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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.
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Pillar III presentation 2 27-15 - redacted version

Apr 14, 2017

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Page 1: Pillar III presentation 2 27-15 - redacted version

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.

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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

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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

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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!

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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)

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

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ANNEX I:CONNECTIVITY MEASURES

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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

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GAMLSS

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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.

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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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