Article 42 | Delegated Regulation 2024/1085

Article 42 - Assessment of the calculation of the partial expected shortfall measures

Article 42

Assessment of the calculation of the partial expected shortfall measures

1. When assessing whether an institution’s internal model is implemented with integrity as required by Article 325bi(1) of Regulation (EU) No 575/2013 in relation to the calculation of the partial expected shortfall measures referred to in Article 325bc of that Regulation, competent authorities shall:

(a)	verify whether the estimator used by the institution to estimate the expected shortfall risk measures is conceptually sound and reasonably accurate;

(b)

verify whether, when calculating partial expected shortfall measures

and

as required by Article 325bc(1) of Regulation (EU) No 575/2013, the institution identifies effective liquidity horizons of the risk factors of a given position, taking into account the maturity of the position in accordance with Article 325bd(4) of that Regulation;

(c)

verify whether, as part of the internal policies referred to in Article 325bi(1), point (e), of Regulation (EU) No 575/2013, the institution has established objective criteria that are appropriate for choosing the risk factors forming the subset of modellable risk factors referred to in Article 325bc(2), point (a), of that Regulation;

(d)	verify whether risk factors that are not part of the subset of modellable risk factors chosen by the institution in accordance with Article 325bc(2), point (a), of Regulation (EU) No 575/2013 are kept constant when computing and ;

(e)	verify whether the techniques used to calculate and those used to calculate are the same, except for those deviations necessary to ensure the fulfilment of requirements set out in Article 325bc(2) to (4) of Regulation (EU) No 575/2013;

(f)	verify whether, when calculating the , the institution uses equally weighted data in the observation period;

(g)

in relation to the identification of the stress period, verify whether the 12-month rolling windows tested to determine the stress period starts at least from 1 January 2007 as referred to in Article 325bc(2), point (c), of Regulation (EU) No 575/2013 and that the internal policies of the institution specify the frequency of update of the stress period for the calculation of the partial expected shortfall measures, and the other applicable criteria triggering its update.

For the purposes of point (e), competent authorities shall obtain an overview of the differences in the techniques employed by the institution when calculating the partial expected shortfall measures calibrated on the recent 12-month period and on the stress period, and verify whether those differences do not go beyond what is needed to achieve compliance with the requirements set out in Regulation (EU) No 575/2013.

For the purposes of point (g), competent authorities shall verify, also on the basis of past updates, whether the stress period is updated at least with a quarterly frequency and that the institution has followed any possible criteria specified in the internal policies.

2. For the purposes of paragraph 1, point (a), competent authorities:

(a)	shall verify how the institution choses the estimator it uses and the analysis made to support such choice;

(b)

verify whether the expected shortfall estimator corresponds either to the integral of the estimator for the Value-at-Risk numbers referred to in Article 325bf of Regulation (EU) No 575/2013 understood as a function of the tail probability from zero to one minus the relevant confidence level, and dividing by one minus the relevant confidence level, or to a more conservative choice;

(c)

may compare the Value-at-Risk and expected-shortfall estimators used by the institution against the estimators included in Table 1.

Table 1

Value-at-risk estimators

Expected shortfall estimators

;

Where:

denotes the i-th lowest value in the sample

used for the estimation, i.e.

is the most severe loss in a profit-and-loss sample and typically a large negative number;

N denotes the number of values in the sample

used for the estimation;

α denotes the tail probability, i.e. one minus the confidence level;

denotes the integer part of an argument;

and for the expected shortfall assuming

, i.e. computing for a left tail of a sample;

and for the expected shortfall assuming that

, i.e. more than one loss is in the α-tail of a profit-and-loss sample;

(d)	where the calculation of the expected shortfall risk measures is based on Monte Carlo simulations, verify whether the number of simulations ensures convergence towards stable results.

For the purposes of point (d), competent authorities shall review the tests performed by the institution to set the number of simulations, and the statistical tests ensuring that the randomness properties of the sequences used to generate the simulation are appropriate. Where the competent authority deems those tests insufficient, it may use the assessment method referred to in paragraph 4.

3. For the purposes of paragraph 1, point (b), competent authorities shall:

(a)	require the institution to provide the Monte Carlo statistical error at 95 % confidence level, and verify whether the method employed to measure such statistical error is sound;

(b)	require the institution to calculate the expected shortfall risk measures with several different seeds, all other assumptions being equal;

(c)	assess whether the differences in the expected shortfall risk measures with a different seed resulting from the calculation in accordance with point (b) are compatible with the statistical error referred to in point (a).

(d)	where competent authorities deem the results referred to in point (c) incompatible, assess the root cause of such incompatibility, and assess the number of simulations needed to ensure that the statistical error is below 5 %.

4. For the purposes of paragraph 1, point (c), competent authorities shall:

(a)

obtain an overview of the risk factors chosen by the institution and verify:

(i)	whether the criteria ensure a sufficient level of coverage in the modellable risk factors’ types chosen compared to the full set of modellable risk factors to which the institution is exposed;

(ii)	whether the criteria are such that the threshold referred to in 325bc(2), point (a), of Regulation (EU) No 575/2013 is expected to be exceeded over time;

(iii)

whether the institution tests alternative subsets of modellable risk factors to ensure that its choice does not underestimate the own funds requirements;

(iv)

whether the institution, in its choice, favours the selection of risk factors for which data in the stress period exist over risk factors for which proxies are used, and where that is not the case, competent authorities shall assess the reason why the institution did not implement such a criterion, and whether a different choice would improve the quality of the unconstrained and partial expected shortfall measure.

(b)	verify whether, where the position has a maturity of less than 10 days, the effective liquidity horizon of all risk factors is set to 10 days, and that such position does not impact the calculation of for ;

(c)

where the position has a maturity of Mat days, with

, verify whether:

(i)	all risk factors of that position with a liquidity horizon have been assigned to an effective liquidity horizon that is the shortest liquidity horizon among the liquidity horizons provided in Table 1 of Article 325bc(1) of Regulation (EU) No 575/2013 that is greater than or equal to Mat;

(ii)	the position does not impact the calculation of for all j corresponding to a liquidity horizon that is greater than the shortest liquidity horizon among the liquidity horizons provided in Table 1 of Article 325bc(1) of Regulation (EU) No 575/2013 that is greater than or equal to Mat;

(d)	verify whether, where the position has a maturity of Mat days, with , the institution has assigned all risk factors of that position to an effective liquidity horizon corresponding to the liquidity horizon SubCatLH assigned to the risk factors;

(e)	verify whether, when computing , the institution keeps constant those risk factors with an effective liquidity horizon that is lower than the liquidity horizon corresponding to the index j.

For the purposes of point (a)(ii), competent authority shall assess by which margin the institution exceeded the threshold in the previous quarters.

For the purposes of point (a)(iii), competent authorities may, where they deem insufficient the testing of alternative subsets carried out by the institution, require the institution to test alternative subsets and assess whether alternative choices lead to material differences in terms of own funds requirements.

CHAPTER 1 - GENERAL PROVISIONS (Article 1-4)

CHAPTER 2 - ASSESSMENT OF QUALITATIVE REQUIREMENTS (Article 5-21)

CHAPTER 3 - ASSESSMENT OF THE INTERNAL RISK-MEASUREMENT MODEL USED TO COMPUTE THE EXPECTED SHORTFALL RISK MEASURE AND THE STRESS SCENARIO RISK MEASURE (Article 22-44)

SECTION 1 - Overview of the assessment (Article 22)

SECTION 2 - Assessment of the internal risk measurement model’s risk factors set-up and properties (Article 23-33)

SECTION 3 - Assessment of proxies and data quality (Article 34-35)

SECTION 4 - Assessment of compliance with requirements relating to the back-testing and profit-loss attribution test (Article 36-38)

SECTION 5 - Assessment of compliance with requirements relating to the treatment of foreign-exchange and commodity risk in the non-trading book (Article 39)

SECTION 6 - Assessment of the calculation of the expected shortfall risk measures and the stress scenario risk measure (Article 40-44)

Subsection 1 - Assessment of aspects that are relevant both for the calculation of the expected shortfall risk measures and the stress scenario risk measure (Article 40)

Subsection 2 - Assessment of aspects that are relevant for the calculation of the expected shortfall risk measures (Article 41-43)Article 41 - Assessment of the calculation of the expected shortfall risk measure Article 42 - Assessment of the calculation of the partial expected shortfall measures Article 43 - Assessment of distributional and statistical assumption

Subsection 3 - Assessment of aspects that are relevant for the calculation of the stress scenario risk measure (Article 44)

CHAPTER 4 - ASSESSMENT OF THE INTERNAL DEFAULT RISK MODEL USED TO COMPUTE THE ADDITIONAL OWN FUNDS REQUIREMENT FOR DEFAULT RISK (Article 45-52)

CHAPTER 5 - FINAL PROVISIONS (Article 53)

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Article 42 - Assessment of the calculation of the partial expected shortfall measures

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