pillar iii presentation 2 27-15 - redacted version
TRANSCRIPT
MARKET-BASED INDICATORS APPROACHTO STRESS TESTING: FINAL RESULTSBENJAMIN 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.
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
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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
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SYSTEMIC RISK DASHBOARD
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 5
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SyRinDerives widely-applicable financial stability indicators and systemic loss measures to detect direct/indirect linkages among institutions/sectors within a given financial system
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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
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CONTINGENT CLAIMS ANALYSIS
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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SAMPLE INSTITUTIONSNumber Selection Criteria
Asset Managers 41 10 billion USD plus market capNBFIs 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 capBanks 46 20 billion USD plus market cap
GSEs 2 Must have entered government conservatorship
Foreign Insurers and Foreign Banks 32
All banks and insurers designated by the FSB as GSIB/GSII plus largest non-US
domiciled global insurersTotal 210
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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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DEFAULT PROCESS IN THE CCA STRUCTURAL MODEL
Valu
e of
Ass
ets
/ Lia
bilit
ies
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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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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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
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HISTORICAL RECAP
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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 ProbabilityFinancial Institution
Rating Percent FractionAA+ 0.057 0.00057A‐ 0.18 0.0018
BBB+ 0.23 0.0023BBB‐ 0.37 0.0037BB+ 0.46 0.0046BB‐ 0.72 0.0072B+ 1 0.01B‐ 2.05 0.0205
CCC+ 3.65 0.0365CC 12.84 0.1284
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MODELING FRAMEWORKAN INTRODUCTION TO GAMLSS
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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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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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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)
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STRESS TEST RESULTS
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DEFAULT PROBABILITY PROJECTIONS
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MACRO CONTRIBUTIONS TO SYSTEM DEFAULT RISK
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March 9, 2009 June 16, 2016
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SECTOR CONTRIBUTIONS TO SYSTEM DEFAULT RISK
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March 9, 2009 June 16, 2016
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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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DOMESTIC AND CROSS-BORDER SPILLOVERS*
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* Results represent linear spillover estimates only (domestic system result withstanding)
Orig
inat
ing
Sect
or
Receiving Sector
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THE EFFECT OF CONNECTIVITY ON CREDIT RISK
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ASSESSING CROSS-BORDER SPILLOVER RISK
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THANK YOU!
DIAGNOSTICSTHE AGGREGATE FINANCIAL SYSTEM MODEL
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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)
39Model normalized quantile residuals appear completely normal which means the choice of distributional model was correct
ANNEX I:CONNECTIVITY MEASURES
SPEARMAN RANK CORRELATION TESTS
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GLOBAL CLUSTERING COEFFICIENT
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PRUNED EXACT LINEAR TIME
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ANNEX II:GAMLSS METHODOLOGY
GAMLSS
GAMLSS
46* 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.
REFERENCES
Blancher, Nicolas, and others, 2013, “Systemic Risk Monitoring “Sysmo” Tool Kit - A User Guide”, IMF Working 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 School Working Paper No. 09/15 (Cambridge).
Gray, Dale, and Samuel Malone, 2008, Macrofinancial Risk Analysis (London: Wiley Finance).
US Financial Stability Stress Testing 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, NYU Vlab.
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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