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Quantifying and Stress Testing Operational Risk with Peer Banks’ Data

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Abstract

One of the main challenges that banks face in quantifying operational risk is the instability of risk estimates caused by heavy-tailed and insufficient loss data. To address these issues, we propose a loss scaling method to combine a bank’s internal loss data with loss data of peer banks. In this method, we scale tail losses using total assets and a measure of risk management quality as scaling factors. Using supervisory operational loss data from large U.S. bank holding companies, we demonstrate that our method of incorporating scaled external data improves the stability of operational risk estimates. In addition, we show that our scaling method can be applied for stress testing operational losses to macroeconomic shocks by better depicting the relationship between losses and macroeconomic variables.

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Notes

  1. Using publicly available information of 11 large bank holding companies (BHCs), Abdymomunov et al. (2019) report that the share of risk-weighted assets (RWA) for operational risk amounts to, on average, 27% of total RWA, relative to 8% and 65% for market and credit risks, respectively.

  2. See the Wall Street Journal http://www.wsj.com/articles/home-depot-breach-bigger-than-targets-1411073571

  3. In general, a VaR model simulates a loss distribution and risk is measured by a selected tail quantile. Jorion (2007) describes a VaR model in detail and its application in various risk areas. For example, Barber and Copper (1996), Singh (2004), Almeida and Vicente (2009) describe VaR models applied to market and interest rate risks. Embrechts et al. (2005), Embrechts and Puccetti (2006) describe applications of a VaR model to operational risk.

  4. For a detailed description of the FR Y-14Q reporting form and instructions visit http://www.federalreserve.gov/apps/reportforms/.

  5. The FR Y-9C form reports consolidated financial statements for holding companies. Details can be found at https://www.federalreserve.gov/apps/reportforms/

  6. We set the modeling threshold at $100,000 for only two BHCs because of their higher data collection thresholds and their similar business focuses. However, we set our modeling threshold at $20,000 for all other BHCs to use more observations in our data.

  7. SR 04-18 document of the Federal Reserve System describes the BHC rating system and is available at http://www.federalreserve.gov/boarddocs/srletters/2004/sr0418.htm.

  8. We do not include index q in 𝜖i,k because the error term varies for each individual loss i rather than for a given quarter.

  9. In our application of the scaling method, we always find a distribution that passes the goodness of fit tests. We do, however, have a very small number of such cases for individual bank’s data. The application of the bootstrap method to the individual bank’s data does not favor our scaling method in our analysis of the stability of risk estimates relative to the individual banks’ models.

  10. We constrain the parameters of the Generalized Extreme Value and the Generalized Pareto distributions to have a finite first moment in order to avoid unstable and unrealistic estimates. This constraint is not binding in our scaling method. However, it happens to be binding for the individual banks. Thus, this constraint does not favor our scaling method in the stability analysis.

  11. The macroeconomic variables are constructed using data obtained from the St. Louis FRED database.

  12. In addition to de Jongh et al. (2015), please see Ergashev (2012) and Abdymomunov et al. (2015) for extensive discussions of a 1-in-c- years scenario.

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Authors and Affiliations

  1. Federal Reserve Bank of Richmond, 530 East Trade Street, Charlotte, NC, 28202, USA

    Azamat Abdymomunov & Filippo Curti

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  1. Azamat Abdymomunov
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  2. Filippo Curti
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Correspondence to Filippo Curti.

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The views expressed in this paper are those of the authors and do not necessarily reflect the position of the Federal Reserve Bank of Richmond or the Federal Reserve System. We thank the Editor and the Referee, as well as Adam Ashcraft, Alexander Cavallo, Jens H. E. Christensen, participants at the 2015 Federal Reserve Stress Testing Research Conference, the 2015 ABA Risk Modeling Forum, the 18th OpRisk North America conference, and the 2017 IBEFA Summer Meeting for their thoughtful comments. All remaining errors are our own.

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Abdymomunov, A., Curti, F. Quantifying and Stress Testing Operational Risk with Peer Banks’ Data. J Financ Serv Res 57, 287–313 (2020). https://doi.org/10.1007/s10693-019-00320-w

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