1. Introduction

A regulation on bank’s large exposures was issued in 2019 by the Bank for International Standards (Basel Committee) and is being implemented by countries within the Basel Accord following local implementation schedules. In Mexico, the regulation entered into effect in October 2023. The large exposures regulation is a tool to deal with credit risk concentration, specifically “name concentration”. However, questions on the effectiveness of this regulation were raised regarding the adequacy of the capital requirement. Thus, there is a need to analyze if the current capital requirement is aligned with the charge of capital implicit in this regulation regarding credit risk concentration. Due notice is given to the fact that the credit risk due to concentration accounts for an important share or capital at risk, measured through the computed add-ons.

Concentration risk arises basically from two kinds of concentration of credit risk: The so-called “name risk” referred to as the one resulting from a single counterparty or a group of connected counterparties, and the concentration in economic sectors. This work addresses the “name concentration” problem since this is the focus of the large exposures regulation.

The Basel regulation placed its initial focus on credit risk capital requirements given that it is the main component of capital for most banks. The regulatory framework included two approaches:

At the beginning (2000-2004) there was a proposal to include a component of the capital requirement resulting from the concentration level of the bank’s portfolio. Eventually, the Basel Committee did not include this capital component, and the discussion on how to deal with credit risk concentration remained open. After years of discussion, the proposal for a different approach emerged in 2014 and concluded in 2019. This was called the large exposures approach or LEX. This work looks retrospectively and links the initial discussion with the final proposal.

2. Objective

This work seeks to determine the add-on implicit in the large exposures regulation (LEX, following the Bank for International Settlements-BIS-practice) and to assess its importance in the regulatory capital. The regulation has followed a different path from computing and assigning a specific supplement of capital due to credit risk concentration, relying more upon the complete Basel framework, as well as on current and in-process capital supplements. Therefore, it is important to quantify the risk implicit in the new LEX rule. The difference between the capital requirement without concentration, measured by the capital requirement through the Basel IRB formula, and the requirement including concentration in the credit portfolio will be the adjustment add-on-the share of risk not included in the regulatory requirement. To do so we will go from a capital requirement with only a systemic risk to a capital requirement including an idiosyncratic risk derived from the risk concentrated in a single counterparty or a group of connected counterparties. We hypothesize that the concentration credit risk has an important share of capital at risk since realworld portfolios are heavily concentrated.

3. Previous Studies on Credit Risk Concentration and add-on Computation

The problem of credit risk concentrations has been extensively addressed in the past. Works can be classified according to the problems addressed from 2000 to the present.

4. The Large Exposures (LEX) Regulation Components and their Implications

In this work, we will use the global regulation (^{Financial Stability Institute, 2022}) and the specific implementation in Mexico for examples, parameters, and precise implications.

The BIS LEX framework was concluded and released by the BIS to enter into effect as of January 1^st, 2023. It was implemented in Mexico in 2023 and became effective in October 2023 for systemic banks. The BIS assessed Mexico as LEX regulatorycompliant in December 2023 (^{BCBS, 2023, p. 7}).

Main components of the ^{Financial Stability Institute, 2022}:

Let us rethink the LEX regulation and its implications in the management of the credit concentration risk and the metrics to manage the credit risk.

The LEX regulatory approach does not include a specific capital requirement for credit risk concentration but requires the development of a framework to manage such risk. Nonetheless, the LEX regulation’s components have important implications for the parameters used to compute the capital requirement under the IRB framework. As shown in Table 1, we can align the components with the credit risk key parameters that are important to determine the capital requirement (see Table 1).

In theory, all those elements provide a framework to manage the concentration risk. In Figure 1 all the elements of the framework are joined and show at the center the management of the concentration risk (see Figure 1). We can trace how every component affects the credit risk parameters, as shown in Figure 2 (see Figure 2). Our objective is to model portfolios derived from the LEX regulation and to compute the concentration component that is completely absent from the Basel IRB formula.

Source: Prepared by the author.

Figure 1 Components of Large Exposures Regulation and Effect on Risk Management and Risk Metrics Parameters 

* In the case of Mexico, only subordinated debt convertible to capital is allowed. The law must be modified to permit the use of other absorbing losses debt to be used.

Source: Prepared by the author.

Figure 2 Components of Large Exposures Regulation and Effect on Risk Management and Risk Metrics Parameters 

Before addressing the task of computing capital requirements, it is worth pointing out that the LEX regulation is not the only component of the Basel regulation dealing with handling credit risk concentration. The complete framework is important to deal with this risk, but of course, not only with this risk. The next section addresses this issue.

5. The Basel Regulation Framework and its Connection with the Concentration Risk

At the end of the day, the LEX regulation is looking to avoid impacts on the financial system derived from large losses in banks due to large exposures in loans granted and other credit exposures.

As explained in the Large exposures standard: executive summary (^{Financial Stability Institute, 2022}) document, the LEX standard is part of the Basel III reform package that complements the Basel Committee on Banking Supervision’s risk-based capital framework to achieve a:

Thus, it is not only important to study the complete framework but also to compute the impacts on capital according to the implicit risks in the LEX.

First, let’s address the BIS framework’s components and their connection with the credit concentration risk. For our purpose, the relevant components are as follows:

Figure 3 shows the integration of the pieces into a complete framework (see Figure 3). For our purposes, we place the credit concentration risk in the center but is a complementary piece of the framework.

Source: Prepared by the author.

Figure 3 Concentration Risk and its Integration into the BIS Regulation Framework 

The author presents this framework in articulated form to understand the role that every piece has in managing concentration risk.

The 2008 banking crisis triggered important initiatives that will be reflected in specific regulations later. The focus of those initiatives was oriented to the resilience and stability of the financial system and of course to protect the economy, as explained by the Basel Committee on Banking Supervision:

This consultative document presents the Basel Committee’s proposals to strengthen global capital and liquidity regulations with the goal of promoting a more resilient banking sector. The objective of the Basel Committee’s reform package is to improve the banking sector’s ability to absorb shocks arising from financial and economic stress, whatever the source, thus reducing the risk of spillover from the financial sector to the real economy. (^{BCBS, 2009, p. 1}).

In that sense, we must interpret the articulation of the regulation pieces explained before. The regulation addresses the main systemic components of the financial system-the important part is the system, not a specific group of banks.

Let us use Figure 4 to complete the articulation of the pieces (see Figure 4).

1. The rule in Mexico is a maximum between 6.5% of the risk-weighted assets or 3.75% of the risk-adjusted assets for leverage ratio computation purposes. 2. In Mexico the supplement is assigned by the regulator to every bank designated as locally systemically important or D-SIB. The size of the supplement depends on the systemic impact of the bank. ^{Financial Stability Institute (2019)}.

Source: Prepared by the author

Figure 4 Role of the Pieces of the BIS Regulation Framework in Managing Credit Concentration Risk 

We can notice, on the one hand, that systemic banks have two heavy capital supplements to deal with losses: G-SIB and D-SIB losses (from 0.6% to 1.5%) and the TLAC supplement of approximately 6.5% of the bank’s risk-weighted assets. On the other hand, the rest of the banks are only obliged to form the capital conservation supplement, not the TLAC supplement, as shown in Table 2 (see Table 2).

There are minimum regulatory capital requirements-including the supplements. Regulatory reporting ensures that those minimums are complied with. To assess any potential risk, banks must conduct a regulatory Internal Capital Adequacy Assessment Process (ICAAP) annually. In the manual and template to conduct such assessment, the Comisión Nacional Bancaria y de Valores (^{CNBV, 2023, pp. 32-33}), the Mexican regulator, includes in Section 3.4.15 Sensitivity Analysis, the following: a) Simultaneous write-offs of the ten main counterparties or group of connected counterparties, (write-offs adjusted by loss given default). Sensitivity must include Public Sector Entities (PSEs such as Petróleos Mexicanos [Pemex] and Comisión Federal de Electricidad [CFE]).

The effect of this sensitivity on the regulatory capital (through the capital ratio) must be computed and disclosed to the regulator.

We need to point out several issues about this sensitivity.

The simultaneous write-off assumption is very heavy for any portfolio since a Bank that uses the maximum concentration limits, by definition, among the 10 main counterparties must include the four maximum large exposures, that in its limit would sum the 100% of the Tier 1 capital, and the next six large exposures below those four.

That implies a perfect correlation among the ten main counterparties or group of connected counterparties regardless of sectorial connections and activity, including Public Sector Entities (PSEs).

The reader can easily guess that a loss of this size would be an important share of any bank’s capital.

As an important reference to assess the relevance of concentration risk in the Mexican financial system, let us review the information presented in Table 3. This shows the vulnerabilities identified by regulators in the ICAAP for the years 2017 to 2023 (see Table 3). On average, fifteen banks showed vulnerabilities due to credit concentration. In 2022 ICAAP showed a vulnerability in sixteen banks involving 12.1% of the assets of the banking system (see notes included in Table 3). Note as well that, on average, eight banks presented capital shortfall in the ICAAP exercise.

Although the result of this sensitivity does not imply a failed (ICAAP) regulatory exercise, the bank may eventually face the question of how it would recover from a loss of this size. In such a case the action plan that the bank must outline in its contingency plan (CP) should be enough to face such losses. A bank with an important risk in this sensitivity at least will be on a watch list. Therefore, results from one exercise (ICAAP) can be linked to another (CP) straightforwardly, which is one of the benefits of the integrated framework from a regulatory point of view.

Obviously, there is an offset of the write-offs. The risk-weighted assets will also be reduced, but in any case, the net effect is important.

That risk is present in all banks, but the supplements for systemic banks are enough to cover any loss of this size. A regular (non-systemic) bank has only the capital conservation supplement of 2.5%. We will address this issue later when we compute the capital concentration add-on.

The LEX regulation is oriented to all banks including those that use the standard approach to compute their regulatory capital. For this reason, instead of including a specific capital requirement in the IRB formula, the approach is to control important parameters that have to do with the capital requirement, regardless of the bank being systemic or not, or uses the IRB or the standard approach to compute its capital requirement. The parameters are as follows:

The process that we will follow to determine the add-on is the following:

6. Levels of Concentration Implicit in the LEX Regulation

LEX regulations released by the BIS and CNBV in Mexico have implications for credit portfolio concentration, regardless of whether the bank computes the capital requirement measured with the IRB formula or determined with the standard model.

The IRB formula assumes infinite granularity in the portfolio. For practical purposes, we reduce the problem dimension based on Yi Xiao and Finger’s research.

The problem we face is the same one that ^{Yi Xiao and Finger (2002)} addressed since, in both cases, we are parting from homogeneous and fine-grained portfolios. In our case, a corporate one under the Basel IRB Basel formula, that assumes infinite granularity and homogeneous risk, homogeneity and fine-grained exposures in the case of retail exposures, in both cases the dimension of the problem is reduced to analyze the problem in a more tractable size.

Consider a portfolio with an average default probability of 5%, an average recovery rate of 50%, and an average correlation of 10%. Assuming there are 20, 100, 500, or 2500 exposures in this portfolio, each to a distinct obligor, we carry out fullblown Monte Carlo simulations with 100,000 scenarios for each case. The distribution of the portfolio is calculated from the simulation and shown as a histogram in Figure 1. With a small number of exposures in the portfolio, the distribution is rather discrete, dominated by the properties of individual positions.

With more and more exposures in the portfolio, the default of a single exposure has less and less impact on the total pool, and the distribution becomes progressively smoother. The distribution eventually converges to the homogeneous and fine-grained limit shown as solid lines in Figure 1. (^{Yi Xiao & Finger, 2002, p. 3}. Please note that the following Figure 1 is part of the quote).

Source: ^{Yi Xiao and Finger (2022, p.3)}.

Figure 1 Convergence of a loan pool to the homogeneous and fine-grained limit. 

On the one hand, in the quotation above note that in Xiao and Finger convergence was at 100,000 trials in a Monte Carlo simulation exercise.

On the other hand, we will use the one presented by the ^{Committee on Banking Supervision (2006)} as a reference yardstick.

Credit concentration is sometimes known as lack of granularity. This section discusses how to extend the ASRF model to incorporate the effect of granularity.

To fix ideas, consider how economic capital (credit VaR) varies over a sequence of loan portfolios with the following structure: they all contain a number of exposures to similar credits which are all of the same size with the exception of one that is ten times that size. Table 1 depicts the tail of the simulated loss distribution for seven such portfolios of different sizes ranging from 10 to 3000 credits. As the number of credits increases the importance in the portfolio of the single large exposure declines and the economic capital converges to the one corresponding to the infinitely granular case (^{BCBS, 2006, p. 9}).

The following Table 4 (Table 1 of the ^{BCBS, 2006, p. 9}, and Table 4 in this text) appears on page 9 of the BCBS document (see Table 4).

Table 4. Scenarios Present in BSI’s Basel Committee on Banking Supervision (^{BSCS, 2006}) Working Paper 15

With this information, we can infer a simple add-on, if we know the increase in concentration, assuming that the 3000 exposures portfolio mimics the granular portfolio case. For instance, at a 99.9% level of confidence passing from three thousand loans to one hundred implies an add-on of 3.37% using the VaR risk metric.

In this same document, the following question is asked: “How important is the effect of name concentration on economic capital?” (^{BCBS, 2006, p. 9}) The answer is important for our purposes:

The 3000 exposures portfolio size is similar to the one proposed by ^{Xiao and Finger (2002)}.

In our exercise, we assumed that we had a portfolio of 3000 granular exposures (same size and risk), and we derived alternative concentrated portfolios as follows, according to the main sizes found in ^{Basel Committee on Banking Supervision (2006)}:

The monetary amount of the portfolio and loans was selected as follows:

If we were to consider the Tier 1 capital of systemic banks, the level of concentration would be higher, but we can calculate the add-on with a rule we can derive from our results.

We also worked on the 3000-size portfolio with equal-size exposures in Table 5 (see Table 5).

In the first line, we will compute the add-ons for all scenarios, and based on the results, we will infer the rest of the cases.

In the BCBS’s framework, we find the following reference regarding the “Maximum permissible concentration under EU large exposures rules. Such calculations give estimates of 13% to 21% higher portfolio value-at-risk for this highly concentrated portfolio versus a perfectly granular one that is comparable in all other dimensions.” (^{BCBS, 2004}). Also, note 8 states the following: “Directive 93/6/EEC of 15 March 1993. An estimate of the HHI for such a portfolio would be about 0.0156”; following the HHI inverse rule (^{Márquez Diaz-Canedo, 2003, pp. 198-199}) that number would be around 64 loans, so that estimate falls within our scenarios.

According to the Banco de México (the Mexican Central Bank) in its second semester report of 2023 on financial stability (^{Banco de México, 2023}) the concentration (measured by the Herfindahl-Hirschman Index HHI) of Mexican banks ranged from 0.01 to 0.02 during the 2012-2023 period (see Graph 1). This is a significant level of concentration. Using the metric 1/HHI, we find that it is equivalent to portfolios with a number of loans between 50 and 100. As stated before, those numbers are consistent with the scenarios designed for this work.

Source: ^{Banco de México (2023, p. 67)}.

Graph 1 Banco de México Graph on Loan Portfolio Concentration, Default Probability, and Correlation 

Thus, for our purposes, the relevant HHI and associated loan portfolios are between 100 and 50 loans.

The parameters and other assumptions for our exercise are the following:

The model used is a CreditMetrics-like model developed by the author. The Cholesky decomposition is used to obtain credit-correlated default scenarios. The original methodology is disclosed in ^{JP Morgan and Reuters (1996)}.

The metrics to be used to compute the add-on are the Value at Risk of the portfolios and The Conditional Value at Risk (VaR and CVaR). Nonetheless, although we will compare the results from both, CvaR will be the final chosen metric to compute the add-on. We know from ^{Artzner et al (1999)} that VaR fails as a coherent measure of risk, specifically in the subadditivity property at high levels of confidence, as is the case in our research. The CVaR has become the dominant risk metric for many standards.

7. Capital Requirements and VaR Using the Basel IRB Formula

As a comparison yardstick, we computed the capital requirement using the Basel IRB formula. Is important to point out that this formula considers no concentration at all, which is why there is a need to compute the add-on resulting from passing to the real world, where concentration is an important risk factor to be considered.

The capital requirement for a loan under the selected assumptions is computed with the Basel IRB formula as follows.

Capital requirement:

Where the correlation is:

Maturity adjustment:

Ln = natural logarithm

N(x) = standard normal cumulative distribution function

G(x) = standard normal inverse cumulative distribution function

Source: BCBS (2004, para. 272).

Notice that the confidence level of this requirement is 99.9%. To align the formula with our exercise, we fix the term as one year.

The reference capital requirement using this formula and our assumptions is 13.03%.

8. Results Computing the VaR and CVaR of Portfolios with Different Concentration Levels

8.3 Portfolio Composition

To assess the effect of credit concentration in the portfolios we designed the following portfolios. Concentration in a portfolio increases as the number of loans (exposures) decreases.

1. Portfolio A 3000 has all exposures of the same size. In our exercise, this case is the most similar to an IRB granular portfolio.

2. Portfolio B 3000 has four exposures with an individual limit of 25% of Tier 1 Capital. The rest are exposures of the same size. This portfolio includes in a granular portfolio the effect of the maximum credit limit to a counterparty or group of connected counterparties: 25%. We assume that four counterparties or groups of connected counterparties use this limit, so the limit of 100% of Tier 1 capital allocated in four counterparties or groups of connected counterparties is reached.

3. The rest of the portfolios (with sizes of 2000, 1000, 500, 100, 50, 40) have four exposures with an individual limit of 25% of Tier 1 Capital. The rest exposures are homogeneous in size. This follows the same logic of Portfolio B 3000.

Once we defined the portfolio size and composition, we executed the simulation process and computed the risk metrics. The results were as presented in Table 6 (see Table 6).

Table 6 Results of VaR and CVaR for Built Portfolios 

	Value at Risk				Conditional Value at Risk
	VaR Confidence Level				CvaR Confidence Level
Portfolio Size	99.90%	99.50%	99.00%	95.00%	99.71%	98.56%	97.10%	85.40%
3,000 Equal	13.60%	8.53%	6.57%	2.80%	13.59%	8.53%	6.59%	2.86%
3,000 Portfolio	13.90%	8.88%	6.91%	3.06%	13.90%	8.87%	6.97%	3.06%
2,000 Portfolio	14.14%	8.95%	6.98%	3.04%	14.01%	8.93%	6.94%	3.07%
1,000 Portfolio	14.28%	8.28%	6.93%	3.05%	14.13%	8.93%	6.93%	3.07%
500 Portfolio	14.34%	9.02%	7.00%	3.07%	14.19%	9.01%	7.01	3.12%
100 Portfolio	14.85%	10.01%	7.40%	3.66%	15.08%	9.87%	7.30%	3.58%
50 Portfolio	16.51%	10.67%	8.72%	3.56%	16.60%	10.70%	8.67%	3.57%
40 Portfolio	16.68%	11.43%	8.95%	3.97%	17.42%	11.26%	9.05%	3.71%

Source: Prepared by the author.

Recall that our comparison reference value is the VaR implicit in the IRB formula capital requirement-that is, 13.03%.

When a metric changes from VaR to CvaR, it is good practice to select the latter’s confidence level to replicate the risk of the VaR. One example is to use 97.25% for CVaR and 99.9% for VaR, as shown in Graph 2 (see Graph 2). In this work, we determined the CVaR confidence level as 99.71% to align both metrics, as in Graph 3 (see Graph 3). Other works identify a confidence level of 99.72%.

Source: Prepared by the author.

Graph 2 Value at Risk for Every Portfolio at a 99.9% Confidence Level 

Graph 3 Conditional Value at Risk for Every Portfolio at 99.71% Confidence Level 

9. Computing the Concentration add on and Assessment of Results

We obtained the add-ons by comparing the risk metric with a given level of concentration minus the capital requirement with the IRB formula. Not all banks are IRB, but the idea is to get a comparison parameter, and this is a sound one.

Graph 4 shows the resulting VaR and CVaR. It is easy to notice that the CVaR metric is much more stable. This has to do with its coherence, and so we used it to determine the add-one (see Graph 4).

Source: Prepared by the author.

Graph 4 Concentration add-on with VaR and CVaR 

Despite the size of the simulations, it is advisable to correct any deviation coming from the method used and the slow convergence that we noted. For this reason, we obtained a fitted add-on from a linear regression between the HHI and the obtained add-on. Results are shown in Tables 7 and 8 and Graph 5 (see Table 7, Table 8 and Graph 5).

Source: Prepared by the author.

Graph 5 Fitted Concentration add-on with CVaR 

As expected, there is a linear relation between the HHI and the add-on. If we use this relation to obtain the add-on for concentrations of 0.01 and 0.02 (the range of concentrations for the Mexican Bank system as of December 2023) we find add-ons of 2.02% and 3.56%, as shown in the previous graph.

The results are similar to those in other works. We have mentioned the Basel Committee on Banking Supervision (2004) and the EU large exposure rules quoted in that paper.

One extensive study on concentration is ^{Hibbeln (2010)}. This author uses several approaches to compute the add-on. He estimated the add-ons with the following results (see Table 9).

The resulting add-ons for the scenarios initially proposed are presented in Table 10 (see Table 10). Recall that the add-on for a completely grained portfolio of 3000 loans is 0.52. In the next case, it passes from a granular to a concentrated portfolio having the four maximum exposures permitted by the LEX regulation-the add-on is 0.94% for the first 3000-size portfolio scenario, and 1.21% for the last.

The add-on changes little for portfolio sizes of 2000 and 1000, but for sizes of 100 and 50 (with HHI equal to 0.01 and 0.02), in our relevant area, the add-on increases considerably: ranging from 2.19% to 2.21% for the former and 3.59% to 3.77% for the latter.

It is also important to note that “vertically” the increase of the add-on from the best (only 4 maximum large exposures permitted) to the worst scenario (4 maximum LE + 3 D-SIB Exposures +10 Loans larger Than 10% of Tier 1 capital) is moderated (see Table 10, and for complementary support, see Table 11). Therefore, we conclude that the main contribution to concentration is by one of the four largest loans.

“Horizontally” the average increase of the add-on is 2.59%, so the most critical component is the implicit reduction in the number of loans according to the inverse of the HHI. We can take as a concise result of this work the one in Table 10 for concentration levels of HHI= 0.01 and HHI=0.02, which is an add-on ranging from 2.2% to 3.6% in higher concentrations, as in Table 10 (see Table 10).

So, in summary, the vertical behavior (increasing base concentration) is the key driver. Adding more concentration to base scenario does not contribute heavily to capital requirement, as shown in Table 11 (See Table 11).

Please note that the add-on is 4.34% for a forty-loan equivalent portfolio size, and concentration escalates the capital requirement heavily.

Assigned to a specific supplement of capital or not, the conclusion is that credit portfolio concentration implicit in LEX accounts for an important share of the capital at risk. In perspective, it is important to know how important that number is. Consider the following for some Mexican banks: In Table 12 we can see that the amount of required capital due to concentration in LEX regulation is especially important, accounting for more than 50% of the total TLAC supplement, and on average, it represents more than 20% of the regulatory capital (see Table 12).

We explained before that there is not a specific capital requirement for concentration, but the pieces of the whole regulatory framework work together to handle the concentration risk. We also explained that systemic banks have two additional capital buffers apart from the capital conservation supplement and that the last one is a supplement for all banks.

It is true that capitalization ratios are, in general, higher than minimum regulatory ones, but it is important to know the marginal contribution of risk components to total risk and to capital at risk. In Graph 6 we can find the total capital ratio and by type of bank, compare such data with the one in Table 13, which shows the capital requirement for Mexican systemic banks, meaning that those have higher requirements. Recall that for the rest of the banks, the minimum ratio is 10.5% (see Graph 6 and Table 13).

Source: Prepared by the author with data from ^{CNBV (2024b)}.

Graph 6 Mexico, Total Capital Ratio by Type of Bank as of December 2023 

What is capitalization like in the world? In Graph 7 we can notice that world capitalization levels are much higher than 10.5%. Only three countries have ratios lower than 12% and only one with an average capital ratio of 6%. In red labels, we have the ratios of other selected countries: the United States 16.3%; Mexico 17.7%, and Switzerland 19.7% (see Graph 7, in next page). Consider the minimum concentration component that we have computed and keep in mind that those ratios must support several types of losses including concentration implicit in LEX.

Disclaimer of data provider: Deposit takers’ capital adequacy is a ratio of total regulatory capital to their assets held, weighted according to the risk of those assets.

Source: ^{World Bank (n.d.)}.

Graph 7 World Banks’ Regulatory Capital as of 2020 

10. Conclusions

We have explained that the regulation did not follow the approach of computing a specific granularity adjustment for the bank’s capital requirement due to the credit concentration risk. However, a holistic approach through the complete regulatory framework, including the LEX regulation, is a way to limit the concentration risk, and account for consolidated exposures, including not only all those with credit risk but also adding the exposures of all connected counterparties. At the same time, this approach addresses correlation and contagion and is supported by other pieces of the Basel regulation. Nonetheless, the LEX has an implicit minimum concentration and, therefore, a share of capital at risk. We have computed the add-ons and demonstrated that such a share is important. Since there is not a specific capital supplement for concentration, the existing supplements must be enough to absorb any loss, including the losses eventually coming from the concentration risk. We have also pointed out that the whole focus of the Basel regulation is systemic. Finally, we showed that although capital levels are aligned with the add-on, those levels must face any kind of loss. Losses implicit in the LEX due to concentration are particularly important and account for more than half of the TLAC supplement (6.5% of RWAs). This confirms the relevance of the size of the add-on.

The BIS implemented the LEX regulation to address the concentration risk, but once banks adopt the new regulation completely, the residual risk will remain relevant.

In Table 3, the author presents a summary of data from seven years of ICAAP in Mexico (2017-2023) showing that, on average, an important number of banks (15) present a vulnerability due to credit risk concentration. At least in one year, this involves an important share of the total system assets. LEX regulation started in Q4 2023 in Mexico.

If credit concentration would materialize, the results of this work show that for nonsystemic banks, the capital conservation supplement would not be enough (3.6% vs 2.5%). For systemic banks this implies that the add-on represents 55% of the complete TLAC supplement (3.6% vs 6.5%) still in the formation process. A current offset for this risk is the levels of capital shown by Mexican banks. Nonetheless, the stress test scenarios in the ICAAP show vulnerabilities due to credit concentration, meaning that under stress conditions, situations may change considerably.