Using Contingent Claims Analysis (CCA) to Measure and Analyze Systemic Risk, Sovereign and Macro Risk September 13, 2012 Presentation to Macro Financial Modeling Conference Dale Gray, IMF, Monetary and Capital Markets Department The views expressed in this presentation are those of the authors and should not be attributed to the International Monetary Fund, its Executive Board, or its management.
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Dale Gray, IMF, Monetary and Capital Markets Department
Using Contingent Claims Analysis (CCA) to Measure and Analyze Systemic Risk, Sovereign and Macro Risk September 13, 2012 Presentation to Macro Financial Modeling Conference. Dale Gray, IMF, Monetary and Capital Markets Department. - PowerPoint PPT Presentation
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Using Contingent Claims Analysis (CCA) to Measure and Analyze Systemic Risk,
Sovereign and Macro Risk
September 13, 2012
Presentation to Macro Financial Modeling Conference
Dale Gray, IMF, Monetary and Capital Markets Department
The views expressed in this presentation are those of the authors and should not be attributed to the International Monetary Fund, its Executive Board, or its management.
• Sovereign CCA models and Sovereign-Banking Destabilization Spirals
• Integrated Policy Analysis
3
Outline of Presentation (cont.)
Presentation is based on material in: Gray, D. F., Merton R. C. and Z. Bodie, 2008, “A New Framework for Measuring and
Managing Macrofinancial Risk and Financial Stability,” Harvard Business School Working Paper No. 09-015.
Gray, D., A. Jobst, 2011, “Modeling Systemic Financial Sector and Sovereign Risk,” Sveriges Riksbank Economic Review, September.
As well as:
• Book: Macrofinancial Risk Analysis; other IMF, JOIM, Annual Review of Financial Economics (2009 and 2012) and related papers
• Financial Risk Indicators in Monetary Policy Models (joint work with Central Bank of Chile IMF WP 11/228)
• International Transmission of Macro, Sovereign, Financial, and Corporate Distress (joint work with ECB CCA- GVAR Model of EU)
4
Traditional Analysis is Incomplete
Traditional macroeconomic and banking models do not adequately measure risk exposures of financial institutions and sovereigns and cannot be used to understand the transmission and amplification of risk within and between balance sheets in the economy.
Traditional macroeconomic analysis of the government and central bank is almost entirely flow or accounting balance sheet based. Sovereign debt analyses focus on debt sustainability (stocks, flows and debt to GDP), not sovereign risk exposures (contingent liabilities, expected losses on sovereign debt).
A fundamental point is that accounting balance sheets or a flow-of-funds do not indicate risk exposures, which are forward-looking.
5
CCA Balance Sheet Models and Macroeconomic Models
Macroeconomic models are largely based on flow and accounting balance sheets, geared to try to forecast the mean of macro variables (i.e. first moment)
Finance measures risk from stochastic assets relative to threshold (second and third moments critical to risk indicators).
CCA is an excellent tool for analyzing macrofinancial linkages
Time pattern of CCA risk indicators can be linked to macroeconomic variables and to monetary policy, DSGE, and other models
6
Added Dimension of Risk Indicators CCA Risk Analytics Models to Spectrum of Macroeconomic Models
Risk Analytics Models CCA, Credit Risk Macroeconomic Theory Based RBC, GE IS-LM DSGE, MPM VAR Data Based Macroeconomic Models
7
Macrofinancial Risk Analysis
Framework integrates risk-adjusted balance sheets using Contingent Claims Analysis (CCA) of financial institutions, corporates, and sovereigns together and with macroeconomic and monetary policy models
TOOLKIT FOR MACRO RISK ANALYSIS
8
Core Concept of Contingent Claims Analysis (CCA): Merton Model
• Value of liabilities derived from value of assets.
• Liabilities have different seniority.
• Randomness in asset value.
9
CCA is Generalization of Black, Scholes, Merton Option Pricing Theory
Liabilities derive their value from assets
Assets are stochastic (changes driven by income flows, asset sales, or changes in value, including credit risk/guarantees)
Uncertain changes in future asset value, relative to the promised payments on debt are the driver of forward-looking values of equity and risky debt.
Risky debt is default-free debt value minus the expected loss due to default which can be measured with an implicit put option.
Key elements are Asset value (A) at time 0, asset return volatility (σ), default barrier (B = PV of promised payments on debt, time horizon (T) and risk-free rate (r).
Note : one does not have to know the expected returns to use CCA/Merton models for valuation of liabilities!
10
Tradeoffs between Market Capitalization, Market Value of Assets and Default Probability (Moody’s KMV data)
CITIGROUP EXAMPLE: From Sept 9, 2008 to March 9, 2009, Market Capitalization fell from $125 bn to $6 bn, Assets declined and Default Probability went from 0.5% to 24%
To get back to a BBB+ rating (0.3% EDF) combinations of capital injection, asset guarantees, debt-equity swaps can
be evaluated; during TARP 107bn in capital was raised
11
CCA is Based on Proven, Well-tested Calibration Techniques
Tools and techniques for calibrating CCA balance sheets of corporates and financial institutions are decades old (as described in HBR 2008 paper). Even commercial sources available (e.g. Moody’sKMV provide CCA risk indicators daily for 40,000 firms and financial institutions in over 60 countries)
Extensions to sovereigns and economy-wide risk transmission is becoming widespread
Over 20 countries have been calibrated; 35 sovereigns; CCA now included in several IMF FSAPs; recent integration into DSGE/monetary policy models and CCA GVAR (Global and EU)
12
As a result of the crisis, CCA concepts have now found their way into the mainstream
The structural CCA model, with its embedded fundamental volatility, endogenously changes as values change (e.g. shocks to assets endogenously change values of equity and risky debt and credit risk premiums)
It helps explain complex risk, especially expected losses in financial system and “insidiousness” of risk exposures where small changes in value can lead to very large changes in risk due to convexity!
13
CCA has robustness
It does not depend on expected returns;
It does not depend on preferences;
It is designed to be modular (can be integrated with many models of consumption and investment);
Retains the (endogenous) non-linearity of values and risk exposures, and can linked to macro models in different ways.
14
For the remainder if my presentation I will describe several ways CCA can be applied to enhance financial stability and macroeconomic analysis
1. Non-linear risk transmission across sectors of an economy
4. Applying CCA To The Sovereign Balance Sheet; Framework For Sovereign-Bank Feedback Destabilization Processes
5. Unified Macrofinancial Policy Framework
Further Applications
15
1. NON-LINEAR RISK TRANSMISSION ACROSS SECTORS OF AN ECONOMY
Risky debt of households and corporates are assets on financial institution balance sheets and implicit and explicit guarantees of bank’s liabilities are on the sovereign balance sheet
Balance Sheets for the Economic Sectors.
ASSETS LIABILITIES CORPORATE SECTOR
FINANCIAL SECTOR
HOUSEHOLD SECTOR
SOVEREIGN SECTOR (Government and Monetary Authorities)
Source: Gray, Merton and Bodie (2008).
Foreign Currency Reserves
Net Fiscal Asset
(PV of taxes minus expenditures)
Other Public Assets
Financial Guarantees
Foreign-currency Debt
Base Money and
Local-currency Debt
Household Assets (including household income and
savings in the form of deposits and other financial assets)
Net Worth (Subsidiary BS)
Household Net Worth – Claim on Household Assets
Consumption is a “Dividend”
Payment out of Asset Associated With this Claim
Household Real Estate Assets
Household Mortgage and Debt Net Worth (Subsidiary BS)
Loans and other Assets (including loans to corporates, households and sovereign)
Financial Guarantees
Debt and Deposits
Equity
Corporate Assets
Debt
Equity
16
CCA Balance Sheet: Assets Minus Liabilities equal Zero
CCA Balance Sheet
Assets
+or - Implicit or Explicit Guarantees {Implicit Put
Options}
minus
Equity / Jr. Claim {Implicit Call Option}
minus
(Default-free Value of Debt – Implicit Put Option)
= 0
For a sector, sub-sector
or individual institution
17
Stylized Interlinked CCA Balance Sheets for an Economy
Corporates
Households Financial Sector
Sovereign Foreign
H BS H RE Govt. MA Asset
CA
,
FIN
L
H RE
A
A
E
,H REA FA
,
( )
G Other
PV T G
A
,
FX
G
MA Other
R
E
A
ContingentAssets & Liab
FP G FP
Equity/Jr. & Sub. Claims
CE H
H
E
c
,H REE
FE G
SLC SLC
SLC
E
B i
P
BMM
Foreign
Claims
Senior Claims (Default Barrier)
C
C
B
i
,
,
H RE
H RE
B
i
F fB i
SFX SFXB i
Put CP
HP (1 ) FP SFXP
Sum 0 0 0 0 0 0 0
Sectors of an economy can be viewed as interconnected risk-adjusted balance
sheets with portfolios of assets, liabilities, and guarantees—explicit and implicit.
18
Economy-wide CCA Balance Sheet Models Capture Non-linear Risk Transmission
Interlinked implicit options result in compound options that exhibit highly non-linear risk transmission, as seen a variety of financial crises
Note that if asset volatility in CCA balance sheets is set to zero:– Implicit put options go to zero,
– Macroeconomic accounting balance sheets and traditional flow-of-funds are the result
– Measurement of (non-linear) risk transmission is not possible using macroeconomic flow or accounting frameworks when fundamental structural volatility is ignored (i.e. = 0).
19
Examples of Channels of Risk Transmission
Corporates/Households Banks
Banks Sovereigns
Sovereigns Sov Debt Holders
Financial System Risk GDP Growth
Financial Sector Sovereign
GDP Growth
20
Example of Transmission of Risk from Corporate Sector to Banks to Sovereigns: Case of Thailand
My initial work was motivated to try to understand Asia crisis.
First model was a simple: four corporate sectors, two bank sectors, sovereign model for the Thai economy in the 1990s. Large amounts of foreign debt and pegged exchange rate. This simple model showed:
Corporate risk is embedded in the banking risk. The sensitivity (delta) and convexity (gamma) of banking sector risk increased as the exchange rate depreciates (insidious risk).
21
Example of Transmission of Risk from Corporate Sector to Banks to Sovereigns: Case of Thailand (cont.)
In fact, by using forward exchange rate level and volatility plus balance sheet data (available at the
time), the probability distribution of financial sector losses was 25% of GDP, BEFORE the spot rate moved
from its pegged level!
Actual losses reached around 40% of GDP
22
2. ESTIMATING GOVERNMENT CONTINGENT LIABILITIES AND RISK TRANSMISSION TO SOVEREIGN
Implied credit spreads derived from CCA models (i.e. derived from equity information) are frequently higher than the observed market CDS
This is due to the depressing effect of implicit and explicit government guarantees
The ‘market implied’ guarantees (implicit put option values) can be estimated using CCA and observed CDS
23
Citigroup: Example of Implicit Put Option Value Extracted from CDS vs from CCA model and Estimated
Contingent Liability (billions of US$)
0
100
200
300
400
500
600
700
800
30-Apr-07 30-Apr-08 30-Apr-09 30-Apr-10 30-Apr-11
Implicit Put Option Value from CDS
Implicit Put Option Value from CCA (FVCDS)
0
50
100
150
200
250
300
350
400
450
30-Apr-07 30-Apr-08 30-Apr-09 30-Apr-10 30-Apr-11
Estimated “market implied"
government continent liability
Transfer of Risk: Ireland CDS spreads of banks declined following guarantees in 4Q 2008 and sovereign spread increases
Irish Banks and Sovereign CDS Spreads(In basis points)
0
50
100
150
200
250
300
350
400
Jun-07 Sep-07 Dec-07 Mar-08 Jun-08 Sep-08 Dec-08
Allied Irish Bank
Bank of Ireland
Irish Government
Source: Bloomberg L.P.
25
Transfer of Risk to Sovereign: Austria Example – CCA Banking Contingent Liabilities vs Sovereign CDS spread
Total Contingent Liabilities vs 5-yr Sovereign CDS Spread
20
40
60
80
100
120
140
160
180
Bil
lio
ns o
f U
S $
0
50
100
150
200
250
300
So
vere
ign
CD
S S
pre
ad
(B
asis
Po
ints
)
Total Contingent Liabilities (simple sum) Sovereign 5-yr CDS Spread
26
Note how CCA financial sector risk indicators (aggregated financial institution CCA indicator related to expected losses) provides:
A robust measure of financial sector systemic risk;
Frequently a leading indicator of credit growth and GDP/output gap;
Provides a quantitative measure of government contingent liabilities, which affects sovereign risk (e.g. spreads)
27
3. SYSTEMIC CCA: MEASURING AND STRESS TESTING FINANCIAL SECTOR TAIL-RISK LOSSES AND CONTINGENT LIABILITIES
Beginning with CCA models of individual banks, expected losses and market implied contingent liabilities
Multivariate extreme value dependence model is then used to calculate the multivariate density of:
(i) the banking system expected losses, and,
(ii) government’s contingent liabilities accounting for the time-varying and non-linear dependence
(iii) measures of financial sector tail risk (95% VaR or Expected Shortfall)
(See Gray and Jobst Swedish Economic Review 2011, and 2009, 2010, & forthcoming)
28
Extreme Tail Risk Total Expected Losses including dependence structure, 36 largest US financial institutions, 95th percentile
0
1,000
2,000
3,000
4,000
Apr
-07
May
-07
Jun-
07
Jul-0
7
Aug
-07
Sep-
07
Oct
-07
Nov
-07
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
Apr
-09
May
-09
Jun-
09
Jul-0
9
Aug
-09
Sep-
09
Oct
-09
Nov
-09
Dec
-09
Jan-
10
In U
S do
llar b
illio
ns
Total Cont. Liab. (sum of individual expected losses)Total Cont. Liab. (ES, 95th percentile)
LehmanCollapse
Source: IMF US Financial Sector Assessment Program Stress Testing Technical Note 2010
29
Extreme Tail Risk Government Contingent Liabilities including dependence structure, 36 largest financial institutions, 95th percentile
Source: IMF US Financial Sector Assessment Program Stress Testing Technical Note 2010
30
Systemic CCA Shows Nonlinearities of Asset Volatility, Market Capital/Assets, Fair Value Credit Spreads, and Joint Losses – for individual institutions and for the system as a whole (illustrated below)
Aggregate MCAR =Aggregate Market Capitalization/
Aggregate Implied Assets
Aggregate Fair Value Credit Spread
Join
t E
L R
atio
=
Join
t E
xpec
ted
Loss
es (
from
Sys
tem
ic C
CA
)/ A
ggre
gate
M
arke
t C
apita
lizat
ion
Imp
lied
Ass
et
Vo
lati
lity
(Sam
ple
Med
ian)
Systemic Risk Assessment
Jobst and Gray (2012)
31
4. APPLYING CCA TO THE SOVEREIGN BALANCE SHEET; FRAMEWORK FOR SOVEREIGN BANK FEEDBACK DESTABILIZATION PROCESSES
1. Calibrating sovereign balance sheets for emerging market sovereigns with significant foreign currency debt (see Gray, Merton, Bodie 2007 JOIM paper; Gapen et al. IMF Staff Papers 55 #1)
2. Calibrating developed country sovereign balance sheets or government balance sheets in euro area. Calibration uses term structure of CDS/bonds plus debt data to infer sovereign assets, volatility and skew (see Gray, Jobst Swedish Economic Review, page 24 and Appendix 3).
32
Sovereign CCA Balance Sheet, Contingent Liabilities, Joint Bank-Sovereign Stress Testing
Sovereign, or Government, CCA model gives implied sovereign asset value and volatility, whose components can be estimated as shown below:
Liabilities to Financial sector + Other (residual)
Sovereign spreads = f (sovereign assets, volatility, debt default barrier, time horizon, risk-free rate)
Joint stress testing of banks and sovereigns can be carried out: macro variables affect bank CCA, and thus contingent liabilities, and fiscal surplus and in turn sovereign spreads
(Swedish Economic Review paper shows example on page 24 and 25 of base
and adverse stress test of bank expected losses and sovereign spreads.)
33
Linkages between Stylized Financial Sector and Sovereign CCA Balance Sheets
FINANCIAL SECTOR GOVERNMENT
ASSETSAssets (including government debt)/Loans/Other Assets+ Liquid Assets/Reserves+ Asset Guarantees
Present value of (Fiscal Surplusand Guarantee fees)+ Equity (government owned)+ Other Assets
Financial System Credit Risk, Sovereign Credit Risk
Sovereign CCA Balance
Sheet Model
Monetary Policy Model
Interest Rate Term Structure
Financial System Credit Risk
IndicatorFinancial Sector
CCA Model
• Fiscal Policy
• Debt Management
• Reserve Management
• Policy Rate
• Liquidity Facilities
• Quantitative Actions
• Capital Adequacy
• Financial Regulations
• Economic Capital
Fiscal and Debt Policies:
Guarantees
Financial Stability Policies:
Sovereign Credit Risk
Indicator
Monetary Policies:
Household CCA
Balance Sheet(s)
Corporate Sector CCA
Balance Sheet(s)
Sovereign Equity Claims (from Capital Injections)
Global Market Claims
on Sovereign
37
Traditional Flow and Accounting Framework No Risk-Adjusted Balance Sheets (Asset Volatility = 0)
No Credit Risk or Guarantees; No Risk Exposures
GovernmentAccounts Flow of Funds
Monetary Policy Model
Interest Rates
Bank Accounting
Balance Sheets
• Fiscal Policy
• Debt Management
• Reserve Management
• Policy Rate
• Liquidity Facilities
• Quantitative Actions
• Capital Adequacy
• Financial Regulations
Fiscal and Debt Policies:
Financial Stability Policies: Monetary Policies:
Household Accounting
Balance Sheet(s)
Corporate Accounting
Balance Sheet(s)
Capital Injections
Global Market Flows
Credit Flows
38
FURTHER APPLICATIONS – New risk-adjusted GDP and external account measures (from economy-wide CCA balance sheets, slide 17)
Solving for the put option in the financial sector one can see the put option depends on the implicit put options in other sectors. It is the compound nature of this put option which can lead to sudden non-linear increases in value.
( ) ( ) ( )F F F F F F DCF C C DLCF GLC GLC DH H HP E B A E B B P B P B P
Combining all the components of the junior claims or call option values across the economy (households, government, and foreign sector) gives the CCA-based Economic Output
CCAEO = 1 ... H j H n H G EC C EF FE E E E f E f E .
The sum of all foreign claims across the sectors is defined as the risk adjusted external account.
( )
( (1 ) ) ( )EC C EF F DC C C
DF F F GLCH GLC GLC
Risk Adjusted External Account f E f E f B P
f B P f B P
See Gray, D. F., Jobst, A. A., and S. Malone, 2010, “Quantifying Systemic Risk and Reconceptualizing the Role of Finance for Economic Growth,” Journal of Investment Management
39
FURTHER APPLICATIONS (cont.) - Integrating Financial System Risk Indicators into Monetary Policy ModelsGDP is affected by financial stability in the banking
system via: Financial accelerator links; Financial distress in banks and bank’s borrowers
reduces lending as borrower’s credit risk increases; Explicit inclusion of CCA banking system credit risk
indicator in monetary policy models in the output gap equation.
Uses a simple two-module framework:
1. Central Bank of Chile Macro Monetary Policy Model.
2. CCA Financial System Module. See Garcia et al. 2011 “Incorporating Financial Sector into Monetary Policy Models: Case
of Chile” IMF WP/11/228
40
Including CCA Banking Risk Indicator in Bank of Chile Monetary Policy Model: Conclusions
A simple, but powerful model for monetary policy including financial sector risk. Empirical evidence supports the model. Impulse Responses behave according to theory.
Robust efficient frontier (inflation volatility vs output volatility) A stronger reaction of interest rates to financial risk indicator reduces inflation volatility and output volatility.
Base model reaction to dtd: 0.5, 1.0 ,1.5
2.0
3.0
4.0
5.0
6.0
3.0 4.0 5.0 6.0 7.0
Inflation volatility
Out
put
vol
atili
ty
DTD: 0.5
DTD: 1.0
DTD: 1.5
41
FURTHER APPLICATIONS (cont.) - Ongoing Joint work with ECB – CCA-GVAR for EU(Joint work with ECB: Marco Gross, Matthias Sydow, and Joan Paredes)
Framework for analysis the interactions of banking sector risk, sovereign risk, GDP growth, stock markets, and other macro variable for 15 EU countries plus the US.
Uses CCA risk indicators for the banking systems and corporate sectors and sovereigns in each country,
Together with the GVAR (Global Vector Autoregression) model for each country, and weight matrices, impulse responses captures the non-linearity of changes in bank assets, equity capital, bank credit spreads, sovereign spreads and corporate credit risk.
42
CCA-GVAR model framework
CCA bank by bank risk indicators (63)
CCA sovereign credit risk indicators (16)
GDP data (16 series) Stock market index (16)
Other
Copula Simulation
GVAR Model (16 local
country models)
Scenarios and Shock Origins
Weighting Matrices
CCA banking system risk indicators (16)
Scenario Responses
GDP growth IRs Stock market IRs
Banking system IRs (ELRs and spreads)
Sovereign IRs (ELRs and spreads)
EU and Euro Zone Aggregate banking and sovereign
debt expected losses Aggregate bank capital impact
- Contingent liabilities - Borrowing cost changes - Debt to GDP changes
43
Conclusions for CCA GVAR Model
Integrated forward-looking banking system, corporate and sovereign risk indicators in a GVAR with macroeconomy and financial markets;
Large panel of banks, sovereigns, macro, financial markets all fully endogenous;
Stable global model provides meaningful responses in terms of directions and magnitude;
CCA captures nonlinear features related to bank capital, funding cost and sovereign risk;
Allows a range of policy options to be modeled and their risk mitigation impact quantified.
44
Additional references:
Macrofinancial Risk Analysis, Gray and Malone (Wiley Finance book Foreword by Robert Merton)
Gray, Dale F., Robert C. Merton, and Zvi Bodie. (2006) “A New Framework for Analyzing and Managing Macrofinancial Risks of and Economy” Harvard Business School Working Paper, No. 07-026, 2006. (Also NBER Working Paper Series, No. 12637.)
Gray, D. F., Merton R. C. and Z. Bodie, 2007, “Contingent Claims Approach to Measuring and Managing Sovereign Credit Risk, Journal of Investment Management, Vol. 5, No. 4, pp. 5-28.
Gapen M. T., Gray, D. F., Lim C. H., Xiao Y. 2008, “Measuring and Analyzing Sovereign Risk with Contingent Claims,” IMF Staff Papers Volume 55 Number 1 (Washington: IMF).
Gray, D. F., Jobst, A. A., and S. Malone, 2010, “Quantifying Systemic Risk and Reconceptualizing the Role of Finance for Economic Growth,” Journal of Investment Management, Vol. 8, No. 2, pp. 90-110.
Chen, Q., D. Gray, P. N’Diaye, H. Oura 2010 “International Transmission of Bank and Corporate Distress” IMF Working Paper No. 10/124 (Washington: International Monetary Fund).
Garcia, C., D. Gray, L. Luna, J. Restrepo, 2011, “Incorporating Financial Sector into Monetary Policy Models: Application to Chile,” IMF WP/11/22
Gray, D. and S. Malone, 2012, “Sovereign and Financial Sector Risk: Measurement and Interactions” Annual Review of Financial Economics, 4:9.
Gray, D., M. Gross, J. Paredes, M. Sydow, 2012, “Modeling the Joint Dynamics of Banking, Sovereign, Macro, and Financial Risk using Contingent Claims Analysis (CCA) in a Multi-country Global VAR” forthcoming
Gray, D. F., and A. A. Jobst, 2012, “Systemic Contingent Claims Analysis (Systemic CCA) – Estimating Potential Losses and Implicit Government Guarantees to Banks,” IMF Working Paper (Washington: International Monetary Fund), forthcoming.