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February 2 nd , 2004 Séminaire de gestion

February 2 nd , 2004 Séminaire de gestion. How to reduce capital requirement? The case of retail portfolio with small PD Marie-Paule Laurent SOLVAY BUSINESS SCHOOL UNIVERSITÉ LIBRE DE BRUXELLES. Motivation. New Basel Accord Since June 1999 – Today CP3 and QIS3 Objective

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February 2 nd , 2004 Séminaire de gestion

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  1. February 2nd, 2004Séminaire de gestion How to reduce capital requirement? The case of retail portfolio with small PD Marie-Paule LaurentSOLVAY BUSINESS SCHOOLUNIVERSITÉ LIBRE DE BRUXELLES

  2. Motivation • New Basel Accord • Since June 1999 – Today CP3 and QIS3 • Objective • Maintain the overall level of regulatory capital • Be more sensitive to risk • Application for the end of 2006 (?) • In the US: only large international banks • In Europe: all banks through a directive • Concerns • Level playing field • Procyclicality • Calibration of the model MP Laurent

  3. Agenda • Basel framework • Generalities • Retail credit risk • Implication • Empirical testing I • Database: large automotive lease portfolio • Results • Alternative measure of asset return correlation • One factor model • Study of the modified IRBA approach • Empirical testing II • Conclusion MP Laurent

  4. Basel framework: generalities (1) • Three Pillars • Pillar I: minimum capital requirement • Credit risk: SA, IRBF and IRBA • Market risk: SA and IRB • Operational risk: BI, SA and IM • Pillar II: supervisory review • Evaluate risk • Adjust capital • Pillar III: market discipline • Investors information MP Laurent

  5. Basel framework: generalities (2) • General formula KA: capital allocation EAD: earnings at default RW: risk weight K: capital ratio • Capital definition • Tier 1: equity + disclosed reserves • Tier 2: undisclosed res. + asset revaluation res. + gen. provisions+ hybrid debt/equity instruments + subordinated debts • Risk weights • Depends on the approach • Retail exposure • EAD < 1 mio € • No borrower accounts for more than 0.2% of the retail portfolio K MP Laurent

  6. Basel framework: retail credit risk (1) • Standardised approach K= 8% x 0.75 • Internal Rating Based approach PD: probability of default - LGD: loss given default - R: asset return correlation – M: maturity : normal standard cumulative distribution function • IRBF: estimate of PD only • IRBA: estimate of PD, LGD and EAD [Madj=1] MP Laurent

  7. Basel framework: retail credit risk (2) • R is a decreasing function of PD • Riskier firms are less sensitive to systematic risk MP Laurent

  8. Basel framework: retail credit risk (3) • K is an increasing function of PD • The K function is concave for 0<PD <0.049 • convex (slightly) 0.049 <PD <0.152 • concave (slightly) 0.152 <PD <1 MP Laurent

  9. x1 ax1 +(1-a) x2 x2 Basel framework: Implication (1) • Strong concavity for low PD • Capital reduction possible • For “extreme” PD segmentation MP Laurent

  10. Basel framework: Implication (2) • Theoretical case • Total portfolio: • 1000 retail credit loans with maturity of 1 year, EAD=1, LGD=100% • 30 defaults during the year  PD=3% • Calculation under the Basel framework • R= 0.072 • K =0.1381 • Segmentation • Port A:30 defaulted loans & Port B:970 other loans • K(A) = 1 • K(B) = 0 • Total K = 30/1000 x 1 + 970/1000 x 0 = 0.03 MP Laurent

  11. Basel framework: Implication (3) Capital requirement of the total portfolio wrt the size of portfolio B for different segmentation criterion • Possibility of regulatory arbitrage MP Laurent

  12. Empirical testing I: Data (1) • Lease characteristics • Lease financing in the EU = 200 bio € in 2002 • Empirical findings • Low-risk activity • Low asset return correlation • Role of the physical collaterals in reducing the credit risk • Database • 35,787 individual completed automotive lease contracts issued between 1990 and 2000 by a major European leasing company • Ex ante variables • issuance date, cost of the asset, internal rate of return … • Ex post variables • effective payments, final status, recovery… MP Laurent

  13. Empirical testing I: Data (2) • Descriptive statistics of the database • Median contractual term-to-maturity: 48 months • Average cost of the leased asset: 23,302 € • Average interest premium: 3% • 5 distribution networks, 5 regions of origins of the lessor • Overall default rate: 9.1% • Estimation method • PD : life table methodology • EAD : amount due at default date • LGD :1-recovery/amount due (may be positive of negative) • For the global portfolio PD = 2.3% LGD = 31.1% K = 4.0% MP Laurent

  14. Empirical testing I: Results (1) • Summary of the results MP Laurent

  15. Empirical testing I: Results (2) • Significant capital reduction through segmentation • In relative term: 10% reduction by using term-to-maturity • In absolute term : 30bp reduction by using interest premium • LGD has not significant influence • What drives capital reduction? • Differentiation of PD • Not the number of segment  Pooling similar assets reduces the risk? • Problem of asset return correlation • Use a one factor model to estimate R MP Laurent

  16. Alternative measure of R: one factor model (1) • One factor model: one systematic factor probit ordered model • Asset value return of obligation i : • PD of obligator i in a given portfolio : • Obligator i defaults when : • The conditional probability of default: MP Laurent

  17. Alternative measure of R: one factor model (2) • Asset return correlation: • We only observe default Di is a dummy (1 if default; 0 otherwise) • Joint probability of 2 obligators: • Unconditional variation of conditional PD • Estimation of R: calibration of w² in the two last equations MP Laurent

  18. Alternative measure of R: study (1) • R is a decreasing function of PD and an increasing function of STD MP Laurent

  19. Alternative measure of R: study (2) • K is an increasing function of PD and an increasing function of STD MP Laurent

  20. Alternative measure of R: study (3) • Basel framework often overestimates R MP Laurent

  21. Alternative measure of R: study (4) • Basel framework often overestimates K MP Laurent

  22. Empirical testing II: Results (1) • Estimation of STD nk number of contract in segment k, pk the average default frequency • For the global portfolio PD = 2.3% LGD = 31.1% STD = 0.5% K = 1.3% MP Laurent

  23. Empirical testing II: Results (2) • Summary of the results MP Laurent

  24. Empirical testing II: Results (3) • Lower required capital in the model approach (50% on average) • Due to large difference in estimated R • No capital reduction through segmentation • In general, no significant change (absolute term) • For A and F1, significant increase of K (due to high STD in some sub-portfolio) • LGD has not significant influence MP Laurent

  25. Conclusion • Basel II • Better risk allocation • But regulatory arbitrage • Estimation of R • Does not account for the risk profile of the portfolio • Use of a one factor model •  Accuracy of the Basel calibration • Next… • Testing on different portfolio • Factor driving the diversification • … MP Laurent

  26. Question time • Questions ? MP Laurent

  27. 9th Belgian Financial Research Forum • Organised by Solvay Business School - ULB • On May 6th, 2004 • For both junior and senior researchers • Call for Paper: • Abstract for March 31st • Complete paper for April 15st • Information at http://www.solvay.edu/EN/Research/bfrf.php MP Laurent

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