In the framework of this note, the write-of is considered a special case of sale in which the sale price is zero.

LLR are the cumulation (stock) of provisions over time.

Net book value is defined as gross book value net of LLR.

The Excel template uses the concept of haircut expressed as a ratio (defined as [NBV-market price]/NBV), when simulating NPL sales with ad hoc haircut rates (for example, 10 percent). See Section below titled “Step 2: Calculation of the Capital Relief.”

Both the projected losses and the level of provisions are measured at the same (initial) period, which is assumed to be the year of the disposal of the NPL. In the template, this year is the most recent date for which data is available (2018 at the time of writing this note but the template could be updated after publication).

This is an approximation since the original effective interest rate of the loan (to be used for calculating its gross book value) is likely to differ from the market interest rate used to compute the sale price as the sum of discounted cash flows. Therefore, the difference in the interest rate environment between the loan origination (most of the time before the economic shock) and loan sale (after the economic shock) could be another important factor affecting haircut levels.

α measures the fraction of the loan that is expected to be recovered in the future expressed in net present value. We also assume that this ratio incorporates all indirect costs associated with the management of the loan during the recovery period.

The model does not take into account the possibility that the collateral may not be sold at its “fair” value, due, for instance, to the illiquidity of the collateral market.

The prudential treatment described in the note (that is, risk weights assigned to net exposures) is only applied by banks using the standardized approach. Under the IRB approach, risk weights are applied to gross exposures and the difference between expected losses (EL) and provisions is deducted from/added to prudential own funds.

The eligible collateral in the standardized approach includes cash; gold; some categories of debt securities depending on their rating, issuer, or seniority; equities (including convertible bonds) included in a main index or listed on a recognized exchange; undertakings for collective investments in transferable securities; and mutual funds under certain conditions (Basel Committee on Banking Supervision 2019).

Since K = reg . CAR% * RWA ⇒ dK = reg . CAR% * dRWA . Given that dRWA = dCRWA * dRWA / dCRWA, and dCRWA = WNPL * dNPL , the change in capital is dK = reg . CAR% * WNPL * dNPL * dRWA / dCRWA.

In the Fitch Connect bank database, NPLs are classified in these three buckets (substandard, doubtful, loss) according to the numbers of days past due in the respective country’s regulations. Generally, provisioning rates are higher for the oldest/legacy NPLs.

The intuition behind this alternative assumption is that bank risks can be correlated. For instance, when banks remove NPLs from their balance sheets, this can reduce both the credit risk and the operational risk.

The formula can be derived from: K = reg . CAR% * RWA ⇒ dK = reg . CAR% * dRWA . In addition, dCRWA = dRWA * dCRWA / dRWA, and dCRWA = WPL * dPL. Therefore, the change in performing loans is dPL = dK*(l/(WPL*reg. CAR%))* (dCRWA/dRWA), with dK denoting the capital relief.

Future updates of the template may allow using data for subsequent years.

The rule is to set a 150 percent risk weight when specific provisions are less than 20 percent of the outstanding amount of the loan, and a 100 percent risk weight when specific provisions are above 20 percent of the outstanding amount of the loan (see Basel Committee on Banking Supervision 2019).

To be included in the regulatory retail portfolio and risk weighted at 75 percent, claims must meet the following criteria: (i) orientation: individual person or persons or to a small business; (ii) product: revolving credit and lines of credit, personal term loans and leases, and small business facilities and commitments (securities and mortgage loans are excluded); (iii) granularity; and (iv) low value of individual exposures (see Basel Committee on Banking Supervision 2019).

At the time of drafting this note, the coverage of the Fitch Connect bank-level dataset was not sufficiently comprehensive to be able to compute from it accurate average provisioning rates for banking systems in sub-Saharan African countries.

Specific provisions are calculated from the FSI database as the difference between gross NPLs and net NPLs.

The database is available at: https://www.worldbank.org/en/ research/brief/BRSS

While conceptually superior to option 1, the computation of the provision ratio by buckets of NPLs relies on many simplifying assumptions due to missing data in the Fitch Connect bank database: (i) when a particular bank does not report any data by NPL category, it is removed from the country calculation of the country provision rate; (ii) when a bank reports only partial data by NPL category (for example, data is available for sub-standard NPLs but missing for doubtful and loss NPLs), the missing data is inferred by distributing the residual in equal amounts across the remaining NPL categories; (iii) when a country does not report any data by NPL category (meaning that no bank in the country reports data in this format), it is assumed that the country’s ratios for each category (for example, share of substandard NPLs in total NPLs) is equal to the median for sub-Saharan Africa; and (iv) when a provision ratio for a given country and a given NPL category is not available in the World Bank’s Bank Regulation and Supervision Survey database, it is assumed that this specific ratio is equal to the sub-Saharan African median provision ratio for the same NPL category.

See European Banking Authority 2016; Gandrud and Hallerberg 2014; and Croatian National Bank 2020.

The liquidation of problem banks or their orderly resolution without recourse to public funds are, in general, preferable options. The use of public resources to recapitalize private banks should be a last-resort measure, used exclusively when financial stability is threatened. It should only occur after loss absorption by bank owners, and alongside time-bound restructuring plans that address the underlying bank weaknesses and help restore its long-term viability (see Dobler and others 2020).

See example of Croatia for NPL investors’ income per unit of gross NPL value in recent years (Croatian National Bank 2020).

For Europe, indirect costs are assumed to be in the range of 2 percent to 6 percent according to Jobst, Portier, and Sanfilippo (2015) and Ciavoliello and others (2016).

The Doing Business indicator on “enforcing contracts” is used as a proxy to estimate the legal costs of resolution. It is important to note that the Doing Business indicator does not refer to the recovery of bank loans, but a hypothetical case where a commercial debt is recovered through the court system. Bank loans may have different procedures available, and most importantly, the indicator does not refer to the recovery of secured loans. In addition, in August 2020, The World Bank suspended the Doing Business report due to some data irregularities. The authors of this note are aware of the risk and quality concerns over these indicators. However, there are no better alternatives presently.

More precisely, the World Bank Doing Business database provides the individual components of the cost of enforcing a contract, but some costs are likely to be split between the bank and the borrower. As a result, the total enforcement cost for the bank is proxied as the sum of attorney fees, enforcement costs, and half of the court fees. Ten, 75 percent of this value is taken.

To proxy the time to resolution, (i) the default option in the template is to use the time to enforce contracts for going concern businesses from the World Bank Doing Business database, since this series is available for the whole country sample. The series refers to the time required to enforce a contract through the courts (in calendar days), including the time to file and serve the case, the time for trial and to obtain the judgment, and the time to enforce the judgment. Note that the time, which is reported in calendar days in the World Bank database, is converted to years in the template and rounded to the nearest 0.5. (ii) A second option is to use the time to resolve insolvency (also from the World Bank Doing Business database), although this series is not available for some countries and insolvency procedures are not common in the sub-Saharan Africa region (compared to debt enforcement). The series is the time required to recover debt measured in calendar years, including appeals and requests for extension. (iii) A third option in the template is to use the average of the time to enforce contracts and the time to resolve insolvency. Note that, similarly to the assumption on legal costs, we take 75 percent of these series values (for the time to enforcement and the time to insolvency), since the resolution process may have already started for some of the NPLs sold by the banks.

The default calibration of 35 percent is justified as follows. For the consensual route, banks typically proceed to a preliminary segmentation of NPL borrowers to identify the (i) viable, (ii) marginally viable, and (iii) nonviable ones. It is assumed that the shares of these categories are given by the median shares of (i) substandard, (ii) doubtful, and (iii) loss categories of NPLs in sub-Saharan African countries from the Fitch Connect bank database for 2018. These shares are 0.27, 0.29, and 0.44, respectively. It is also assumed that the recovered amounts (in percent of the loan book value) are 75, 50, and 0. This gives an overall recovery ratio of about 35 percent.

See some applications of the template in the 2021 IMF Departmental Paper “Resolving Non-Performing Loans in Sub-Saharan Africa in the Aftermath of the COVID-19 Crisis.”

For policy experiments with a targeted NPL disposal strategy, key parameters should be adjusted to account for the fact that the sale focuses mostly on loss NPLs (and not on “average” NPLs). For instance, management costs may need to be increased; the discount rate should decrease given lower expected returns on legacy NPLs; the probability of consensual recovery would be reduced; and the value recovered through the consensual approach should be significantly lowered, as well as the collateralized portion of the loan.