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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

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MP Laurent |2|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

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MP Laurent |3|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

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MP Laurent |4|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

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MP Laurent |5|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

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MP Laurent |6|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 [M adj =1]

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

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MP Laurent |8|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

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MP Laurent |9|9 Basel framework: Implication (1) Strong concavity for low PD –Capital reduction possible –For extreme PD segmentation x1x1 x2x2 ax 1 +(1-a) x 2

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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

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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

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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…

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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%

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

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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

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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:

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MP Laurent | 17 Alternative measure of R: one factor model (2) –Asset return correlation: –We only observe default D i 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 –

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

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

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

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

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

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

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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

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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 –…

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MP Laurent | 26 Question time Questions ?

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

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