This document provides an overview of a market-based indicators approach to stress testing financial institutions in the United States. It describes using a systemic risk dashboard to monitor risks, a contingent claims analysis model to estimate institutions' default probabilities, and generalized additive models to project default probabilities under stress scenarios. Historical results are also recapped. Key findings on macroeconomic contributions and inter-sector spillovers are presented. Annexes provide details on modeling methodologies.

1. MARKET-BASED INDICATORS APPROACH
TO STRESS TESTING: FINAL 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 for Pillar III
 Projections
 Macro analysis
 Spillover analysis
 Connectivity analysis
Annexes
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
 The Systemic Risk Dashboard is an integral part of the market-based indicator stress testing regime.
It uses established IMF-methodologies* to analyze systemic risk along a number of dimensions
 Some of the metrics that will be featured in the dashboard include:
 SRISK
 SyRin
 Equity-Composite Z-scores
 Financial Cycles
 Other misalignment measures
*For further information see Systemic Risk Monitoring (‘SysMo’)Toolkit, IMF working paper No. 13168
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6. 6
[REDACTED]

7. 7
SyRin
Derives widely-applicable financial stability indicators and systemic loss measures to detect direct/indirect linkages
among institutions/sectors within a given financial system
[REDACTED]

8. 8
Source: IMF staff estimates; *APT: Arbitrage Pricing Theory Source IMF staff estimates; equity market under- or overvaluations are based on deviations of
various equity market valuation indicators from long-term averages (Z scores).
Source: IMF staff estimates; financial cycles are computed using the BIS methodology (BIS, 2014) and capture the co-
movement between credit growth and residential property prices. Empirically, downward inflections in a financial is shown
to be a good predictive measure of an impending domestic financial crisis
Source: IMF staff estimates; defined as the difference of the credit-to-gdp ratio to its long term trend,
calculated using an HP filter with a smoothing parameter of 400000
[REDACTED] [REDACTED]
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9. [REDACTED]

10. [REDACTED]

11. CONTINGENT CLAIMS ANALYSIS

12. CCA APPROACH
CCA was used in the 2010 US FSAP (and in 9 other FSAPs)
2015 US FSAP covers more institutions across wider range of sectors
than before
Analysis is enhanced by integrating macro factor stress testing with
spillover and interconnectedness measures
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13. 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
Banks 46 20 billion USD plus market cap
GSEs 2
Must have entered government
conservatorship
Foreign Insurers
and Foreign Banks
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All banks and insurers designated by the
FSB as GSIB/GSII plus largest non-US
domiciled global insurers
Total 210
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14. 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
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15. 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
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16. 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 a “distance-to-default” indicator. This indicator is then
mapped to one year default probabilities using Moody’s default
database and the CreditEdge 9.0 modeling methodology.
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17. STRESS TESTING APPROACH
 Construct a set of sector regression models to assess the impact of adverse macroeconomic
changes and increased connectivity on median credit/default risk
 Credit risk: ten years of daily CreditEdge default probability data (2004Q3 to 2014Q3)
 Macro risk: IMF/DFAST macro variables
 Connectivity: network clustering coefficient time-series
 Conduct stress tests under “baseline” and “stress” scenarios and forecast default
probabilities for five domestic and two foreign sectors
 Use default probability forecasts to assess potential inward cross-border spillovers
using a separate model for total U.S. financial system 17

18. HISTORICAL RECAP
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19. DEFAULT PROBABILITIES
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 Default probabilities can be
mapped to ratings, note that
investment grade and
above corresponds to BBB-
and above.
 Rule of thumb: “Safe zone”
is default probability of 0.5
percent (0.005 fraction) or
less
One‐year Default Probability
Financial Institution
Rating Percent Fraction
AA+ 0.057 0.00057
A‐ 0.18 0.0018
BBB+ 0.23 0.0023
BBB‐ 0.37 0.0037
BB+ 0.46 0.0046
BB‐ 0.72 0.0072
B+ 1 0.01
B‐ 2.05 0.0205
CCC+ 3.65 0.0365
CC 12.84 0.1284

20. [REDACTED]

21. [REDACTED]

22. MODELING FRAMEWORK
AN INTRODUCTION TO GAMLSS
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23. What is GAMLSS?
 General Adaptive Models of Location, Scale and Shape (GAMLSS) are a flexile class of statistical models which can estimate a quantity of interest
using dozens of different distributional assumptions. This model class also allows for explicit estimation of each distributional parameter (i.e.,
mean, variance, skewness, kurtosis). See Annex II for details.
Why GAMLSS?
 GAMLSS is a practical framework for utilizing the following functionalities to address the following issues and concerns
 [I
Functionality Methodological Issue End-User Concern
Semi- and non-parametric/nonlinear additive
terms
Violation of normality assumption Non-normality
High dimensional model selection algorithms Contemporaneous correlations “Excessive interdependence”
Penalty functions to prevent over fitting Heteroscadisticty
Validation/training/testing regime to assess
model predictive power
Excess skewness and kurtosis “Fat tails/tail risk”
Robust White-Hall standard errors Non-constant (i.e., adaptive) distributional
properties
Non-linearity
GENERAL ADAPTIVE MODELS OF LOCATION, SCALE AND SHAPE
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24. GAMLSS FOR STRESS TESTS
Default probability data is bounded along a 0-1 interval, has a skewed distribution, and can change in response to
macro factors in a non-linear manner. Econometric modeling of macro variables and default probabilities must
account for these characteristics.
Approach
 Beta, generalized gamma, inverse gamma, inverse gaussian, and generalized inverse gaussian distributions were used to
model median sector and aggregate financial system default probabilities
 Semi- and fully-nonparametric additive terms were utilized to capture non-linear and/or localized relationships
 Variable selection algorithms and generalized informational coefficient were used to chose best models
 Penalty functions and training/test sets were used to prevent over-fitting and assess predictive power
 Diagnostic tests were used to consistently check for modeling assumption violations
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25. This connectivity time series was
included as an independent variable
in all GAMLSS models
MEASURING CONNECTIVITY
Three step process to measure
connectivity
1. Perform Spearman Rank Correlation
Tests to identify correlated default
probabilities
2. Create “correlation networks” from test
results
3. Calculate global clustering coefficient
score for entire network
Above process was repeated applied to institution-level
data using 30-day rolling windows
* Pruned exact linear time (PELT) tests were performed to identify significant structural
changes (“regime changes”) in connectivity mean and variance. (See Annex I)
[REDACTED]

26. STRESS TEST RESULTS
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27. DEFAULT PROBABILITY PROJECTIONS
27
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28. [REDACTED]

29. [REDACTED]

30. MACRO CONTRIBUTIONSTO SYSTEM DEFAULT RISK
30
March 9, 2009 June 16, 2016
[REDACTED]

31. SECTOR CONTRIBUTIONSTO SYSTEM DEFAULT RISK
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March 9, 2009 June 16, 2016
[REDACTED]

32. CONNECTIONS AND SPILLOVERS
So far we have:
 Controlled for firm idiosyncratic risk by using the median sector default probability;
 Controlled for macro risk by using the macro variables;
 Controlled for connectivity and the system level via the inclusion of the connectivity measure;
 What remains it the impact of one sectors’ spillover impact on another sector either + or –
See next slide for this spillover effect………………………….
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33. DOMESTIC AND CROSS-BORDER SPILLOVERS*
33
* Results represent
linear spillover
estimates only
(domestic system
result withstanding)
OriginatingSector
Receiving Sector
[REDACTED]

34. THE EFFECT OF CONNECTIVITY ON CREDIT RISK
34
[REDACTED]

35. ASSESSING CROSS-BORDER SPILLOVER RISK
35
[REDACTED]

36. THANKYOU!

37. DIAGNOSTICS
THE AGGREGATE FINANCIAL SYSTEM MODEL
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38. 38
DIAGNOSTICS: THE AGGREGATE FINANCIAL SYSTEM MODEL
Orthogonalized additive
terms greatly decrease
correlation among predictor
variables and help to mitigate
estimation biases. (Shown right:
predictor correlation matrix.)
Worms plot (below) of the aggregate model’s
residuals shows that the model does not violate any
distribution assumptions. (Curved dotted lines are
95% CIs; fitted central red line should look fairly
straight)

39. 39Model normalized quantile residuals appear completely normal which means the choice of distributional
model was correct

40. ANNEX I:
CONNECTIVITY MEASURES

41. SPEARMAN RANK CORRELATIONTESTS
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42. GLOBAL CLUSTERING COEFFICIENT
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43. PRUNED EXACT LINEARTIME
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44. ANNEX II:
GAMLSS METHODOLOGY

45. GAMLSS

46. GAMLSS
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* See Stasinopoulos, D, and R. Rigby, 2007, Generalized Additive Models for Location, Scale and Shape
(GAMLSS) in R, Journal of Statistical Software, v. 23 Issue 7.

47. REFERENCES
Blancher, Nicolas, and others, 2013,“Systemic Risk Monitoring “Sysmo” Tool Kit - A User Guide”, IMFWorking Paper 13/168.
http://www.imf.org/external/pubs/cat/longres.aspx?sk=40791
Gray, Dale. F., R.C. Merton, and Z. Bodie, 2008,“A New Framework for Measuring and Managing Macrofinancial Risk and Financial Stability,”
Harvard Business SchoolWorking Paper No. 09/15 (Cambridge).
Gray, Dale, and Samuel Malone, 2008, Macrofinancial Risk Analysis (London:Wiley Finance).
US Financial Stability StressTesting Note, July 2010, International Monetary Fund
Acharya,V., R. Engle, and M. Richardson, Capital Shortfall:A New Approach to Ranking and Regulating Systemic Risks, AEA, January 7, 2012 ---
SRISK Model, NYUVlab.
Stasinopoulos, D, and R. Rigby, 2007, Generalized Additive Models for Location, Scale and Shape (GAMLSS) in R, Journal of Statistical Software,
v. 23 Issue 7.
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