The usage of proxies under FRTB

Non-modellable risk factors (NMRFs) have been shown to be one of the largest contributors to capital charges under FRTB. The use of proxies is one of the methods that banks can employ to increase the modellability of risk factors and reduce the number of NMRFs. Other potential methods for improving the modellability of risk factors is using external data sources and modifying risk factor bucketing approaches.

Proxies and FRTB

A proxy is utilised when there is an insufficient historical data for a risk factor. A lack of historical data increases the likelihood of the risk factor failing the Risk Factor Eligibility Test (RFET). Consequently, using proxies ensures that the number of NMRFs is reduced and capital charges are kept to a minimum. Although the use of proxies is allowed, regulation states that their usage must be limited, and they must have sufficiently similar characteristics to the risk factors which they represent.

Banks must be ready to provide evidence to regulators that their chosen proxies are conceptually and empirically sound. Despite the potential reduction in capital, developing proxy methodologies can be time-consuming and require considerable ongoing monitoring. There are two main approaches which are used to develop proxies: rules-based and statistical.

Proxy decomposition

FRTB regulation allows NMRFs to be decomposed into modellable components and a residual basis, which must be capitalised as non-modellable. For example, credit spreads for small issuers which are not highly liquid can be decomposed into a liquid credit spread index component, which is classed as modellable, and a non-modellable basis or spread.  

To test modellability using the RFET, 12-months of data is required for the proxy and basis components. If the basis between the proxy and the risk factor has not been identified and properly capitalised, only the proxy representation of the risk factor can be used in the Risk Theoretical P&L (RTPL). However, if the capital requirement for a basis is determined, either: (i) the proxy risk factor and the basis; or (ii) the original risk factor itself can be included in the RTPL.

Banks should aim to produce preliminary analysis on the cost benefits of proxy development – does the cost and effort of developing proxies outweigh the capital which could be saved by increasing risk factor modellability? For example, proxies which are highly volatile may also result in increasing NMRF capital charges.

Approaches for the development of proxies

Both rules-based and statistical approaches to developing proxies require considerable effort. Banks should aim to develop statistical approaches as they have been shown to be more accurate and also more efficient in reducing capital requirements for banks.

Rules-based approach

Rules-based approaches are more simplistic, however are less accurate than the statistical approaches. They find the “closest fit” modellable risk factor using somewhat more qualitative methods. For example, picking the closest tenor on a yield curve (see below), using relevant indices or ETFs, or limiting the search for proxies to the same sector as the underlying risk factor.

Similarly, longer tenor points (which may not be traded as frequently) can be decomposed into shorter-tenor points and cross-tenor basis spread.

Statistical approach

Statistical approaches are more quantitate and more accurate than the rules-based approaches. However, this inevitably comes with computational expense. A large number of candidates are tested using the chosen statistical methodology and the closest is picked (see below).

For example, a regression approach could be used to identify which of the candidates are most correlated with the underlying risk factor. Studies have shown that statistical approaches not only produce the more accurate proxies, but can also reduce capital charges by almost twice as much as simpler rules-based approaches.

Conclusion

Risk factor modellability is a considerable concern for banks as it has a direct impact on the size of their capital charges. Inevitably, reducing the number of NMRFs is a key aim for all IMA banks. In this article, we show that developing proxies is one of the strategies that banks can use to minimise the amount of NMRFs in their models. Furthermore, we describe the two main approaches for developing proxies: rules-based and statistical. Although rules-based approaches are less complicated to develop, statistical approaches show much better accuracy and hence have the potential to better reduce capital charges.