###### Parametric Approaches (II): Extreme Va ...

After completing this reading, you should be able to: Explain the importance and... **Read More**

**After completing this reading**,** the candidate should be able to**:

- Explain the elements of the new standardized approach to measuring operational risk capital, including the business indicator, internal loss multiplier, and loss component, and calculate the operational risk capital requirement for a bank using this approach.
- Compare the SMA to earlier methods of calculating operational risk capital, including the Advanced Measurement Approaches (AMA).
- Describe general and specific criteria recommended by the Basel Committee for the identification, collection, and treatment of operational loss data.

Operational risk is defined as the risk of loss resulting from inadequate or failed internal processes, people, and systems or from external events. It includes events such as fraud, employee errors, criminal activity, and security breaches. However, this definition **excludes** **reputational risk** as well as **strategic risk**.

Following the announcement of Basel III reforms, operational risk should be measured using the **standardized approach** in internationally active banks. It is, indeed, noteworthy that supervisors still have the discretion to apply the standardized approach among non-internationally active lenders.

The minimum operational risk capital (ORC) for a bank is given by:

$$ ORC = BIC × ILM $$

The Business Indicator Component (BIC) is a product of the Business Indicator (BI) and a set of regulatory marginal coefficients \( { a }_{ i } \).

$$ \left( BIC \right) =\sum { \left( { a }_{ i }\times { BI }_{ i } \right) } $$

The BI consists of select items from a bank’s financial statements that are representative of a bank’s operational risk exposure. In particular, the BI has 3 components:

- The interest, leases, and dividends component (ILDC).
- The services component (SC).
- The financial component, FC.

**Important**: All the three components must be calculated as averages over **3** years.

The BIs of large international banks are typically large figures running into billions of Euros – the chosen denomination for operational risk capital calculations. A bank’s BI tells a lot about its operational risk exposure. For this reason, the standardized approach divides banks into 3 buckets according to the size of their BI. Each bucket is associated with a regulatory determined coefficient \( { a }_{ i } \).** **As the BI increases, so do the coefficients. A summary is set out in the table below:

$$

\small{\begin{array}{l|c|c|c}

\textbf{BI Bucket}& \textbf{1} & \textbf{2}& \textbf{3} \\ \hline

\textbf{BI Range} & ≤ €1 \text{ billion} & €1 \text{ billion} < BI ≤ €30 \text{ billion} & ≥€30 \text{ billion} \\ \hline

\textbf{Marginal BI Coefficient, } \bf{{ a }_{ i }} & 0.12 & 0.15 & 0.18 \\ \hline

\textbf{Calculation, } \bf{{ a }_{ i }} & €1bn × 12\%

= €0.12bn & €(30 – 1) × 15\%

= €4.35bn & €(40 – 30) × 18\%

= €1.8bn \\

\end{array}

}$$

By summing the 3 buckets, we arrive at a BIC of **€6.27 billion**.

$$

\small{\begin{array}{l|c|c|c}

\textbf{BI Bucket}& \textbf{1} & \textbf{2}& \textbf{3} \\ \hline

\textbf{BI Range} & ≤ €1 \text{ billion} & €1 \text{ billion} < BI ≤ €30 \text{ billion} & ≥€30 \text{ billion} \\ \hline

\textbf{Marginal BI Coefficient, } \bf{{ a }_{ i }} & 0.12 & 0.15 & 0.18 \\ \hline

\textbf{Calculation, } \bf{{ a }_{ i }} & €1bn × 12\%

= €0.12bn & €(25 – 1) × 15\% = €3.6bn & \\

\end{array}}

$$

By summing the 3 buckets, we arrive at a BIC of **€3.72 billion**.

The internal Loss Multiplier is defined as:

$$ ILM=\ln { \left[ exp\left( 1 \right) -1+{ \left( \frac { LC }{ BIC } \right) }^{ 0.8 } \right] } $$

As can be seen from the equation above, the ILM (the Internal Loss Multiplier) is a function of the BIC and the Loss Component (LC), where the latter is equal to **15 **times a bank’s average historical losses over the preceding 10 years. Firms with less than 10 years of data must use a minimum of 5 years of data while computing the average historical loss.

**Important**:

- When LC = BIC, the ILM factor is equal to 1, and in effect, it becomes the default ILM level in certain circumstances.
- When the LC is greater than the BIC, the ILM is greater than one.
- When the LC is less than the BIC, the ILM is less than one.
- For firms with BI levels less than €1bn, the ILM is set to 1, and therefore internal loss data does not affect the capital calculation.
- Under transitional arrangements, banks without 5-year historical data must set the ILM to 1, although the supervisor in charge maintains the discretion to set higher levels.

The AMA, introduced in Basel II, allows for the estimation of regulatory capital to be based on a diverse range of internal modeling practices conditional on supervisory approval. The method has had a significant degree of flexibility, meaning that banks have been at liberty to use slightly different models while calculating the capital required. It is this flexibility that has resulted in the AMA being replaced since it has resulted in widely incomparable internal modeling practices. This has exacerbated variability in risk-weighted asset calculations and eroded confidence in risk-weighted capital ratios. The SMA has limited flexibility and requires banks to follow precise guidelines in the entire capital calculation process.

To use the Loss Component (LC), banks have to observe certain guidelines:

- A bank must have quality loss data spanning a 10-year period. Under transitional arrangements, banks are allowed to use a minimum of 5 years of loss data.
- A bank must have documented procedures and processes for the identification, collection, and treatment of internal loss data.
- A bank must be ready to map internal loss data onto the relevant Level 1 supervisory category as defined in Annex 9 of the Basel II Framework, on request (by the supervisor).
- The data must capture all material events and exposures from all geographical locations and subsystems. Any loss event of €20,000 or more is considered material.
- A bank must keep records of specific dates when operational risk events occurred or commenced.
- Operational loss events related to credit risk and that are accounted for in credit risk RWAs should not be included in the loss data set.
- For the purpose of calculating minimum regulatory capital under the SMA framework, operational risk losses related to market risk are treated as operational risks.
- A bank must have an independent mechanism to validate and ensure the accuracy of the data.

- A bank must put policies that address various aspects of internal loss data in place. Among others, such aspects include collection dates, gross loss definition, and the grouping of losses.
- Gross loss is a loss before recoveries of any type. Net loss is defined as the loss after taking the impact of recoveries into account.
- Banks must be able to identify gross operational losses and recoveries for all operational risk events.
- Items included in gross loss calculations:
- Direct charges, including impairments and settlements.
- External expenses linked to an operational risk event, e.g., legal expenses.
- Provisions or reserves are accounted for in the P&L against the potential operational loss impact.
- Material “timing losses” resulting from operational risk events impacting the cash flows or financial statements of previous financial accounting periods.
- Temporary losses booked in suspense accounts but not recorded in P&L.

- Items excluded from gross calculations:
- General maintenance costs.
- Internal or external business enhancement costs incurred following a risk event.
- Insurance premiums

## Practice Question

Calculate the BIC of a bank with a BI of €20bn.

A. €3.6 billion.

B.€2.4 billion.

C. €3 billion.

D. €2.97 billion.

SolutionThe correct answer is

D.$$

\small{\begin{array}{l|c|c|c}

\textbf{BI Bucket}& \textbf{1} & \textbf{2}& \textbf{3} \\ \hline

\textbf{BI Range} & ≤ €1 \text{ billion} & €1 \text{ billion} < BI ≤ €30 \text{ billion} & ≥€30 \text{ billion} \\ \hline

\textbf{Marginal BI Coefficient, } \bf{{ a }_{ i }} & 0.12 & 0.15 & 0.18 \\ \hline

\textbf{Calculation, } \bf{{ a }_{ i }} & €1bn × 12\%

= €0.12bn & €(20 – 1) × 15\% = €2.85bn & \\

\end{array}}

$$By summing the 2 buckets, we arrive at a BIC of

€2.97 billion.