february 2 nd , 2004 séminaire de gestion
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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. Motivation. New Basel Accord Since June 1999 – Today CP3 and QIS3 Objective - PowerPoint PPT PresentationTRANSCRIPT
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
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
EADRWKA %8 K
MP Laurent |6
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
MP Laurent |7
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
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
0
5
10
15
20
25
0% 5% 10% 15% 20% 25% 30%
PD
K
MP Laurent |9
Basel framework: Implication (1)
• Strong concavity for low PD – Capital reduction possible – For “extreme” PD segmentation
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]1;0[a
x
f(x)
x1 x2ax1 +(1-a) x2
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
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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%
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 portfolioPD = 2.3%
LGD = 31.1%
K = 4.0%
MP Laurent |14
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
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:
ii ewwxZ 5.02 )1(
)(]Pr[ iZPD
5.021
15.02
1
)1()(
)()1(
)(
wwxPD
PDwwx
PDZ
i
i
i
])1/())([()( 5.021 wwxPDxPD
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–
2),( wZZ ji
)]|)(&)([Pr(][ 11 xPDZPDZEDDE jiji
)),(),((][ 2112 wPDPDDDE ji
222 ][)]([])([)]([ PDDDExPDExPDExPDVar ji
2)]([ STDxPDVar
MP Laurent |18
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
MP Laurent |19
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
MP Laurent |20
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
MP Laurent |21
Alternative measure of R: study (4)
– Basel framework often overestimates K
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0,05
0,10
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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
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 portfolioPD = 2.3%
LGD = 31.1%
STD = 0.5%
K = 1.3%
k
kkk
k
k
nE
ppnEpVarxpVar
11
)1(1)()(
MP Laurent |23
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%
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 athttp://www.solvay.edu/EN/Research/bfrf.php