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Scaling Models for the severity and frequency of external operational loss Data

Scaling Models for the severity and frequency of external operational loss Data. Hela Dahen Georges Dionne April 2007. Outline. Introduction Motivations Literature review Methodology - Severity Scaling Model - Frequency Scaling Model Results Conclusion.

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Scaling Models for the severity and frequency of external operational loss Data

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  1. Scaling Models for the severity and frequency of external operational loss Data Hela Dahen Georges Dionne April 2007

  2. Outline • Introduction • Motivations • Literature review • Methodology - Severity Scaling Model - Frequency Scaling Model • Results • Conclusion

  3. Introduction • Huge operational losses have occurred recently in the financial sector (Barings, Allied Irish Bank, Enron…) • Basel II accord : regulatory capital requirement for operational risk. • Operational risk is defined as the loss resulting from inadequate or failed internal processes, people and systems or from external events • 3 methods for the measurement of regulatory capital : • Basic Indicator Approach (BIA) • Standardized Approach (SA) • Advanced Measurement Approach (AMA)

  4. Motivations • Research is still in its embryonic stage. • Internal operational Loss data is often insufficient. • The use of external losses is a must in the implantation of an advanced measurement approach. • Challenge to using external loss data

  5. Literature Review • Little research was done for the development of scaling models for the severity and frequency of external operational loss data : • Shih, Samad-Khan and Medapa (2000) : Non linear severity scaling model using only the institution’s size. • Na (2004) : • loss amount is split into a common component and an idiosyncratic component • power relationship between the institution size and the idiosyncratic component. • A similar model for scaling frequency • Hartung (2004) : severity scaling model using a normalization formula introducing scaling factors and adjustment parameters.

  6. Objectives • Developing a scaling model for the external operational loss amounts • The use of external data with internal data • Provide more information on the tail of the severity distribution • Developing a scaling model for the number of external operational losses • Determine the number of scaled external losses that we have to introduce in the model

  7. Contributions: • Improve the existing severity scaling model (Shih et al., 2000; Na 2004) • Develop a first frequency scaling model. • Use of zero truncated Poisson and negative binomial regression in the context of operational risk (Hausman et al., 1984; Cameron and Trivedi, 1986; Dionne and Vanasse, 1992…) • Capital calculation based on scaled external loss data.

  8. Data • Fitch data base • 1056 loss observations more than $1M us • 323 financial institutions • Information on : • Loss event, • Location, • Date, • Business line, • Risk type, • The institution where loss occured (Assets, deposits, equity, revenues, number of employees).

  9. Severity scaling : Assumption 1- Loss components (Na, 2004 ): Lossi = Compcommonx g(Compidiosyncratic))i Compcommon: common component to all banks (macroeconomic, geopolitical, cultutal environment, human nature…) Compidiosyncratic : idiosyncratic component : specific risk (bank size, location, business line, risk type…) 2- Non linear relationship between the idiosyncratic component and the different factors composing it. 3- All the other non-observable factors (quality of control environment…) are supposed to remain the same for all banks.

  10. Severity scaling : the model with : Size : Log(assetsi) US, Canada, Europe : binary variables of location (USA, Canada, Europe) BLij: binary variables of business line RTij : binary variables of risk type

  11. Severity scaling : Estimation results • Estimation of the coefficients by OLS method : Variables of size, location (US, Canada), Business line (commercial banking) and risk type (clients, products and business practices) are significantly different from 0. • Results (see table 1) • R2adjusted=10.63%

  12. Severity scaling : Robustness tests for the size variables Model 1 : Regression including only the size (Shih et al., 2000) Model 2 : Regression including the size and the location Model 3 : Regression including the size, the location and the business lines. Model 4 : Regression including only the significantly non null variables Results (see table 2)

  13. Severity scaling : estimation results Normalization formula : With

  14. Severity scaling : validation of the model • Reference Bank : Merrill Lynch with 52 loss events over 1994-2004 in the data base. • Scaling all the losses (1050) included in the data base to Merrill Lynch bank. • Comparaison of the statistics calculated on the sample of 52 observed losses and those calculated on the 1050 losses that could occur in the same bank (after scaling) • Statistics : Table 3 • Impact of the scaling factors on loss amount : Table 4

  15. Frequency scaling : the model • Modelling the number of losses per company over the period [1994 -2004] zero truncated Poisson and negative binomial • Frequency depends on the size and the distribution of banking activities Include a regression component in the model Variables included in the model : • Size : log (assets) • US, Canada, Europe, Others : binary variables (1 if the institution has had losses in this country (continent), 0 otherwise)

  16. Frequency scaling :zero truncated count models Yi : number of losses sustained by company over 1994-2004 • Zero truncated Poisson regression : • Zero truncated negative binomial regression : ~

  17. Frequency scaling : results • Most of the variables introduced in the model are statistically different from 0 • Test for overdispersion (test for truncated regression models : Gurmu, 1991) : Existence of significant overdispersion : The negative binomial model dominates the Poisson. • Results (see table 5)

  18. Capital calculation from external loss data Example : Merrill Lynch • Scale all the external losses contained in the database to Merrill Lynch • Scale the frequency of the external data to Merrill Lynch • Determin the parameters of the negative binomial • Determin the frequency distribution of the annual number of operational losses • Generate a number of losses from the frequency distribution • Make random drawing of scaled loss amounts to Merrill Lynch, according to the number generated. • Calculate the total annual losses • Repeat steps 3; 4 and 5 • Calculate statistics from the annual aggregate distribution of annual losses.

  19. Conclusion and extension • We improve the existing scaling model : • Besides the size, other factors have a significant and more important impact on the external loss amounts than size. These variables have to be introduced in the severity scaling model. • We develop a frequency scaling model : • The negative binomial regression model permits the scaling of the number of the external operational losses and generates a number of scaled losses to a specific bank. • Extensions : • Introducing variables estimating the quality of the control environment, and macroeconomic variables in the common component.

  20. Variable Basic model Constant 0.799 Log (assets) 0.077*** US -0.541*** Canada -1.087*** Europe -0.053 Retail brokerage 0.115 Corporate finance 0.386 Asset management 0.398 Trading and sales 0.417 Commercial banking 0.797*** Retail banking 0.043 Agency services 0.478 Damages to physical assets 1.300 Clients, products, and business practices 1.123* Employment, practices and workplace safety 0.088 External fraud 0.360 Internal fraud 0.731 Execution, delivery, and process management 0.577 F(18, 1037) 8.38 R2 12.07% R2adj 10.63% Table 1: Results from the estimation of the Linear Regression Parameters

  21. Model 1 Model 2 Model 3 Model 4 Constant 1.495*** (0.000) 1.797*** (0.000) 1.713*** (0.000) 1.379*** (0.000) Log (assets) 0.076** (0.007) 0.084*** (0.003) 0.077*** (0.006) 0.082*** (0.001) US -0.583*** (0.000) -0.446** (0.001) -0.595*** (0.000) Canada -1.219*** (0.000) -1.055*** (0.000) -1.102*** (0.000) Europe 0.020 (0.907) 0.083 (0.624) Retail brokerage -0.275 (0.271) Corporate finance 0.423 (0.166) Assets management 0.369 (0.225) Trading and sales 0.148 (0.599) Commercial banking 0.455* (0.062) 0.665*** (0.000) Retail banking -0.200 (0.398) Agency services 0.383 (0.327) Clients, products and businesspractices 0.633*** (0.000) F 7.6 (0.000) 12.91 (0.000) 8.39 (0.000) 22.84 (0.000) R2 0.69% 4.68% 8.12% 9.81% R2adj 0.60% 4.32% 7.16% 9.38% Table 2 : Robustness Tests

  22. Table 3 : Comparaison between statistics on observed and scaled

  23. Table 4 : Impact of Scaled Variables on Loss amounts

  24. Truncated Poisson regression model Truncated negative binomial regression model Constant -5.876*** (-15.28) -10.439*** (-8.35) Log (assets) 1.176*** (15.30) 1.783*** (8.45) United States 1.432*** (14.20) 2.000*** (6.60) Canada 0.559*** (5.51) 1.721*** (2.83) Europe 0.141* (1.73) -0.111 (-0.34) Other countries 0.191** (2.43) 0.457 (1.52) 4.347 (1.53) Log (likelihood function) -695.314 -439.414 Score test 34.637 Table 5 : Results of the Estimation of the Coefficients in the Frequency Model

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