## 1. Set of Shocks Depleting the Stocks of Dynamic Provisions

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### Introduction: procyclicality and incurred-loss provisioning
- Procyclicality amplifies fluctuations during a business cycle and is exacerbated by backward-looking loan loss provisioning rules that fail to recognize credit-risk build-up in boom phases.
- Empirical evidence cited shows credit risks build up during an upswing and banks postpone provisioning until lending conditions deteriorate.
- The incurred-loss model with backward-looking provisioning rules does not adequately recognize the build-up of credit risks during expansionary phases and fails to provide the right incentives for prudent loan origination.

### Dynamic provisioning: purpose and mechanism
- Dynamic loan loss provisioning aims to mitigate procyclicality by deliberately building loan loss reserves during good times to absorb losses in bad times.
- Under dynamic provisioning:
  - Banks build provisions in line with the estimate of long-run expected (through-the-cycle) loan losses rather than incurred losses.
  - During an upswing, the stock of dynamic provisions grows rapidly as loan origination is high and loan losses are typically low; in downturns, additional provisions for actual loan losses are covered by drawing on the stock.
  - Once the stock has reached a sufficiently high level, monthly provisioning charges should effectively become independent of current loan losses and, if anything, grow in line with the rate of credit expansion.
- Dynamic provisioning provides profit-smoothing properties and lessens earnings management by curbing the effect of specific loan loss provisions on bank profits.
- For agreement with international accounting standards, historical data on loan defaults are used in setting dynamic provisioning rates, but these rates ought to be broadly in line with loan losses expected for the ongoing or upcoming credit cycle.

### Calibration, limits, and interactions with capital policy
- Key calibration points:
  - Dynamic provisioning rates need to be devised in accordance with the loan default history spanning at least a full credit cycle to avoid over- or underprovisioning.
  - Imprecise estimation of historic default rates and miscalibration can cause an excessive burden on banks or an insufficient cushion in a downturn.
- Limits and complementarities:
  - Dynamic provisioning cannot by itself prevent credit booms: attempting to contain a credit boom primarily through dynamic provisioning would require prohibitively high provisioning rates.
  - Provisions and capital assume complementary roles as buffers for expected and unexpected losses, respectively; capital requirements also need to become more forward-looking to significantly reduce procyclicality.

### Findings from the Uruguay-focused study and simulation results
- Scope and method:
  - The study assesses protection that dynamic provisions in Uruguay afford and compares, using simulations, to systems used in Spain, Peru and Bolivia.
  - The BCU credit risk model is subjected to a set of growth, exchange rate and interest rate shocks; simulations cover September 2001 to June 2009.
- Key findings:
  - The present stock of dynamic provisions would suffice to fully absorb a medium-sized shock in terms of offsetting the cost of additional specific provisions, but it would fail to withstand a severe crisis.
  - Alternative dynamic provisioning formulas produce distinct accumulation paths; some produce paths that have a high correlation with credit growth along the cycle and feature a markedly countercyclical buildup and drawdown of dynamic provisions.
  - Some formulas also have desirable properties for mitigating procyclicality.
- Additional analytical points:
  - The timing of provisioning is more important than the level; a sufficient “war chest” reduces the likelihood of failure from capital deficiency.

### II. The Uruguayan System of Dynamic Provisioning
- Implementation and rule:
  - Uruguay introduced dynamic loan loss provisioning in September 2001, following the Spanish model.
  - Regulation: banks contribute to their individual dynamic provisioning funds, DPt, the difference between the monthly statistical net losses on loans to the non-financial private sector (NFPS) and the realized net loan loss in that month:
    - Σ12 i=1 ßiCit − LLt = ΔDPt (formula as presented in source).
  - Statistical losses derived from multiplying 1/12 of the expected rate of loss for five loan categories, ßi, by respective loan volumes, Cit.
  - The five loan categories and rates: loans with public sector guarantees (0.1 percent); loans with other guarantees (0.5 percent); other loans (1.1 percent); consumer loans (1.4 percent); credit card loans (1.8 percent).
  - Net loan loss, LLt, is the cost of additional specific provisions recorded in profit-and-loss, net of deactivations of specific provisions and recoveries of defaulted loans already written off.
  - At inception, beta parameters reportedly distributed around average annual loan loss during 1990-2000, which was 1 percent of loans.
  - Dynamic provisions fund of each bank is bounded between 0 and 3 percent of total loans to be provisioned.
- System performance and dynamics:
  - Countercyclical system took effect toward end of previous credit cycle; when the 2002/03 crisis hit the cushion was insufficient and funds remained more or less depleted.
  - With recovery, overall stock approached 3 percent limit, reaching 2.7 percent of loans to the NFPS at system level in June 2009.
  - At more than 5 times non-performing loans, total loan loss provisions are much higher than in other countries (as cited).
- Interplay with specific provisions:
  - Overall provisions remained fairly stable post-crisis due to interplay between specific and dynamic provisions.
  - Reclassifications toward better risk categories contributed to drop in specific provisions after crisis in 2004/05 and again in mid-2007.
  - Total provisions dropped thereafter when declines in specific provisions could not be fully offset by rising dynamic provisions because banks increasingly hit the 3 percent ceiling.
- Drivers of dynamic-provisions accumulation in post-crisis:
  - Strong credit growth and, to some extent, decline in impaired loans.
  - Build-up volatile during 2005-07; constrained by 3 percent ceiling in 2008 when many banks reached that limit.
- Impact on profitability:
  - Continued accumulation in expansionary phase came at cost to banks’ profitability.
  - Figure 4 described: RoAA of Uruguayan banking system—banks’ bottom line since 2004 been consistently lower than without dynamic provisioning.
    - Two largest differences: hypothetical increment in RoAA of 0.5 and 0.3 percentage points for 2004 and 2007, respectively.
    - Marginal benefit of 0.04 percentage points in 2002 and 2003.
  - Measurable costs weighed against resilience benefits given only moderate rise in delinquencies in 2009.

### III. THE SUFFICIENCY OF DYNAMIC PROVISIONS UNDER MACROECONOMIC SHOCKS
A. Empirical Approach
- Method:
  - Use the credit risk model of the BCU to subject loan portfolios of the 13 Uruguayan banks to macroeconomic shocks calibrated to produce default rates and loan losses that will exhaust individual stocks of dynamic provisions.
  - Main input variables: (i) rate of GDP growth; (ii) Uruguayan Peso-US dollar exchange rate; (iii) Uruguayan Bond Index (UBI).
  - Different credit risk models for peso and dollar loans; BCU routinely applies an “adverse” scenario and a “crisis” scenario.
- Calibration details:
  - Variation in exchange rate based on historic correlation with GDP growth during 2002–09; changes in UBI reflect correlation with GDP growth during 2004-09.
  - Correlations used: -0.6 for exchange rate and +0.3 for the UBI.
  - Example calibration: for every ten percent increase in negative GDP growth rate vis-a-vis the adverse scenario of the BCU (this implying a 0.37 percentage point drop), exchange rate set to depreciate by 6 percent (corresponding to a 0.8 percentage point change) and bond spread to rise by 3 percent (i.e., an increase of about 20 basis points).
  - BCU model also includes unemployment rate, foreign interest rates, inflation rate; these were kept constant in optimization for ease.

B. Simulation Results
- Average shocks depleting dynamic provisions (Table 1):
  - Change in GDP in percent: -4.93 (Standard Deviation (2.33))
  - Exchange Rate Depreciation in percent: 15.78 (Standard Deviation (5.01))
  - Uruguayan Bond Index (basis points): 811 (Standard Deviation (141))
  - Memorandum item: Dynamic Provisions in percent of Loans*: Average 2.97** (Standard Deviation (0.81))
    - *As of July 2009. For technical reasons, the stock of provisions may temporarily exceed the 3 percent limit.
    - **Unweighted arithmetic average of individual provisioning ratios. The overall (weighted) average is 2.68 percent.
- Interpretation:
  - On average, shocks that would deplete dynamic provisions: a 5 percent drop in economic activity, an exchange rate depreciation of about 15 percent, and a rise in the UBI to slightly above 800 basis points (250 b.p. higher than in June 2009).
  - Having mostly attained maximum dynamic provisions funds, 85 percent of banks are within one standard deviation of the magnitude of the average shock.
- Coverage under BCU stress scenarios (Table 2):
  - BCU adverse scenario:
    - ∆ GDP: -3.64%
    - ∆ Exchange Rate*: +13.02%
    - Bond Spread**: 733
    - Dynamic Provisions†: 158.8
    - Expected Loan Losses†: 100.0
    - Coverage of Losses by Dyn. Prov.: 100.0%
  - BCU crisis scenario:
    - ∆ GDP: -8.00%
    - ∆ Exchange Rate*: +31.70%
    - Bond Spread**: 1000
    - Dynamic Provisions†: 158.8
    - Expected Loan Losses†: 383.6
    - Coverage of Losses by Dyn. Prov.: 41.4%
  - Crisis of 2002/03:
    - ∆ GDP: -11.00%
    - ∆ Exchange Rate*: +50.00%
    - Bond Spread**: 2000
    - Dynamic Provisions†: 158.8
    - Expected Loan Losses†: 1,246.6
    - Coverage of Losses by Dyn. Prov.: 12.7%
  - Notes: *Increase = depreciation of the local currency; ** Uruguayan Bond Index; † millions of US dollars
- Conclusions from simulations:
  - Dynamic provisions would more than cover additional loan losses under the BCU adverse scenario.
  - Under the BCU crisis scenario (∆ GDP -8.00%, exchange rate +31.70%), coverage only 41.4 percent.
  - Under a shock similar to 2002/03, coverage falls to 12.7 percent.
  - Heterogeneity across banks implies some would have higher- or lower-than-average coverage; bank-specific provisioning rates could accommodate differing exposures but require accurate through-the-cycle loss estimates.

### IV. SIMULATIONS USING ALTERNATIVE PROVISIONING FORMULAS
A. Characteristics of Alternative Formulas
- General observation:
  - Size of dynamic provision funds converged toward regulatory limit of 3 percent, reaching 2.7 percent system level in June 2009.
  - Stock should diminish during slowdown with stagnant or falling credit; in early 2009 dynamic provisions did not fall significantly despite temporary negative GDP and credit growth.
- Spanish formula (summary):
  - ΔDPt = Σ6 i=1 (αi ΔCit) + Σ6 i=1 (ßi Cit) − ΔSPt (structure as presented).
  - Differences from Uruguayan rule: (1) subtracts flow of specific provisions rather than net loan loss; (2) includes alpha component capturing expected loss of new loans.
  - Spanish parameter examples (as presented): e.g., High risk—credit card exposures and overdrafts—α=2.50%, β=1.64%; other categories listed in source.
  - Spanish caps: banks required to provision between 0 and 2.5 percent of increase in provisionable loans (alpha) and beta rates 0 to 1.64 percent; cap of 125 percent of the latent loss and a floor of 0.1 percent of loans.
  - Simulation calibration: alpha parameters set 0.1 percentage points higher than Uruguayan beta parameters; specific simulated alpha and beta values used (0.1 percent for A-loans with liquid guarantees; 0.7 percent for other guaranteed loans; 1.6 percent for consumer loans; 2.0 percent for credit card loans; 1.3 percent for all other loans). Uruguayan 3 percent cap assumed for comparability.
- Uruguayan formula (calibration notes):
  - Beta parameters set according to average annual provisioning rates during the simulation period; post-crisis (2004-09) average provisioning rate of 1.1 percent was used.
- Peruvian formula:
  - Introduced November 2008; no cumulative fund; procyclical element activates only if GDP growth rises above thresholds.
  - Banks maintain a stock of general provisions of between 0.7 and 1.0 percent of loans in the non-activation period; during activation banks add between 0.3 and 1.5 percent of loans.
  - Activation rule: procyclical component activated if either the average annualized rate of GDP growth has been above 5 percent in the past 30 months or the average change in GDP growth has been greater than 2 percent in the past 12 months (deactivation thresholds in reverse).
  - In simulation, activation begins in October 2003 after a 2.8 percent increase in GDP over previous four quarters.
  - Peruvian surcharges applied to Uruguayan beta parameters in simulation: 1 percent for consumer loans, 1.5 percent for credit card loans, and 0.5 percent for other non-guaranteed loans.
  - Additional provisions during activation are phased in over six months; Peruvian formula includes a general provision floor preventing full depletion in deep crises.
- Bolivian formula:
  - Enacted December 2008; prescribes a general provision on prime quality loans between 1.5 and 5.5 percent of loans.
  - During contraction, banks may access up to half of the additional specific provisions in a given month, provided loan quality has deteriorated for six consecutive months and the dynamic provision was fully phased in.
  - Replenishment rule: when six-month moving average of the indicator improves, banks add each month 2.78 percent of the total required provision over 36 months.
  - Simulation assignments: 1.9 percent to “other loans” and 2.3 percent to consumer and credit card loans; Bolivian loan quality indicator proxied by share of overall specific provisions in total loans.
  - Applied to Uruguayan data: access period begins in July 2002 and ends six months later; because banks can cover as much as half of the increase in specific provisions, the stock can be depleted within 6 months under severe downturns.
- Hybrid and Colombian systems:
  - Hybrid Uruguayan-Spanish: adds Spanish alpha component to Uruguayan methodology; 3 percent regulatory cap relaxed in simulation to illustrate alpha effect.
  - Colombian system: uses specific provisions and transition matrices; not applied here due to data requirements.

B. Simulation results — dynamics, correlations, and volatility
- General patterns:
  - Peruvian and Bolivian formulas yield relatively smooth provision development over time.
  - Spanish and Uruguayan formulas produce more volatile responses.
  - Peruvian formula tends to produce larger stocks through the cycle because of its minimum general provision requirement.
  - Spanish and hybrid systems display faster buildup and drawdown of dynamic provisions linked to credit growth thanks to the alpha term.
- Correlations (Table 3, 2004-09):
  - Correlation between Dynamic Provisions/Credit Growth:
    - Bolivian Formula: 0.46
    - Peruvian Formula: 0.50
    - Spanish Formula: 0.32
    - Hybrid Formula: 0.17
    - Uruguayan Formula: -0.07
  - Correlation between Dynamic Provisions/Change in Economic Activity*:
    - Bolivian Formula: 0.28
    - Peruvian Formula: 0.25
    - Spanish Formula: -0.09
    - Hybrid Formula: 0.14
    - Uruguayan Formula: 0.09
    - *Measured by the official monthly index of economic activity (IMAE)
  - Correlation between Total Provisions/Credit Growth:
    - Bolivian Formula: -0.01
    - Peruvian Formula: 0.10
    - Spanish Formula: 0.57
    - Hybrid Formula: -0.05
    - Uruguayan Formula: -0.16
  - Correlation between Dynamic Provisions/Specific Provisions:
    - Bolivian Formula: -0.04
    - Peruvian Formula: -0.04
    - Spanish Formula: -0.96
    - Hybrid Formula: 0.08
    - Uruguayan Formula: 0.12
  - Standard Deviation, Flows of Dyn. Prov. (US$ mn.):
    - Bolivian Formula: 2.5
    - Peruvian Formula: 4.2
    - Spanish Formula: 8.0
    - Hybrid Formula: 6.9
    - Uruguayan Formula: 7.3
- Interpretation:
  - Desired property: flow of dynamic provisions should align with credit growth. Bolivian and Peruvian formulas achieve this (correlation ~0.5); Spanish formula to a lesser extent (0.32). Uruguayan and hybrid formulas show correlations close to zero.
  - Spanish formula produces a highly negative correlation between dynamic and specific provisions (-0.96), smoothing total provisions by counterbalancing swings in specific provisions.
  - Bolivian and Peruvian formulas lack a beta component, explaining near-zero correlation between dynamic and specific provisions; Uruguayan near-zero correlation driven by netting loan recoveries.
  - Standard deviations show Spanish and Uruguayan formulas generate higher volatility in provisioning flows than Bolivian and Peruvian systems.

### Conclusions, tradeoffs, and further research directions
- Coverage and resilience:
  - The current stock of Uruguay’s dynamic provisions would cushion a medium-sized macroeconomic shock; most banks are at the regulatory limit of their stocks.
  - It would take a relatively large shock for banks to experience loan losses that can no longer be covered by dynamic provisions; provisions are not designed to cover the most extreme events.
- Tradeoffs and costs:
  - Tradeoff between financial stability (maintain ample provisions) and banking system efficiency (reasonable loan loss provisioning).
  - Simulated impact on profitability: hypothetical return on average assets without dynamic provisions exceeds the actual return by as much as 0.5 percentage point, indicating non-negligible costs during tranquil periods; two largest differences noted were 0.5 and 0.3 percentage points for 2004 and 2007, respectively.
- Adequacy uncertainty and policy implications:
  - Simulations cannot definitively determine adequacy of stocks produced by any formula; limited rise in delinquencies toward the end of the credit cycle leaves uncertainty.
  - If future downturns are milder than past crises, the system may be over-provisioned: arbitrarily halving loan loss rates in the 2002-03 crisis would yield an average loan loss over the cycle of 0.4 percent—below the assumed loss rate of 1 percent.
  - Periodic revisits of the provisioning system are recommended to ensure stock levels align with potential credit risks.
- Further research:
  - Apply hypothetical dynamic provisioning rules to other countries or simulate different credit cycles to assess properties of various provisioning systems.
  - Such exercises would inform supervisory authorities and complement Basel Committee work on mitigating procyclicality, including promoting forward-looking loan loss provisioning.

*Source: Excerpt from “1. Set of Shocks Depleting the Stocks of Dynamic Provisions” (IMF working paper content provided in the source PDF).*

### 1. Set of Shocks Depleting the Stocks of Dynamic Provisions ...............................................10

### 1. Set of Shocks Depleting the Stocks of Dynamic Provisions

### Introduction: procyclicality and incurred-loss provisioning
- Procyclicality amplifies fluctuations during a business cycle and is exacerbated by backward-looking loan loss provisioning rules that fail to recognize credit-risk build-up in boom phases.
- Empirical evidence cited shows credit risks build up during an upswing and banks postpone provisioning until lending conditions deteriorate.
- The incurred loss model with backward-looking provisioning rules does not adequately recognize the build-up of credit risks during expansionary phases and fails to provide the right incentives for prudent loan origination.

### Dynamic provisioning: purpose and mechanism
- Dynamic loan loss provisioning aims to mitigate procyclicality by deliberately building loan loss reserves during good times to absorb losses in bad times.
- Under dynamic provisioning:
  - Banks build provisions in line with the estimate of long-run expected (through-the-cycle) loan losses rather than incurred losses.
  - During an upswing, the stock of dynamic provisions grows rapidly as loan origination is high and loan losses are typically low; in downturns, additional provisions for actual loan losses are covered by drawing on the stock.
  - Once the stock has reached a sufficiently high level, monthly provisioning charges should effectively become independent of current loan losses and, if anything, grow in line with the rate of credit expansion.
- Dynamic provisioning provides profit-smoothing properties and lessens earnings management by curbing the effect of specific loan loss provisions on bank profits.
- For agreement with international accounting standards, historical data on loan defaults are used in setting dynamic provisioning rates, but these rates ought to be broadly in line with loan losses expected for the ongoing or upcoming credit cycle.

### Calibration, limits, and interactions with capital policy
- Reaping merits requires careful calibration:
  - Dynamic provisioning rates need to be devised in accordance with the loan default history spanning at least a full credit cycle to avoid over- or underprovisioning.
  - Imprecise estimation of historic default rates and miscalibration can cause an excessive burden on banks or an insufficient cushion in a downturn.
- Dynamic provisioning cannot by itself prevent credit booms:
  - Although it gives incentives for more careful loan origination and provisioning charges on new loans cause a decline in banks’ capital (which for a given or desired leverage will restrain credit growth to a limited extent), attempting to contain a credit boom primarily through dynamic provisioning would require prohibitively high provisioning rates.
  - Provisions and capital assume complementary roles as buffers for expected and unexpected losses, respectively; capital requirements also need to become more forward-looking to significantly reduce procyclicality.

### Findings from the Uruguay-focused study and simulation results
- Scope and method:
  - The study assesses protection that dynamic provisions in Uruguay afford and compares, using simulations, to systems used in Spain, Peru and Bolivia.
  - The credit risk model of the central bank (Banco Central del Uruguay (BCU)) is subjected to a set of growth, exchange rate and interest rate shocks (see Section III for details in the source).
  - Simulations for the period of September 2001 to June 2009 are used to compare alternative dynamic provisioning formulas.
- Key findings:
  - The present stock of dynamic provisions would suffice to fully absorb a medium-sized shock in terms of offsetting the cost of additional specific provisions, but it would fail to withstand a severe crisis.
  - Alternative dynamic provisioning formulas produce distinct accumulation paths; some produce paths that have a high correlation with credit growth along the cycle and feature a markedly countercyclical buildup and drawdown of dynamic provisions.
  - Some formulas also have desirable properties for mitigating procyclicality.
- Additional analytical points:
  - The timing of provisioning is more important than the level; a sufficient “war chest” reduces the likelihood of failure from capital deficiency.
  - Numerical examples that do not consider the impact of credit growth on provisions are noted (see footnote reference in source).

### Organization of the paper (as presented)
- Section II: characteristics of the Uruguayan dynamic provisioning system; descriptive statistics on the evolution of credit and of specific versus dynamic provisions; estimate of the additional cost of dynamic provisioning in terms of a lower return on assets than otherwise obtained.
- Section III: assessment of whether the current stock of dynamic provisions suffices to provide protection against sizable economic downturns via simulations using the BCU credit risk model and a set of growth, exchange rate and interest rate shocks.
- Section IV: simulations of the evolution of dynamic provisions based on the dynamic provisioning formulas used in Spain, Peru and Bolivia and assessment of merits of each alternative system.

*Source: Excerpt from “1. Set of Shocks Depleting the Stocks of Dynamic Provisions” (IMF working paper content provided in the source PDF).*

### Section V concludes and discusses a number of policy implications.

### _wp10125 - Section V concludes and discusses a number of policy implications.

### II. The Uruguayan System of Dynamic Provisioning
- Uruguay introduced dynamic loan loss provisioning in September 2001, following the Spanish model launched one year earlier.
- Regulation: banks contribute to their individual dynamic provisioning funds, DPt, the difference between the monthly statistical net losses on loans to the non-financial private sector (NFPS) and the realized net loan loss in that month:
  - Σ12 i=1 ßiCit − LLt = ΔDPt (formula expressed in source text).
- Statistical losses derived from multiplying 1/12 of the expected rate of loss for five loan categories, ßi, by respective loan volumes, Cit.
  - The five loan categories and rates: loans with public sector guarantees (0.1 percent); loans with other guarantees (0.5 percent); other loans (1.1 percent); consumer loans (1.4 percent); credit card loans (1.8 percent).
- Net loan loss, LLt, is the cost of additional specific provisions recorded in profit-and-loss, net of deactivations of specific provisions and recoveries of defaulted loans already written off.
- At inception, beta parameters reportedly distributed around average annual loan loss during 1990-2000, which was 1 percent of loans.
- Dynamic provisions fund of each bank is bounded between 0 and 3 percent of total loans to be provisioned.
- System performance and dynamics:
  - Countercyclical system took effect toward end of previous credit cycle; when the 2002/03 crisis hit the cushion was insufficient.
  - During crisis banks’ dynamic provisions funds remained more or less depleted.
  - With recovery, overall stock approached 3 percent limit, reaching 2.7 percent of loans to the NFPS at system level in June 2009.
  - At more than 5 times non-performing loans, total loan loss provisions are much higher than in other countries (see Adler et al., 2009, as cited in source).
- Interplay with specific provisions:
  - Overall provisions remained fairly stable post-crisis due to interplay between specific and dynamic provisions.
  - Reclassifications toward better risk categories contributed to drop in specific provisions after crisis in 2004/05 and again in mid-2007.
  - Total provisions dropped thereafter when declines in specific provisions could not be fully offset by rising dynamic provisions because banks increasingly hit the 3 percent ceiling.
- Drivers of dynamic-provisions accumulation in post-crisis:
  - Strong credit growth and, to some extent, decline in impaired loans.
  - Build-up volatile during 2005-07; constrained by 3 percent ceiling in 2008 when many banks reached that limit.
- Impact on profitability:
  - Continued accumulation in expansionary phase came at cost to banks’ profitability.
  - Dynamic provisioning intended to bring recognition of losses forward without increasing total buffers significantly above prudent expected losses through cycle; over normal cycle profitability should not be impaired.
  - If cycle deviates from standard or profitability assessed only during part of cycle, profitability may be impaired.
  - Figure 4 (described): RoAA of Uruguayan banking system—banks’ bottom line since 2004 been consistently lower than without dynamic provisioning.
    - Two largest differences: hypothetical increment in RoAA of 0.5 and 0.3 percentage points for 2004 and 2007, respectively.
    - Marginal benefit of 0.04 percentage points in 2002 and 2003.
  - Apparent cost must be weighed against benefit of strengthened financial stability; measurable costs arguably outweighed intangible resilience benefits given only moderate rise in delinquencies in 2009.

### III. THE SUFFICIENCY OF DYNAMIC PROVISIONS UNDER MACROECONOMIC SHOCKS
A. Empirical Approach
- Method: use the credit risk model of the BCU to subject loan portfolios of the 13 Uruguayan banks to macroeconomic shocks calibrated to produce default rates and loan losses that will exhaust individual stocks of dynamic provisions.
- Main input variables historically impacting expected loan losses in BCU model:
  - (i) rate of GDP growth; (ii) Uruguayan Peso-US dollar exchange rate; (iii) Uruguayan Bond Index (UBI).
  - Different credit risk models for peso and dollar loans; BCU routinely applies an “adverse” scenario and a “crisis” scenario.
- Exercise: set additional loan losses to deplete each bank’s stock of dynamic provisions and solve backward for shocks that produce such losses.
- Correlations used in modeling:
  - Variation in exchange rate based on historic correlation with GDP growth during 2002–09.
  - Changes in UBI reflect correlation with GDP growth during 2004-09.
  - Correlations found: -0.6 for exchange rate and +0.3 for the UBI (as used in calibration).
  - Example: for every ten percent increase in negative GDP growth rate vis-a-vis the adverse scenario of the BCU (this implying a 0.37 percentage point drop), exchange rate set to depreciate by 6 percent (corresponding to a 0.8 percentage point change) and bond spread to rise by 3 percent (i.e., an increase of about 20 basis points).
- Additional model notes:
  - BCU credit risk model also includes unemployment rate, foreign interest rates, inflation rate; kept constant in optimization for ease.

B. Simulation Results
- Average shocks depleting dynamic provisions (Table 1):
  - Change in GDP in percent: -4.93 (Standard Deviation (2.33))
  - Exchange Rate Depreciation in percent: 15.78 (Standard Deviation (5.01))
  - Uruguayan Bond Index (basis points): 811 (Standard Deviation (141))
  - Memorandum item: Dynamic Provisions in percent of Loans*: Average 2.97** (Standard Deviation (0.81))
    - *As of July 2009. For technical reasons, the stock of provisions may temporarily exceed the 3 percent limit.
    - **Unweighted arithmetic average of individual provisioning ratios. The overall (weighted) average is 2.68 percent.
- Interpretation:
  - On average, shocks that would deplete dynamic provisions: a 5 percent drop in economic activity, an exchange rate depreciation of about 15 percent, and a rise in the UBI to slightly above 800 basis points (250 b.p. higher than in June 2009).
  - Having mostly attained maximum dynamic provisions funds, 85 percent of banks are within one standard deviation of the magnitude of the average shock.
- Coverage under BCU stress scenarios (Table 2):
  - BCU adverse scenario:
    - ∆ GDP: -3.64%
    - ∆ Exchange Rate*: +13.02%
    - Bond Spread**: 733
    - Dynamic Provisions†: 158.8
    - Expected Loan Losses†: 100.0
    - Coverage of Losses by Dyn. Prov.: 100.0%
  - BCU crisis scenario:
    - ∆ GDP: -8.00%
    - ∆ Exchange Rate*: +31.70%
    - Bond Spread**: 1000
    - Dynamic Provisions†: 158.8
    - Expected Loan Losses†: 383.6
    - Coverage of Losses by Dyn. Prov.: 41.4%
  - Crisis of 2002/03:
    - ∆ GDP: -11.00%
    - ∆ Exchange Rate*: +50.00%
    - Bond Spread**: 2000
    - Dynamic Provisions†: 158.8
    - Expected Loan Losses†: 1,246.6
    - Coverage of Losses by Dyn. Prov.: 12.7%
  - Notes: *Increase = depreciation of the local currency; ** Uruguayan Bond Index; † millions of US dollars
- Conclusions:
  - Banks could withstand a medium-sized shock without having to record additional specific provisions; dynamic provisions would more than cover additional loan losses under the adverse scenario.
  - Under the BCU crisis scenario (∆ GDP -8.00%, exchange rate +31.70%), coverage only 41.4 percent.
  - Under shock similar to 2002/03, coverage falls to 12.7 percent.
  - Given Uruguay’s relatively favorable performance during the current global economic crisis (only one quarter of moderately negative GDP growth), cushion regarded as comfortable.
  - Heterogeneity: Standard deviations indicate some banks would have higher- or lower-than-average coverage reflecting diverging risk profiles.
  - Policy consideration: allow bank-specific dynamic provisioning rates to accommodate differing exposures; this would require accurate through-the-cycle loss estimates per institution and recalibrations when risk profiles change.

### IV. SIMULATIONS USING ALTERNATIVE PROVISIONING FORMULAS
A. Characteristics of Alternative Formulas
- System convergence:
  - Size of dynamic provision funds converged toward regulatory limit of 3 percent, reaching 2.7 percent system level in June 2009.
  - Basic idea: stock should diminish during slowdown with stagnant or falling credit; in early 2009 dynamic provisions did not fall significantly despite temporary negative GDP and credit growth.
- This section applies provisioning formulas used in Spain, Peru, and Bolivia to Uruguayan data to assess alternative accumulation paths.

Spanish Formula (summary of characteristics and mechanics)
- Spanish formula—in place since July 2000—is conceptually similar but differs in two elements:
  - (1) subtracts the flow of specific provisions rather than the net loan loss from required contribution;
  - (2) includes an additional component capturing expected loss of new loans (alpha component).
- Spanish formula computes general provisions with a countercyclical component. Formula expressed in source:
  - ΔDPt = Σ6 i=1 (αi ΔCit) + Σ6 i=1 (ßi Cit) − ΔSPt  (structure as presented in source).
- Elements:
  - ΔDPt: increase in general dynamic provision (provisioning flow) to be added quarterly;
  - αi: average estimate of the credit loss in a year neutral from a cyclical perspective for loans in risk category i;
  - ΔCit: change in stock of loans of risk category i in current period;
  - ßi: historical average rate of specific provisions for loans of category i;
  - ΔSPt: specific provision made in current period.
- Spanish parameters and caps:
  - Depending on risk, banks required to provision between 0 and 2.5 percent of increase in provisionable loans (alpha component) in addition to beta (countercyclical) component with rates 0 to 1.64 percent.
  - Spanish system features a cap of 125 percent of the latent loss and a floor of 0.1 percent of loans.
- Risk-category examples and parameter values (as presented in source for Spain):
  - 1. Negligible risk—α=0.00%, β=0.00%;
  - 2. Low risk—α=0.60%, β=0.11%;
  - 3. Medium-low risk—α=1.50%, β=0.44%;
  - 4. Medium risk—α=1.80%, β=0.65%;
  - 5. Medium-high risk—α=2.00%, β=1.10%;
  - (additional categories and full parameterization described in source).

*Source: _wp10125 - Section V concludes and discusses a number of policy implications.*

### 6. High risk—credit card exposures and overdrafts—α=2.50%, β=1.64%.

### 6. High risk—credit card exposures and overdrafts—α=2.50%, β=1.64%.

### Design and calibration of alternative dynamic provisioning formulas
- Spanish formula
  - Beta part should average to zero over the credit cycle if the average rate of specific provisions is properly calibrated.
  - Alpha component accelerates build-up of dynamic provisions during an upswing and increases downward pressure when credit growth turns negative.
  - In the simulation, alpha parameters were set to be 0.1 percentage points higher than the Uruguayan beta parameters. The difference is predicated on the average annual loan loss rate of 1.1 percent recorded over the credit cycle of 2001-08.
  - The Spanish formula prescribes taking the rate of loan loss in a cyclically neutral year, but because 2007 had a negative loan loss rate (-0.5 percent), the simulation deviated and used the average loss rate over the cycle.
  - Alpha and beta parameters in the simulation (footnote summary): 0.1 percent for A-loans with liquid guarantees, 0.7 percent for other guaranteed loans, 1.6 percent for consumer loans, 2.0 percent for credit card loans, and 1.3 percent for all other loans.
  - For comparability in the simulation, the Uruguayan regulatory limit of 3 percent of loans was assumed rather than the Spanish cap of 125 percent of latent loss.

- Uruguayan formula (calibration notes)
  - Beta parameters were set according to the average annual provisioning rates during the simulation period. The post-crisis (2004-09) average provisioning rate of 1.1 percent was used (the full-period average, including the 2002-03 crisis, was 3.8 percent and considered excessive).

- Peruvian formula
  - Introduced November 2008; differs substantially: no cumulative fund; procyclical element activates only if GDP growth rises above thresholds.
  - Banks maintain a stock of general provisions of between 0.7 and 1.0 percent of loans in the non-activation period.
  - During activation, banks add between 0.3 and 1.5 percent of loans.
  - Activation rule (footnote): the procyclical component is activated [deactivated] if either the average annualized rate of GDP growth has been above [below] 5 percent in the past 30 months or the average change in GDP growth has been greater than 2 percent [-4 percent] in the past 12 months.
  - In the simulation, the activation period begins in October 2003 after a 2.8 percent increase in GDP over the previous four quarters.
  - Peruvian surcharges applied to the Uruguayan beta parameters in the simulation: 1 percent for consumer loans, 1.5 percent for credit card loans, and 0.5 percent for other non-guaranteed loans.
  - By regulation, additional provisions during activation are phased in over six months.
  - Peruvian formula unique feature: an embedded general provision floor that prevents full depletion even in deep crises.

- Bolivian formula
  - Enacted December 2008; prescribes a general provision on prime quality loans that can be drawn upon fully during slowdown.
  - Dynamic provision required by loan type: between 1.5 and 5.5 percent of loans.
  - During contraction, banks may access up to half of the additional specific provisions in a given month, provided loan quality has deteriorated for six consecutive months and the dynamic provision was fully phased in.
  - Loan quality deterioration measured as the sum over loan categories of (share of category in total loans × actual rate of specific provisions for that category).
  - Replenishment rule: when the six-month moving average of the indicator improves, banks add each month 2.78 percent of the total required provision over 36 months.
  - Simulation assumptions: assigned 1.9 percent to “other loans” (average of mortgage and prime corporate provisioning rates) and 2.3 percent to consumer and credit card loans; Bolivian loan quality indicator proxied by share of overall specific provisions in total loans.
  - Applied to Uruguayan data: access period found to begin in July 2002 and end six months later; if countercyclical provisions are fully constituted at start, banks can use accrued dynamic provisions from July to December 2002.
  - Because banks can cover as much as half of the increase in specific provisions, the stock of countercyclical provisions can be depleted within 6 months under severe downturns.

- Hybrid and Colombian systems
  - Hybrid Uruguayan-Spanish: adds the Spanish alpha component to the Uruguayan methodology; 3 percent regulatory cap relaxed in simulation to illustrate alpha effect.
  - Colombian system: uses specific provisions and transition matrices attaching empirically-derived probabilities of default per loan classification. Countercyclical provision is difference between rates derived from two transition matrices; SFC decides annually which matrix applies. Not applied in this study due to data requirements.

### Simulation results — dynamic provision trajectories and properties
- General patterns and volatility
  - Peruvian and Bolivian formulas yield relatively smooth provision development over time.
  - Spanish and Uruguayan formulas produce more volatile responses.
  - Peruvian formula tends to produce larger stocks through the cycle because of its minimum general provision requirement.
  - Spanish and hybrid systems display faster buildup and drawdown of dynamic provisions linked to credit growth thanks to the alpha term.

- Specific behavior by formula (qualitative)
  - Spanish formula
    - Produces a broadly similar path to Uruguay’s actual dynamic provisions but would not have prevented the rapid drawdown during 2002-03; overall stock never reaches zero due to a Spanish floor of 0.1 percent of loans.
    - From mid-2007 the Spanish path recovers toward the actual one due to lower loan recoveries and stronger credit growth, with the alpha component driving provisions on incremental credit.
  - Peruvian formula
    - Smoother path; begins to rise in October 2003 when procyclical component phased in and then traces actual Uruguayan provisions closely (coincidence from offsetting effects).
    - The general provision floor ensures the stock is never fully depleted.
  - Bolivian formula
    - Similar to Peruvian but allows faster access to the stock; with access up to half of increased specific provisions, the stock is quickly depleted and then reconstituted gradually and less volatilely.
  - Hybrid Uruguayan-Spanish
    - Stock rises faster during high credit growth and falls faster when credit diminishes.
  - Uruguayan formula
    - Netting of recoveries of charged-off loans mitigates loan losses and produces a path somewhat less volatile than the Spanish formula but more volatile than Bolivian and Peruvian formulas.

- Correlations (Table 3: Correlations Between Provisioning Flows and Changes in Credit & Activity, 2004-09)
  - Correlation between Dynamic Provisions/Credit Growth:
    - Bolivian Formula: 0.46
    - Peruvian Formula: 0.50
    - Spanish Formula: 0.32
    - Hybrid Formula: 0.17
    - Uruguayan Formula: -0.07
  - Correlation between Dynamic Provisions/Change in Economic Activity*:
    - Bolivian Formula: 0.28
    - Peruvian Formula: 0.25
    - Spanish Formula: -0.09
    - Hybrid Formula: 0.14
    - Uruguayan Formula: 0.09
    - *Measured by the official monthly index of economic activity (IMAE)
  - Correlation between Total Provisions/Credit Growth:
    - Bolivian Formula: -0.01
    - Peruvian Formula: 0.10
    - Spanish Formula: 0.57
    - Hybrid Formula: -0.05
    - Uruguayan Formula: -0.16
  - Correlation between Dynamic Provisions/Specific Provisions:
    - Bolivian Formula: -0.04
    - Peruvian Formula: -0.04
    - Spanish Formula: -0.96
    - Hybrid Formula: 0.08
    - Uruguayan Formula: 0.12
  - Memorandum item: Standard Deviation, Flows of Dyn. Prov. (US$ mn.)
    - Bolivian Formula: 2.5
    - Peruvian Formula: 4.2
    - Spanish Formula: 8.0
    - Hybrid Formula: 6.9
    - Uruguayan Formula: 7.3

- Interpretation of the correlations and volatility
  - Desired property: flow of dynamic provisions should align with credit growth. This is achieved by Bolivian and Peruvian formulas (correlation ~0.5) and to a lesser extent by Spanish formula (0.3). Uruguayan and hybrid formulas show correlations close to zero.
  - The Spanish formula produces a highly negative correlation between dynamic and specific provisions (-0.96), which smooths total provisions by counterbalancing swings in specific provisions.
  - Bolivian and Peruvian formulas lack a beta component, explaining near-zero correlation between dynamic and specific provisions; Uruguayan near-zero correlation is driven by netting loan recoveries in the dynamic provisioning requirement.
  - Standard deviations show Spanish and Uruguayan formulas generate higher volatility in provisioning flows than Bolivian and Peruvian systems.

### Conclusions, tradeoffs, and further research directions
- Coverage and resilience
  - The current stock of Uruguay’s dynamic provisions would cushion a medium-sized macroeconomic shock; most banks are at the regulatory limit of their stocks.
  - It would take a relatively large shock for banks to experience loan losses that can no longer be covered by dynamic provisions. Provisions are not designed to cover the most extreme events.

- Tradeoffs and costs
  - There is a tradeoff between financial stability (maintain ample provisions) and banking system efficiency (reasonable loan loss provisioning).
  - Simulated impact on profitability: hypothetical return on average assets without dynamic provisions exceeds the actual return by as much as half a percentage point, indicating non-negligible costs during tranquil periods.

- Adequacy uncertainty and policy implications
  - Simulations cannot definitively determine whether stocks produced by any formula are adequate; the jury is still out given only slight loan delinquency rise toward the end of the credit cycle.
  - If future downturns are milder than past crises, the system may be over-provisioned: arbitrarily halving loan loss rates in the 2002-03 crisis would yield an average loan loss over the cycle of 0.4 percent—below the assumed loss rate of 1 percent.
  - Periodic revisits of the provisioning system are opportune to ensure stock levels align with potential credit risks.

- Further research
  - Apply hypothetical dynamic provisioning rules to other countries or simulate different credit cycles to assess properties of various provisioning systems.
  - Such exercises would inform supervisory authorities and complement Basel Committee work on mitigating procyclicality, including promoting forward-looking loan loss provisioning.

*Source: _wp10125 - 6. High risk—credit card exposures and overdrafts—α=2.50%, β=1.64%.*

### REFERENCES

### REFERENCES

### Academic articles, working papers, and books
- Adler, G., M. Mansilla and T. Wezel, 2009, “Modernizing Bank Regulation in Support of Financial Deepening: The Case of Uruguay”, IMF Working Paper 09/199 (Washington: International Monetary Fund).
- Balla, E. and A. McKenna, 2009, “Dynamic Provisioning: A Countercyclical Tool for Loan Loss Reserves”, Federal Reserve Bank of Richmond Economic Quarterly, Vol. 95, 383-418.
- Bikker, J.A. and P.A.J. Metzemakers, 2005, “Bank provisioning behaviour and procyclicality”, International Financial Markets, Institutions and Money (15), 141-157.
- Bouvatier, V. and L. Lepetit, 2006, “Banks’ procyclicality behavior: does provisioning matter?”, Centre d’Economie de la Sorbonne Working Paper 2006.35
- Brunnermeier, M., A. Crockett, C. Goodhart, A. Persaud, and H. Shin, 2009, “The Fundamental Principles of Financial Regulation”, (London: Centre for Economic Policy Research).
- Cavallo, M. and G. Majnoni, 2001, “Do Banks Provision for Bad Loans in Good Times? Empirical Evidence and Policy Implications,” World Bank Policy Research Working Paper No. 2619 (Washington: The World Bank Group).
- Fernández de Lis, S., J. Martínez Pagés and J. Saurina, 2000, “Credit Growth, Problem Loans and Credit Risk Provisioning in Spain,” Banco de España Working Paper No. 18.
- Jiménez, G. and J. Saurina, 2006, “Credit cycles, credit risk, and prudential regulation” International Journal of Central Banking (2), 65-98.
- Laeven, L. and G. Majnoni, 2003, “Loan Loss Provisioning and Economic Slowdowns: Too Much, Too Late?” Journal of Financial Intermediation (12): 178-197.
- Mann, F. and I. Michael, 2002, “Dynamic Provisioning: issues and application”, Bank of England Financial Stability Review, December 2002.
- Martínez, O., F. Pineda and D. Salamanca, 2005, “Esquema de Provisiones anticíclicas para Colombia”, Central Bank of Colombia, Temas de Estabilidad Financiera, July.
- Panetta, F., P. Angelini, U. Albertazzi, F. Columba, W. Cornacchia, A. Di Cesare, A. Pilati, C. Salleo and G. Santini, 2009, “Financial sector pro-cyclicality – Lessons from the crisis”, Banca d’Italia Occasional Paper No. 44.
- Pérez, D., V. Salas and J. Saurina, 2006, “Earning and Capital Management in Alternative Loan Loss Provision Regulatory Regimes”, Banco de España Working Paper No. 614.
- Sacasa, N., 2010, “Implementing Rules-Based Stabilizers for Banks: A Simplified Simulation for the United States 1992-2007”, IMF Working Paper, forthcoming (Washington: International Monetary Fund).
- Saurina, J., 2009, “Dynamic Provisioning – The Experience of Spain,” World Bank Crisis Response Note No. 7 (Washington: The World Bank Group).
- Shin, H.S., 2009, “Financial Intermediation and the Post-Crisis Financial System”, Working Paper Princeton University, mimeo.

### Reports, presentations, and international body outputs
- Financial Stability Forum, 2009, “Report of the FSF Working Group on Provisioning”, www.financialstabilityboard.org/fsb_publications
- International Accounting Standards Board, 2009, “Spanish Provisions under IFRS”, Presentation at the joint IASB-FASB meeting of March 2009.
- Roldan, J.M. and J. Saurina, 2009, “Dynamic Provisioning in Spain”, Presentation at the IASB meeting of June 2009.

### Central bank, supervisory, and regulatory publications
- Banco Central del Uruguay, 2008, “Comunicación 2008/023 – Instituciones de Intermediación Financiera – Actualización N o 177 a las Normas Contables y Plan de Cuentas”, Montevideo.
- Superintendencia de Banca, Seguros y AFP Peru, 2008, “Resolución 11356 – 2008.”
- Superintendencia de Bancos y Entidades Financieras Bolivia, 2008, “Modificaciones al Anexo I – Evaluación y Calificación de la Cartera de Créditos de las Directrices Generales para la Gestión del Riesgo de Crédito”, Circular No. 604/2008.
- Superintendencia Financiera de Colombia, 2007, “Guia para la Implementación del Modelo de Referencia de Cartera Comercial – MRC”.

*Source: REFERENCES (content unit: _wp10125 - REFERENCES).*

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