Financial Stability Measures Miguel Segoviano* and Raphael Espinoza [email protected] RE i [email protected] @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

References • •

• • • • • • •

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