1. Introduction

One of the main missions of the Basel Committee of Banking Supervision (BCBS), incorporated in its Tableer, is to set the standards for the prudential regulation and supervision of banks. In general terms, it expects full implementation of its standards by its members and their internationally active banks, albeit BCBS standards constitute minimum requirements and its members may evaluate to go beyond them.

BCBS’s guidance comes in waves, usually in response to big financial crises, as was the case for Basel I, Basel II and Basel III^{1 2}. In this instance, it appears that the BCBS detected may flaws in the current Capital Accord, and decided to correct it enacting an entire overhaul of the market risk framework, both for the Standardized and the Internal Models Approaches (SA and IMA respectively). The initial glance at the new set of specifications determines that the Minimum Capital Requirements (MCR) will undoubtedly rise, but although the BCBS intended to counter the argument stating that the changes would only exert a minimal impact in the overall capital requirements, further analysis shows that the new market risk rules will heavily affect banks with significant investment activities.

However, many organizations like the Global Financial Markets Association (GFMA), the Institute of International Finance (IIF) and the International Swaps and Derivatives Association (ISDA) challenged the BCBS and stressed that the rules may have a negative impact on banks’ capital market activities and reduce market liquidity.

It is relevant to analyze the effect that the new regulations could exert on the banks’ capital levels emphasizing one of the most volatile markets, i.e. the stock market. The article focuses on Mexico, the second largest Latin American economy, with the motivation fueled by the fact that Mexican banks have not participated in the Quantitative Impact Studies (QIS) carried out by the BCBS that defined the final structure of the schemes and the value of the respective parameters. Furthermore, in consideration of the fact that the relationship between SA and IMA was completely revamped and banks using the latter must also compute the former, it is imperative to evaluate whether the latest version of the IMA could be the right one and, additionally, if the incentives to develop modelling innovations are aligned with the final outcome or, on the contrary, if the BCBS seems to be pushing institutions to utilize the SA. The study is carried out hypothesizing that Basel IV entails a profound change in the relationship between SA and IMA with a tilt towards the former in view of the intricate network of validation tests for the latter that, alongside the output floor, severely hampers the election of the latter, particularly during periods of heightened market volatility.

The paper unfolds as follows. Section 2 briefly introduces the incoming Standardized and Internal Models Approaches; Section 3 sketches the literature review; Section 4 outlines the Methodology; Section 5 describes the Results and, finally, Section 6 synthetizes the conclusions and implications.

2. Introduction to the SA and IMA

3. Literature review

In view of the recent enactment of the latest regulations, the academic literature on the subject is not very profuse, and, in that sense, supervisory agencies and professional bodies provide the bulk of the references.

Magnus et. al. (²⁰¹⁷), from the Directorate-General for Internal Policies (IPOL) in 2017 sketched a review of the main characteristics of the road to Basel IV which reflects the main patterns of the previous Basel Accords, their pitfalls, and the solutions intended to address them. Particularizing on the capital floor and considering that Basel III still broadly maintains Basel I framework the authors highlight that, at the moment of reviewing Basel III’s capital output, the incumbent configuration did not tackle, among other issues, the following ones: the use of low capital levels to boost financial leverage, the unexpected large losses in low capital portfolios and the lack of market confidence in capital floors. These aspects, alongside the interaction between the input data, the output floors and the leverage ratio were to be addressed and finally configured after a comprehensive QIS (^{BCBS, 2016a}). Regarding the capital floors, Neisen (²⁰¹⁶) hypothesized the five objectives that Basel IV’s capital floors should accomplish: i) ensure that the capital level across banking system does not fall below a certain level; ii) mitigate IMA’s model risk and measurement error; iii) enhance the comparability of capital outcomes across banks; iv) reduce the variation in capital ratios across banks due to bank-specific models assumptions, and v) diminish the incentives for exploitation of internal models. However, it cautions that given that the new floor will replace the existing Basel I complemented with the extrinsic ratios in Basel III, the relationship with the IMA must be carefully analyzed. On this regard, Neisen and Schutlte-Mattler (²⁰²¹) pioneer a method to soften the impact of the SA inversely, i.e., adjusting the composition of the portfolio instead of working on the specifications. Therefore, it would be possible to optimize the capital allocation if the business model included, additionally, the internal risk appetite and the cost of capital in the pricing model.

Koch et. al. (²⁰¹⁷) concentrate on the expected capital impact, albeit for the European banking industry, mentioning that banks with significant trading books will bear the brunt of the new market risk framework, adding that those institutions that do not meet the general criteria and the qualitative and quantitative standards would suffer a substantial blow given that they should move from an IMA to the new SA. Furthermore, their study highlights the different impact magnitudes citing that Sweden, Denmark, Belgium and the Netherlands will suffer the greatest shock, followed by Germany, France, Spain and the UK according to the phase-in provisions of Basel IV. On the other hand, they remark that in contrast to the European perspective, the US would result less affected on the grounds that the Federal Reserve has already adopted a 100% Standardized capital floor under Section 171 of the Dodd-Frank Act (^{United States of America in Congress assembled, 2010}). Buberkoku (²⁰²³) performs a study for the Turkish stock market and foreign exchange market using only two variants of IMA (FHS and EVT) and ascertained that Basel IV regulations may increase capital requirements for those risks. Notwithstanding the importance of those articles, the scope is circumscribed to Europe, with Latin America and many other regions lying outside its reach.

Jackson (²⁰¹⁶) makes a point about the complexity of the SA regarding the calculation of the risk sensitivities, the DRC and the RRAO, mentioning that earlier estimations show that banks with large investment operations would face very large increases in capital requirements. The author concludes that Basel IV will have a considerable effect on the total capital required by some banks, furthermore cautioning about the implementation of the SA in view of its highly prescriptive nature and the difficulty in the enhancement to current data, data attributes and processes in banks.

Dankenbring et. al. (²⁰¹⁶) stress that, while Basel III primarily focused on the numerator of the MCR ratio, Basel IV overtly aimed at the denominator of the capital ratio, i.e., the calculation of credit, market and operational risk exposures. Furthermore, they pour doubts on the final outcome of Basel IV underlying that the effect of the new wave of regulations will exceed banks’ capital, funding, implementation costs and risk sensitivity as all those factors will exert downward pressure on profitability, simultaneously raising questions about the viability and sustainability of their business models. On this line, Leake et. al. (²⁰¹⁵) regard investment banking as likely to be more affected than retail banking because the trading book is targeted directly, warning that the proposals, leverage ratio, liquidity requirements, large exposure limits, clearing and initial margins requirements are additional challenges for the (already) besieged investment banking business model. Finally, the authors alert that those banks may need to ponder whether their ROI (Return on Investment) will be viable in the long term. Accordingly, Oyetade et. al. (²⁰²³) carry out a study of the effects of Basel IV on simulated balance sheets of selected African banks and suggest that new Basel IV regulation would presage a negative impact on -at least- their short-term performance, albeit warning about the high uncertainty of an unapplied policy.

There is, then, a schism between BCBS, on the one hand, and the academics and practitioners on the other in the treatment of SA. While the former hails the approach for reducing the complexity, mimic the risks and enhance the comparability, the latter group brands the SA as almost inadequate to calculate MCR (^{Gaumert and Kemmer, 2015}) because of its inability to capture risks, simultaneously proposing few measures to bolster the confidence in the IMA, albeit theoretically circumscribing to the Basel IV boundaries.

Some academics questioned some aspects of the route taken by the BCBS in the application of ES. Among the most innovative, Ahelejbey et. al. (²⁰²¹) propose the Extreme Downside Hedge (EDH) and the Extreme Downside Correlation (EDC), by means of which they discover that assets can be clustered into “givers” and “receivers” of tail risk -though for the cryptocurrency market-, simultaneously criticizing Basel IV’s failure to address systemic risk and Fang et. al. (²⁰²³) put forward a method to take into account and forecast systemic risk and, furthermore, backtest it. Other authors venture beyond the official ES-based IMA and advocate for the adoption of other risk measures like the Expectiles Risk Measure (ERM), like Tsvetelin et. al. (²⁰²³), casting doubts on the non-elicitability of ES, which is the main reason why Backtesting in Basel IV is grounded on VaR, and Burzoni et. al. (²⁰²²) refine ES introducing a set of convex risk measures controlling the expected losses associated with different sectors of the tail distribution.

Another point of conflict is the validation criteria set out in Basel IV, triggered by the lack of elicitability of ES. The financial literature has come up with numerous alternatives like the traditional Acerbi and Szekely (²⁰¹⁴), Constanzino and Curran (²⁰¹⁸), Emmer et. al. (2015), Moldenhauer and Pitera (²⁰¹⁹), Righi and Ceretta (²⁰¹⁵) and the more recent ones in Bayer and Dimitriadis (²⁰²²) via a combined regression featuring VaR and ES, Marcin and Schmid (2022) with an ingenious and efficient way to curb the backtesting shortcomings rooted in VaR, ES and ERM or Molina Muñoz et. al. (²⁰²²) through an innovative combination of EVT and Gram-Charlier distributions. However, all the aforementioned proofs were overlooked by BCBS in an attempt to simplify matters and, accordingly, the new normative only contains a series of tests based on backtesting VaR.

The present paper contributes to the literature body going beyond to show that, even for simple exposures like stock portfolios in the Mexican market, the SA does not properly reflect the true risk; on the contrary, it obliges banks to constitute unnecessarily high capital levels. Consequently, it should not be considered a ‘credible fallback solution’ to IMA as both the official IMA and simpler alternatives related to it can still provide adequate coverage without freezing funds unproductively.

4. Methodology

The study is carried out on Mexico, one of the major economies in Latin America. As of 15/01/2020, every company quoting on the S&P BMV/IPC (Standard & Poor’s Bolsa Mexicana de Valores / Indice de Precios y Cotizaciones) is classified in accordance with the scheme of risk buckets in Table 2.1, bearing in mind that BCBS considers Mexico a developed country given that it belongs to the TLAC alongside USA and Canada. The data set is then split into two periods for parameter estimation (^{BCBS, 2019}) and evaluation of market risk forecasts (one year minimum), thus complying with Basel indications, as in Mapa (²⁰⁰³) and Hansen and Lunde (²⁰⁰⁵). The first one spans ten years, from 15/01/2010 to 15/01/2020, again abiding by BCBS’s requirements (^{BCBS, 2019}), while the second comprises the following year, i.e., from 16/01/2020 to 15/01/2021, for general evaluation and backtesting procedures¹². Primary data about stock prices was previously retrieved from Refinitiv® and converted into inputs via logarithmic returns. Using the sample of the initial 10 years, and companies are ranked in descending order in terms of 1) volatility (using beta with reference to S&P BMV/IPC, highest beta first), and 2) market capitalization (highest market capitalization first, valued as of 15/01/2020). For every set, the first five companies corresponding to each risk bucket are selected and market cap weighted, thus making, at this stage, two portfolios of twenty assets each¹³. Additionally, subsets of portfolios in each category are constructed deleting the last three and four companies and reweighing the remaining components. Hence, briefly stated, the exercise deals with six portfolios calculated with the general criteria explained in Table 4.1, with Table 4.2 informing their precise composition¹⁴.

Portfolios 1 to 6 have then, its MCRs calculated via SA (Section 2.1) and IMA (Section 2.2). For the former, HBR = 1 (11) as only long positions are used and DRC (12) is obtained employing the latest credit rating available at the start of 2020 (Refinitiv ®). For the latter, given that BCBS does not require a specific VaR model, several approaches are employed¹⁵: Historical Simulation (HS), Filtered Historical Simulation (FHS) and Conditional Volatility (CV) via GARCH-Normal, GARCH-t(d), EGARCH-Normal, EGARCH-t(d) and Extreme Value Theory (EVT). HS values are obtained through rolling windows; CV and FHS (GARCH-EGARCH) via Maximum Likelihood (ML), and FHS through Quasi-ML with GARCH-Normal, GARCH-t(d), EGARCH-Normal and EGARCH-t(d) specifications to generate the distribution of Standardized residuals. EVT follows the Peaks-Over-Thresholds (POT) approach with the Method of Moments (MM) applied to obtain Generalized Pareto Distribution (GPD) parameters after GARCH pre-whitening (McNeil, Frey and Embrechts (²⁰⁰⁵) and Embrechts, Klüppelberg and Mikosch (¹⁹⁹⁷)). However, in order to circumscribe the scope of the analysis and avoid masking artificial capital increases, EVT, i.e. the model that performs best without Backtesting penalties in the evaluation period is selected for ES and VaR calculations throughout the process. Additionally, again complying with BCBS (²⁰¹⁹), S&P BMV/IPC is the reduced factor (RS) contemplated in (13), as it reasonably drives the behavior of the six portfolios¹⁶. IMA calculations follows two different strands: the first one closely resembles the official approach exposed in Section 2.3., while the second one suppresses the reduced factor modelling, simply computing:

with the model validation standards in Section 2.2.1.

SA and both IMA variants are further calculated for every day of the evaluation period, and several parameters computed as a means to ascertain the respective capital levels, stability and relative slack compared to the losses experienced by the base portfolios. Finally, the relationship between both IMAs and SA is calculated to gauge the latter as a credible capital floor in view of the scheme proposed by BCBS (²⁰¹⁹).

5. Results

Tables 5.1, 5.2 and 5.3 picture an overview of the kind of movement that the pandemic brought about on the portfolios, most notably the increase in standard deviation, skewness and kurtosis, which alongside the growth in the tails of the distribution, indicate that the distributions of all the portfolios became more leptokurtic than the sample period. This fact, that appears more marked in P5 and P6, is indeed a foregone conclusion given the diversification present in more granulated portfolios. Aprioristically, this point would pave the way for models featuring a special treatment of the extremes, thus the expected result for EVT in Backtesting.

Some interesting elements appear in Table 5.4, which breaks down the components of SA. The high correlation regime gives the maximum MCR for every portfolio, with an increase in the region of 10% with reference to the ‘normal’ case, which is one of the innovations of the new SA (Table 5.4, Column [5]). HBR = 1 makes the portfolios bear the full brunt of DRC given the absence of offsetting short positions to net. Although it appears strange, the behavior of the DRC is not closely related with diversification as it depends on the credit rating of the weightier allocations¹⁷. The total MCR, ranges from 39% and 41% for P1 and P2 respectively, to 1%-2% more for P3, P4, P5 and P6, slightly ascending where the quantity of assets (and the diversification benefit) is reduced.

Rossignolo, Fethi and Shaban (²⁰¹³) introduced the LCR, a simple measure of the extent of capital coverage of the trading desk. In this sense, Table 5.4 Column [12] shows that SA in Basel IV provides more than 5.4 times the largest loss of the backtesting period, indeed a substantial amount that banks ought to immobilize as a result of the new regulations and high threshold to be attained by IMA.

From the tables below, it could be deduced that the behavior of the portfolios became more extreme in the forecast period as the volatility of the portfolios (as measured by the standard deviation) of the distributions increased. Predictably, the kurtosis and the negative skew also augmented -particularly for the intermediate portfolios- on the grounds of the weights gained by the most volatile bucket, i.e., bucket 5. Strangely enough, the S&P BMV/IPC saw the kurtosis reverted, mainly due to the fall in the capitalization of its most volatile components.

Section 4 mentioned that EVT was the specification selected to perform the rest of the study, based on the evidence deployed in Table 5.5, as, in effect, it is the only one capable of avoiding Backtesting penalties in the evaluation period. The performance stems from the very foundations of the Theory of Extremes at the time of dealing with huge variations between the sample and evaluation periods. As for the rest of the techniques, it does not seem possible to extract definite conclusions about their behavior, bar from the unsuitability of Historical Simulation and linear models. In terms of the traditional VaR Backtesting, FHS and CV deliver somewhat mixed results, with GARCH variants faring slightly better than EGARCH counterparts in FHS category (Columns [3] to [6]) and GARCH-t and EGARCH-t in FHS (Columns [7] to [10]), which appears to signal the relative preeminence of the specification for the FHS and the distributional assumption for CV. Therefore, it would not seem sensible to apply any other model than EVT, as their performance across the board implies¹⁸.

Table 5.6 depicts the capital levels at the start of the evaluation period. A simple look shows that both specifications do not suffer Backtesting penalties (Table 5.6 Columns [3] to and [13] to [15]), hence their capital values are not in principle deemed to be distorted by those surcharges. Furthermore, the fact that both Spearman and Kolmogorov-Smirnov tests fall into the Green Zone translates in the absence of the surcharge envisaged in (17) and (18) for both variants (Table 5.6 Columns [6] to [7] and [16] to [17]). The comparison between the Basel IV model and the Simplified specification in terms of the capital levels brings about a handful of implications and, in this sense, a first glance at Columns [11] and [21] shows that the official formula nearly triples its alternative due to the stressed calibration, thus taking the LCR to levels in excess of 4.65 in contrast to the figure of the more limited approach, 1.82. Consequently, both models provide coverage against the significant market slumps recorded after the pandemic, albeit the alternative in (20) would appear somewhat tight, with only 82% to spare.

Table 5.7 deals with the concept of the capital floor, in terms of the comparison between SA, the official IMA and the Simplified Specification. As Columns [4] and [6] convey, the average coverage¹⁹ of the capital floor established by the SA reaches 88% in the case of the official IMA, descending to 27% for the Simplified Specification. The table also shows another option, i.e., a very straightforward adaptation of (20), increasing the 1.5 multiple in (15) to 3 and embedding it. This latest option delivers encouraging results, as the capital levels raise to 22% bringing the floor coverage to 53%. Given the timetable established by the BCBS (²⁰²⁰), by means of which IMA must meet SA levels by 50% in 2023, 55% in 2024, 60% in 2025, 65% in 2026, 70% in 2027 and 72.50% in 2028, the official specification would be granted approval since 2023, the Simplified Specification could not surpass the minimum threshold and the Alternative specification may remain in line for the year 2023 and in need to raise the game onwards.

Table 5.8 deploys the average, standard deviation, average surplus (as the difference between portfolio returns and the respective MCR), the average floor coverage (in relation with the SA) and its standard deviation. Across the board, the official model nearly doubles the Simplified technique, again mainly due to the stressed calibration of the reduced factors (S&P BMV/IPC). However, the flip side of the increased capital is its instability as long as the quantity of assets is reduced (the standard deviation raises from 2.73% and 2.61% to 7.06% and 5.31% for P1 and P2 respectively (Table 5.8 Column [2] against [10] and [4} against [12], second line), in turn deriving from the ES_FC (i.e., a portfolio of 4 assets each) as the rest of the factors of (13) remain unaltered; conversely, the path for simple ES does not appear spiky as the diversification decreases (Table 5.8 Columns [3], [5], [7], [9], [11] and [13], second line). The average capital surplus reflects the modelling nature, with maximum and minimum values of around 43% and 26% (Table 5.8 Columns [10] and [8] respectively) versus 23% and 13% (Table 5.8 Columns [11] and [5] respectively)²⁰.

Finally, the proportion of floor coverage also delivers interesting implications given that, once more, the official specification shows satisfactory levels albeit with rising instability as diversification erodes, whereas the Simplified system appears relatively more stable showcasing lesser coverage levels. This is, in turn, a relevant derivation because it hints that much more simple models can provide capital levels enough to withstand crises of considerable magnitudes but would still be disallowed by the regulatory authorities.

6. Conclusions

In the very words of the BCBS, Basel IV has been enacted to remedy many flaws of Basel III, principally around four axes: the trading book/banking book boundary, the measurement of risk of market illiquidity, enhancement of the robustness and risk sensitivity of the SA and finally, improvement of the capture and capitalization against tail risk. The paper could -completely achieving the objectives stated- carry out the complete cycle of MCR determination for the Mexican stock market and the results confirmed the initial hypothesis, given that the relationship between SA and IMA looks completely transformed. However, the bias towards the former appears clearer and on the other hand, the adoption of the latter may be hampered by the inherent complexity in its construction and the stringent validation criteria, the extent of which is pushed forward during market crises. Hence, in consideration of the outcomes, and even acknowledging that equity risk is only one of the main risks mentioned, the BCBS certainly seems to have achieved its aims, albeit at a potentially high cost which, at least, should merit a review.

The SA looks completely revamped, with a logical attempt to embed risk via the classification in risk buckets, the correlation coefficients and regimes and the sensitivities method. However, the outcome poses interesting questions because, in principle, the output floor looks somewhat elevated as it would provide coverage many times the highest loss of the backtesting period. Although ultimately it is a matter of empirical assessment, the scheme appears orientated to be computed using stressed values, with the standalone capital requirement (risk weights) already delivering sizeable cushions and, on top of this, a questionable correlation matrix rooting in an arguable sector classification. Admittedly, both the individual risk weights and the correlation within and among the risk buckets play a very important part at the time of increasing the threshold, which is augmented by the inclusion of the DRC. It is clear that the rigidness of the approach pushed the BCBS to introduce a credit risk element in market risk measurements (the deterioration of the credit standards is not reflected in the whole scheme) and, time and again, the flexibilization of the coefficients would appear healthy. Ultimately, it boils down to empirical verification whether their relaxation and adaptation to the different market moments could bring about a softening of the floor, but everything may point in that direction.

In view of the outcomes, the IMA has suffered an important crackdown by the BCBS, and its reflections blaming the models for its poor performance in the event of the major subprime crisis do reveal its beliefs. Not only has it increased the market risk estimates by substituting VaR for ES -fact logical from a theoretical point of view - but it has made life harder by imposing stringent and complex validating criteria which leaves in practical terms highly leptokurtic specifications like those rooted in the theory of extremes one of the few capable of overcoming them. This consequently translates into elevated minimum capital requirements which, besides enacting a sizeable coverage, may still fall behind the levels demanded by the SA. Delving into the mechanics of the formula, it is useful to compare it to the yardstick represented by the Simplified model, and it is clear that the stressed calibration of the reduced factor ES raises the level of MCR. The results convey that even though the plain vanilla technique provides sufficient coverage against relatively major market slumps, the presence of the strained factor increases the output, and a detailed assessment would elucidate whether the removal of the stressed calibration and the utilization of an enhanced variant (i.e., increasing the fixed multiple but still keeping the leptokurtic modelling) would be enough to provide coverage in stressed times, but, initially, the results should encourage a likely path forward.

The BCBS attained its aims at the time of raising the MCR, albeit at the expense of cornering the IMA (formulation, validation criteria and high capital floor) and enabling a relatively inflexible SA. True as it may be, this facilitates the comparison across jurisdictions and the harmonization of standards, but in principle would stifle the financial innovation, increase the cost of capital, decrease profit measures like ROA or ROI and shrink banking credit.