Financial Stability Measures
Miguel Segoviano* and Raphael Espinoza
msegoviano@cnbv.gob.mx
RE i
REspinoza@imf.org
@i f
Financial Markets Group - Bank of England Conference
London-January 25, 2011
*O temporall leave
*On
l
f
from
the
h IMF.
IMF The
Th views
i
expressed
d iin this
hi presentation
i are those
h
off the
h author
h and
dd
do
not necessarily represent those of the IMF, CNBV or IMF,CNBV policy. Any errors remain attributable to the
authors.
Outline
I. Objective.
II. Main points of Modelling Framework.
III. Financial Stability and Systemic Risk Assessment:
Distress Dependence Amongst FIs.
Financial Stability Indicators
Financial Stability Indicators.
Systemic Macro‐Financial ST.
Second‐round effects
IV. Financial Stability and Sovereign Risk.
Spillover Coefficient.
Index of Global Risk Aversion.
Fundamentals.
V. Conclusions.
2
Modeling Framework
We assume that the financial system is a portfolio of FIs.
Macroeconomic
Risk Factors
Financial Risk Factors
Commercial Banking
PoD
Pension Funds
PoD
Mutual Funds
POD
Develpmt Bking Insurance Cos
PoD
POD
Brokers
PoD
Others
Financial System´s
Multivariate Density
EAD
LGD
0 . 2
0 . 1 5
0 . 1
0 . 0 5
0
4
2
4
2
0
Systemic
Loss Simulation
0
-2
-2
-4
-4
Systemic Stress
Indicators
Contagion
Indicators
Systemic Loss
Indicators
Sovereign Risk
Assessment
3
Objective
Framework to estimate consistently:
•
Complementary financial stability indicators.
•
Q
Quantification of expected and extreme losses at the systemic level.
ifi i
f
d d
l
h
i l l
•
Quantification of the marginal contribution to systemic risk of Quantification
of the marginal contribution to systemic risk of
individual institutions.
•
Assessment of the underlying factors causing sovereign risk to spread.
•
Stress Testing
Stress Testing.
4
Main Points
• It is a comprehensive coverage: The methodology allows for the inclusion of banking and non‐banking financial institutions (FIs)/sectors.
• It captures contagion effects: It takes into account interlinkages (direct and indirect) amongst Fis.
• It captures changes across the economic cycle of distress dependence amongst FIs and sovereigns.
dependence amongst FIs and sovereigns.
• It integrates complementary information: It uses micro‐
f
founded supervisory data and market‐based information.
d d
i
d t
d
k t b di f
ti
• It
It incorporates a wide set of factors: It accounts for a wide incorporates a wide set of factors: It accounts for a wide
set of macroeconomic and financial risk factors.
5
Main Points
• It
It provides robust estimations: It benefits from robust provides robust estimations: It benefits from robust
estimation with restricted data (under the PIT criterion).
• It can be extended to capture second round effects: It allows to take into account second‐round effects and macro‐
financial linkages.
financial linkages.
• It is being extended to different applications with national authorities around the world.
h ii
d h
ld
6
Implementation Map
IMF
ECB
USA , Canada / FSAP
Egypt FSAP
South Africa
FSAP
Denmark FSAP
Bank of Lithuania /
FSAP
Banque de France
Norges Bank
Banca d’Italia
CNBV México
Bank of Japan
Bank of Jordan
Deutshe Bundesbank
Sveriges Riksbank
Central Bank of UAE
Bank of Malaysia
7
Distress Dependence
Segoviano and Goodhart (2009)
Distress dependence between institutions is incorporated via joint Distress
dependence between institutions is incorporated via joint
movements of their PoDs, which in turn move in tandem due to
Systemic shocks
h k
Indirect Links
Lending to common sectors
Proprietary Trades
Direct Links
InterI t -Bank
Inter
B kD
Deposit
it M
Markets
k t
Syndicated Loans
The recent crisis underlined that proper estimation of distress dependence amongst FIs in a financial system is essential for financial stability FI i fi
i l
i
i l f fi
i l bili
assessment.
Contagion through
Idi
Idiosyncratic
i Shocks
Sh k
G dh
Goodhart, Sunirand, Tsomocos (2004).
S i d T
(2004)
8
The CIMDO Methodology
•
•
•
Problem: ‘how to estimate P(A,B) if we have P(A) and P(B)?’
( )
( )
( )
We can assume a known parametric distribution (e.g. multivariate normal), and estimate/calibrate parameters using data on A and B, but it seldom fits the data…
…or, we can try to “match” the data with a non‐parametric distribution ‐‐> CIMDO.
Advantages:
•
Robust: Without imposing unrealistic parametric assumptions.
•
It can be estimated from partial information: From PoDs on marginals, without the need to explicitly
to
explicitly set correlation structures.
set correlation structures
•
It characterizes the full “distributional dependence”: Rather than just linear dependence (correlations) or relations in the first few moments.
•
It embeds effects of changing macroeconomic conditions/shocks (via PoDs): It allows measurement of changes in dependence after shocks.
Source: Segoviano (2006)
9
CIMDO‐Density
Empirical
I f
Information
ti
10
CIMDO‐Copula
Lett X and
L
d Y be
b two
t
random
d
variables
i bl with
ith continuous
ti
di t ib ti functions
distribution
f
ti
F and
d H respecitvely,
it l
then the Spearman Correlation of X and Y is defined and denoted by the following:
S ( X , Y )   ( F ( X ), H (Y ))  12  [C (u , v)  uv]dudv  12  C (u, v)  3
2
I2
I
Where I  [0,1]x[0,1] and ρ(F(X),H(Y)) is the Pearson Correlation of the transformed uniform
random variables F(X) and G(Y).
2
11
Complementary Indicators
SYSTEMIC INDICATORS
MICRO-BASED INDICATORS
Market-based
Information
Supervisory
Information
Supervisory
Information
Market-based
Information
M to M Assets
PD Credit
Card
PD
ConsCre
PD
Housing
Ho
sing
PD
Commercial
Systemic Stress Indicators
PoD
Banks
SI
PoD
Banks
MI
Joint
Probability
of Distress
Financial
Stability
Index
PD
Governmental
C t i Indicators
Contagion
I di t
PD
Financial
PoD
Developt
B k
Banks
PoD
Pension
Funds
PoD
Mutual
Funds
PoD
Insurance
C
Co
PoD
Brokers
Distress
Dependence
Matrix
Contagion
Index
Spillover
Coefficient
Systemic Loss Indicators
Extreme
Systemic
Loss
Marginal
Contribution
to Systemic
Risk
Sovereign
Risk
A
Assessment
t
Cascade
Effects
Probability
PoD from Supervisory Information
PLD Baseline Scenario
PLD Stressed Scenario
St
Stressed
dV
VaR
R
Expected Loss
Unexpected Loss
PLD Baseline Scenario
PLD Stressed Scenario
Stressed PoD
PoD
Benchmark
13
Systemic Stress Indicators: U.S. Financial Stability Index: Expected number of FIs in distress given that p
g
at least one became distressed (left scale).
Joint Probability of Distress (JPoD):
Likelihood of common distress of all the FIs in the system (right scale).
3.5
3.0
0.025
1.
2.
3.
4.
Bear Stearns episode (3/11/08)
Lehman Bankruptcy
p y and AIG bailout (9/15-16/08)
(
)
TARP I bill failure (9/30/08)
Global central bank intervention (10/8/08)
1
2 34
0.020
2.5
2.0
Bank Stability Index
(Number of banks, left scale)
0.015
1.5
0 010
0.010
1.0
JPoD
(Probability of default %, right scale)
0.005
0.5
0.0
Jan 07
Jan-07
0.000
May 07
May-07
Sep 07
Sep-07
Jan 08
Jan-08
May 08
May-08
Sep 08
Sep-08
14
Systemic Stress Indicators: Mexico
Financial Stability Index: Expected number of FIs in distress given that
Expected number of FIs in distress given that at least one became distressed (left scale).
Joint Probability of Distress (JPoD):
Likelihood of common distress of all the FIs in the system (right scale).
JPOD-FSI: México
FSI
BSI
4
35
3.5
3
2.5
2
1.5
1
0.5
0
1. Lehman spillover, derivatives’ market
crisis and mutual funds
funds’ crisis (Oct2008).
2. H1N1 crisis (March-April-2009).
JPOD
JPOD
0.002
1
2
0.0018
0.0016
0.0014
0.0012
0.001
0.0008
0.0006
0.0004
0.0002
0
15
Systemic Stress Indicators
They incorporate changes in distress‐dependence that are consistent with They
incorporate changes in distress dependence that are consistent with
the economic cycle.
30
3.0
Joint probability of distress
2.5
Average probability of distress
20
2.0
1.5
1.0
0.5
0.0
-0.5
-1.0
J
Jan-07
07
M
May-07
07
S
Sep-07
07
J
Jan-08
08
M
May-08
08
S
Sep-08
08
16
Contagion Indicators: DiDe U.S.
Distress Dependence Matrix: Probability that FI (row) falls in distress given that FI (column) falls in distress.
July 1 2007 September 12, 2008
July 1, 2007‐
September 12 2008
July 1, 2007
Citi
BAC
JPM
Wacho
WAMU
GS
LEH
MER
MS
AIG
Citigroup
Bank of America
JPMorgan
Wachovia
Washington Mutual
Goldman Sachs
Lehman
Merrill Lynch
y
Morgan Stanley
AIG
Column average
1.00
0.12
0 15
0.15
0.12
0.16
0.17
0.22
0.19
0.19
0.07
0.24
0.14
1.00
0 42
0.42
0.33
0.28
0.25
0.32
0.32
0.31
0.14
0.35
0.11
0.27
1 00
1.00
0.24
0.21
0.28
0.32
0.33
0.28
0.10
0.31
0.11
0.27
0 31
0.31
1.00
0.23
0.21
0.26
0.25
0.24
0.10
0.30
0.08
0.11
0 13
0.13
0.11
1.00
0.11
0.15
0.17
0.14
0.05
0.21
0.09
0.11
0 19
0.19
0.12
0.12
1.00
0.43
0.33
0.35
0.07
0.28
0.08
0.10
0 16
0.16
0.10
0.12
0.31
1.00
0.31
0.28
0.06
0.25
0.09
0.12
0 19
0.19
0.12
0.16
0.28
0.35
1.00
0.30
0.07
0.27
0.09
0.12
0 18
0.18
0.12
0.13
0.31
0.33
0.31
1.00
0.06
0.26
0.08
0.15
0 17
0.17
0.14
0.15
0.17
0.20
0.20
0.16
1.00
0.24
September 12, 2008
Citi
BAC
JPM
Wacho
WAMU
GS
LEH
MER
MS
AIG
Citigroup
Bank of America
JPMorgan
W h i
Wachovia
Washington Mutual
Goldman Sachs
Lehman
Merrill Lynch
Morgan Stanley
AIG
Column average
1.00
0.14
0.13
0 34
0.34
0.93
0.15
0.47
0.32
0 21
0.21
0.50
0.42
0.20
1.00
0.29
0 60
0.60
0.97
0.19
0.53
0.41
0 28
0.28
0.66
0.51
0.19
0.31
1.00
0 55
0.55
0.95
0.24
0.58
0.47
0 29
0.29
0.59
0.52
0.14
0.18
0.16
1 00
1.00
0.94
0.13
0.43
0.30
0 19
0.19
0.53
0.40
0.07
0.05
0.05
0 17
0.17
1.00
0.06
0.25
0.16
0 09
0.09
0.29
0.22
0.17
0.16
0.19
0 36
0.36
0.91
1.00
0.75
0.53
0 40
0.40
0.54
0.50
0.13
0.10
0.11
0 27
0.27
0.88
0.18
1.00
0.37
0 22
0.22
0.43
0.37
0.14
0.13
0.14
0 31
0.31
0.92
0.20
0.59
1.00
0 27
0.27
0.49
0.42
0.16
0.15
0.16
0 34
0.34
0.91
0.27
0.62
0.48
1 00
1.00
0.47
0.46
0.11
0.11
0.09
0 29
0.29
0.89
0.11
0.37
0.26
0 14
0.14
1.00
0.34
Row
average
0.19
0.24
0 29
0.29
0.24
0.26
0.31
0.36
0.34
0.33
0.17
0.27
Row
average
0.23
0.23
0.23
0 42
0.42
0.93
0.25
0.56
0.43
0 31
0.31
0.55
0.41
17
Contagion Indicators: DiDe Mexico
Distress Dependence Matrix: Probability that FI (row) falls in distress given that FI (column) falls in distress.
July 1, 2007‐ October 22, 2008
01/01/07
Banamex
BBVA
Santander
Banorte
HSBC
Inbursa
Scotiabank
ING
Bajío
Interacciones
IXE
Azteca
Prom
Columna
22/10/08
Banamex
BBVA
Bancomer
Santander
Banorte
HSBC
Inbursa
Scotiabank
Inverlat
ING
Bajío
Interacciones
IXE
Azteca
Prom
Columna
Banamex
BBVA
Santander
Banorte
HSBC
Inbursa
Scotiabank
ING
Bajío
Interacciones
IXE
Azteca
Prom
Renglón
1.00
0.25
0.25
0.24
0 27
0.27
0.18
0.31
0.25
0.31
0.11
0.11
0.19
0.26
1.00
0.72
0.29
0 42
0.42
0.15
0.25
0.47
0.42
0.11
0.12
0.19
0.25
0.69
1.00
0.29
0 41
0.41
0.16
0.25
0.44
0.41
0.11
0.11
0.19
0.24
0.28
0.29
1.00
0 27
0.27
0.18
0.23
0.28
0.31
0.11
0.11
0.18
0.27
0.40
0.41
0.26
1 00
1.00
0.15
0.25
0.37
0.61
0.11
0.11
0.18
0.18
0.14
0.16
0.17
0 15
0.15
1.00
0.16
0.15
0.22
0.11
0.10
0.22
0.32
0.24
0.25
0.22
0 26
0.26
0.17
1.00
0.23
0.29
0.11
0.12
0.17
0.25
0.45
0.44
0.27
0 36
0.36
0.15
0.23
1.00
0.36
0.11
0.11
0.18
0.30
0.39
0.40
0.30
0 60
0.60
0.22
0.28
0.36
1.00
0.10
0.11
0.43
0.11
0.11
0.11
0.10
0 11
0.11
0.12
0.11
0.11
0.11
1.00
0.11
0.10
0.11
0.11
0.11
0.11
0 11
0.11
0.11
0.12
0.11
0.11
0.11
1.00
0.11
0.19
0.18
0.19
0.18
0 18
0.18
0.23
0.17
0.18
0.43
0.10
0.11
1.00
0.29
0.35
0.36
0.29
0 35
0.35
0.23
0.28
0.33
0.38
0.18
0.18
0.26
0.29
0.37
0.36
0.29
0.34
0.23
0.28
0.33
0.38
0.18
0.18
0.26
0.29
Banamex
BBVA
Bancomer
Santander
Banorte
HSBC
Inbursa
Scotiabank
Inverlat
ING
Bajío
Interacciones
IXE
Azteca
Prom
Renglón
1.00
0.49
0.48
0.46
0.49
0.39
0.54
0.47
0.53
0.29
0.29
0.40
0.49
0.46
0.47
0.47
0.50
0.38
1.00
0.83
0.52
0.63
0.35
0.79
1.00
0.52
0.62
0.35
0.48
0.50
1.00
0.49
0.37
0.58
0.60
0.49
1.00
0.34
0.34
0.36
0.39
0.36
1.00
0.46
0.48
0.46
0.49
0.37
0.62
0.62
0.50
0.58
0.35
0.59
0.61
0.53
0.75
0.42
0.27
0.29
0.28
0.29
0.28
0.28
0.29
0.30
0.29
0.27
0.37
0.39
0.40
0.39
0.42
0.52
0.54
0.49
0.53
0.41
0.50
0.48
0.52
0.29
0.25
0.41
0.45
0.67
0.61
0.30
0.26
0.40
0.45
0.64
0.60
0.30
0.26
0.40
0.42
0.50
0.51
0.28
0.25
0.39
0.45
0.57
0.72
0.29
0.25
0.39
0.35
0.36
0.43
0.29
0.24
0.44
1.00
0.46
0.51
0.29
0.26
0.39
0.42
1.00
0.56
0.29
0.25
0.39
0.48
0.58
1.00
0.29
0.26
0.61
0.27
0.29
0.28
1.00
0.24
0.26
0.28
0.29
0.29
0.28
1.00
0.29
0.36
0.39
0.59
0.26
0.25
1.00
0.45
0.52
0.55
0.35
0.31
0.45
0.48
0.54
0.53
0.47
0.52
0.41
0.48
0.50
0.55
0.34
0.35
0.44
0.47
18
DiDe: Mexico
DiDe: México- IFs Españolas
MEXICO-BBVA
MEXICO-SANTANDER
Probabilida
ad
1
0.8
0.6
0.4
0.2
0
Jun-2007
Oct-2007
Feb-2008
Jun-2008
Oct-2008
Feb-2009
Jun-2009
Oct-2009
Feb-2010
Jun-201
DiDe: IF´s Españolas-México
Probabilidad
d
BBVA-MEXICO
SANTANDER-MEXICO
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
Jun-2007
Oct-2007
Feb-2008
Jun-2008
Oct-2008
Feb-2009
Jun-2009
Oct-2009
Feb-2010
Jun-201
Contagion Indicators: Spillover Coefficient
Spillover Coefficient (SC): Vulnerability of a country/FI given distress in other countries/Fis.
P(A)
P(B)
P(C)
CIMDO
Methodolog
y
 P( A / A) P( A / B ) P( A / C ) 


 P( B / A) P( B / B ) P( B / C ) 


 P(C / A) P(C / B) P(C / C ) 
P(A,B,C)  JPoD
P(A B); P(A,C);
P(A,B);
P(A C); P(B,C)
P(B C)
Bayes’
Bayes
Law
For e.g. country (A)/FI(A):
SC(A)=P(A/B)*P(B) + P(A/C)*P(C)
20
Contagion Indicators: SC Europe
Spillover Coefficient: European
p
p
Region
g
0.35
0.3
0.25
0.2
GER
GRE
0.15
IRE
SWE
0.1
0.05
0
03/01/05
03/01/06
03/01/07
03/01/08
03/01/09
03/01/10
21
Contagion Indicators: Contagion Index
Contagion Index (CI): Toxicity of the distress of a country/FI on other countries/FIs.
P(A)
P(B)
P(C)
CIMDO
Methodolog
y
 P( A / A) P( A / B ) P( A / C ) 


 P( B / A) P( B / B ) P( B / C ) 


 P(C / A) P(C / B) P(C / C ) 
P(A,B,C)  JPoD
P(A B); P(A,C);
P(A,B);
P(A C); P(B,C)
P(B C)
Bayes’
Bayes
Law
For e.g. country (A)/FI(A):
CI(A)=P(A)+P(B/A)*P(A) + P(C/A)*P(A)
22
Contagion Indicators: Probability of Cascade Effects
Probability of Cascade Effects (PCE): Probability that at least one FI becomes distressed given that a given FI becomes distressed.
PCE Lehman/AIG (September 12).
100
90
Lehman
AIG
80
70
60
50
40
30
20
10
9/1/2008
8
8/1/2008
8
7/1/2008
8
6/1/2008
8
5/1/2008
8
4/1/2008
8
3/1/2008
8
2/1/2008
8
1/1/2008
8
12/1/2007
7
11/1/2007
7
10/1/2007
7
9/1/2007
7
8/1/2007
7
7/1/2007
7
6/1/2007
7
5/1/2007
7
4/1/2007
7
3/1/2007
7
2/1/2007
7
1/1/2007
7
0
23
Output: Cross-region Spillovers
1.00
0.90
0.80
0.70
0.60
0.50
0 40
0.40
0.30
0.20
0.10
0.00
C it i-M exico
C it i-Lat
C it i-EE
i EE
5/
20
09
09
7/
9/
2/
2/
20
09
09
20
20
2/
2/
20
3/
11
1/
/2
2/
/2
00
8
09
08
08
20
20
2/
9/
7/
3/
2/
08
08
20
2/
2/
20
20
2/
1/
11
5/
7
08
07
00
/2
/2
07
20
2/
20
2/
7/
5/
9/
07
20
2/
20
20
2/
2/
3/
1/
07
C it i-A sia
07
Prob ab ility
Probability of dis tre s s of C itigrou p con dition al on dis tre s s of an oth e r e n tity
Probability of dis tre s s of an e n tity con dition al on dis tre s s of C itigrou p
0.60
Prob ab ility
0.50
0 40
0.40
B A C -C it i
0.30
U B S-C it i
0.20
D B -C it i
0.10
09
20
09
3/
9/
5/
7/
3/
3/
20
09
20
09
09
20
3/
1/
3/
3/
20
00
8
08
/2
11
9/
/3
3/
20
08
20
08
5/
7/
3/
3/
20
08
20
3/
20
3/
3/
11
1/
/3
/2
00
7
08
07
07
20
9/
7/
5/
3/
3/
20
07
07
20
3/
20
3/
1/
3/
3/
20
07
0.00
1.00
0.90
0.80
0.70
0.60
0.50
0.40
0.30
0.20
0.10
0 00
0.00
C it igroup
U BS
DB
09
3/
20
3/
20
09
9/
09
20
3/
5/
7/
09
09
20
3/
3/
20
8
00
/2
3/
1/
/3
11
9/
3/
20
08
08
08
20
3/
7/
5/
3/
20
08
3/
3/
20
08
00
1/
3/
20
7
07
11
/3
/2
07
20
3/
9/
20
3/
7/
20
3/
5/
20
3/
3/
07
07
BA C
07
20
3/
1/
Prob ab ility
C as cade Effe cts
24
Systemic Loss Indicators
Commercial Banking
PoD
Pension Funds
PoD
Mutual Funds
POD
Develpmt Bking Insurance Cos
PoD
POD
Brokers
PoD
Others
Financial System´s
Multivariate Density
EAD
LGD
Systemic
L
Loss
Si
Simulation
l ti
0 . 2
0 . 1 5
0 . 1
0 . 0 5
0
4
2
4
2
0
0
-2
-2
-4
Systemic Loss
Indicators
MCSR
-4
Systemic Stress
Indicators
Contagion
Indicators
Sovereign Risk
Indicators
25
Systemic Loss Indicators
E
Extreme Systemic Loss
S
i L
PLD
Independent IFs
PLD
Stressed PoDs
Independent IFs
PLD
Stressed PoDs
Stressed Distress Dependence
Expected Loss
Unexpected Loss
25-45%
26
14.0%
10.0%
1999Q2
2000Q1
2000Q4
2001Q3
2002Q2
2003Q1
2003Q4
2004Q3
2005Q2
2006Q1
2006Q4
2007Q3
2008Q2
2009Q1
2009Q4
2010Q3
2011Q2
2012Q1
2012Q4
2013Q3
2014Q2
2015Q1
2015Q4
Forecasted PoD Under Assumed
Macroeconomic Scenarios
Baseline
12.0%
Min
Mean
Max
8.0%
6.0%
4.0%
2.0%
0.0%
Risk-Neutral and Subjective PoD
0.045
0.040
0.035
Comparing Risk‐Neutral Default Probability and Adjusted Real‐world Probability
0.030
0.025
0.020
RN‐Median
0.015
Real‐Median
0.010
0.005
0.000
•
For loss estimation purposes, we convert risk neutral CDS-PoDs to subjective PoDs.
((Espinoza
p
and Segoviano,
g
, 2011).
)
Systemic Expected Losses
B li
Baseline
•
•
2007
2008
2009
2010
2011
2012
2013
$000
% Assets
27,144,218
0.22
123,251,952
0.96
58,981,703
0.45
109,916,227
0.84
77 632 877
77,632,877
0 59
0.59
33,721,172
0.26
22,758,454
0.17
T t l
Total
453 406 602
453,406,602
3 50
3.50
Ad
Adverse
% GDP
0.19
0.85
0.42
0.77
0 53
0.53
0.22
0.15
3 14
3.14
$000
% Assets
27,144,218
0.22
123,251,952
0.96
60,233,379
0.46
127,844,040
0.98
83 131 248
83,131,248
0 64
0.64
77,552,119
0.59
59,380,397
0.45
558 537 354
558,537,354
4 31
4.31
% GDP
0.19
0.85
0.43
0.90
0 57
0.57
0.52
0.39
3 84
3.84
Potential Losses the system
y
could incur.
Through-time pattern of losses is highly consistent with assumed
macroeconomic scenarios.
Systemic Unexpected Losses
2007
2008
2009
2010
2011
2012
2013
Bas eline
Advers e
VaR 99%
VaR 99%
$000
% As s ets
162 523 198
162,523,198
1.33
1
33
356,360,895
2.78
238,209,910
1.82
334,112,073
2.56
270 050 643
270,050,643
2 07
2.07
180,355,988
1.38
148,846,513
1.14
% GDP
1 15
1.15
2.47
1.70
2.34
1 84
1.84
1.20
0.97
$000
% As s ets
162 523 198
162,523,198
1.33
1
33
356,360,895
2.78
245,110,532
1.87
368,703,692
2.82
295 548 717
295,548,717
2 26
2.26
278,878,012
2.13
242,699,313
1.86
% GDP
1 15
1.15
2.47
1.74
2.59
2 02
2.02
1.85
1.57
1,690,459,220
13.07
11.67
1,949,824,359
15.06
13.40
Memo item
2009 total equity 1,022,994,436
7.82
7.28
1,022,994,436
7.82
7.28
Total
•
Extreme Losses that the system could incur with 1 percent probability.
•
Cumulative extreme losses could be significant in both scenarios, especially
compared to 2009 capital levels.
Marginal Contribution to Systemic Risk
Marginal Contribution to Systemic Risk (MCSR): It takes into account of size and interconnectedness.
Commercial Banking
PoD
Pension Funds
PoD
Mutual Funds
POD
Develpmt Bking Insurance Cos
PoD
POD
Brokers
PoD
Others
Financial System´s
Multivariate Density
EAD
LGD
Systemic
L
Loss
Si
Simulation
l ti
0 . 2
0 . 1 5
0 . 1
0 . 0 5
0
4
2
4
2
0
0
-2
-2
-4
Syste c Loss
Systemic
oss
Indicators
Expected Shortfall
Shapley Value
-4
Systemic Stress
Indicators
Contagion
Indicators
Sovereign Risk
Indicators
MCSR
31
Shapley Value
•
Let F be a sub-group of members of the financial system containing the financial institution I, we define the “contribution of institution I to F” as
V(F)-V(F-{I}).
The Shapley Value of institution I could be viewed as the weighted average of the contributions of I over all the sub-groups of the
financial system containing institution I.
Let´s assume three financial institutions A, B , C
Sub‐Group
Loss
Contribution A to Sub‐group
Contribution B to Sub‐group
Contribution C to Sub‐group
A
B
C
A,B
A,C
B,C
A,B, C
Shapley Value
MCSR
1
3
5
3.5
5.5
7
8.5
1
None
None
0.5
0.5
None
1.5
1
0.12
None
3
None
2.5
None
2
3
2.75
0.32
None
None
5
None
4.5
4
5
4.75
0.56
Permutation
Sub‐Group of all instituions before A including A
Sub‐Group of all instituions before A including A
Calculation of Contribution of A
Calculation of Contribution of A
Contribution of A
Contribution of A ABC
ACB
BAC
CAB
BCA
CBA
A
A
B,A
C,A
B,C,A
C,B,A
Shapley Value of A
V(A) ‐ V(0) = 1‐0 = 1 V(A) ‐ V(0) = 1‐0 = 1 V(B,A) ‐V(B) = 3.5 ‐ 3 = 0.5
V(C,A) ‐ V( C) = 5.5 ‐5=0.5 V(C,B,A) ‐ V(C,B) = 8.5 ‐ 7 = 1.5
V(C,B,A) ‐ V(C,B) = 8.5 ‐ 7 = 1.5
Weighted Average
1
1
0.5
0.5
1.5
1.5
1
MCSR
0.12
•
Additivity. The sum of the shapley values of all the members of our financial system gives us the systemic risk of all the financial system.
•
Intuitive Indicator. The Shapley Value of a financial institution captures the systemic importance of it in only one number.
•
Flexibility. Can be applied to any measure of system-wide risk.
Marginal Contribution to Systemic Risk
Marginal Contribution to Systemic Risk:
g
y
It takes into account of size and interconnectedness.
0.4
0.016
0.35
0.014
0.3
0.012
0.25
0.01
0.2
0.008
0.15
0.006
0.1
0.004
0.05
0.002
MCSR
POD AIG
Spearman Corr AIG
Mar-09
Feb-09
Jan-09
Dec-08
Nov-08
Oct-08
Sep-08
Aug-08
Jul-08
Jun-08
May-08
Apr-08
Mar-08
Feb-08
Jan-08
0
Dec-07
0
Contagion Index AIG
Right Axis for CI
AIG Factors
Second-Round Effects
Macroeconomic
Factors
Comm Banks
PoD
Dvlpmt Banks
PoD
GSEs
PoD
Financial System’s
Returns
Pension Funds
PoD
Insurance
PoD
Mutual Funds
PoD
Financial System´s
Tail Risk (JPoD)
Macroeconomic
Factor
Comm Banks
PoD
Exposures
Financial
Factors
Dvlpmt Banks
PoD
LGDs
Systemic
Loss Simulation
Marginal Contribution
to Systemic Risk
GSEs
PoD
Financial
Factors
Pension Funds
PoD
Insurance
PoD
Mutual Funds
PoD
Financial System´s
y
Multivariate Density
Financial System’s
Loss Distribution
Financial Stability
Measures
34
Financial Stability Measures: Additional Applications
Additional Applications:
1.
Macro‐Financial stages over time.
2.
Spillovers between the banking and corporate sectors.
3.
Sovereign Risk Assessment (Caceres Guzzo Segoviano IMF WP 10/120)
(Caceres, Guzzo, Segoviano, IMF WP 10/120).
35
Financial Stability Over Time
•
Markov Switching VAR
Definition of alternative risk zones given specific values of JPoD
and
d other
th variables
i bl
0.002
MSIAH(2)-VAR(1), 1999 (7) - 2009 (3)
Jpodrev
dlhouse
0.000
-0.002
1.0
2000
2001
2002
Probabilities of Regime 1
filtered
predicted
2003
2004
2005
2006
2007
2008
2009
2003
2004
2005
2006
2007
2008
2009
2003
2004
2005
2006
2007
2008
2009
smoothed
0.5
1.0
2000
2001
2002
Probabilities of Regime 2
filtered
predicted
di d
smoothed
0.5
2000
•
•
2001
2002
Probability of being in different economic
actual/assumed ((in ST)) economic shocks.
Analysis of IRFs in different enconomic regimes
regimes
due
to
36
10/1/2009
7/1/2009
4/1/2009
1/1/2009
10/1/2008
7/1/2008
4/1/2008
1/1/2008
10/1/2007
7/1/2007
4/1/2007
1/1/2007
10/1/2006
7/1/2006
0.7
4/1/2006
1/1/2006
10/1/2005
7/1/2005
4/1/2005
1/1/2005
10/1//2009
7/1//2009
4/1//2009
1/1//2009
10/1//2008
7/1//2008
4/1//2008
1/1//2008
10/1//2007
7/1//2007
4/1//2007
1/1//2007
10/1//2006
7/1//2006
4/1//2006
1/1//2006
10/1//2005
7/1//2005
4/1//2005
1/1//2005
Spillovers Between Financial
and Corporate Sectors
0.08
PoD: Banks & Corporates
0.07
0.06
0.05
0.04
0.03
Average Bank
0.02
Average Corp
0.01
0.00
Distress Dependence: Banks & Corporates
0.6
0.5
0.4
0.3
Bank-Bank
02
0.2
Bank-Corp
Corp-Bank
Corp
Bank
0.1
Corp-Corp
0
37
Sovereign Risk Assessment: Four Phases
EUR Sovereign 10Y Swap Spreads
1,000
800
600
400
200
GER
FRA
ITA
SPA
NET
BEL
AUT
GRE
IRE
POR
Sovereign
Risk
Systemic
Response
p
Systemic
Outbreak
Financial Crisis Build‐Up
0
Jul‐22010
May‐22010
Mar‐22010
Jan‐22010
Nov‐22009
Sep‐22009
Jul‐22009
May‐22009
Mar‐22009
Jan‐22009
Nov‐22008
Sep‐22008
Jul‐22008
May‐22008
Mar‐22008
Jan‐22008
Nov‐22007
Sep‐22007
Jul‐22007
‐200
38
Some Existing Literature on Sovereign Spreads
• Models with Risk Aversion based on observable measures ( corporate –
(e.g
t Treasury spread):
T
d)
– Fiscal situation has temporary and limited impact on sovereign spreads (Afonso and Strauch, 2004).
spreads (Afonso
and Strauch, 2004).
– Short‐term interest rates are the main driver (Manganelli and Wolswijk, 2007) but international risk factors and liquidity premia
also matter (Bernoth et al., 2004).
– Sovereign spreads widen when the prospects of a domestic financial sector worsen (Mody 2009)
sector worsen (Mody, 2009).
Risk Aversion as a common factor:
Aversion as a common factor:
• Risk
– common factor using a Kalman filter (Geyer et al, 2004). y g
y
g
– Time‐varying common factor estimated with Bayesian filtering technique (Sgherri and Zoli, 2009).
39
Data and Construction of the Variables:
3 Types of ‘Measures’
• Measure of “contagion”: the Spillover Coefficient (SC). Segoviano and Goodhart, IMF WP 09/4.
g
• Measure of “risk aversion”: the Index of Risk Aversion (IRA).
f
( )
(Espinoza and Segoviano, IMF WP, forthcoming 2011).
• Country‐specific fiscal fundamentals:
– Overall Budget Balance (% of GDP).
Overall Budget Balance (% of GDP).
– Public Debt (% of GDP).
40
The Index of Risk Aversion (IRA)
Espinoza and Segoviano, IMF WP forthcoming, 2011.
• Global risk aversion proxies tend to be ‘over simplistic’ (e.g. US corporate bond spreads to Treasuries).
• Statistically sophisticated methods depend on the sample: global risk aversion is assigned to a common trend
g
or common factor
f
((i.e. ‘filtering’).
– common factors might be capturing ‘distress dependence’ as well as ‘risk aversion’

• O
Our IRA is the ‘factor’ linking risk‐neutral probabilities (extracted IRA i th ‘f t ’ li ki
ik
t l
b biliti  ( t t d
e.g. from CDS spreads) to the actual probabilities of nature . This 
factor is the market price of risk in situations of distress
p
– It does not depend on the sample used
41
The Index of Risk Aversion (IRA)
• The price of an asset reflects
– Market expectations of the asset´s returns – The price of risk: what investors are willing to pay for receiving income in distress states of nature. The linear (one factor) pricing and the risk‐neutral pricing formulae 
1
Pt  Et [mt 1 xt 1 ]    t 1 ( s )mt 1 ( s ) xt 1 ( s ) 
 t 1 ( s ) xt 1 ( s )
F 
1  rt s
s
t1(s)mt1(s)
where is the price of a security paying $1 in state s
and 
 t 1 ( s )  (1  rt F ) t 1 ( s )mt 1 ( s )
is the risk‐neutral probability that is given by CDS spreads
42
The Index of Risk Aversion (IRA)
• Market price of risk under distress:
Et mt 1 | distress  Et mt 1 | mt 1   
 ( t )
 Et mt 1   vart (mt 1 )
1   1[ t ]
where  t 
 t  Et (mt 1 )
vart (mt 1 )
(1)
(2)
• The threshold τ can be exogenous, or such that the probability that the market‐price of risk exceeds the threshold p
τ is equal to q
the actual probability of distress:
 t  Et (mt 1 )  1[1   t ] * var(mt 1 )
(3)
43
The Index of Risk Aversion (IRA)
• Market price of risk under distress:
mt

Et ( mt 1 | mt 1   ) 
Et (mt 1 )
 t 1
(1  rt F ) t 1

1[1   t ] * var(mt 1 )
44
The Index of Risk Aversion (IRA)
Et[mt+1 | mt+1 > τ]
3.2
3.0
2.6
2.8
2.4
2.2
2.0
1.8
45
Estimation: Methodology
• Simple GARCH(1,1) model to estimate sovereign swap (Yt) spreads as a function of: – its lag Yt‐1
– The Spillover Coefficient p
– Index of Risk aversion
Xt
– debt/GDP and fiscal balance
debt/GDP and fiscal balance
Yt  Yt 1   ' X t   t
 t2     t21   t21
• Estimated by Maximum Likelihood
46
Estimation: Main Results
GER
Mean equation:
Constant
Lag dep.variable
IRA
SC
Overall balance
Debt ratio
-0.122***
(0 025)
(0.025)
0.933***
(0.006)
-0.217***
(0 034)
(0.034)
0.083***
(0.026)
-0.002***
(0 001)
(0.001)
0.000
(0.000)
Variance
V
i
equation:
i
Constant
0.000***
(0.000)
ARCH term
0.381***
(0 034)
(0.034)
GARCH term
0.702***
(0.017)
R-squared
d
No. of observations
0.981
0
981
1,194
FRA
ITA
SPA
NET
-0.042**
(0 019)
(0.019)
0.971***
(0.005)
-0.202***
(0 032)
(0.032)
0.176***
(0.034)
-0.002***
(0 001)
(0.001)
0.001**
(0.000)
0.039
(0 030)
(0.030)
0.981***
(0.005)
-0.046
(0 038)
(0.038)
0.137***
(0.035)
-0.002***
(0 001)
(0.001)
0.001*
(0.000)
-0.140***
(0 013)
(0.013)
0.943***
(0.008)
-0.074***
(0 027)
(0.027)
0.268***
(0.037)
-0.000
(0 000)
(0.000)
0.002***
(0.000)
-0.077***
(0 015)
(0.015)
0.966***
(0.005)
-0.118***
(0 033)
(0.033)
0.154***
(0.030)
-0.000
(0 000)
(0.000)
0.000**
(0.000)
0.000***
(0.000)
0.095***
(0 007)
(0.007)
0.918***
(0.005)
0.000***
(0.000)
0.074***
(0 007)
(0.007)
0.933***
(0.005)
0.000*** 0.000***
(0.000)
(0.000)
0.283*** 0.089***
(0 023)
(0.023)
(0 009)
(0.009)
0.789*** 0.926***
(0.014)
(0.006)
0.984
0
984
1,194
0.993
0
993
1,194
0.992
0
992
1,194
0.986
0
986
1,194
47
Estimation: Main Results (2)
BEL
Mean equation:
Constant
GRE
IRE
POR
-0.028
(0 034)
(0.034)
0.962***
(0.006)
-0.098***
(0 032)
(0.032)
0.177***
(0.025)
-0.002***
(0.000)
0.000
(0.000)
-0.258***
(0 035)
(0.035)
0.956***
(0.006)
-0.052
(0 035)
(0.035)
0.579***
(0.073)
-0.001*
(0.000)
0.002***
(0.000)
-0.059*
(0 030)
(0.030)
1.008***
(0.004)
-0.053**
(0 024)
(0.024)
0.183***
(0.037)
0.002***
(0.000)
0.000
(0.000)
Variance equation:
Constant
0.000*** 0.000***
(0.000)
(0.000)
ARCH term
0 113*** 0.076
0.113
0 076***
(0.011)
(0.007)
GARCH term
0.913*** 0.935***
(0.008)
(0.005)
0.000***
(0.000)
0 066***
0.066
(0.005)
0.945***
(0.004)
0.000*** 0.000***
(0.000)
(0.000)
0 289*** 0.150
0.289
0 150***
(0.023)
(0.010)
0.800*** 0.885***
(0.011)
(0.005)
Lag dep. variable
IRA
SC
Overall balance
Debt ratio
-0.090***
(0 016)
(0.016)
0.953***
(0.007)
-0.097***
(0 032)
(0.032)
0.278***
(0.024)
-0.000
(0.001)
0.000*
(0.000)
AUT
R-squared
0.991
No. of observations 1,194
0.993
1,194
0.996
1,194
0.998
1,194
-0.018
(0 020)
(0.020)
0.950***
(0.007)
-0.316***
(0 035)
(0.035)
0.631***
(0.059)
0.000
(0.000)
-0.002***
(0.000)
0.993
1,194
48
Global Risk Aversion, Contagion or Fundamentals?
Contributions to 10-year Swap Spread
3.0
2.5
2.0
15
1.5
1.0
0.5
0.0
-0.5
-1.0
-1.5
20
-2.0
-2.5
Germany
Jul 07 Sep 08 Oct 08 Mar
09
Fundamentals
Contagion
Apr 09 Sep Oct 09 Feb 10
09
Global Risk Aversion
49
Global Risk Aversion, Contagion or Fundamentals?
Contributions to 10-year Swap Spread
8.0
Italy
6.0
4.0
2.0
0.0
-2.0
-4.0
-6.0
-8.0
Jul 07 Sep 08 Oct 08 Mar Apr 09 Sep Oct 09 Feb 10
09
09
Fundamentals
Contagion
g
Global Risk Aversion
50
Global Risk Aversion, Contagion or Fundamentals?
Contributions to 10-year Swap Spread
250.0
200.0
150.0
100.0
50.0
0.0
-50.0
50.0
-100.0
-150.0
-200.0
-250.0
250 0
-300.0
Greece
Jul 07 Sep 08 Oct 08 Mar
09
Fundamentals
Contagion
Apr 09 Sep Oct 09 Feb 10
09
Global Risk Aversion
51
Global Risk Aversion, Contagion or Fundamentals?
Contributions to 10-year Swap Spread
20.0
Ireland
15.0
10.0
5.0
0.0
-5.0
-10.0
Jul 07 Sep 08 Oct 08 Mar
09
Fundamentals
Contagion
Apr 09 Sep Oct 09 Feb 10
09
Global Risk Aversion
52
Estimation: Index of Risk Aversion
• When Risk Aversion rises, swap spreads widen, as sovereign yields fall further below swap yields (flight‐to‐quality leads to i ld f ll f th b l
i ld (fli ht t
lit l d t
capital flowing away from risky assets).
• Not the case for some high‐debt, lower‐rated issuers (notably Greece and Italy) that do not benefit from flight‐to‐quality. • Outside the euro area, the US and the UK benefit from rising Risk Aversion. For Sweden (and to some extent Japan), risk aversion is (
)
not significant.
• The impact of the IRA on US swap spreads is larger than the impact on the spreads for the other three countries (US is a “safe p
p
haven”).
53
Estimation: Contagion and Fundamentals
• Contagion: sovereign bond yields rise when the probability
of a credit event rises (because of contagion from another sovereign issuer). • High‐debt, lower‐rated sovereigns exhibit larger sensitivities as these countries are vulnerable to even remote probabilities of distress among higher‐rated issuers.
• Fundamentals : significant relationship with sovereign spreads. Wh b d t d fi it i
When budget deficits increase, sovereign bond yields rise i b d i ld i
(versus swap yields).
54
But Contagion from Where?
• Contagion can further broken down across sources of g
distress.
• For a given probability of distress in a specific sovereign, we find the most significant sources of contagion.
• Our measure of distress dependence (contributions to the changes in each country’s SC) taken from the Contagion Matrices.
55
Contagion from Where? Systemic outbreak (1)
– October 2008‐March 2009: countries weighing adversely on other sovereigns were those whose financial institutions were hit hard by the
sovereigns were those whose financial institutions were hit hard by the financial crisis (Austria, Ireland, and Italy).
USA
JPN
UK
GER
FRA
ITA
SPA
NET
BEL
AUT
GRE
IRE
O
POR
SWE
AVG
USA JPN
5.2
3.7
3.7
5.3
55
5.5
48
4.8
4.1
5.1
3.5
5.3
34
3.4
51
5.1
4.1
5.0
3.6
5.5
39
3.9
58
5.8
3.4
5.9
3.8
5.9
3.2
5.6
4.1
5.1
3.5
5.0
UK
8.3
8.4
8.8
8
8
8.8
9.2
89
8.9
9.4
8.9
91
9.1
8.6
9.1
8.5
9.4
8.3
GER FRA ITA
7.2
5.6
8.1
4.5
5.0
8.9
5.1
5.4
9.7
65
6.5
88
8.8
6.2
8.7
4.9
5.1
52
5.2
57
5.7
92
9.2
5.4
6.2
9.7
5.1
5.5
8.9
46
4.6
4 8 10
4.8
10.4
4
4.4
4.7
9.7
4.5
4.5 10.2
4.9
5.4
8.6
5.2
5.7
9.7
4.6
4.9
8.7
SPA NET BEL AUT GRE IRE POR SWE
6.4
8.4
6.7 11.4 7.6 11.0 5.2
9.0
6.8
7.3
7.1 12.2 9.4 12.2 6.5
7.9
7.4
8.6
7.2 11.9 8.6 11.8 6.1
9.2
74
7.4
84
8.4
7 2 10.3
7.2
10 3 7.5
7 5 10.0
10 0 6.1
61
87
8.7
7.8
9.2
7.3 10.2 7.6
9.4
6.4
9.1
7.3
8.4
6.9 12.9 9.2 12.5 5.9
9.0
85
8.5
6 7 12.4
6.7
12 4 8.7
8 7 11.5
11 5 5.8
58
92
9.2
7.8
7.9 10.7 8.0 10.6 6.4
8.9
6.8
8.8
12.0 8.5 11.5 5.9
9.0
79
7.9
75
7.5
75
7.5
9 8 13.5
9.8
13 5 7.0
70
83
8.3
7.3
7.3
7.0 12.8
14.3 6.5
8.1
7.4
7.5
7.2 13.8 11.0
6.5
8.5
6.8
8.1
6.7 12.7 9.0 11.6
8.7
7.9
8.3
7.5 11.2 8.3 11.3 6.4
6.8
7.5
6.6 11.1 8.2 10.9 5.8
8.0 56
Conclusions
• Readily implementable in terms of data needs.
• Reliable in the sense of being robust under data‐restricted environments.
• Interpretable, so that the approach itself and its output can be used as an input to policy development. • Incorporates distress dependence among FIs and its changes across the economic cycle.
• Includes all the relevant IFs and Sectors.
• Framework
Framework that produces complementary measures in a consistent that produces complementary measures in a consistent
manner.
• Integrates
Integrates complementary information (micro‐founded supervisory data complementary information (micro‐founded supervisory data
and market‐based).
57
Conclusions (ctd.)
• Debt sustainability and appropriate management of sovereign balance sheets are necessary conditions for preventing sovereign risk from feeding back into broader financial stability concerns.
• Rising sovereign risk requires credible medium‐term fiscal consolidation plans as well as a solid public debt management framework.
• Emphasis should be given to the presence of significant contingent risk on sovereign balance sheets and the need for sovereigns to gradually disengage
sovereign balance sheets and the need for sovereigns to gradually disengage from a number of measures supporting the financial sector.
• Immediate steps should be taken to reduce the possibility of projecting longer‐
term sovereign credit risks into short‐term financing concerns.
58
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g p , /
61