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)

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.

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.

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.

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?

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.

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

)

.

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.

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.

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.

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

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

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

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.

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

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.

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

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).

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).

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

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

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.