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Global credit risk cycles, lending standards, and limits to cross border risk diversification
SYstemic Risk TOmography:
Signals, Measurements, Transmission Channels, and Policy Interventions
Bernd Schwaab, European Central Bank Siem Jan Koopman, VU University Amsterdam and Tinbergen Institute André Lucas, VU University Amsterdam and Tinbergen Institute SYRTO Code Workshop Workshop on Systemic Risk Policy Issues for SYRTO July, 2 2014 - Frankfurt (Bundesbank-ECB-ESRB)
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Mitigation : Credit Cycle and Linkages
A review of two papers :
• Nowcasting and forecasting global financial sector stress
and credit market dislocation, by SKL (2014, InternationalJournal of Forecasting).
• Global credit risk cycles, lending standards, and limits to
cross border risk diversification, by SKL (2014, DiscussionPaper).
Econometric methodology :
• High-dimensional mixed-measurement dynamic factor
model for Gaussian and non-Gaussian panel time series.
• State space importance sampling methods: integrating out the
unobserved dynamic factors from the data (signal extraction) and
from the likelihood function (parameter estimation) using efficient
simulation methods.
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Contributions
We decompose global default risk conditions into its different
systematic risk components at the world, regional, and industry-level
using a new methodological framework.
New framework? We suggest a mixed-measurement dynamic factor
model for both Gaussian and non-Gaussian high-dimensional panel
data to model global default risk and macro developments
simultaneously.
How to decompose default risk? We use a CreditMetrics firm
value model to disentangle (i) global and regional business cycle
effects, (ii) global and regional default-specific variation/frailty, (iii)
industry-specific dynamics, (iv) unsystematic/ idiosyncratic risk.
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Why is this important?
It is well known that corporate defaults cluster in time. Less is known
about the relative contribution of the different sources of systematic
default risk. What causes (excess) default clustering, and to
what extent?
If systematic default risk is not well explained by observed (macro,
financial, firm-level) information, but rather due to unmodeled (frailty,
contagion) dynamics, then implied risk measures are inaccurate.
Our factor model yields an integrated framework for estimation,
inference, and forecasting of corporate default rates at the global
level. Use as inputs for VaR levels, stress testing, loan pricing.
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Additional motivation: credit risk literature
• Unobserved risk factors matter. A few observables are not
enough, see Das, Duffie, Kapadia, Saita (JF, 2007).
• Econometric problem for frailty models: No analytic expression
for p(UC|NG data) and log-likelihood.
• Simulation based techniques required. Duffie, Eckner, Horel,
Saita (JF, 2009) use Simulated EM with Gibbs Sampling.
Wendin and McNeil (JEF, 2007) are fully Bayesian.
• KLS (2011, 2012) use simulation methods based on importance
sampling for non-Gaussian models in state space form.
• How important are observed and unobserved factors for non-U.S.
firms? Is X-border credit risk diversification always beneficial?
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Summary of main results
• There is a distinct world credit risk cycle, different from the
worlds’ macro cycles.
• In addition to macro factors, firms from all world regions load on
unobserved risk factors, excess clustering.
• Frailty factors are persistent: substantial decoupling from
macro-economic fundamentals before returning to their means.
• Global macro factors explain 4-11% of total default risk
variation, regional macro < 1%, global frailty 6-31%, regional
frailty 0-14%, and industry-specific 20-36%, depending on
industry and location.
• Approximately 0-80% of total default risk is diversifiable,
depending on sector and location. 20-40% is systematic.
• Risk bearing capacity of a global lender is not necessarily
superior to that of a nationally active lender.
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Firm-value model
As in Merton (1974), CreditMetrics (2007), we assume that a firm i
defaults if its log asset value Vit falls below a default threshold λi,
where
Vit =[
a′ifgt +b
′
ifmt +c′if
ct+d
′
ifdt +e
′
ifit
]
(systematic risk)
+√
1− a′ia′
i − b′ib′
i − ...− e′ie′
i · uit (idiosyncratic)
= w′
ift+√
1− w′
iwiuit, t = 1, ..., T.
A default occurs when Vit< λi ⇐⇒ uit<λi−w′
ift√1−w′
iw′
i
.
The conditional default probability is πit = Pr
(
uit<λi−w′
ift√1−w′
iw′
i
∣
∣
∣
∣
ft
)
.
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Empirical model
Assume firms (i = 1, .., I) can be pooled into groups (j = 1, .., J ),then
yj,t|f t ∼ Binomial(kj,t, πj,t),
πj,t = [1 + e−θj,t ]−1,
θj,t = χj+α′
jfgt +β
′
jfmt +γ
′
jfct+δ
′
jfdt +ǫ
′
jfit ,
where χj , αj , βj , γj, δj , ǫj are parameters to be estimated.
If uit is logistically distributed, then ∃ a 1-1 correspondence between
the parameters of the firm-value and the empirical model.
Define systematic risk of firm i as the variance of its firm asset value
process due to the systematic risk component, Var[Vit|uit] = w′
iwi.
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The joint credit risk/macro modelModel in state space form
Obs eq yj,t|f t ∼ Binomial(kj,t, πj,t) Act defaults
Fx,t|f t ∼ Normal(µx,t,Σx) Macro principal components
θz,t|f t ∼ Normal(µz,t, Σz) Log odds EDF factors
πj,t = [1 + e−θj,t ]−1default probability firm j
Signals θj,t = χj+α′
jfgt +β
′
jfmt +γ
′
jfct+δ
′
jfdt +ǫ
′
jfit
Factors ft = (f g′t , fm′
t ; f c′t ; fd′t ; f
i′t )
′
= Φf t−1+ηt, ηt∼NID(0, I −ΦΦ′)
Consider 18=3+4+1+4+6 latent factors, orthonormal.
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Parameter estimation
The observation density of Y = (Y ′
1 , ..., Y′
T )′ can be expressed as
p(Y ;ψ) =
∫
p(Y |f ;ψ)p(f ;ψ)df,
see Durbin and Koopman (1997) and KLS (2011, 2012).
A MC estimator of p(Y ;ψ) based on importance sampling is given by
p(Y ;ψ) = g(Y ;ψ)M−1M∑
k=1
p(Y |f (k);ψ)g(Y |f (k);ψ)
, f (k) ∼ g(f |Y ;ψ).
Remarks:
* Importance density g(f |Y ;ψ) is Laplace approximation to
p(f |Y ;ψ).* IS weights stable due to antithetic variables, despite high
dimensions.
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Default and exposures data(Moody’s DRD, 1980Q1-2013Q3)
total defaults, U.S. total defaults, U.K. total defaults, euro area total defaults, asia pacific
1980 1985 1990 1995 2000 2005 2010
25
50total defaults, U.S. total defaults, U.K. total defaults, euro area total defaults, asia pacific
total exposures, U.S. total exposures, U.K. total exposures, euro area total exposures, asia pacific
1980 1985 1990 1995 2000 2005 2010
1000
2000
3000total exposures, U.S. total exposures, U.K. total exposures, euro area total exposures, asia pacific
agg default fractions, U.S. agg default fractions, U.K. agg default fractions, euro area agg default fractions, asia pacific
1980 1985 1990 1995 2000 2005 2010
0.01
0.02
0.03agg default fractions, U.S. agg default fractions, U.K. agg default fractions, euro area agg default fractions, asia pacific
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EDF data(Moody’s Analytics)
EDF financial firms, 1 year ahead, U.S. EDF non−financial firms, 1 year ahead, U.S.
1995 2000 2005 2010
0.025
0.050
0.075
EDF financial firms, 1 year ahead, U.S. EDF non−financial firms, 1 year ahead, U.S.
EDF financial firms, 1 year ahead, U.K. EDF non−financial firms, 1 year ahead, U.K.
1995 2000 2005 2010
0.005
0.010
0.015
0.020
0.025EDF financial firms, 1 year ahead, U.K. EDF non−financial firms, 1 year ahead, U.K.
EDF financial firms, 1 year ahead, euro area EDF non−financial firms, 1 year ahead, euro area
1995 2000 2005 2010
0.01
0.02
0.03
0.04 EDF financial firms, 1 year ahead, euro area EDF non−financial firms, 1 year ahead, euro area
EDF financial firms, 1 year ahead, asia pacific EDF non−financial firms, 1 year ahead, asia pacific
1995 2000 2005 2010
0.025
0.050
0.075EDF financial firms, 1 year ahead, asia pacific EDF non−financial firms, 1 year ahead, asia pacific
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Macro principal componentsGlobal (three) and regional (four) macro factors
E[global macro f_t|data] 95% SE band first flobal PC
1985 1990 1995 2000 2005 2010 2015
−5.0
−2.5
0.0
2.5
E[global macro f_t|data] 95% SE band first flobal PC
E[global macro f_t|data] 95% SE band second global PC
1985 1990 1995 2000 2005 2010 2015
−2.5
0.0
2.5
E[global macro f_t|data] 95% SE band second global PC
E[global macro f_t|data] 95% SE band third global PC
1985 1990 1995 2000 2005 2010 2015
−2.5
0.0
2.5E[global macro f_t|data] 95% SE band third global PC
E[US macro f_t|data] 95% SE band regional PC
1985 1990 1995 2000 2005 2010 2015
−2.5
0.0
2.5
E[US macro f_t|data] 95% SE band regional PC
E[UK macro f_t|data] 95% SE band regional PC
1985 1990 1995 2000 2005 2010 2015
−2.5
0.0
2.5
E[UK macro f_t|data] 95% SE band regional PC
E[EA macro f_t|data] 95% SE band regional PC
1985 1990 1995 2000 2005 2010 2015
−2.5
0.0
2.5E[EA macro f_t|data] 95% SE band regional PC
E[AP macro f_t|data] 95% SE band regional PC
1985 1990 1995 2000 2005 2010 2015
−2.5
0.0
2.5E[AP macro f_t|data] 95% SE band regional PC
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Frailty factor estimatesOne global and three regional frailty factors
E[common / global frailty | data] 95% SE band
1985 1990 1995 2000 2005 2010 2015
−2
0
2
E[common / global frailty | data] 95% SE band
E[U.S. regional frailty | data] 95% SE band
1985 1990 1995 2000 2005 2010 2015
−2
0
2
E[U.S. regional frailty | data] 95% SE band
E[euro area regional frailty | data] 95% SE band
1985 1990 1995 2000 2005 2010 2015
−2.5
0.0
2.5 E[euro area regional frailty | data] 95% SE band
1985 1990 1995 2000 2005 2010 2015
−2.5
0.0
2.5
E[Asia−Pacific regional frailty | data] 95% SE band
U.K. frailty factor is insignificant.
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Industry-specific risk factorsfinancials; energy; industrials; technology; retail; consumer goods.
E[financial industry f_t | data] 95% SE band
1985 1990 1995 2000 2005 2010−2
0
2E[financial industry f_t | data] 95% SE band E[transport and energy f_t | data]
95% SE band
1985 1990 1995 2000 2005 2010−2.5
0.0
2.5E[transport and energy f_t | data] 95% SE band
E[industrials f_t | data] 95% SE band
1985 1990 1995 2000 2005 2010
−2
0
2E[industrials f_t | data] 95% SE band
E[technology f_t | data] 95% SE band
1985 1990 1995 2000 2005 2010
−2
0
2E[technology f_t | data] 95% SE band
E[retail and distribution f_t | data] 95% SE band
1985 1990 1995 2000 2005 2010−2.5
0.0
2.5E[retail and distribution f_t | data] 95% SE band
E[consumer industries f_t | data] 95% SE band
1985 1990 1995 2000 2005 2010−2
0
2E[consumer industries f_t | data] 95% SE band
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Model fit and loss ratesGood fit, mainly due to frailty and industry factors.
0.000 0.005 0.010 0.015 0.020
100
200
300
400
Actual losses fg, fm fg, fm, fc, fd fg, fm, fc, fd, fi
1980 1985 1990 1995 2000 2005 2010
0.005
0.010
0.015observed (global) default rate Fit, only macro factors fg, fm Fit, all factors fg, fm, fc, fd, fi
diamonds: observed aggregate default fractions, Moody’s DRD, all firms;
black line: fitted rates, based on full model with five sets of factors;
green line: variation due to global and regional macro factors only.
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Global default hazard ratesTime-variation in fitted rates at the industry-level across regions
Financial sector, U.S. U.K. euro area asia pacific
1985 1990 1995 2000 2005 2010 2015
0.5
1.0Financial sector, U.S. U.K. euro area asia pacific
Transportation, utilities, and energy, U.S. U.K. euro area asia pacific
1985 1990 1995 2000 2005 2010 2015
0.5
1.0
1.5
2.0 Transportation, utilities, and energy, U.S. U.K. euro area asia pacific
Capital goods, U.S. U.K. euro area asia pacific
1985 1990 1995 2000 2005 2010 2015
2
4
Capital goods, U.S. U.K. euro area asia pacific
Technology firms, U.S. U.K. euro area asia pacific
1985 1990 1995 2000 2005 2010 2015
1
2
3
Technology firms, U.S. U.K. euro area asia pacific
Retail and distribution, U.S. U.K. euro area asia pacific
1985 1990 1995 2000 2005 2010 2015
1
2
3 Retail and distribution, U.S. U.K. euro area asia pacific
Consumer industries, U.S. U.K. euro area asia pacific
1985 1990 1995 2000 2005 2010 2015
1
2
3Consumer industries, U.S. U.K. euro area asia pacific
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Decomposition of systematic default riskU.S. firms
Reg. Ind. GloM RegM GloF RegF Ind %SR1 %SR2
U.S. financial 4.0% 0.0% 9.5% 8.4% 31.0% 22.1% 53.0%
transport 4.0% 0.0% 9.5% 8.4% 31.5% 21.9% 53.4%
industrials 4.2% 0.0% 10.0% 8.8% 28.0% 23.0% 51.0%
technology 4.4% 0.0% 10.4% 9.2% 24.7% 24.1% 48.7%
retail 4.1% 0.0% 9.6% 8.5% 30.5% 22.2% 52.7%
consumer 3.8% 0.0% 8.9% 7.9% 35.9% 20.5% 56.4%
%SR1 is based on macro and frailty factors (columns 3-6),
%SR2 is based on all factors (columns 3-7, including industry-specific).
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Decomposition of systematic default riskAsia-Pacific firms
Reg. Ind. GloM RegM GloF RegF Ind %SR1 %SR2
A.P. financial 5.3% 1.0% 12.6% 13.0% 27.0% 32.0% 59.0%
transport 5.3% 1.0% 12.5% 12.9% 27.5% 31.8% 59.3%
industrials 5.5% 1.1% 13.1% 13.5% 24.3% 33.2% 57.5%
technology 5.8% 1.1% 13.6% 14.0% 21.3% 34.5% 55.8%
retail 5.4% 1.1% 12.7% 13.1% 26.6% 32.2% 58.8%
consumer 5.0% 1.0% 11.8% 12.2% 31.6% 30.0% 61.6%
%SR1 is based on macro and frailty factors (columns 3-6),
%SR2 is based on all factors (columns 3-7, including industry-specific).
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Credit risk deviations from fundamentalsco-vary with bank lending standards (Fed, BoE, ECB, BoJ)
Credit risk deviations, capital goods industry, U.S. U.K. euro area asia pacific
1985 1990 1995 2000 2005 2010 2015
−2
0
2
Credit risk deviations, capital goods industry, U.S. U.K. euro area asia pacific
U.S. Bank Lending Standards (FED SLO) U.K. BLS (BoE) E.A. BLS (ECB) Japanese BLS (BoJ)
1990 1995 2000 2005 2010 2015
−25
0
25
50
75
100 U.S. Bank Lending Standards (FED SLO) U.K. BLS (BoE) E.A. BLS (ECB) Japanese BLS (BoJ)
Net tightening bank lending standards, U.S. (FED SLO) changes in credit risk deviations, capital goods industry, U.S., yoy
1990 2000 2010
−2
0
2
Net tightening bank lending standards, U.S. (FED SLO) changes in credit risk deviations, capital goods industry, U.S., yoy
Net tightening BLS, U.K. (BoE) Changes in CRD, U.K., changes yoy
1990 2000 2010
−2
0
2
Net tightening BLS, U.K. (BoE) Changes in CRD, U.K., changes yoy
Net tightening BLS, E.A. (ECB) changes in CRD, euro area, changes yoy
1990 2000 2010
−2
0
2
Net tightening BLS, E.A. (ECB) changes in CRD, euro area, changes yoy
Net tightening BLS, Japan (BoJ) changes in CRD, asia pacific, yoy
1990 2000 2010
−2
0
2
Net tightening BLS, Japan (BoJ) changes in CRD, asia pacific, yoy
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Does diversification lower portfolio risk?Likely, but not necessarily
Loss fraction PF1, actual Loss density, full model Loss density, only macro factors
0.00 0.01 0.02 0.03 0.04
100
200
ES=2.49%
Loss fraction PF1, actual Loss density, full model Loss density, only macro factors
Loss fractions PF2, actual Loss density, full model Loss density, only macro factors
0.00 0.01 0.02 0.03 0.04
100
200
ES=1.79%
Loss fractions PF2, actual Loss density, full model Loss density, only macro factors
Loss fractions PF3, actual Loss density, full model Loss density, only macro factors
0.00 0.01 0.02 0.03 0.04
100
200
300
ES=2.02%
Loss fractions PF3, actual Loss density, full model Loss density, only macro factors
Loss as fraction of PF 4 Loss density M0 Loss density M3
0.00 0.01 0.02 0.03 0.04
100
200
300
ES=2.00%
Loss as fraction of PF 4 Loss density M0 Loss density M3
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This project has received funding from the European Union’s
Seventh Framework Programme for research, technological
development and demonstration under grant agreement n° 320270
www.syrtoproject.eu
This document reflects only the author’s views.
The European Union is not liable for any use that may be made of the information contained therein.