Measure variations

Details of each of the measure variations. Jump to the relevant section:

• Euler
• High-Low
• Imported
• Incremental
• Long-Short
• Netted
• Pro-Rata
• Rank
• Reported
• Spot

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Euler

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Euler capital allocation

Naming pattern: Measures with “Euler” behavior follow the name pattern: Main Measure Name Euler. Euler is one of the approaches implemented in to decompose a non-linear measure down to additive components. For instance, the Euler variation of the IMCC measure is called IMCC (Euler). The IMCC (Euler) measure enables allocating a result (for instance, at firm level) down to individual components (typically, desks).

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Overview of Euler calculations

The theory behind Euler Calculations is based on these facts:

• Use of Euler’s theorem of homogeneous functions
• Capital Charges are homogeneous functions of degree 1
• Euler Capital Allocation is the evaluation of the derivative on a sub-portfolio

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Analytical vs numerical Euler

The difference between Analytical and Numerical Euler is in how the calculations are performed:

• For Analytical Euler, the functions are differentiated and the derivative is evaluated (this gives the exact value).
• For Numerical Euler, the Existing Capital Charge calculations are used to numerically approximate the derivative.

Follow this link to see the measures with the described behavior: Euler Measures. In both methods the charge computed at ReferenceLevel is decomposed into additive components. Additionally, the impact of query filters on the results can be controlled using ReferenceLevelVisualTotalsMode.

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High-Low

The “high” and “low” measure variations represent the high correlation scenario and low correlation scenario (resp.) for the SBM calculations.

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Imported

Deprecated: Imported measures are deprecated and only provided for backwards compatibility with older EBA reporting templates. In a future version these measures will be hidden. Naming pattern: Measures with “Imported” behavior follow the name pattern:Main Measure Name Imported. Imported is one of the optional approaches implemented in to allow you to import values to be included in the cube for reporting purposes via an optional file and its corresponding store. Each imported value is identified by legal entity and measure name. Each value will be added to the capital charge calculations whenever the corresponding legal entity is included. The imported values only impact a specific set of measures. These comprise measures with the “Imported” suffix and those with the “(reported)” suffix. They also include the following measures, which are the ones requested in the CRR2 reporting template:

• “risk-class risk-measure Risk Charge scenario”
• “risk-class Delta Sensitivities direction”
• “drc-risk-class Default Risk Charge”
• “drc-risk-class Gross JTD direction”
• “RRAO Exotic”
• “RRAO Other”

Where: Additionally, the SA measures that follow on from the list of CRR2 reporting template measures above are also impacted, up to the “Portfolio Risk Charge”. The Reported measure variation includes the impact of the netting sets and imported values. For example, “Portfolio Risk Charge (reported)”. The netting sets and imported values do not currently impact the unmodified measures; for example, “Portfolio Risk Charge” is not changed.

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Overview of imported calculations

The imported values are identified by legal entity, parameter set, and measure name (and as-of date). The measure name must be one from the list above. The parameter set and measure name are sourced from the LegalEntityImports input store via the technical Legal Entity Import Parameter Set and Legal Entity Import Measure Name hierarchies, used internally to look up imported values and not intended for direct end-user navigation.

• The imported measures are not included when drilling down. For example, if a query filters on a desk or node from the booking hierarchy, then the imported measures will not be included.
• A configuration option allows you to specify for which hierarchies to ignore filters. For example, if you have added a “sensitivity-type” hierarchy and add that to the list to ignore, then the imported values will still be included even if a query filters by “sensitivity-type”.

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Incremental

Naming pattern: Measures with “Incremental” behavior follow the name pattern:Main Measure Name Incremental. The Incremental measures evaluate the impact of a trade or a group of trades (‘current scope’) on the result at a selected ReferenceLevel, by comparing it with a computation as if the considered trade or aggregate of trades were hypothetically removed. $M^{incremental}(\text{scope})= M(\text{portfolio}) - M(\text{portfolio excl scope})$

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Example

In the following example, the IMCC measure is showing the impact of individual desks on the firm-level IMCC number.

• In this example, the ReferenceLevel is set to Enterprise.
• IMCC for desk “Bonds” is -17 mio, which means, that this portfolio is reducing firm-level IMCC by 17 mio.

To validate the incremental measure for desk “Bonds”, compute firm-level IMCC with a filter excluding the desk: From the screenshot above, IMCC is approximately 17 mio higher (109.7 - 92.6) if the “Bonds” desk positions were closed-out. Follow this link to see the measures with the described behavior: Incremental Measures.

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Long-Short

The “long” and “short” measure variations are used with the SBM Delta sensitivities. They were introduced for the EBA reporting template. In evaluating these measures, Delta sensitivities are aggregated to the risk-factor level, then sorted into “long” or “short” depending on if the aggregate sensitivities are positive or negative.

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Netted

Netted is an optional approach for calculating capital charges independently for each netting set and IRT Desk. Naming pattern: Measures with “Netted” behavior follow the name pattern: Main Measure Name Netted. Netted is an optional approach implemented in to map Legal Entities (and hence all sensitivities) to “netting sets” via an optional file and its corresponding store. Additionally, each book can be flagged as belonging to the “IRT Desk” or not. The capital charges can be calculated independently for each netting set and IRT Desk, then summed. The netting sets only impact a specific set of measures. These comprise measures with this suffix and those with the “(reported)” suffix. They also include the following measures, which are the ones requested in the CRR2 reporting template:

• “risk-class risk-measure Risk Position scenario”
• “risk-class risk-measure Risk Charge scenario”
• “risk-class Curvature Sb scenario”
• “risk-class Delta Sensitivities direction”
• “drc-risk-class Default Risk Charge”
• “drc-risk-class Gross JTD direction”
• “drc-risk-class Net JTD direction”
• “drc-risk-class WtS Ratio”
• “RRAO Exotic”
• “RRAO Other”

Where: Additionally, the SA measures that follow on from the above list are also impacted, up to the “Portfolio Risk Charge”. The reported measure variation includes the impact of the netting sets and imported values. For example, “Portfolio Risk Charge (reported)”. The netting sets and imported values do not currently impact the unmodified measures; for example, “Portfolio Risk Charge” is not changed.

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Overview of Netted Calculations

A Netting Set hierarchy allows for filtering by netting set. The capital charge calculations are performed with the netting sets as the leaf level, so that:

• The capital charges are calculated without offsetting sensitivities across netting sets and IRT desks.
• After the capital charges are calculated (independently) for each netting set and IRT desk, they are summed.
• As with the “(reported)” suffix, the same set of measures are directly and indirectly impacted.

See Netted Measures for the measures with the described behavior.

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Pro-Rata

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Pro-rata capital allocation

Naming pattern: Measures with “Pro-rata” behavior follow the name pattern: Main Measure Name Pro-Rata. Pro-Rata is one of the approaches implemented in to decompose a non-linear measure down to additive components. Depending on the specified context values, a Pro-Rata measure behaves as:

• bottom-up calculation: charges computed at leaf level (usually, trades) are scaled proportionally. They then sum to a charge computed at ReferenceLevel. Scaled leaf-level charges are additive and can be rolled up to any level; Pro-Rata Capital Allocation := Leaf * Scale
• “Russian Doll” calculation: charges are computed recursively along the levels in a specified hierarchy (for instance, organizational hierarchy), so that the sum at each level is equal to the pro-rata charge for a parent. Scale := Parent / {sum of Siblings} Several hierarchies can be combined, as described under ProRataHierarchy.

In both methods the charge computed at ReferenceLevel is decomposed into additive components. Additionally, the impact of query filters on the results can be controlled using ReferenceLevelVisualTotalsMode. The main difference between the approaches is that the capital allocation per “Russian Doll” method will take into account the netting within aggregation nodes, whereas in bottom-up approach only the leaf-level netting matters. Follow this link to see the measures with the described behavior: Pro-Rata Measures.

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Rank

Naming pattern: Measures with “Rank” behavior follow the name pattern: Main Measure Name Rank. Rank measures are derived from vectors of P&L values. The P&L values are sorted lowest to highest and assigned an integer value from 1 to the size of the vector. The sort order of the ranks matches the sort order of the P&L values. The Rank measure can be used to manually check tail measures such as VaR and ES. For example, the 97.5% ES on a vector of 250 P&L values will be the average of the bottom 6-7 values. These will be the values whose rank is between 1 and 7. Follow this link to see the measures with the described behavior: Rank Measures

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Reported

Naming pattern: Measures with “Reported” behavior follow the name pattern: Main Measure Name (reported). Reported is one of the optional approaches implemented in to include the impact of the netting sets and imported values. For example, “Portfolio Risk Charge (reported)”. The following measures have a Reported variation:

• “risk-class risk-measure Risk Position scenario”
• “risk-class risk-measure Risk Charge scenario”
• “risk-class Curvature Sb scenario”
• “risk-class Delta Sensitivities direction”
• “drc-risk-class Default Risk Charge”
• “drc-risk-class Gross JTD direction”
• “drc-risk-class Net JTD direction”
• “drc-risk-class WtS Ratio”
• “RRAO Exotic”
• “RRAO Other”

Where: Additionally, the SA measures that follow on from the above list are also impacted, up to the “Portfolio Risk Charge”. Follow this link to see the measures with the described behavior: Reported Measures.

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Spot

This page describes the Spot measures, a group of measures that focus on the most recent observation date only.

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Spot analysis

Naming pattern: Measures with “Spot” behavior follow the name pattern: Main Measure Name Spot. The capital requirement $C_A$ in BCBS 457 must respect the past history of $IMCC$ and $SES$ according to this equation: $C_A = max\left\{ IMCC_{t-1} + SES_{t-1};\ m_c \cdot IMCC_{avg} + SES_{avg} \right\}$ A group of measures has been implemented, which allow focusing on the most recent observation date only: $C_A^{MostRecent} = \left\{ IMCC_{t-1} + SES_{t-1} \right\}$ Follow this link to see the measures with the described behavior: Spot Measures.