Credit Risk Transfer and Systemic Risk. Study Case on Romania Coordonator: PhD. Professor Moisa...
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Transcript of Credit Risk Transfer and Systemic Risk. Study Case on Romania Coordonator: PhD. Professor Moisa...
Credit Risk Transfer and Systemic Risk. Study Case on Romania
Coordonator: PhD. Professor Moisa ALTARStudent: Irina LUPA
Introduction
Remarks by Chairman Alan Greenspan (1998) “In the context of bank capital adequacy, supervisors increasingly must be
able to assess sophisticated internal credit risk measurement systems, as well as gauge the impact of the continued development in securitization and credit derivative markets. It is critical that supervisors incorporate, where practical, the risk analysis tools being developed and used on a daily basis within the banking industry itself. If we do not use the best analytical tools available, and place these tools in the hands of highly trained and motivated supervisory personnel, then we cannot hope to supervise under our basic principle -- supervision as if there were no safety net.”
(1999) “Heavier supervision and regulation designed to reduce systemic risk would likely lead to the virtual abdication of risk evaluation by creditors of such entities, who could--in such an environment--rely almost totally on the authorities to discipline and protect the bank. The resultant reduction in market discipline would, in turn, increase the risks in the banking system, quite the opposite of what is intended. Such a heavier hand would also blunt the ability of U.S. banks to respond to crisis events. Increased government regulation is inconsistent with a banking system that can respond to the kinds of changes that have characterized recent years, changes that are expected to accelerate in the years ahead.”
Literature Review
• D. Baur and E. Joossens (2005)
• M. Davis and V. Lo (2001)
• Upper and Worms (2004)
• C. H. Furfine (2003)
• O. De Bandt and P. Hartmann (2000)
• F. Allen and D. Gale (2000)
SPV
Exposures portfolio
Defaults
Investor holdings scenarios
LOSS
Investors state of default
Inter-bank linkages matrix
Default of credit institutions by
contagion effect
The measurement
of the aggregated
impact
The conceptual model of the impact a securitization might have on financial stability
Data
Logit Model:
• Credit Register – the status of default of companies in debt (Dec. 2004 and
Dec. 2005)
• Ministry of Finance – financial statements of companies (Dec. 2004)
Securitization:
• Credit Register – value of loan exposures to companies (Dec. 2004)
Contagion:
• the matrix of inter-bank exposures (Dec. 2005)
• the level of own funds for each bank (Dec. 2005)
• the value of assets for each bank (Dec. 2005)
• the value of the risk-weighted assets for each bank (Dec. 2005)
Portofoliul institutiei de credit initiatoare
0
100
200
300
400
500
600
700
800
900
1000
1 601 1201 1801 2401 3001 3601 4201 4801 5401 6001 6601 7201 7801 8401 9001 9601 10201 10801 11401 12001 12601
Numar debitori
va
loa
re e
xp
un
eri
in
mil
ioa
ne
le
i
Individual value of exposures (mil
lei)
Number of exposures
% in the total
number
Cumulated value of the exposures
% in the total value of the loan portfolio
<1 11856 0.914674 1719.8538 0.124591
<2 482 0.037186 681.70502 0.049385
<3 180 0.013887 435.45774 0.031546
<5 185 0.014272 719.12073 0.052095
>=5 259 0.019981 10247.82 0.742383
Total 12962 1 13803.957 1
Loan portfolio structurestructure of the originator
Originator’s Loan Portfolio
Loan portfolio of the originator
The securitization will only include a fraction of the institution’s company loans portfolio. The securitized exposure amounts will affect the institution’s total risk-weighted assets (RWA). In order to determine the appropriate weighted exposure amount we develop a logit model that evaluates debtor’s probability of default (PD). The RWA will be calculated according to the provisions of Basel II.
Originator’s Loan Portfolio
Correlation (R) = 0.12 × (1 –EXP(-50 ×PD)) /(1 –EXP(-50)) + 0.24 ×[1 –(1 –EXP(-50 × PD))/(1 –EXP(-50))]
Maturity adjustment (b) = (0.11852 – 0.05478 × ln(PD))^2
Capital requirement (K) =[LGD×N[(1 – R)^-0.5×G(PD)+(R/(1 – R))^0.5×G(0.999)]–PDxLGD]x(1–1.5 x b)^-1×(1+(M– 2.5)×b)
Risk-weighted assets (RWA) = K x 12.5 x EAD
• LGD – loss given value has been considered to be 45%• M – the maturity is considered 2.5 yrs.
The variables, that have the highest discriminatory power, and are included in
the model are:
a) the term of recovery of receivables (trc);
b) the rate of repaying short-termed debt (tmps);
c) net cash-flow rate (tn12at).
Logit Model
iii
iii
xc
xc
iij
e
ecxyP
1
),,|1(
Dependent Variable: DEF
Method: ML - Binary Logit (Quadratic hill climbing)
Sample: 1 35512
Included observations: 35512
Convergence achieved after 9 iterations
Covariance matrix computed using second derivatives
Variable Coefficient Std. Error z-Statistic Prob.
TMPS -0.258722 0.029835 -8.671706 0.0000
TN12AT -2.360039 0.209011 -11.29144 0.0000
TRC 0.003279 0.000454 7.227984 0.0000
C -4.290552 0.124839 -34.36864 0.0000
Mean dependent var 0.013038 S.D. dependent var 0.113438
S.E. of regression 0.112832 Akaike info criterion 0.127369
Sum squared resid 452.0579 Schwarz criterion 0.128324
Log likelihood -2257.559 Hannan-Quinn criter. 0.127673
Restr. log likelihood -2469.342 Avg. log likelihood -0.063572
LR statistic (3 df) 423.5659 McFadden R-squared 0.085765
Probability(LR stat) 0.000000
Obs with Dep=0 35049 Total obs 35512
Obs with Dep=1 463
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Aroc=76.54%
0.72 0.73 0.74 0.75 0.76 0.77 0.78 0.79 0.8 0.810
20
40
60
80
100
120
140indice roc
AUROC value after 1000 bootstrap iterations
Roc curve of the model
Logit Model Statistics
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10
500
1000
1500
2000
2500PD estimat
Estimated Default Probabilities
5.31%
17.52%
29.21%
18.01%
14.55% 14.28%
1.12%
0%
5%
10%
15%
20%
25%
30%
35%
c1 c2 c3 c4 c5 c6 c7
Rating Scale
Distribution among debtors
Securitized exposures according to rating classes
0.000
0.100
0.200
0.300
0.400
0.500
0.600
0.700
0.800
0.900
1.000
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08
PD
Lei M
il.
The Holding of Securitizations
•junior securitizations
0 500 1000 1500 2000 2500 3000 3500 4000 45000
1
2
3
4
5
6
7
8
9x 10
9
a1
a2
a3
0 500 1000 1500 2000 2500 3000 3500 4000 45000
1
2
3
4
5
6
7
8x 10
10
x1
x2
x3
•senior securitizations
(1) sxxx nnn 321 , where sx ni ,0 , 3,1i , Nn and s represents a number of
percents of the entire issue. 100,0s
(2) jaaa nnn 321 , where ja ni ,...,2,1,0 , 3,1i , j represents the number of
percents of the entire issue. 100,0j , and 100 js
The initial shock in the system is generated by a random number of defaults in the securitized portfolio. The value of the absolute loss is generated by adding up exposures, in a descending default probability manner, until the total defaulted number is equal to that of the random number. The effect of the absolute loss on the value of the securitizations is:
0,100
max3
1
3
1
' La
aV
j
a
aa
ii
i
ii
ii
100,)
100(
100
100,
3
1
3
1
' jVL
x
xjVLV
s
x
x
jVLx
x
ii
i
ii
i
i
i
Where a’i and x’
i represent the value of the junior and senior securitizations after the loss, V is the portfolio value, L is the level of loss, s and j are those discussed above.
The Value of Securitizations after Inflicted Loss
0
10
20
30
0
10
20
30
0
0.2
0.4
0.6
0.8
Banca
X: 30Y: 23Z: 0.1717
X: 15Y: 6Z: 0.1728
X: 8Y: 6Z: 0.5183
X: 9Y: 23Z: 0.4121
X: 5Y: 23Z: 0.6868
Banca
The matrix of inter-bank exposures highlights the inter-bank assets of each credit institution to the other (n-1) banks in the system (left picture). The weight of inter-bank exposures compared to own funds show there are only a few banks that could default due to the loss of all their inter-bank exposures (right picture).
Inter-bank Linkages
0
10
20
30
0
10
20
30
0
1
2
3
4
5
6
x 104
•Inter-bank linkages determine an incomplete structure (according to Allen&Gale (2000))
•only 4 banks are exposed to insolvency if they lost all of their inter-bank exposures
If the inter-bank matrix is:
Then, the propagation of loss takes place the following way:
nnnjn
iniji
nj
IB
xxx
xxx
xxx
M
1
1
1111
, where xij is the gross exposure of bank “i” to bank „j”.
pn
x
p
x
p
x
p
x
p
x
p
x
p
x
p
x
p
x
MRP
nn
j
njn
n
in
j
iji
n
n
j
j
IB
1
1
1
1
11
1
11 , where xij has the same meaning as above and pj represents inter-bank liabilities of bank “j”.
Insolvency occurs whenever the insolvency indicator (IS) drops under 2%. When a bank defaults, it is removed from the matrix and analyses are continued the next round. Then IS is calculated for the remaining non-defaulted banks in the system.
Inter-bank Linkages
Results
0 500 1000 1500 2000 2500 3000 3500 4000 45000.5
1
1.5
2
2.5
3
s1
s1 minims1 maxim
s1 mediu
0 500 1000 1500 2000 2500 3000 3500 4000 45000.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.1
sever1
sever1 minimsever1 maxim
sever1 mediu
Average number of investor-banks that default in the first round (s1)
Average share of the system assets that default in the first round (atd)
Average number of banks that default by contagion in the following rounds (m1)
0 500 1000 1500 2000 2500 3000 3500 4000 45000
2
4
6
8
10
12
14x 10
-3
sever11
sever11 minimsever11 maxim
sever11 mediu
Average share of the system assets that default by contagion in the following rounds (sever1)
0 500 1000 1500 2000 2500 3000 3500 4000 45000
0.01
0.02
0.03
0.04
m11
m11 minimm11 maxim
m11 mediu
Indicator Average Median Standard Deviation
s1 2,623 2,906 0,467
atd 6,599% 6,773% 0,013
m1 0,005 0,001 0,011
sever1 0,026% 0,000% 0,001
0
10
20
30
0
10
20
30
0
0.5
1
1.5
2
2.5
X: 24Y: 6
Z: 0.6911
Banca
X: 30Y: 32Z: 0.4365
X: 8Y: 6Z: 1.037
X: 5Y: 17Z: 2.353
X: 5Y: 23Z: 1.538
Banca
Results
Inter-bank exposures are multiplied by 2
0 500 1000 1500 2000 2500 3000 3500 4000 45000
2
4
6
8
10
12x 10
-3
sever11
sever11 minimsever11 maxim
sever11 mediu
Average number of banks that default by contagion in the following rounds (m1)
Average share of the system assets that default by contagion in the following rounds (sever1)
Only in some cases does the amount of inter-bank exposures exceed the credit institution’s level of own funds. The labeled values mark these institutions at risk.
0 500 1000 1500 2000 2500 3000 3500 4000 45000
0.02
0.04
0.06
0.08
0.1
0.12
m11
m11 minimm11 maxim
m11 mediu
Indicator Average Median Standard Deviation
s1 2,623 2,906 0,4671
atd 6,60% 6,77% 0,0131
m1 0,018 0,005 0,024
sever1 0,048% 0,006% 0,0011
Inter-bank exposures are multiplied by 3
Average number of banks that default by contagion in the following rounds (m1)
Average share of the system assets that default by contagion in the following rounds (sever1)
There are more situations where the amount of interbank exposures exceed the credit institution’s level of own funds in this case. The labeled values mark these institutions at risk.
0 500 1000 1500 2000 2500 3000 3500 4000 45000
1
2
3
4
5
6
7
8
9x 10
-3
sever11
sever11 minimsever11 maxim
sever11 mediu
0
10
20
30
0
10
20
30
0
1
2
3
4
X: 24Y: 6Z: 1.037
Banca
X: 30Y: 32Z: 0.6547
X: 8Y: 6Z: 1.555
X: 8Y: 10Z: 1.086
X: 19Y: 32Z: 0.3273
X: 5Y: 17Z: 3.53
X: 5Y: 23Z: 2.308
Banca
0 500 1000 1500 2000 2500 3000 3500 4000 45000.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
m11
m11 minimm11 maxim
m11 mediu
Indicator Average Median Standard Deviation
s1 2,623 2,906 0,4671
atd 6,60% 6,77% 0,0131
m1 0,075 0,058 0,0348
sever1 0,082% 0,038% 0,0011
Results
Results
We assume that three credit institutions default simultaneously. This would mean that automatically all their loans on the inter-bank market will be considered losses to other banks. This is the maximum effect that can take place on the inter-bank market.
Inter-bank exposures are not multiplied
Inter-bank exposures are multiplied by 2
Inter-bank exposures are multiplied by 3
Indicator Maxim Value Average Standard Deviation
No. of defaulted institutions 2.000 0.117 0.3844% Defaulted Assets 0.007 0.000 0.001143
Indicator Maxim Value Average Standard Deviation
No. of defaulted institutions 5.000 0.394 0.817% Defaulted Assets 0.026 0.001 0.003
Indicator Maxim Value Average Standard Deviation
No. of defaulted institutions 6.000 1.071 1.297% Defaulted Assets 0.028 0.004 0.005
Conclusions
• credit risk transfer does not have major implications on the financial
stability, given that the credit institutions are capitalized.
• the inter-bank market is characterized by both a low degree of
connectivity (10.43%) and a low level of exposure amounts, issues that
will significantly reduce contagion risk, given that investors will default as
the result of very poor quality of the purchased securitizations. Generally,
the banks that are affected by contagion are the small ones and even so
the average number of banks that default is 0.005. The average
defaulted assets due to contagion is around 0.026% and the maximum
number of contagion rounds is 2.
Bibliography
• Baur, D., E. Joossens (2005), "The effect of credit risk transfer on financial stability", European
Commission, Joint Research Centre, Ispra (VA), Italy
• Davis, M.H.A, Lo, V. (2001) "Infectious defaults", Quantitative Finance, 1 (4). pp. 382-387
• De Bandt, O., P. Hartmann (2000), "Systemic Risk: A Survey", European Central Bank Working
Paper Series, Working Paper No. 35
• Furfine, C H (2003): "Interbank Exposures: Quantifying the Risk of Contagion", Journal of
Money,Credit and Banking, vol 35, pp 111-28.
• Hartmann, P., S. Straetmans, C. de Vries (2007), "Banking System Stability a Cross-Atlantic
Perspective", in "Risk Measurement and Systemic Risk"
• Upper, C., A. Worms (2002), "Estimating Bilateral Exposures in the German Interbank Market:
Is there a Danger of Contagion?", Discussion Paper no. 9, Economic Research Center of the
Deutsche Bundesbank
Thank you for your attention!