February 2nd, 2004

Séminaire de gestionHow to reduce capital requirement?The case of retail portfolio with small PD

Marie-Paule LaurentSOLVAY BUSINESS SCHOOLUNIVERSITÉ LIBRE DE BRUXELLES

MP Laurent |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

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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

EADRWKA %8 K

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Basel framework: retail credit risk (1)

• Standardised approachK= 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]

adjMRRPDRLGDK )999.0())1(()()1( 15.015.0

(.)

]1

11[%17

1

1%2

35

35

35

35

e

e

e

eR

PDPD

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Basel framework: retail credit risk (2)

– R is a decreasing function of PD

– Riskier firms are less sensitive to systematic risk

0,00

0,04

0,08

0,12

0,16

0,20

0% 5% 10% 15% 20% 25% 30%

PD

Co

rrel

atio

n

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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

0

5

10

15

20

25

0% 5% 10% 15% 20% 25% 30%

PD

K

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Basel framework: Implication (1)

• Strong concavity for low PD – Capital reduction possible – For “extreme” PD segmentation

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]1;0[a

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f(x)

x1 x2ax1 +(1-a) x2

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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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Basel framework: Implication (3)

Capital requirement of the total portfolio wrt the size of portfolio B for different segmentation criterion

– Possibility of regulatory arbitrage

0,00

0,02

0,04

0,06

0,08

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0,14

0,16

1000 975 950 925 900 875 850 825 800

Size of Portfolio B

K o

f th

e to

tal

po

rtfo

lio

100%

80%

60%

40%

20%

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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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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 portfolioPD = 2.3%

LGD = 31.1%

K = 4.0%

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Capital required % of reduction Capital required % of reduction Mean Mean Asset LGD included LGD not included LGD Correlation

No segmentation 4,00% 12,83% 3,21 8,71% Segmentation by:

A - Issuance date 3,94% 1,5% 12,74% 0,8% 3,24 8,77% B – Term-to-maturity 3,55% 11,3% 11,29% 12,1% 3,18 9,89% C - Cost of the leased asset 3,88% 2,9% 12,85% -0,1% 3,31 8,68% D - Distribution network 3,94% 1,3% 12,69% 1,1% 3,22 8,89% E - Region of origin of the lessor 4,01% -0,3% 12,79% 0,4% 3,19 8,77% F1 - Interest premium 3,70% 7,4% 12,15% 5,4% 3,28 9,36% F2 - Interest premium (decile) 3,69% 7,7% 11,97% 6,7% 3,25 9,48% H - Control 3,99% 0,1% 12,83% 0,1% 3,21 8,72%

Empirical testing I: Results (1)

• Summary of the results

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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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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:

ii ewwxZ 5.02 )1(

)(]Pr[ iZPD

5.021

15.02

1

)1()(

)()1(

)(

wwxPD

PDwwx

PDZ

i

i

i

])1/())([()( 5.021 wwxPDxPD

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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–

2),( wZZ ji

)]|)(&)([Pr(][ 11 xPDZPDZEDDE jiji

)),(),((][ 2112 wPDPDDDE ji

222 ][)]([])([)]([ PDDDExPDExPDExPDVar ji

2)]([ STDxPDVar

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Alternative measure of R: study (1)

– R is a decreasing function of PD and an increasing function of STD

0,010,06

0,110,16

0,5%1,0%

1,5%2,0%

0%2%4%6%8%10%12%14%16%18%20%22%24%26%28%

R

PD S

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Alternative measure of R: study (2)

– K is an increasing function of PD and an increasing function of STD

0,01 0,06 0,11 0,160,5%

1,0%

1,5%2,0%

0%2%4%6%8%10%12%14%16%18%20%22%24%26%28%

K

PD

S

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Alternative measure of R: study (3)

– Basel framework often overestimates R

0%

5%

10%

15%

20%

25%

30%

0,01 0,03 0,05 0,07 0,09 0,11 0,13 0,15 0,17 0,19

PD

R

S=0.5% S=1% S=1.5% S=2% Basel

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Alternative measure of R: study (4)

– Basel framework often overestimates K

0,00

0,05

0,10

0,15

0,20

0,25

0,30

0,35

0,40

0,01 0,03 0,05 0,07 0,09 0,11 0,13 0,15 0,17 0,19

PD

K

S=0,5% S=1% S=1,5% S=2% Basel

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Empirical testing II: Results (1)

• Estimation of STD

nk number of contract in segment k, pk the average default frequency

• For the global portfolioPD = 2.3%

LGD = 31.1%

STD = 0.5%

K = 1.3%

k

kkk

k

k

nE

ppnEpVarxpVar

11

)1(1)()(

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Empirical testing II: Results (2)

• Summary of the results

Capital required

% of reduction

Capital required

% of reduction Mean Mean Mean Asset

LGD included LGD not included LGD STD Correlation

No segmentation 1,35% 4,32% 3,21 0,513% 0,87% Segmentation by: A - Issuance date 3,09% -129,8% 9,61% -122,5% 3,11 1,346% 5,32% B – Term-to-maturity 1,81% -34,5% 5,19% -20,2% 2,87 0,620% 4,94% C – Cost of the leased asset 1,34% 0,6% 4,41% -2,2% 3,30 0,518% 0,99% D - Distribution network 1,48% -9,9% 4,77% -10,5% 3,23 0,598% 1,34% E - Region of origin of the lessor 1,45% -7,9% 4,65% -7,6% 3,20 0,581% 1,14% F1 - Interest premium 3,68% -173,6% 12,12% -180,7% 3,29 0,883% 11,07% F2 - Interest premium (decile) 2,12% -57,4% 6,80% -57,4% 3,21 0,847% 5,35% H – Control 1,29% 4,1% 4,15% 4,0% 3,22 0,474% 0,77%

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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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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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Question time

• Questions ?

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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 athttp://www.solvay.edu/EN/Research/bfrf.php