FX-at-Risk (5th-percentile FX-at-Risk scenario): - ZAR continues to appreciate against USD by 49 percent over the five years. - Historical precedent: ZAR appreciated against USD by 52 percent during 2001/12–2004/11. - Appreciation reduces foreign interest income → accumulated realized earnings are smaller → equity decreases slowly. - The equity will reach 1.4 percent in 2028Q4. - Note: Forecasts of FX-at-Risk use moving averages to smooth seasonal patterns for long-term projections. ### Quantifying the GFECRA Buffer (VaR-based approach) - Method: - Estimate mean and volatility of log returns of exchange rates by currency. - Apply VaR formula for each currency and aggregate VaR-based unexpected revaluation losses across currencies. - Key findings: - A smaller percentile and longer time horizon increases the GFECRA buffer (Table 4). - The corresponding log return for each selected percentile and time horizon is shown for reference; magnitudes are below historical worst returns from January 2000 to July 2024 (example: three-year log return from 2001/12/31 to 2004/11/30 is −72.5 percent). - SARB’s current calibration of the GFECRA buffer (ZAR 250 billion) is close to the 5th-percentile with 2-year time horizon (243 billion ZAR). - Recommendation: - SARB should employ a quantitative VaR-based approach for annual recalibrations, reflecting: - (i) size of exposure for each currency; - (ii) exchange rate uncertainty (statistical moments such as volatility); - (iii) risk tolerance parameters (percentile and time horizon of VaR), which are policy decisions. ### Assessing the adequacy of the equity buffer - Current equity buffer: 142 billion ZAR. - Assessment approach: - Use combination of FX-at-Risk and Inflation-at-Risk scenarios. - Rather than direct adequacy computation, calculate number of years to deplete equity. - Turn off additional distribution of GFECRA to equity beyond scheduled transfer for interpretability. - For this purpose, VaR-based GFECRA buffer is assumed at 1-percentile over a two-year horizon (highly conservative; illustrative). - Findings: - Lower percentile of FX-at-Risk and higher percentile of Inflation-at-Risk → fewer years to deplete equity (Table 5). - Under the severest combination of FX-at-Risk and Inflation-at-Risk, equity (currently ZAR 142 billion) will remain positive over the next 13 years. - Buffer estimates sensitive to assumptions: - If SARB purchases USD over next five years, cost of financing the USD purchase adds to excess reserves → larger interest expenses → buffer could decrease. - Risks from SARB’s lender of last resort function not captured; including them could lead to a higher buffer. - Changes in CiC dynamics would affect buffer estimates. - Historical context and plausible appreciation scenarios: - Rand has long-term downward trend, but plausible scenarios exist for appreciation, including with higher inflation and interest rates (Box 1). - Mean reversion of USD and unwinding of South Africa’s country risk premium since 2014 could result in rand appreciation nearing 30 percent (Box 2). ### Boxes summarizing key historical and modeled scenarios - Box 1 — Combined Shocks of ZAR Appreciation and High Inflation: - Historical analysis 2000–2024 identifies three periods where ZAR appreciated while inflation exceeded 75 percent of recorded instances. - Box 2 — Possible Scenario of a Significant ZAR Appreciation: - Estimated USD/ZAR equation: FX_t = α0 + α1 I_t + α2 CDS_t. - Estimated results (table): - α0 estimate: 0.0013; Standard Error 0.015; t-value 0.083; Pr(>|t|) 0.934. - α1 estimate: ***-1.1936; Standard Error 0.054; t-value -22.040; Pr(>|t|) 0.000. - α2 estimate: ***-0.1157; Standard Error 0.006; t-value -19.301; Pr(>|t|) 0.000. - Adjusted R-Square 0.385; Durbin-Watson Test Statistic = 2.286. - *** indicates statistical significance at the 99.9-percentile level. - Interpretation: - FX_t is USD in 1 ZAR; I_t is nominal broad U.S. dollar index; CDS_t is 5-year sovereign CDS spread; daily data 2014–2024. - Regression implies ZAR expected to appreciate by approximately 29.73 percent assuming specified decreases in U.S. dollar index and CDS to 2014 levels. - A 24 percent decrease in U.S. dollar index → 28.17 percent ZAR appreciation; a 14 percent reduction in CDS → 1.57 percent ZAR appreciation. ### Sensitivity analyses (policy decision impacts on policy solvency) - Scenarios examined: - (i) Constant required reserves. - (ii) 20 percent increase in gross foreign reserves (foreign reserve accumulation). - GFECRA buffer assumed at 1 percentile and two years for sensitivity checks. - Constant required reserves scenario: - Constant required reserves increase interest expenses on excess reserves because excess reserves are larger (no increase in required reserves). - Equity will reach 1.8 percent in 2028Q4, which is 0.1 percent lower than under the base scenario. - Foreign reserve accumulation scenario (increase foreign reserves by 20 percent in USD terms): - Accumulation increases interest expenses on excess reserves due to financing net USD purchase; foreign interest income increases but less than the increase in interest expenses. - Equity will start to decline in 2026Q1 and will be lower than under the base scenario. - Equity will reach 1.6 percent in 2028Q4, which is 0.3 percent lower than under the base scenario. ### At-Risk methodology (Annex I) - Overview: - “At-risk” models forecast conditional distributions for real GDP growth, inflation, and ZAR/USD using four steps: - (i) dimensionality reduction on explanatory variables; - (ii) conditional average prediction using the Theil-Sen model; - (iii) skewness estimation using the Firth model; - (iv) parameterize an asymmetrical Gaussian distribution assuming Theil-Sen variance. - Method developed for an IMF Financial Sector Assessment Program mission to WAEMU. - Data reduction: - Synthetic variables obtained through partial least squares regression (PLS) across thematic variable sets (Tables A1–A3). - Model specifications: - Conditional mean: Theil-Sen estimator (jackknife variant described). - Skewness/asymmetry: Firth penalized-likelihood logistic regression estimating probability of exceeding threshold. - Variance: assumed unconditional equal to Theil-Sen residual variance (constant heteroskedasticity). - Distribution fit: asymmetrical Gaussian parameterized from estimated mean, variance, and skewness. - At-risk percentiles used: - Growth, inflation, and FX-at-risk scenarios use 95th percentile for adverse inflation and 5th percentile for real GDP growth and FX appreciation as worst outcomes. - Historical distribution benchmarks: - From 2000–2023 quarterly: highest inflation 13 percent; lowest real GDP growth −17 percent. - Highest appreciation of ZAR was 31 percent (2001–2023 series). - Synthetic regressor groupings (selected entries preserved exactly as in source): - Growth At-Risk model includes: Real GDP growth lag; Private consumption (percentage change); Central government deficit/surplus as percentage of GDP (first difference); Gross fixed capital formation (percentage change); Industrial production; Gold Index (percentage change); Crude Oil Index (percentage change); USA real GDP growth; China real GDP growth; REER (percentage change); Import (percentage change); Export (percentage change); Inflation (first difference); Policy rate (first difference); Predominant overdraft rate (first difference); Interbank rate (first difference); 3-month CD rate (first difference); FTSE/JSE all-share price index (percentage change). - Inflation-at-Risk model includes: Real GDP Growth; Import (percentage change); Export (percentage change); FTSE/JSE all-share price index (percentage change); USD/ZAR (first diff.); USD/EUR (first diff.); USD/SDR (first diff.); REER (percentage change); Policy rate (first diff.); Predominant overdraft rate (first diff.); Interbank rate (first diff.); 3-month CD rate (first diff.). - Exchange Rate-at-Risk model includes: Real GDP growth; FTSE/JSE all-share price index (percentage change); Inflation; Policy rate (first diff.); Predominant overdraft rate (first diff.); Interbank rate (first diff.); 3-month CD rate (first diff.); Current account balance to GDP (first diff.); Reserves and related items (first diff.); Financial account balance (first diff.). - Modeling advantages and constraints: - Asymmetric Gaussian chosen for analytical tractability with three moments available (mean, variance, skewness). - Nonparametric or heavier-tailed asymmetric distributions not used due to limited sample size and requirement of additional moments (e.g., kurtosis). *Source: IMF staff.* --- _Source: https://www.imf.org/-/media/files/publications/tar/2025/english/tarea2025051-print-pdf.pdf_