A Framework forMacro-financial Stress Testingg

CNBV (México)

I Meeting on Financial Stability

Mexico CityNovember 3-4, 2011

*On temporal leave from the IMF. The views expressed in this presentation are those of the author and do not necessarily represent those of the IMF, CNBV or IMF,CNBV policy. Any errors remain attributable to the author

Outline

I. Objective and Modelling Framework.

I.  Pillars I ‐II: Individual Bank Perspective

III. Pillars III‐IV‐V: Systemic Risk Perspective.

IV. ST with Second Round Effects.

V. Pillar V: Contagion.

2

Objective

Provide the CNBV a methodological framework for risk i dassessment in order to:

• Support the design policy to minimize the potential negative effects of macroeconomic‐ financial shocks in the Mexican financial systemfinancial system.

• Implement a risk based regulatory framework• Implement a risk‐based regulatory framework.

• Validate financial institutions (FIs) IRB models;• Validate financial institutions (FIs) IRB models;

3

Stress Test Modeling Framework

Individual Bank Perspective Systemic Macro-Financial Perspective

Market-BasedInformation

p

SupervisoryInformation

y p

Information

Pillar III:Systemic

Risk-Based ST

Pillar IV:Financial Stability

Indicators

Pillar V:ContagionIndicators

Pillar II:Enhanced

Ri k B d ST

Pillar I:Balance Sheet ST

Macro-Financial Scenarios

Macro-Financial Scenarios

Risk-Based ST

Macro-Financial Scenarios

MCSR•Portfolio growth and composition.

Liquidity Risk

Portfolio

Financial StabilityMeasures

Mx SubsBHCs

Portfolio Losses

MarketRisk

EL

•Financial Margin.

•Net Result

••Portfolio Multivariate

Density.•Unexpected Losses.

• Portfoliocomposition

• Significantrisk factors.

• VaR

EL

e-CAR •SVaRCAR

Modelling Contributions

• 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 d d i d t d k t b d i f tifounded supervisory data and market‐based information.

• It incorporates a wide set of factors: It accounts for a wideIt incorporates a wide set of factors: It accounts for a wide set of macroeconomic and financial risk factors.

5

Main Points

• It provides robust estimations: It benefits from robust• It 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.

• Framework implemented and scrutinized by supervisors d l k d h ldand Central Banks around the world.

6

Implementation Map

Projects with I t ti l

IMF/GFSR

ECB /FSR

International Authorities

ECB /FSR

USA FSAP

India FSAP Banca D’Italia

Bank of Japan

Banque de France

Denmark FSAPBank of Jordan

Norges Bank

Central Bank of UAE

Canada FSAP

Central Bank of S Korea

Lithuania FSAPRisksbank (Sweden)

Deutshe BundesbankCentral Bank of UAE

Central Bank of Indonesia

Central Bank of S Korea

Central Bank of Croatia

Complementary Sources of Information

Supervisory Information Market Information

PD/LGD Credit Card

PD /LGDConsumption

Credit

InterbankFinancing Cost

Credit

PD/LGDMortgage

Loans

PD /LGDCorporate

Credit

PD/LGDPD/LGDCredit to States and

Municipalities

PD/LGDCredit to FIs

8

Complementary Sources of Information

Supervisory “Micro founded Information”

Assets Types MortgageConsumer

C dit C d

Portfolio Loss Distribution for

Financial I tit tiCredit Card

CommercialInstitutions

Merton TypeC dit D f lt S d P D

MarketInformation

Credit Default Swaps spreadsBond SpreadsOption Prices

PoDMarket

Information

Advantages- Actual Portfolio Composition

- Information of Concentration / Driver s effects

Disadvantages

- It does not consider off-balance sheet items

- It does not account for risk of complex derivatives- Signals market perceptions that might consider risks not captured by supervisory Data

- Daily data with no lags

- Can serve as early warning indicator of issues to be

It does not account for risk of complex derivatives

- Low frequency and lagged

- Market perceptions not always correct

- Issues with thin markets- Can serve as early warning indicator of issues to be explored by Supervisory data

Pillars I-II: Individual Bank Perspective

Balance Sheet Stress Test

CNBV: Base and Adverse Scenarios

CNBV Analysis

Credit AssumptionsLoss Given Default

Probabability of DefaultCAR &

CAR SensitivityIncrease in

LiabilitiesMonthly stocks

Flows, stock (quarterly)Liabilities

Macroeconomic AssumptionsGDP

Unemployment rateHousing Index

Increase in expected loss

Decrease in loan origination

Liability structurechanges

CapitalizationNet capital, Risk Weighted

Assets)ICAP

CAR (2013)

Financial AssumptionsTIIEFX

changesFunding structure

changesDecrease in

Financial marginIncrease in Adm. &Balance

Loan PortfolioCorporate

SMESta&Muns

Fi i l I tit ti

Bank: Base and Adverse Scenarios

Increase in Adm. & Promotionalexpenses

Other incomeeliminationFinancial

Monthly stock

Cash FlowInterest, loan payments

Financial InstitutionsRevolving credit

Non revolving creditProjections (Quarterly)

Balance sheetIncome statement

Capital RatioCredit Origination

intermediationelimination

Loan ProvisionExpected loss

Income StatementI t tCredit Origination Interest

ST of Individual FIs: Modeling Framework

Stressed PoDStressedMacro

Variables

LGD(CoPoD)

MacroeconomicScenarioDesign

Step 1 Step 2

Bank’sStressed Portfolio

Multivariate Density

0 . 1

0 . 1 5

0 . 2

Bank’s E t

Bank s Exposure to Asset type X

(CIMDO)- 4

- 20

24

- 4- 2

0

240

0 . 0 5

St 3

Exposure to Asset type Y

SimulationStressed

Economic Capital

Step 3

Stressed PLDSimulationp

(VaR)Step 4 12

Macroeconomic Scenarios

Macroeconomic Scenario

Defined jointly between IMF and CNBV in consultation with SHCP.

• Baseline: Consistent with WEO projections• Baseline: Consistent with WEO projections.

• Adverse: Consistent with last period of financial, macroeconomic Distress.

BASELINEVariable 07‐Dic 08‐Dic 09‐Dic 10‐Dic 11‐Dic 12‐Dic 13‐Dic

PERCENT CHANGE NOMINAL GDP Y/Y 10.84% 2.53% 3.50% 2.59% 6.58% 7.11% 6.67%INFLATION LEVEL Y/Y 3.76% 6.53% 3.57% 4.40% 3.51% 2.99% 2.99%UNEMPLOYMENT RATE LEVEL 3.54% 4.26% 5.33% 5.36% 4.50% 3.90% 3.50%TIIE28 LEVEL 7.93% 8.70% 4.92% 4.88% 4.85% 5.85% 6.48%

BASELINE

TIIE28 LEVEL 7.93% 8.70% 4.92% 4.88% 4.85% 5.85% 6.48%PERCENT CHANGE DOMESTIC CREDIT 16.40% 7.70% 14.88% 13.00% 12.86% 15.31% 16.53%PERCENT CHANGE HOUSING PRICES INDEX 6.08% 5.68% 3.64% 4.60% 4.52% 4.45% 4.95%IPC LEVEL 29,536.83    22,380.32    32,120.47    38,550.79    39,903.17    41,095.1530    42,325.79    CURRENCY RATE MXP/USD M/M 10.92            13.83            13.07            12.35            11.84            12.0200            12.19           VIMEX LEVEL 26.74          50.37          23.09          20.74           22.16          36.92              31.00         

Variable 07‐Dic 08‐Dic 09‐Dic 10‐Dic 11‐Dic 12‐Dic 13‐DicPERCENT CHANGE NOMINAL GDP Y/Y 10.84% 2.53% 3.50% 2.59% 3.74% 3.29% 3.52%INFLATION LEVEL Y/Y 3.76% 6.53% 3.57% 4.40% 4.18% 5.98% 5.47%

ADVERSE

UNEMPLOYMENT RATE LEVEL 3.54% 4.26% 5.33% 5.36% 5.21% 5.06% 4.26%TIIE28 LEVEL 7.93% 8.70% 4.92% 4.88% 5.49% 7.12% 6.57%PERCENT CHANGE DOMESTIC CREDIT 16.40% 7.70% 14.88% 13.00% 9.91% 8.41% 16.05%PERCENT CHANGE HOUSING PRICES INDEX 6.08% 5.68% 3.64% 4.60% 4.45% 2.42% 4.92%IPC LEVEL 29,536.83    22,380.32    32,120.47    38,550.79    32,075.00    22,259.95         27,272.26   

14

 CURRENCY RATE MXP/USD M/M 10.92          13.83          13.07          12.35           12.33          13.8443          13.32         VIMEX LEVEL 26.74            50.37            23.09            20.74            26.12            50.37                36.92           

Macroeconomic Scenario

15

PD Modelling:f(macro-financial factors)

Summary PD Modeling

TYPE OF CREDIT LOAN ADJUSTED R^2 VARIABLE SIGN LAG BETA P‐VALUECONSTANT ‐ ‐‐‐‐‐ 2.06617 0.0001PERCENT CHANGE NOMINAL GDP Y/Y ‐ 14 0.685319 0.0031INFLATION LEVEL Y/Y + 0 5.368116 0TIIE28 LEVEL + 1 3.029672 0.0835

MODELS

Corporatives 0.977125

VIMEX LEVEL + 5 0.000877 0AR(1) + ‐‐‐‐‐ 0.986921 0CONSTANT ‐ ‐‐‐‐‐ 1.229176 0DOMESTIC CREDIT/GDP ‐ 10 0.918431 0.0071INFLATION LEVEL Y/Y + 0 2.091662 0.007TIIE28 LEVEL + 11 1.664722 0.0002VIMEX LEVEL + 0 0.00055 0.0001

SME's 0.972802

0 0 00055 0 000AR(1) + ‐‐‐‐‐ 0.973609 0CONSTANT ‐ ‐‐‐‐‐ 1.543225 0.0113PERCENT CHANGE NOMINAL GDP Y/Y ‐ 14 0.877081 0.0955PERCENT CHANGE IPC M/M ‐ 1 0.094635 0.0144INFLATION LEVEL Y/Y + 0 7.273109 0.0033AR(1) + ‐‐‐‐‐ 0.980313 0CONSTANT ‐ ‐‐‐‐‐ 2.239624 0

Sta & Mun's 0.977609

CONSTANT 2.239624 0PERCENT CHANGE NOMINAL GDP Y/Y ‐ 14 0.710064 0PERCENT CHANGE IPC INDEX M/M ‐ 1 0.076908 0INFLATION LEVEL Y/Y + 0 5.192735 0TIIE28 LEVEL + 0 1.848745 0.0036VIMEX LEVEL + 5 0.001097 0AR(1) + ‐‐‐‐‐ 0.983825 0CONSTANT ‐ ‐‐‐‐‐ 1 175139 0 0001

Financial Institutions 0.976715

CONSTANT ‐ ‐‐‐‐‐ 1.175139 0.0001PERCENT CHANGE CURRENCY RATE MXP/USD M/M + 7 0.184682 0.0432DOMESTIC CREDIT/GDP ‐ 8 0.905785 0.0364INFLATION LEVEL Y/Y + 2 3.246666 0.0777TIIE28 LEVEL + 0 3.102642 0.0099AR(1) + ‐‐‐‐‐ 0.946654 0CONSTANT ‐ ‐‐‐‐‐ 0.788277 0.0001DOMESTIC CREDIT/GDP 6 1 31564 0 0147

Credit Card 0.983347

DOMESTIC CREDIT/GDP ‐ 6 1.31564 0.0147INFLATION LEVEL Y/Y + 3 2.390412 0.1577VIMEX LEVEL + 3 0.000942 0.0589AR(1) + ‐‐‐‐‐ 0.925927 0CONSTANT ‐ ‐‐‐‐‐ 2.173912 0PERCENT HOUSING PRICES INDEX ‐ 1 1.013343 0.0828PERCENT CHANGE IPC INDEX M/M ‐ 21 0.10354 0.03DOMESTIC CREDIT/GDP 2 1 769317 0 0023M t 0 960473

Not Revolving Consumption 0.963588

17

DOMESTIC CREDIT/GDP ‐ 2 1.769317 0.0023UNEMPLOYMENT RATE LEVEL + 8 9.828639 0.0107TIIE28 LEVEL + 6 13.27227 0AR(1) + ‐‐‐‐‐ 0.892155 0

Mortgagees 0.960473

PDs by Asset Class

10.00%

15.00%

20.00%

25.00%

0.00%

5.00%

1/09

/200

4

1/03

/200

5

1/09

/200

5

1/03

/200

6

1/09

/200

6

1/03

/200

7

1/09

/200

7

1/03

/200

8

1/09

/200

8

1/03

/200

9

1/09

/200

9

1/03

/201

0

1/09

/201

0

1/03

/201

1

1/09

/201

1

1/03

/201

2

1/09

/201

2

1/03

/201

3

1/09

/201

3

01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01

PD's SYSTEM BASELINE Revolving Credit

PD's SYSTEM ADVERSE Revolving Credit

18

PDs by Asset Class

10.00%

15.00%

20.00%

25.00%

0.00%

5.00%

1/09

/200

4

1/03

/200

5

1/09

/200

5

1/03

/200

6

1/09

/200

6

1/03

/200

7

1/09

/200

7

1/03

/200

8

1/09

/200

8

1/03

/200

9

1/09

/200

9

1/03

/201

0

1/09

/201

0

1/03

/201

1

1/09

/201

1

1/03

/201

2

1/09

/201

2

1/03

/201

3

1/09

/201

3

01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01

PD's SYSTEM BASELINE Revolving Credit

PD's SYSTEM ADVERSE Revolving Credit

19

PDs by Asset Class

20

Results

21

Regulatory Capital Ratio Measures

C t C t ICAP L l C t MCategory Category ICAP Levels Category MeasuresCategory I ICAP≥10% No measuresCategory II 8%≤ICAP<10% The FI will abstain from realizingCategory II 8%≤ICAP<10% operations that will cause their ICAP to

fall below the levels requred by theCapitalization Rules.

Category III 7%≤ICAP<8% 1. Suspend all payments of dividends tostockholdersstockholders.

2. Suspend all compensations and bonuses to the director general of theFI.

3. Present a plan for restaurationsubject to various obligationssubject to various obligationsrequired by the CNBV

Category IV 4%≤ICAP<7% All measures required for FI undercategory are readily applicable forcategory IV. Aditionally the FI must askf th i ti b th CNBV t i t ifor authorization by the CNBV to invest in non-financial assets, open new branchesor realizing operations other than theones normally realized by the FI.

Category V ICAP≤4% All measures applicable for FI underCategory V ICAP≤4% ppCategory IV will be applied.

Banking Sector

23

24

25

eCAR Graphs

26

27

Pillars III-IV-V: Systemic Macro-Financial

PerspectivePerspective

Modeling Framework

Supervisory Information Market Information

Commercial BankingPoD

Pension FundsPoD

Mutual FundsPOD

Develpmt BkingPOD

Insurance CosPoD

BrokersPoD Others

EAD

Financial System´sMultivariate Density

LGD 0 . 2

SystemicLoss Simulation

Systemic StressIndicators

- 4- 2

02

4

- 4- 2

0

240

0 . 0 5

0 . 1

0 . 1 5

Systemic LossIndicators

Sovereign Risk

ContagionIndicators

Sovereign RiskAssessment

30

Marginal contribution toSystemic Risk

Distress Dependence

Segoviano and Goodhart (2009)

Distress dependence between institutions is incorporated via jointDistress dependence between institutions is incorporated via joint movements of their PoDs, which in turn move in tandem due to

h kh kIndirect LinksIndirect Links

Systemic shocksSystemic shocks Lending to common sectorsLending to common sectorsProprietaryProprietary TradesTrades

Contagion throughContagion throughIdi i Sh kIdi i Sh k

Direct LinksDirect LinksI tI t B k D it M k tB k D it M k t

The recent crisis underlined that proper estimation of distress dependence FI i fi i l i i l f fi i l bili

Idiosyncratic ShocksIdiosyncratic Shocks InterInter--Bank Deposit MarketsBank Deposit MarketsSyndicated LoansSyndicated Loans

amongst FIs in a financial system is essential for financial stability assessment.

G dh S i d T (2004)Goodhart, Sunirand, Tsomocos (2004).31

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 set correlation structuresto explicitly 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.

32Source: Segoviano (2006)

CIMDO‐Density

EmpiricalI f tiInformation

33

CIMDO-Density

34

CIMDO‐Copula

L t X d Y b t d i bl ith ti di t ib ti f ti F d H it lLet X and Y be two random variables with continuous distribution functions F and H respecitvely, then the Spearman Correlation of X and Y is defined and denoted by the following:

22

3),(12]),([12))(),((),(I

vuCI

dudvuvvuCYHXFYXS

2

35

Where and ρ(F(X),H(Y)) is the Pearson Correlation of the transformed uniformrandom variables F(X) and G(Y).

]1,0[]1,0[2 xI

Distress Dependence: CIMDO-Copula

CIMDO-Copula. (Segoviano, 2008)

Maintains the benefits of copula modeling butMaintains the benefits of copula modeling but

• Allows for changing dependence as empirical PoDsh hil t diti l t i l f tichange, while traditional parametric copula functions

assume it constant.

• Avoids copula choice problem.

• Outperforms commonly used parametric copula functions• Outperforms commonly used parametric copula functions under the PIT criterion.

R dil i l t bl ith il bl d t (P D )• Readily implementable with available data (PoDs).

36

PoDMarket InformationMarket Information

37

PoDs Graphs

38

Pillar III:Marginal Contribution to Systemic RiskMarginal Contribution to Systemic Risk

39

B1B4

B2

B3

B5

B3

40

Marginal Contribution to Systemic Risk:Mexico

Mexican Bank P Mexican Bank S

0.050.10.150.2

0.050.1

0.150.2

0.250.3

0.220.230.240.250.260.27

0.050.1

0.150.2

0.250.3

000 05

01/0

3/20

0701

/06/

2007

01/0

9/20

0701

/12/

2007

01/0

3/20

0801

/06/

2008

01/0

9/20

0801

/12/

2008

01/0

3/20

0901

/06/

2009

01/0

9/20

0901

/12/

2009

01/0

3/20

1001

/06/

2010

01/0

9/20

1001

/12/

2010

0.210.22

00.05

01/0

3/20

0701

/06/

2007

01/0

9/20

0701

/12/

2007

01/0

3/20

0801

/06/

2008

01/0

9/20

0801

/12/

2008

01/0

3/20

0901

/06/

2009

01/0

9/20

0901

/12/

2009

01/0

3/20

1001

/06/

2010

01/0

9/20

1001

/12/

2010

Tamaño PoD

Spearman Correlation Shapley ValueTamaño PoD

Spearman Correlation Shapley Value

41

Marginal Contribution to Systemic Risk:U.S

Marginal Contribution to Systemic Risk:g yIt takes into account of size and interconnectedness.

AIG Factors

0.014

0.016

0.35

0.4

Axi

s fo

r CI

0.008

0.01

0.012

0.2

0.25

0.3

Rig

ht

0.002

0.004

0.006

0.05

0.1

0.15

00

Dec

-07

Jan-

08

Feb-

08

Mar

-08

Apr

-08

May

-08

Jun-

08

Jul-0

8

Aug

-08

Sep

-08

Oct

-08

Nov

-08

Dec

-08

Jan-

09

Feb-

09

Mar

-09

MCSR POD AIG Spearman Corr AIG Contagion Index AIG

Pillar IV:Banking Stability MeasuresBanking Stability Measures

43

Tail Risk Indicators: Mexico

Financial Stability Index: 

Expected number of FIs in distress given that

Joint Probability of Distress (JPoD):Likelihood of common distress of all the FIs Expected number of FIs in distress given that 

at least one became distressed (left scale). in the system (right scale).

JPOD-FSI: México

211. Lehman spillover, derivatives’ marketcrisis and mutual funds’ crisis (Oct- 0 0018

0.002

3 5

4

JPOD-FSI: MéxicoBSI JPODFSI JPOD

crisis and mutual funds crisis (Oct-2008).

2. H1N1 crisis (March-April-2009).

0.0012

0.0014

0.0016

0.0018

2.5

3

3.5

0.0006

0.0008

0.001

1.5

2

0

0.0002

0.0004

0

0.5

1

44

Tail Risk Indicators under Scenarios

45

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 2008July 1, 2007‐ September 12, 2008July 1, 2007 Citi BAC JPM Wacho WAMU GS LEH MER MS AIG Row

averageCitigroup 1.00 0.14 0.11 0.11 0.08 0.09 0.08 0.09 0.09 0.08 0.19Bank of America 0.12 1.00 0.27 0.27 0.11 0.11 0.10 0.12 0.12 0.15 0.24JPMorgan 0 15 0 42 1 00 0 31 0 13 0 19 0 16 0 19 0 18 0 17 0 29JPMorgan 0.15 0.42 1.00 0.31 0.13 0.19 0.16 0.19 0.18 0.17 0.29Wachovia 0.12 0.33 0.24 1.00 0.11 0.12 0.10 0.12 0.12 0.14 0.24Washington Mutual 0.16 0.28 0.21 0.23 1.00 0.12 0.12 0.16 0.13 0.15 0.26Goldman Sachs 0.17 0.25 0.28 0.21 0.11 1.00 0.31 0.28 0.31 0.17 0.31Lehman 0.22 0.32 0.32 0.26 0.15 0.43 1.00 0.35 0.33 0.20 0.36Merrill Lynch 0.19 0.32 0.33 0.25 0.17 0.33 0.31 1.00 0.31 0.20 0.34yMorgan Stanley 0.19 0.31 0.28 0.24 0.14 0.35 0.28 0.30 1.00 0.16 0.33AIG 0.07 0.14 0.10 0.10 0.05 0.07 0.06 0.07 0.06 1.00 0.17Column average 0.24 0.35 0.31 0.30 0.21 0.28 0.25 0.27 0.26 0.24 0.27

September 12, 2008 Citi BAC JPM Wacho WAMU GS LEH MER MS AIG Row average

Citigroup 1.00 0.20 0.19 0.14 0.07 0.17 0.13 0.14 0.16 0.11 0.23Bank of America 0.14 1.00 0.31 0.18 0.05 0.16 0.10 0.13 0.15 0.11 0.23JPMorgan 0.13 0.29 1.00 0.16 0.05 0.19 0.11 0.14 0.16 0.09 0.23W h i 0 34 0 60 0 55 1 00 0 17 0 36 0 27 0 31 0 34 0 29 0 42Wachovia 0.34 0.60 0.55 1.00 0.17 0.36 0.27 0.31 0.34 0.29 0.42Washington Mutual 0.93 0.97 0.95 0.94 1.00 0.91 0.88 0.92 0.91 0.89 0.93Goldman Sachs 0.15 0.19 0.24 0.13 0.06 1.00 0.18 0.20 0.27 0.11 0.25Lehman 0.47 0.53 0.58 0.43 0.25 0.75 1.00 0.59 0.62 0.37 0.56Merrill Lynch 0.32 0.41 0.47 0.30 0.16 0.53 0.37 1.00 0.48 0.26 0.43Morgan Stanley 0 21 0 28 0 29 0 19 0 09 0 40 0 22 0 27 1 00 0 14 0 31Morgan Stanley 0.21 0.28 0.29 0.19 0.09 0.40 0.22 0.27 1.00 0.14 0.31AIG 0.50 0.66 0.59 0.53 0.29 0.54 0.43 0.49 0.47 1.00 0.55Column average 0.42 0.51 0.52 0.40 0.22 0.50 0.37 0.42 0.46 0.34 0.41

46

Contagion Indicators: DiDe Mexico

47

Contagion Indicators: Toxicity Index

P(A)

Toxicity Index (TI): Toxicity of the distress of a country/FI on other countries/FIs.

P(A)

P(B) CIMDOMethodolog

P(A,B,C) JPoD

P(A B); P(A C); P(B C)P(C)Methodolog

yP(A,B); P(A,C); P(B,C)

Bayes’Bayes Law

)/()/()/()/()/()/()/()/()/(

CCPBCPACPCBPBBPABPCAPBAPAAP

For e.g. country (A)/FI(A):

)()()(

For e.g. country (A)/FI(A):

TI(A)=(P(B/A) + P(C/A))/n-1

48

Contagion Indicators:Toxicity IndexMexico

49

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

70

80

90LehmanAIG

50

60

70

30

40

0

10

20

7 7 7 7 7 7 7 7 7 7 7 7 8 8 8 8 8 8 8 8 8

1/1/

2007

2/1/

2007

3/1/

2007

4/1/

2007

5/1/

2007

6/1/

2007

7/1/

2007

8/1/

2007

9/1/

2007

10/1

/200

7

11/1

/200

7

12/1

/200

7

1/1/

2008

2/1/

2008

3/1/

2008

4/1/

2008

5/1/

2008

6/1/

2008

7/1/

2008

8/1/

2008

9/1/

2008

50

Contagion Indicators: Probability of Cascade EffectsMexico

51

Pilar V: Contagion

52

53

54

55

56

PoD Mexico & Mexican Banks

57

PoDs: Mexico & Foreign Banks

58

DiDe Mexico/Sovereigns

59

DiDe Mexican Subs/Parents

60

Second-Round Effects

61

Second-Round Effects

MacroeconomicFactors

FinancialFactors

Financial System´sFinancial System’sReturns

Comm BanksPoD

Dvlpmt BanksPoD

GSEsPoD

Pension FundsPoD

InsurancePoD

Mutual FundsPoD

Tail Risk (JPoD)Returns

MacroeconomicFactor

FinancialFactors

Comm BanksPoD

Dvlpmt BanksPoD

GSEsPoD

Pension FundsPoD

InsurancePoD

Mutual FundsPoD

ExposuresFinancial System´sMultivariate DensitySystemic

LGDs

ySystemicLoss Simulation

Financial System’sLoss Distribution

Financial Stability Measures

Marginal Contributionto Systemic Risk 62

Macro-financial Risk Zones

63

Macro-financial Risk Zones

Objective: Definition of “risk zones” based on the joint interaction ofmacroeconomic and financial indicators (JPoD).(Segoviano and Malik (2011) IMF WP forthcoming).( g ( ) g)

0.000

0.002 MSIAH(2)-VAR(1), 1999 (7) - 2009 (3)Jpodrev dlhouse

2000 2001 2002 2003 2004 2005 2006 2007 2008 2009-0.002

0 5

1.0 Probabilities of Regime 1filtered predicted

smoothed

2000 2001 2002 2003 2004 2005 2006 2007 2008 2009

0.5

1.0 Probabilities of Regime 2filtered predicted

smoothed

2000 2001 2002 2003 2004 2005 2006 2007 2008 2009

0.5

Based on a Markov Switching VAR that allows to quantify:

• Probability of migrating between different “risk zones”.• The impact that different macro-financial shocks have on those probabilities.

64

Thank You

65

References

• Athanosopoulou, M., Segoviano, M., and Tieman A., (2011), “Banks’ Probability of Default:  Which Methodology, When, and Why?”, IMF Working Paper (forthcoming).

Cá C G V S i M (2010) “S i S d Gl b l Ri k• Cáceres, C., Guzzo, V., Segoviano, M., (2010), “Sovereign Spreads: Global Risk Aversion, Contagion or Fundamentals?”, IMF Working Paper WP/10/120.

• Espinoza, R. and Segoviano, M. (2011). “Probabilities of Default and the Market Price of Risk in a Distressed Economy” IMF Working Paper WP/11/75of Risk in a Distressed Economy , IMF Working Paper WP/11/75.

• Goodhart, C., Hofmann, B. and Segoviano, M. (2004), “Bank Regulation and Macroeconomic Fluctuations,” Oxford Review of Economic Policy, Vol. 20, No. 4, pp. 591–615.

• Goodhart, C., Hofmann B., and Segoviano M., (2006), “Default, Credit Growth, and Asset Prices”, IMF Working Paper 06/223.

• Segoviano, M. (2006). “Consistent Information Multivariate Density Optimizing Methodology” Financial Markets Group Discussion Paper No 557Methodology . Financial Markets Group, Discussion Paper No. 557.

• Segoviano, M. and Goodhart, C. (2009). “Banking Stability Measures”, IMF WP/09/4.• Segoviano, M., (2006), “The Conditional Probability of Default Methodology,” 

Financial Markets Group, London School of Economics, Discussion Paper 558.Financial Markets Group, London School of Economics, Discussion Paper 558.• Segoviano, M., (2011), “The CIMDO‐Copula. Robust Estimation of Default 

Dependence under Data Restrictions”, IMF Working Paper (forthcoming).• Segoviano, M. and  Padilla, P., (2006), “Portfolio Credit risk and Macroeconomic 

Shocks: Applications to Stress Testing under Data Restricted Environments ” IMF

66

Shocks: Applications to Stress Testing under Data Restricted Environments,  IMF WP/06/283.