Using Capital Attribution to Understand Your FRTB Capital Requirements

Industry surveys show that FRTB may lead to a 60% increase in regulatory market risk capital requirements, placing significant pressure on banks. As regulatory market risk capital requirements rise, it is imperative that banks employ robust techniques to effectively understand and manage the drivers of capital. However, isolating these drivers can be challenging and time-consuming, often relying on inefficient and manual techniques. Capital attribution techniques provide banks with a solution by automating the analysis and understanding of capital drivers, enhancing their efficiency and effectiveness in managing capital requirements.

In this article, we share our insights on capital attribution techniques and use a simulated example to compare the performance of several approaches.

The benefits of capital attribution

FRTB capital calculations require large amounts of data which can be difficult to verify. Banks often use manual processes to find the drivers of the capital, which can be inefficient and inaccurate. Capital attribution provides a quantification of risk drivers, attributing how each sub-portfolio contributes to the total capital charge. The ability to quantify capital to various sub-portfolios is important for several reasons:

An overview of approaches

There are several existing capital attribution approaches that can be used. For banks to select the best approach for their individual circumstances and requirements, the following factors should be considered:

• Full Allocation: The sum of individual capital attributions should equal the total capital requirements,
• Accounts for Diversification: The interactions with other sub-portfolios should be accounted for,
• Intuitive Results: The results should be easy to understand and explain.

In Table 1, we summarize the above factors for the most common attribution methodologies and provide our insights on each methodology.

Table 1: Comparison of common capital attribution methodologies.

Comparison of approaches: A simulated example

To demonstrate the different performance characteristics of each of the allocation methodologies, we present a simulated example using three sub-portfolios and VaR as a capital measure. In this example, although each of the sub-portfolios have the same distribution of P&Ls, they have different correlations:

• Sub-portfolio B has a low positive correlation with A and a low negative correlation with C,
• Sub-portfolios A and C are negatively correlated with each other.

These correlations can be seen in Figure 1, which shows the simulated P&Ls for the three sub-portfolios.

Figure 1: Simulated P&L for the three simulated sub-portfolios: A, B and C.

The capital allocation results are shown below in Figure 2. Each approach produces an estimate for the individual sub-portfolio capital allocations and the sum of the sub-portfolio capitals. The dotted line indicates the total capital requirement for the entire portfolio.

Figure 2: Comparison of capital allocation methodologies for the three simulated sub-portfolios: A, B and C. The total capital requirement for the entire portfolio is given by the dotted line.

Zanders’ verdict

From Figure 2, we see that several results do not show this attribution profile. For the Standalone and Scaled Standalone approaches, the capital is attributed approximately equally between the sub-portfolios. The Marginal and Scaled Marginal approaches include some estimates with negative capital attribution. In some cases, we also see that the estimate for the sum of the capital attributions does not equal the portfolio capital.

The Shapley method is the only method that attributes capital exactly as expected. The Euler method also generates results that are very similar to Shapley, however, it allocates almost identical capital in sub-portfolios A and C.  

In practice, the choice of methodology is dependent on the number of sub-portfolios. For a small number of sub-portfolios (e.g. attribution at the level of business areas) the Shapley method will result with the most intuitive and accurate results. For a large number of sub-portfolios (e.g. attribution at the trade level), the Shapley method may prove to be computationally expensive. As such, for FRTB calculations, we recommend using the Euler method as it is a good compromise between accuracy and cost of computation.

Conclusion

Understanding and implementing effective capital attribution methodologies is crucial for banks, particularly given the increased future capital requirements brought about by FRTB. Implementing a robust capital attribution methodology enhances a bank's overall risk management framework and supports both regulatory compliance and strategic planning. Using our simulated example, we have demonstrated that the Euler method is the most practical approach for FRTB calculations. Banks should anticipate capital attribution issues due to FRTB’s capital increases and develop reliable attribution engines to ensure future financial stability.

For banks looking to anticipate capital attribution issues and potentially mitigate FRTB’s capital increases, Zanders can help develop reliable attribution engines to ensure future financial stability. Please contact Dilbagh Kalsi (Partner) or Robert Pullman (Senior Manager) for more information.