Operational Risk Capital: An Analysis Kabir Dutta ARIA Conference, Washington DC August 7, 2006

1. Operational Risk Capital: An Analysis Kabir Dutta ARIA Conference, Washington DC August 7, 2006 The views expressed in this presentation do not necessarily reflect those of the Federal Reserve System.

2. Agenda • Characteristics of Data • Capital Estimation • Results

3. Data

4. Background • Under the AMA, Banks must use a combination of the following four elements in quantifying operational risk exposure: • internal loss event data • external loss event data • scenario analysis • business environment and internal control factor assessments • These elements must be combined in a manner that most effectively enables quantification of operational risk exposure.

5. Data Observations • Results from QIS-4 and the Benchmarking Exercise suggest the following: • Institutions have made considerable progress in developing internal loss data collection systems. • Many institutions have acquired external databases, but use of external data varies considerably.

6. Data Observations (Continued) • Institutions have begun using scenario analysis, but significant work remains in this area. • Many institutions are using some form of tools to assess Business Environment and Internal Control Factors (BE&ICF).

7. Unit of measure • The level of granularity seen in QIS-4 varied significantly, with the number of units of measure ranging from 1 to over 100. • Several banks submitted only ‘Enterprise Level’ capital computations. • The others computed capital at business level or loss event type level, or some combination of the two.

8. Operational Loss Frequency (LDCE)

9. Operational Loss Severity (LDCE)

10. LDCE Sample Descriptive Details

11. Data Characteristics and Challenges • Internal Data • Not too old • Data quality appears to vary across institutions • Loss thresholds • Rounding of loss amounts • Length of time series available • Accuracy of loss timestamps

12. References (continued) • AMA Benchmarking Exercise, QIS-4, and LDCE results: • http://www.bos.frb.org/bankinfo/qau/pd051205.pdf • Summary findings of QIS-4: • http://www.federalreserve.gov/boarddocs/press/bcreg/2006/20060224/default.htm

13. Capital Calculation

14. Overview • We found some degree of central tendency among number of institutions using an AMA along some important dimensions. • Capital estimates vs. total assets and other exposure indicators. • Capital estimates in QIS4 vs. the number of losses reported in LDCE. • Use of Loss Distribution Approach

15. Overview (CONT) • There is significant variation across all the institutions, with outliers identified along many different dimensions. • This variation could arise from several different sources. • Cross-firm differences in risk profile. • Differences in data completeness. • Differences in methodology, including use of the four elements.

16. Reference • A Tale of Tails: An Empirical Analysis of Loss Distribution Models for Estimating Operational Risk Capital. White Paper of the Federal Reserve Board, July 2006. • http://www.federalreserve.gov/generalinfo/basel2/whitepapers.htm

17. Important Questions • Operational Risk Characteristics • Which techniques fit the loss data and result in meaningful capital estimates? • Which commonly used techniques do not fit the loss data? • Is there a single model that can be used in all cases? • consistently in some cases • How do the capital estimates vary with respect to the model assumptions across different institutions classified by assets size, income, and other criteria?

18. Some Believe and Suggestions: • Operation Loss Data will be impossible to model • Data Contamination and Outliers • Ignore the Outliers • Truncate Severity Distribution • Impossible to Measure the Risk at 99.9% level • The Operational Risk has to be an application of Extreme Value Theory (EVT) • Body and tail can’t be fitted using same distribution

19. The Problem:Modeling skewness and kurtosis • Finding appropriate leptokurtic behavior in the loss data • Constructing and calibrating models to reflect the observed leptokurtic behavior • Testing of model behavior

20. Exploratory Data Analysis • Various experiments were performed • Skewness and kurtosis are not absolute concepts • They are relative • LDCE data vary with many types of kurtosis values but similar skewness • Heavy-tailed loss severity • Distributions that can’t model the kurtosis variability will not be able to model the data.

21. Performance Measures • We use these criteria to measure the performance of our models: • Good Fit • Realistic • Well Specified • Flexible • Simple • Model performance measured at the enterprise, business line, and event type levels

22. Hoaglin, Mosteller, and Tukey (1985) Using Quantiles to Study Shapes (Chapter 10).Summarizing the Shape Numerically: The g-and-h Distribution(Chapter 11) . In Exploring Data Tables Trend and Shapes

23. g-and-h distribution is a functional transformation of the standard normal variable: • g = 0 is a h-distribution (no skewness) • h= 0 is a g-distribution (no kurtosis)

24. Q-Q Plot – Body and Lower Tail

25. Q-Q Plot – Upper Tail

26. Q-Q Plot – Extreme Tail

27. Tail Shapes for Various Distributions

28. Enterprise Level Capital

29. Enterprise Level Capital

30. Summed ET Capital Estimates

31. Summed BL Capital Estimates

32. Enterprise Distribution Rankings

33. Summary of 99.9% Capital Estimates Summary for g-and-h

34. Conclusion • Flexibility in terms of skewness-Kurtosis is needed to model oprisk data • Oprisk data can be modeled using LDA and at 99.9% and at all levels • Our analysis can be used for product development and securitization in oprisk and other insurance areas