ANNEX II METHODOLOGY FOR THE PRESENTATION OF RISK

Market risk assessment

1. (1)

   Market risk is measured by the annualised volatility corresponding to the value-at-risk (VaR) at a confidence level of 97,5 % over the recommended holding period, unless stated otherwise. The VaR is the percentage of the amount invested, that is returned to the retail investor.

2. (2)

   The PRIIP shall be assigned a MRM class according to the following table:

   MRM class	VaR-equivalent volatility (VEV)
   1	< 0,5 %
   2	0,5 % - 5,0 %
   3	5,0 % - 12 %
   4	12 % - 20 %
   5	20 % - 30 %
   6	30 % - 80 %
   7	> 80 %

1. (3)

   For the purposes of determining market risk, PRIIPs are divided into four categories.

2. (4)

   Category 1 covers the following:

   1. (a)

      PRIIPs where investors could lose more than the amount they invested;

   2. (b)

      PRIIPs that fall within one of the categories referred to in paragraphs 4 to 10 of Part 1 of Schedule 2 to the Financial Services and Markets Act 2000 (Regulated Activities) Order 2001;

   3. (c)

      PRIIPs or underlying investments of PRIIPs which are priced on a less regular basis than monthly, or which do not have an appropriate benchmark or proxy, or whose appropriate benchmark or proxy is priced on a less regular basis than monthly.

3. (5)

   Category 2 covers PRIIPs which, either directly or on a synthetic basis, offer non-leveraged exposure to the prices of underlying investments, or a leveraged exposure on underlying investments that pays a constant multiple of the prices of those underlying investments, where at least 2 years of historical daily prices, or 4 years of historical weekly prices, or 5 years of monthly prices are available for the PRIIP, or where existing appropriate benchmarks or proxies are available, provided that such benchmarks or proxies fulfil the same criteria for the length and frequency of the price history.

4. (6)

   Category 3 covers PRIIPs whose values reflect the prices of underlying investments, but not as a constant multiple of the prices of those underlying investments, where at least 2 years of daily prices of the underlying assets, 4 years of weekly prices or 5 years of monthly prices, or where existing appropriate benchmarks or proxies are available, provided that such benchmarks or proxies fulfil the same criteria for the length and frequency of the price history.

5. (7)

   Category 4 covers PRIIPs whose values depend in part on factors not observed in the market, including insurance-based PRIIPs which distribute a portion of the PRIIP manufacturer's profits to retail investors.

Where appropriate benchmarks or proxies are used by a PRIIP manufacturer, those benchmarks or proxies shall be representative of the assets or exposures that determine the performance of the PRIIP. The PRIIP manufacturer shall document the use of such benchmarks or proxies.

1. (8)

   The MRM class for Category 1 PRIIPs shall be 7, with the exception of PRIIPs referred to in point 4(c) of this Annex, where the MRM class shall be 6.

1. (9)

   The VaR shall be calculated from the moments of the observed distribution of returns of the PRIIP's or its benchmark or proxy's price during the past 5 years. The minimum frequency of observations is monthly. Where prices are available on a daily basis, the frequency shall be daily. Where prices are available on a weekly basis, the frequency shall be weekly. Where prices are available on a bi-monthly basis, the frequency shall be bi-monthly.

2. (10)

   Where data on daily prices covering a period of 5 years are not available, a shorter period may be used. For daily observations of a PRIIP's or its benchmark or proxy's price, there shall be at least 2 years of observed returns. For weekly observations of a PRIIP's price, there shall be at least 4 years of observed data. For monthly observations of a PRIIP's price, there shall be observed data covering a period of at least 5 years.

3. (11)

   The return over each period is defined as the natural logarithm of the ratio of the price at the market close at the end of the current period to the market close at the end of the preceding period.

4. (12)

   The VaR measure in return space is given by the Cornish-Fisher expansion, as follows:

   

   where N is the number of trading periods in the recommended holding period; and σ, μ¼₁, μ¼₂ are respectively the volatility, skew and excess kurtosis measured from the return distribution. The volatility, skew and excess kurtosis are calculated from the measured moments of the distribution of returns in accordance with the following:

   • the zero moment, M₀, is the count of the number of observations in the period as under point 10 of this Annex
   • the first moment, M₁, is the mean of all the observed returns in the sample
   • the second M₂, third M₃ and fourth M₄ moments are defined in the standard manner:

   • 
     ,

   • 
     ,

   • ,

     

   • where ri is the return measured on the ith period in the history of returns.
   • • the volatility, σ, is given by
       
       .
     • the skew, μ¼_1, is equal to M₃/σ³.
     • the excess kurtosis, μ¼₂, is equal to M₄/σ⁴ - 3.

5. (13)

   The VEV is given by:

   

   where T is the length of the recommended holding period in years.

6. (14)

   For PRIIPs that are managed according to investment policies or strategies that pursue certain reward objectives by participating through flexible investment in different financial asset classes (e.g. in both equity and fixed-income markets), the VEV that shall be used shall be determined as follows:

   1. (a)

      where there has been no revision of the investment policy over the period referred to in point 10 of this Annex, the VEV that shall be used is the highest of the following VEVs

      1. (i)

         the VEV computed in accordance with points 9 to 13 of this Annex;

      2. (ii)

         the VEV of the returns of the pro-forma asset mix that is consistent with the reference asset allocation of the fund at the time of the computation;

      3. (iii)

         the VEV which is consistent with the risk limit of the fund, if any and appropriate.

   2. (b)

      where investment policy has been revised during the period referred to in point 10 of this Annex, the VEV that shall be used is the highest of the VEVs referred to in point (a)(ii) and (iii).

7. (15)

   The PRIIP shall be assigned to a MRM class as laid down under point 2 of this Annex depending on the VEV. In the case of a PRIIP having only monthly price data, the MRM class assigned under point 2 of this Annex shall be increased by one additional class.

1. (16)

   The VaR in price space shall be calculated from a distribution of PRIIP values at the end of the recommended holding period. The distribution shall be obtained by simulating the price or prices, which determine the value of the PRIIP, at the end of the recommended holding period. The VaR shall be the value of the PRIIP at a confidence level of 97,5 % at the end of the recommended holding period discounted to the present date using the expected risk-free discount factor from the present date to the end of the recommended holding period.

2. (17)

   The VEV is given by:

   

   where T is the length of the recommended holding period in years. Only in cases where the product is called or cancelled before the end of the recommended holding period according to the simulation, the period in years until the call or cancellation is used in the calculation.

3. (18)

   The PRIIP shall be assigned to a MRM class as laid down in point 2 of this Annex, depending on the VEV. In the case of a PRIIP having only monthly price data, the MRM class assigned under point 2 of this Annex shall be increased by one additional class.

4. (19)

   The minimum number of simulations is 10000.

5. (20)

   The simulation is based on bootstrapping the expected distribution of prices or price levels for the PRIIP's underlying contracts from the observed distribution of returns for these contracts with replacement.

6. (21)

   For the purposes of the simulation referred to in points 16 to 20 of this Annex, there are two types of market observables that may contribute to a PRIIP's value: spot prices (or price levels) and curves.

7. (22)

   For each simulation of a spot price (or level), the PRIIP manufacturer shall:

   1. (a)

      calculate the return for each observed period in the past 5 years, or the years referred to in point 6 of this Annex, by taking the logarithm of the price at the end of each period divided by the price at the end of the previous period;

   2. (b)

      randomly select one observed period which corresponds to the return for all underlying contracts for each simulated period in the recommended holding period (the same observed period may be used more than once in the same simulation);

   3. (c)

      calculate the return for each contract by summing the returns from the selected periods and correcting this return to ensure that the expected return measured from the simulated distribution of returns is the risk-neutral expectation of the return over the recommended holding period. The final value of the return is given by:

      

      Where:

      • the second term corrects for the impact of the mean of the observed returns;
      • the third term corrects for the impact of the variance of the observed returns;
      • the last term corrects for the quanto impact if the strike currency is different from the asset currency. The terms contributing to the correction are as follows:
      • • ρ is the correlation between the asset price and the relevant F_x rate — measured over the recommended holding period;
        • σ is the measured volatility of the asset;
        • σ_ccy is the measured volatility of the F_x rate.

   4. (d)

      calculate the price of each underlying contract by taking the exponential of the return.

8. (23)

   For curves, a principal component analysis (PCA) shall be performed to ensure that the simulation of the movements of each point on the curve over a long period results in a consistent curve.

   1. (a)

      The PCA is performed by:

      1. (i)

         collecting the historical record of tenor points that define the curve for each trading period over the past 5 years, or the years referred to in point 6 of this Annex;

      2. (ii)

         ensuring that each tenor point is positive — where there is a negative tenor point, all tenor points shall be shifted by the minimum whole number or percentage to ensure positive values for all tenor points;

      3. (iii)

         calculating the return over each period for each tenor point by taking the natural logarithm of the ratio between the price/level at the end of each observed period and the price/level at the end of the preceding period;

      4. (iv)

         correcting the returns observed at each tenor point so that the resulting set of returns at each tenor point has a zero mean;

      5. (v)

         calculating the covariance matrix between the different tenors by summing over returns;

      6. (vi)

         calculating the eigenvectors and eigenvalues of the covariance matrix;

      7. (vii)

         selecting the eigenvectors that correspond to the three largest eigenvalues;

      8. (viii)

         forming a matrix with 3 columns where the first column is the eigenvector with the largest eigenvalue; the middle column is the eigenvector with the second-largest eigenvalue and the last column is the eigenvector with the third-largest eigenvalue;

      9. (ix)

         projecting the returns onto the 3 principal eigenvectors calculated in the previous step by multiplying the N×M matrix of returns obtained in point (iv) by the M×3 matrix of eigenvectors obtained in point (viii);

      10. (x)

          calculating the matrix of returns to be used in the simulation by multiplying the results in point (ix) with the transpose of the matrix of eigenvectors obtained in point (viii). This is the set of values to be used in the simulation.

   2. (b)

      The curve simulation is performed as follows:

      1. (i)

         the time step in the simulation is one period. For each observation period in the recommended holding period select a row at random from the calculated matrix of returns. The return for each tenor point, T, is the sum over the selected rows of the column corresponding to tenor point, T.

      2. (ii)

         the simulated rate for each tenor point T, is the current rate at tenor point T:

         • multiplied by the exponential of the simulated return,
         • adjusted for any shifts used to ensure positive values for all tenor point, and
         • adjusted so that the expected mean matches current expectations for the rate at tenor point T, at the end of the recommended holding period.

9. (24)

   For PRIIPS in Category 3 that are characterized by an unconditional protection of capital, the PRIIP manufacturer may assume that the VaR at a confidence level of 97,5 % is equal to the level of the unconditional capital protection at the end of the recommended holding period, discounted to the present date using the expected risk-free discount factor.

1. (25)

   Where the PRIIP performance depends on a factor or factors unobserved in the market or to some extent under the control of the PRIIP manufacturer, or this is the case for a component of the PRIIP, the PRIIP manufacturer shall follow the method in this section to account for this factor or factors.

2. (26)

   The different components of the PRIIP that contribute to the performance of the PRIIP shall be identified, in order for those components that are not wholly or partly dependent on a factor or factors that are unobserved in the market to be treated according to the relevant methods set out in this Annex for Category 1, 2 or 3 PRIIPs. For each of these components a VEV shall be calculated.

3. (27)

   The component of the PRIIP that depends wholly or partly on a factor or factors that are unobserved in the market shall follow robust and well recognised industry and regulatory standards for determining relevant expectations as to the future contribution of these factors and the uncertainty that may exist in respect of that contribution. Where the component is not wholly dependent on a factor that is unobserved in the market, a bootstrap methodology shall be used to account for the market factors, as set out for Category 3 PRIIPs. The VEV for the component of the PRIIP shall be the result of the combination of the bootstrap methodology and robust and well recognised industry and regulatory standards for determining relevant expectations as to the future contribution of these factors that are unobserved in the market.

4. (28)

   The VEV of each component of the PRIIP shall be weighted proportionally in order to arrive at an overall VEV of the PRIIP. When weighing the components, product features shall be taken into account. Where relevant, product algorithms mitigating the market risk as well as specificities of the with-profit component shall be considered.

5. (29)

   For Category 4 PRIIPs that are characterized by an unconditional protection of capital, the PRIIP manufacturer may assume that VaR at a confidence level of 97,5 % is equal to the level of unconditional capital protection at the end of the recommended holding period, discounted to the present date using the expected risk-free discount factor.

Methodology for assessing credit risk

I.

GENERAL REQUIREMENTS

1. (30)

   A PRIIP or its underlying investments or exposures shall be taken to entail credit risk where the return of the PRIIP or its underlying investments or exposures depends on the creditworthiness of a manufacturer or party bound to make, directly or indirectly, relevant payments to the investor. A PRIIP with a MRM of 7 is not required to assess credit risk.

2. (31)

   Where an entity directly engages to make a payment to a retail investor for a PRIIP, credit risk shall be assessed for the entity that is the direct obligor.

3. (32)

   If all payment obligations of an obligor or one or more indirect obligors are unconditionally and irrevocably guaranteed by another entity (the guarantor), the credit risk assessment of the guarantor can be used if it is more favourable than the credit risk assessment of the respective obligor or obligors.

4. (33)

   For PRIIPs which are exposed to underlying investments or techniques, including PRIIPs which themselves entail credit risk or in turn make underlying investments that entail credit risk, the credit risk shall be assessed in relation to the credit risk entailed both by the PRIIP itself and the underlying investments or exposures (including exposures to other PRIIPs), on a look-through basis and adopting a cascade assessment where necessary.

5. (34)

   Where the credit risk is entailed solely at the level of underlying investments or exposures (including to other PRIIPs), the credit risk shall not be assessed at the level of the PRIIP itself but instead at the level of these underlying investments or exposures on a look-through basis. Where the PRIIP is an Undertaking for Collective Investment in Transferable Securities (UCITS) or an Alternative Investment Fund (AIF), the UCITS or AIF itself shall be taken to entail no credit risk, whereas the underlying investments or exposures of the UCITS or AIF shall be assessed where necessary.

6. (35)

   Where a PRIIP is exposed to multiple underlying investments entailing a credit risk exposure, the credit risk entailed by each underlying investment representing an exposure of 10 % or more of the total assets or value of the PRIIP shall be separately assessed.

7. (36)

   Underlying investments or exposures to exchange-traded derivatives or cleared OTC derivatives shall be assumed for the purposes of the credit risk assessment to carry no credit risk. No credit risk shall be taken to be entailed where an exposure is fully and appropriately collateralised, or where uncollateralised exposures that entail credit risk amount to less than 10 % of the total assets or value of the PRIIP.

II.

CREDIT RISK ASSESSMENT

1. (37)

   Where available, a PRIIP manufacturer shall define ex-ante one or more external credit assessment institutions (ECAI) certified or registered with:

   1. (a)

      the European Securities and Markets Authority (ESMA) immediately after IP completion day in accordance with Regulation (EC) No 1060/2009 of the European Parliament and the Council, as it has effect in the European Union; or

   2. (b)

      the Financial Conduct Authority in accordance with Regulation (EC) No 1060/2009,

   whose credit assessments will consistently be referred to for the purpose of the credit risk assessment. Where multiple credit assessments are available according to that policy, the median rating shall be used, defaulting to the lower of the two middle values in case of an even number of assessments.

2. (37A)

   The ability of a PRIIP manufacturer to define an ECAI certified or registered with ESMA for the purpose of the credit risk assessment shall not otherwise affect the application of Article 4(1) of Regulation (EC) No 1060/2009 of the European Parliament and of the Council of 16 September 2009 to a PRIIP manufacturer to which that Regulation also applies.

3. (38)

   The level of credit risk of the PRIIP and each relevant obligor shall be assessed on the basis of, as applicable:

   1. (a)

      the credit assessment assigned to the PRIIP by an ECAI;

   2. (b)

      the credit assessment assigned to the relevant obligor by an ECAI;

   3. (c)

      in the absence of a credit assessment under either (a) or (b) or both, a default credit assessment as set out in point 43 of this Annex.

1. (39)

   The allocation of credit assessments of ECAIs to an objective scale of credit quality steps shall be based on Commission Implementing Regulation (EU) 2016/1800.

2. (40)

   In the case of credit risks assessed on a look-through basis, the credit quality step assigned shall correspond to the weighted average credit quality steps of each relevant obligor for which a credit assessment needs to be undertaken, in proportion to the total assets they respectively represent.

3. (41)

   In the case of credit risks assessed on a cascade basis, all credit risk exposures shall be separately assessed, per layer, and the credit quality step assigned shall be the highest credit quality step, being understood that between a credit quality step set at 1 and a credit quality step set at 3, the higher of the two is 3.

4. (42)

   The credit quality step pursuant to point 38 of this Annex shall be adjusted to the maturity or recommended holding period of the PRIIP, according to the following table, except where a credit assessment has been assigned that reflects that maturity or recommended holding period):

   Credit quality step pursuant to point 38 of this Annex	Adjusted credit quality step, in the case where the maturity of the PRIIP, or its recommended holding period where a PRIIP does not have a maturity, is up to one year	Adjusted credit quality step, in the case where the maturity of the PRIIP, or its recommended holding period where a PRIIP does not have a maturity, ranges from one year up to 12 years	Adjusted credit quality step, in the case where the maturity of the PRIIP, or its recommended holding period where a PRIIP does not have a maturity, exceeds 12 years
   0	0	0	0
   1	1	1	1
   2	1	2	2
   3	2	3	3
   4	3	4	5
   5	4	5	6
   6	6	6	6

5. (43)

   If the obligor has no external credit assessments, the default credit assessment as referred to in point 38 of this Annex shall be:

   1. (a)

      credit quality step 3, if the rating of the state in which the obligor is domiciled would be credit quality step 3 and if the obligor is regulated as a credit institution or an insurance undertaking under:

      1. (i)

         the law of the United Kingdom;

      2. (ii)

         the law of a Member State for the purposes of Union law; or

      3. (iii)

         the legal framework deemed equivalent under United Kingdom or Union law;

   2. (b)

      credit quality step 5, for any other obligor.

III.

CREDIT RISK MEASURE

1. (44)

   A PRIIP shall be allocated to a credit risk measure (CRM) on a scale ranging from 1 to 6 on the basis of the mapping table laid down in point 45 of this Annex and by applying the credit risk mitigating factors under points 46, 47, 48 and 49 of this Annex, or the credit risk escalating factors under points 50 and 51 of this Annex, as appropriate.

2. (45)

   Table on the mapping of credit quality steps into a CRM:

   Adjusted credit quality step	Credit risk measure
   0	1
   1	1
   2	2
   3	3
   4	4
   5	5
   6	6

3. (46)

   The CRM may be assigned as 1 where the assets of a PRIIP or appropriate collateral, or assets backing the payment obligation of the PRIIP, are:

   1. (a)

      at all times until maturity equivalent to the payment obligations of the PRIIP to its investors;

   2. (b)

      held with a third party on a segregated account under equivalent terms and conditions as those laid down in Directive 2011/61/EU of the European Parliament and of the Council or Directive 2014/91/EU, as those directives had effect immediately before IP completion day, or in those enactments which were relied on immediately before IP completion day to implement those directives; and

   3. (c)

      not, under any circumstances, accessible to any other creditors of the manufacturer under applicable law.

4. (47)

   The CRM may be assigned as 2 where the assets of a PRIIP or appropriate collateral, or assets backing the payment obligation of the PRIIP, are:

   1. (a)

      at all times until maturity equivalent to the payment obligations of the PRIIP to its investors;

   2. (b)

      identified and held on accounts or registers, based on applicable law, including Articles 275 and 276 of Directive 2009/138/EC of the European Parliament and of the Council, as those Articles had effect immediately before IP completion day, or those enactments which were relied on immediately before IP completion day to implement those Articles; and

   3. (c)

      such that the claims of retail investors have priority over the claims of other creditors of the PRIIP manufacturer or party bound to make, directly or indirectly, relevant payments to the investor.

5. (48)

   Where credit risk is to be assessed on a look-through or cascade basis, the mitigation factors under point 46 and 47 of this Annex may also be applied when assessing credit risk in relation to each underlying obligor.

6. (49)

   Where a PRIIP is not able to satisfy the criteria under point 47 of this Annex, the CRM pursuant to point 45 of this Annex may be reduced by one class where the claims of retail investors have priority over the claims of ordinary creditors, as set out in Article 108 of Directive 2014/59/EU, as that Article had effect immediately before IP completion day, or those enactments which were relied on immediately before IP completion day to implement that Article, of the PRIIP manufacturer or party bound to make, directly or indirectly, relevant payments to the investor, in so far as the obligor is subject to relevant prudential requirements in respect of ensuring an appropriate matching of assets and liabilities.

7. (50)

   The CRM pursuant to point 45 of this Annex shall be increased by two classes where the claim of a retail investor is subordinate to the claims of senior creditors.

8. (51)

   The CRM pursuant to point 45 of this Annex shall be increased by three classes where a PRIIP is part of the own funds of the PRIIP obligor, as defined in Article 4(1)(118) of Regulation (EU) No 575/2013 of the European Parliament and of the Council, or in that Article as it has effect in the European Union, or in Article 93 of Directive 2009/138/EU or those enactments which were relied on immediately before IP completion day to implement that Article.

Aggregation of market and credit risk into the summary risk indicator

1. (52)

   The overall summary risk indicator (SRI) is assigned according to the combination of the CRM and the MRM classes, in accordance with the following table:

   MRM class CRM class	MR1	MR2	MR3	MR4	MR5	MR6	MR7
   CR1	1	2	3	4	5	6	7
   CR2	1	2	3	4	5	6	7
   CR3	3	3	3	4	5	6	7
   CR4	5	5	5	5	5	6	7
   CR5	5	5	5	5	5	6	7
   CR6	6	6	6	6	6	6	7

Monitoring data with relevance for the summary risk indicator

1. (53)

   The PRIIP manufacturer shall monitor market data relevant to the calculation of the MRM class and, if the MRM class changes to a different MRM class, the PRIIP manufacturer shall attribute the corresponding MRM class to the MRM class which the PRIIP has matched for the majority of the reference points over the preceding four months.

2. (54)

   The PRIIP manufacturer shall also monitor credit risk criteria relevant to the calculation of the CRM and, if according to these criteria the CRM would change to a different CRM class, the PRIIP shall re-attribute the CRM to the relevant CRM class.

3. (55)

   A review of the MRM class shall always be carried out following a decision by the PRIIP manufacturer in respect of the PRIIP's investment policy and/or strategy. In those circumstances, any changes to the MRM shall be understood as a new determination of the PRIIP's MRM class, and consequently, be carried out according to the general rules concerning the determination of an MRM class for the PRIIP category.

Liquidity risk

1. (56)

   A PRIIP shall be considered as having a materially relevant liquidity risk where either of the following criteria are fulfilled:

   1. (a)

      the PRIIP is admitted to trading on a secondary market or alternative liquidity facility and there is no committed liquidity offered by market makers or the PRIIP manufacturer, so that the liquidity depends only on the availability of buyers and sellers on the secondary market or alternative liquidity facility, taking into account that regular trading of a product at one point in time does not guarantee the regular trading of the same product at any other point in time;

   2. (b)

      the average liquidity profile of the underlying investments is significantly lower than the regular reimbursement frequency for the PRIIP, when and to the extent liquidity offered by the PRIIP is conditional to the liquidation of its underlying assets;

   3. (c)

      the PRIIP manufacturer estimates that the retail investor may face significant difficulties in terms of time or costs for disinvesting during the life of the product, subject to specific market conditions.

2. (57)

   A PRIIP shall be considered illiquid, whether contractually or not, if either of the following criteria are fulfilled:

   1. (a)

      the PRIIP is not admitted to trading on a secondary market, and no alternative liquidity facility is promoted by the PRIIP manufacturer or a third party, or the alternative liquidity facility is subject to significant limiting conditions, including significant early exit penalties or discretionary redemption prices, or where there is an absence of liquidity arrangements;

   2. (b)

      the PRIIP offers potential early exit or redemption possibilities prior to the applicable maturity, but these are subject to significant limiting conditions, including significant exist penalties or discretionary redemption prices, or to the prior consent and discretion of the PRIIP manufacturer;

   3. (c)

      the PRIIP does not offer potential early exit or redemption possibilities prior to the applicable maturity.

3. (58)

   A PRIIP shall be considered liquid in all other cases.