Redacted version of presentation delivered as part of the 2015 US FSAP stress testing regime

1. MARKET-BASED INDICATORS APPROACH
TO STRESS TESTING: PRELIMINARY RESULTS
BENJAMIN HUSTON
DALE GRAY
This presentation and its findings are intended as background for discussions with the U.S. stress
testing experts in the context of the FSAP. Some findings have not undergone a full internal review
and should not be shared outside the technical team involved in the US FSAP stress testing exercise.

2. U.S FSAP PILLAR III:
MARKET-BASED INDICATOR STRESS TESTING REGIME
 Overview
 Systemic Risk Dashboard
 Contingent Claims Analysis (CCA) model, data, and historical outputs
 CCA stress testing approach for Pillar III
 Macro factor satellite model to project CCA risk indicators for scenarios
 Network analysis
 SyRin stress testing approach for Pillar III
2

3. WHY MARKET-BASED INDICATORS?
 Supervisory data is confidential and often cannot be utilized for FSAP stress testing purposes
 Market prices contain valuable information that can be used to corroborate traditional stress
testing methodologies and findings
 Stress tests can be extended to sectors that are not traditionally subject to bank-like
supervisory oversight
3

4. SYSTEMIC RISK DASHBOARD

5. SYSTEMIC RISK DASHBOARD (FORTHCOMING)
 The market-indicator based stress tests will be prefaced by a “dashboard” which will use an
established IMF framework to answer a series of questions to analysis systemic risk*
 The dashboard will use an assortment of metrics to address key risks
 Some of the metrics that will be featured in the dashboard include:
 SRISK (Engle, 2010)
 CoVaR (Andrian, 2008)
 network/contagion analysis
 SyRin:
 Contingent Claims Analysis (CCA
*For further information see Systemic Risk Monitoring (‘SysMo’) Toolkit, IMF working paper No. 13168
5

6. CONTINGENT CLAIMS ANALYSIS

7. PREVIEW OF PROPOSED CCA APPROACH AND ITS BENEFITS
The CCA was used in the 2010 US FSAP (and in 9 other FSAPs)
The proposed approach for this US FSAP will cover more institutions and have broader coverage
across the financial and corporate sectors than before
The analysis will be enhanced by integrating macro factor stress testing with measures of network
interconnectedness
The outputs for base and adverse scenarios will include default probabilities, expected loss values, capital/asset ratios, fair
value credit spreads, and capital shortfalls (i.e., the capital required to attain a “safe” credit risk level as measured by default
probability and credit spreads)
7

8. CORE CONCEPT: CONTINGENT CLAIMS ANALYSIS (CCA)
Assets = Equity + Risky Debt
= Equity + PV of Debt Payments – Expected Loss due to Default
= Implicit Call Option + PV of Debt Payments – Implicit Put Option
Assets
Equity
or Jr
Claims
Risky
Debt
•Value of liabilities
derived from value of
assets
• Uncertainty in asset
value
8

9. DEFAULT PROCESS IN THE CCA STRUCTURAL MODEL
ValueofAssets/Liabilities
Timet = 0 T = 1 year
Notional value of liabilities =
Default Barrier
XT
Distribution of market
value of assets
E[AT] = μ
Probability of
Default ≈ EDF
Distance to
default (DD) in σ
σ
Asset Volatility
9

10. CALIBRATION AND DERIVED RISK INDICATORS
Market capitalization, equity volatility, and book values of debt are used to calculate
implied value of assets and asset volatility. For each institution, these are used to
calculate the:
(i) Probability of Default (one year PD)
(ii) Expected Losses (EL), Implicit Put Option
(iii) Implied credit spread called the “Fair-value CDS” (FVCDS) spread in basis points (= f
(EL, t, risk-free rate))
(iv) The market implied government guarantee or contingent liability can be estimated
from the difference between the (higher) FVCDS and the (lower) observed CDS
spread (implicit guarantee lowers CDS)
10
* Based on Credit Edge Data; see Annex 1 for details

11. TRADEOFFS BETWEEN MARKET CAPITALIZATION, MARKETVALUE
OF ASSETS AND DEFAULT PROBABILITY
 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%.
 A 0.5% EDF is near investment grade
0
20,000
40,000
60,000
80,000
100,000
120,000
140,000
1,400,0001,500,0001,600,0001,700,0001,800,0001,900,0002,000,0002,100,000
Market Value of Assets (million $)
MarketCapitalization(million$)
0
20,000
40,000
60,000
80,000
100,000
120,000
140,000
0 5 10 15 20 25 30
EDF, One Year Default Probability in Percent
MarketCapitalization(million$)

12. SAMPLE INSTITUTIONS
Number Selection Criteria
Asset Managers 41 10 billion USD plus market cap
NBFIs 13 10 billion USD plus market cap
Insurers 44 20 billion USD plus market cap
Corporates 32
Must be one of the largest non-financial
DJIA public companies, or an auto maker
that received government support, or an
iconic “new economy” technology
company with a large and rapidly growing
market cap
US Banks 46 20 billion USD plus market cap
GSEs 2
Must have entered government
conservatorship
Non-US GSIBs 20
Must have been designated by the FSB as a
GSIB and not be domiciled in the U.S.
Total 198
12

13. PROPOSED APPROACH
 Fit models using DFAST macro variables as regressors and default probabilities, expected
losses, and fair-value CDS spreads as dependent variables
 For capturing credit risk, use CreditEdge data from 2001 to present
 For macro risk, use publicly available DFAST data
 Conduct stress tests using three macro scenarios that coincide with those used in Pillar II
and calculate impact on capital ratios and CCA credit risk indicators
 Use a risk appetite factor, calibrated using the 2008-09 crisis, that is consistent with
scenario adversity
 Apply interconnectedness measures described in more detail in subsequent Network
Analysis section 13

14. HYPOTHETICAL EXAMPLE:
CAPITAL/ASSET RATIOVS 1-YR PROBABILITY OF DEFAULT (PD)
y = 0.0734x‐0.483
R² = 0.9339
0
0.05
0.1
0.15
0.2
0.25
0.3
0.00 0.50 1.00 1.50 2.00 2.50 3.00
MarketCap/Assets(%)
Probability of Default (%)
14

15. HYPOTHETICAL EXAMPLE:
USE OF SATELLITE MODEL TO PROJECT PD UNDER STRESS
ProbabilityofDefault(%)
0.00
0.50
1.00
1.50
2.00
2.50
3.00
3.50
9/1/2014
12/1/2014
3/1/2015
6/1/2015
9/1/2015
12/1/2015
3/1/2016
6/1/2016
9/1/2016
12/1/2016
3/1/2017
6/1/2017
9/1/2017
EDF Baseline
EDF Adverse 2
EDF Adverse 1
15

16. HYPOTHETICAL EXAMPLE:
PROJECTED CAPITAL / ASSET RATIO UNDER STRESS
*Dashed line is near-investment grade capital ratio threshold
Capital/AssetsRatio(%)
0
0.05
0.1
0.15
0.2
0.25
9/1/2014
1/1/2015
5/1/2015
9/1/2015
1/1/2016
5/1/2016
9/1/2016
1/1/2017
5/1/2017
9/1/2017
Baseline
Adverse 2
Adverse 1
16

17. HYPOTHETICAL EXAMPLE:
5-YR CREDIT SPREADS UNDER STRESS
*Scenario Adverse 2 with higher market price of risk increases FVCDS spread
Basispoints
17
0
500
1000
1500
2000
2500
9/1/2014
12/1/2014
3/1/2015
6/1/2015
9/1/2015
12/1/2015
3/1/2016
6/1/2016
9/1/2016
12/1/2016
3/1/2017
6/1/2017
9/1/2017
FVCDS Baseline
FVCDS Adverse 2
FVCDS Adverse 1
Adverse 2 with
higher MPR

18. HYPOTHETICAL EXAMPLE:
CAPITAL SHORTFALL UNDER STRESS
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
9/1/2014
12/1/2014
3/1/2015
6/1/2015
9/1/2015
12/1/2015
3/1/2016
6/1/2016
9/1/2016
12/1/2016
3/1/2017
6/1/2017
9/1/2017
Baseline
Adverse 1
Adverse 2
CapitalShortfall(%)
18

19. MEASURING FINANCIAL SYSTEM PROBABILITIES OF DEFAULT
19
[REDACTED]

20. MEASURING FINANCIAL SYSTEM EXPECTED LOSSES
20
[REDACTED]

21. NETWORK ANALYSIS

22. MOTIVATION FOR UTILIZING NETWORK INFORMATION
 Prospectively use network connectivity statistics as an interaction term to inform our stress testing models (e.g.,
an entity or sector in-degree/out-degree variable combined with credit growth rates)
 May yield better predictions of capital shortfalls in stressed scenarios
 Network analysis can provide both a qualitative picture (graph) and quantitative measures of financial system
dynamics over time
 Capture potential domestic/international spill-over and contagion risks
22

23. NETWORK EXAMPLES
*Illustrative examples of historical and scenario based Granger-Causality networks 23
Historical Network
(2007 – 2013)
Base Scenario Adverse Scenario

24. DERIVINGTHE NETWORKS
 At the entity- and sector- levels:
1. Use algorithms to fit satellite models using DFAST macro variables as predictors and default probabilities and expected
losses as dependent variables
2. Apply Granger-Causality tests to model residuals and derive adjacency matrices and networks
3. Describe networks in terms of topology (who is connected to who and to what extent), centrality (who is most
important), and community structure (which parts of the network cluster together and share common features), and
entropy (how much network “information” is there)
adjacency matrixresiduals network graph communities
24

25. THANKYOU!

26. SYRIN
SYSTEMIC RISK AND INTERCONNECTEDNESS MEASURES

27. SYRIN: SYSTEMIC RISK AND INTERCONNECTEDNESS MEASURES
Approach
 See forthcoming IMF working paper for analytical details (Segoviano et al; 2014) and (Goodhart, Segoviano; 2006)
 Derives widely-applicable financial stability indicators and system loss measures to detect direct/indirect linkages
among institutions/sectors within a given financial system
27
[REDACTED]

28. SYRIN
28
[REDACTED]

29. ANNEX I:
CONTINGENT CLAIMS ANALYSIS

30. DIFFERENCE BETWEEN ACTUAL AND RISK-NEUTRAL DEFAULT
PROBABILITY
Asset Value
Expected Asset
Distributions of Asset value at T
Drift of μ
Distress Barrier
A0
T Time
“Actual “
Probability
of Default
Drift of r
“Risk Adjusted “ Probability
of Default
,A M
r
SR





30

31. MARKET PRICE OF RISK IN CCA/MKMV MODELS
To get the Risk-neutral Default Probability one must use the EDF and the Market
Price of Risk
MKMV uses CAPM, the excess return of a security is equal to the beta of the
security times the market risk premium.
Beta is equal to the correlation of the asset with the market times the volatility of
the asset divided by the volatility of the market.
Here SR is the Sharpe Ratio for the market.
So, the market price of risk is:
( )Mr r    
,
cov( , )
var( )
V M
A M
M M
r r
r

 

  , ,
( )M
A M A M
M
r
r SR

    


  
,A M
r
SR





1
,( )Risk Neutral A MktEDF N N EDF SR T

   
31

32. FAIRVALUE CDS – FVCDS
Using Risk-Neutral EDF and the Loss Given Default (LGD for FVCDS is from the banking sector
average LGD) FVCDS is Calculated
 , c
1
ln 1 *Risk Neutral Banking Se tor Ave Risk NeutralFVCDS LGD EDF
T
   
Note that in designing scenarios, the market Sharp ratio can be changed to reflect
the anticipated market price of risk for the particular scenario. For example a
severe Adverse 3 scenario could be associated with a market Sharpe ratio similar
to the level during after the Lehman crisis. Thus FVCDS and bank funding cost
would increase reflecting the change in global risk appetite
32

33. ANNEX II:
NETWORK ANALYSIS

34. GRANGER-CAUSALITYTESTS
34

35. NETWORKTOPOLOGY: IN-DEGREE AND OUT-DEGREE
35

36. CENTRALITY MEASURES: DEGREE CENTRALITY
36

37. CENTRALITY MEASURES: EIGENVECTOR CENTRALITY
37

38. SHANNON ENTROPY
38

39. INFORMATION-CRITERIA BASED MODEL SELECTION AND
BAYESIAN MODEL AVERAGING
Fit millions of models and select top 100
with best information criteria scores
(below the red line)
Assess probability a top model is the
“true model”
(red line is cumulative 95% probability)
Assess how often specific variables
appear in top models
(those exceeding redline are likely in
the “true model”) 39

40. ANNEX III:
HISTORICAL CCA RISK INDICATORS

41. CCA ASSESSMENT OF U.S. FINANCIAL SYSTEM RISK
CRISIS PERIOD: MARCH 9, 2009
41
[REDACTED]

42. CCA ASSESSMENT OF U.S. FINANCIAL SYSTEM RISK
PRESENT PERIOD: SEPTEMBER 30, 2014
42
[REDACTED]

43. CCA ASSESSMENT OF U.S. FINANCIAL SYSTEM RISK
SPILLOVER THREATS: CRISIS (LEFT) AND PRESENT (RIGHT) PERIODS
43
[REDACTED]

44. CCA ASSESSMENT OF U.S. FINANCIAL SYSTEM RISK
SPILLOVER THREATS: CRISIS AND PRESENT PERIODS (CONTINUED)
44
[REDACTED]

45. ANNEX IV:
HISTORICAL EXAMPLE OF CCA RISK ZONE ANALYSIS

46. CCA RISK ASSESSMENT EXAMPLE: CITIGROUP
CCA-based “risk-zones” can be used to assess an institution's level of credit risk from given market information
46

47. ENTITY- AND SECTOR-LEVEL CCA ANALYSIS
CCA-indicators gave predictive warning of the Lehman collapse and the trouble at Citigroup.
They can be utilized at both the entity and sector levels.
MarketCap/Assets(%)
47

48. EXAMPLE: CITIGROUP (POST-LEHMAN)
From the time of the Lehman collapse until the time the financial crisis peak began to abate, Citigroup’s credit risk was well-captured by a concurrent
CCA market-based indicator
48