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Financial MarketLinkages During

Crises

Werner Barthel

Introduction

The GeneralModel

Related Models

Spillover andContagion

Data

Modelspecification

Estimation

Results

Conclusion

Financial Market Linkages During CrisesAn empirical approach to contagion and spillover

effects

Werner Barthel

December 2, 2008


Crises

Werner Barthel

Introduction

The GeneralModel

Related Models


Data

Modelspecification

Estimation

Results

Conclusion

Overview

I This talk is based on "‘Unraveling Financial MarketLinkages During Crises"’ by Mardi Dungey andVance L. Martin in Journal of Applied Econometrics,2007.

I Related work:I Source for the definition of contagion and spillovers:

"‘Contagion: Monsoonal Effects, Spillovers, andJumps between Multiple Equilibria"’ by Paul Massonin IMF Working Paper, 1998.

I More detailed description of the simulation estimator:"‘A Multifactor Model of Exchange Rates withUnanticipated Shocks: Measuring Contagion in theEast Asian Currency Crises"’ by Mardi Dungey andVance L. Martin in Journal of Emerging MarketFinance, 2004.


Crises

Werner Barthel

Introduction

The GeneralModel

Related Models


Data

Modelspecification

Estimation

Results

Conclusion

Overview

I Empirical model of multiple asset classes acrosscountries

I Application to linkages between currency and equitymarkets during the East Asian crisis

I Two asset classes in each country: equities andcurrencies

I Countries of the crises region as well as developedcountries are included.

I Financial market linkages during periods of financialcrises are formally specified.

I Contagion and Spillover effectsI Type of the empirical model:

I Latent factor model with common and idiosyncraticfactors

I Autocorrelation structure of the factorsI GARCH structure of autocorrelation residuals


Crises

Werner Barthel

Introduction

The GeneralModel

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Data

Modelspecification

Estimation

Results

Conclusion

Factor models in general

I Factor models are a special case of the state spacerepresentation of multivariate time series.

I We assume that a set of K observed variables Ytdepends linearly on N unobserved common factorsFt and on individual or idiosyncratic components ut ,where N < K .

I Yt = LFt + utI where L is a (K × N) matrix of factor loadings.I This can be seen as the measurement equation in

the state space terminology.I In our model the observed returns of equity and

currency markets in the different countries will bedriven by unobserved common factors andidiosyncratic components.


Crises

Werner Barthel

Introduction

The GeneralModel

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Data

Modelspecification

Estimation

Results

Conclusion

Classification of common factors andidiosyncratic components

I The idiosyncratic component has impacts upon aparticular asset market within a particular country

I Russian bond default (August 1998)I Shocks to the market factor impact upon a specific

asset class within a group of countriesI East Asian Crisis (1997-98), assumed to have

started as currency crisesI Shocks to the country factor impact upon all asset

classes of a countryI The effects of entering IMF negotiations, such as for

Argentina in 2001-2I Shocks to the global factor (Wt) impact upon all

asset classes across all countriesI No specific crises cited in the paper, but US interest

rates may be an example of having such generalimpacts.


Crises

Werner Barthel

Introduction

The GeneralModel

Related Models


Data

Modelspecification

Estimation

Results

Conclusion

The general modelI Build on standard latent factor finance modelsI N + 1 countries (i) each with J asset markets (j)I Latent factor model for demeaned returns Ri,j,t :

Ri,j,t = δi,jWt + λi,jMj,t + ωi,jCi,t + φi,jui,j,t (1)

I Common factors:I The Global factor (Wt) captures shocks that impact

upon all asset markets across all countries.I The Market factor (Mj,t) captures shocks that impact

upon a particular asset class j across all countries.I The Country factor (Ci,t) captures shocks that

impact upon all asset markets within a country.I Idiosyncratic shocks (ui,j,t) impact on a particular

asset market within a particular country.I The strength of the specific factors is measured by

the loading parameters δi,j , λi,j , ωi,j , and φi,j .


Crises

Werner Barthel

Introduction

The GeneralModel

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Data

Modelspecification

Estimation

Results

Conclusion

Dynamics of the latent factors (1)I Serial correlation in the mean:

Wt = ρW Wt−1 + νt

Mj,t = ρM,jMj,t−1 + εj,t

Ci,t = ρC,iCi,t−1 + ζi,t

ui,j,t = ρu,i,jui,j,t−1 + ηi,j,t

I where the residuals are assumed to be conditionallydistributed:

νt ∼ N (0,hW ,t)

εj,t ∼ N (0,hM,j,t)

ζi,t ∼ N (0,hC,i,t)

ηi,j,t ∼ N (0,hu,i,j,t)


Crises

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Introduction

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Data

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Estimation

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Conclusion

Dynamics of the latent factors (2)

I Conditional volatilities allow us to model theobserved volatility clustering

I → GARCH(1,1):

hW ,t = 1− αW − βW + αWν2t−1 + βW hW ,t−1

hM,j,t = 1− αM,j − βM,j + αM,jε2j,t−1 + βM,jhM,j,t−1

hC,i,t = 1− αC,i − βC,i + αC,iζ2i,t−1 + βC,ihC,i,t−1

hu,i,j,t = 1− αu,i − βu,i + αu,iη2i,j,t−1 + βu,ihu,i,j,t−1

I The intercept restriction serves as a normalization toidentify the volatility of each factor.


Crises

Werner Barthel

Introduction

The GeneralModel

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Data

Modelspecification

Estimation

Results

Conclusion

Variance covariance matrix of asset returns

I A feature of the model is the informativeinterpretation of the asset returns’ variancecovariance matrix.

I Sub-classes of related models are presented bydecomposing the covariances into the contributionsof the different factors.

I The sub-classes concentrate on different interactionsbetween asset markets.


Crises

Werner Barthel

Introduction

The GeneralModel

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Data

Modelspecification

Estimation

Results

Conclusion

Unconditional volatility of asset returns

I Assumption of independent factors

E [R2i,j,t ] =

δ2i,j

1− ρ2W

+λ2

i,j

1− ρ2M,j

+ω2

i,j

1− ρ2C,i︸︷︷︸

systematic

+φ2

i,j

1− ρ2u,i,j︸︷︷︸

idiosyncratic

I Relative contributions of the four factors to thevolatility of each asset return


Crises

Werner Barthel

Introduction

The GeneralModel

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Data

Modelspecification

Estimation

Results

Conclusion

Interaction between asset markets (1)

I Commonality across national borders of the sameasset class

I In the general model the unconditional covariancebetween country i and country k for the j th asset isgiven by:

E [Ri,j,tRk ,j,t ] =δi,jδk ,j

1− ρ2W︸︷︷︸

world

+λi,jλk ,j

1− ρ2M,j︸︷︷︸

market

I Forbes and Rigobon (2002) and others used thissub-class of models for contagion tests


Crises

Werner Barthel

Introduction

The GeneralModel

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Data

Modelspecification

Estimation

Results

Conclusion


I Commonality across asset classes within a countryI In the general model the unconditional covariance

between asset markets j and l in country i is givenby:

E [Ri,j,tRi,l,t ] =δi,jδi,l

1− ρ2W︸︷︷︸

world

+ωi,jωi,l

1− ρ2C,j︸︷︷︸

country

I Fang and Miller (2002) and others


Crises

Werner Barthel

Introduction

The GeneralModel

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Data

Modelspecification

Estimation

Results

Conclusion


I Commonality across national borders and acrossasset classes

I In the general model the unconditional covariancebetween asset market j in country i and asset marketl country k is given by:

E [Ri,j,tRk ,j,t ] =δi,jδk ,l

1− ρ2W︸︷︷︸

world

I Equivalent to the basic one-factor ICAPM by Solnik(1974)


Crises

Werner Barthel

Introduction

The GeneralModel

Related Models


Data

Modelspecification

Estimation

Results

Conclusion

Definition of spillover and contagion(Masson(1998,1999))

I Spillovers are the transmission at time t or later ofshocks which occurred at time t − 1

I → Response to expected propagation pathsI Contagion is the contemporaneous or later

transmission of unexpected shocksI → Residual transmission after accounting for all

other sources of transmissions including spilloversI This model views the difference between contagion

and spillovers as referring to the timing of the initialimpact of the shock.


Crises

Werner Barthel

Introduction

The GeneralModel

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Data

Modelspecification

Estimation

Results

Conclusion

Idiosyncratic source of the shockI Shock is located in a particular country’s (k) asset

market (s) (uk ,s,t )I Remember: uk ,s,t = ρu,k ,suk ,s,t−1 + ηk ,s,t

I We augment equation (1) by a spillover and acontagion term:

Ri,j,t = δi,jWt + λi,jMj,t + ωi,jCi,t + φi,jui,j,t+

L∑l=1

θi,j,luk ,s,t−l︸︷︷︸spillover

+L∑

l=0

γi,j,lηk ,s,t−l︸︷︷︸contagion

I The spillover term reflects information that isavailable to agents in other markets at time t − 1.

I Contagion occurs over and above the linkages whichare included in the information sets of agents.


Crises

Werner Barthel

Introduction

The GeneralModel

Related Models


Data

Modelspecification

Estimation

Results

Conclusion

Asset market source of the shock

I Shock is located in a particular asset market (Ms,t )I Remember: Ms,t = ρM,sMs,t−1 + εs,t

I We augment equation (1) again by a spillover and acontagion term:


L∑l=1

θi,j,lMs,t−l︸︷︷︸spillover

+L∑

l=0

γi,j,lεs,t−l︸︷︷︸contagion

I → parsimonious representation of modelling a largenumber of potential linkages between asset marketsthrough the asset market factor Ms,t and itsunanticipated term εs,t


Crises

Werner Barthel

Introduction

The GeneralModel

Related Models


Data

Modelspecification

Estimation

Results

Conclusion

Country source of the shock

I Shock is located in a particular country (Ck ,t )I Remember: Ck ,t = ρC,kCk ,t−1 + ζk ,t

I We augment equation (1) once again by a spilloverand a contagion term:


L∑l=1

θi,j,lCk ,t−l︸︷︷︸spillover

+L∑

l=0

γi,j,lζk ,t−l︸︷︷︸contagion

I As with the asset market source, this specificationcan be extended further by including feedbackbetween countries.


Crises

Werner Barthel

Introduction

The GeneralModel

Related Models


Data

Modelspecification

Estimation

Results

Conclusion

Data description

I The above model is now applied to testing thetransmission between currency and equity marketsduring the East Asian financial crises of 1997-98

I Sample period: 2 July 1997 to 31 August 1998 (304daily observations)

I Indonesia, Korea, Malaysia, and Thailand : includedto identify the linkages amongst financial marketswithin the same geographical region which aredirectly exposed to the crises.

I US and Australia: included to identify transmissionmechanisms to countries outside the East Asianregion

I US: identify common shocks as well as identifyingnumeraire shocks as all exchange rates aredenominated in terms of the US dollar


Crises

Werner Barthel

Introduction

The GeneralModel

Related Models


Data

Modelspecification

Estimation

Results

Conclusion

Contemporaneous structure

Figure: Correlation matrices of equity and currency returns


Crises

Werner Barthel

Introduction

The GeneralModel

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Data

Modelspecification

Estimation

Results

Conclusion

Autocorrelation structure

I Preliminary identification of the autocorrelationstructure

I VAR(1) to VAR(5) containing all eleven returns seriesare estimated.

I AIC and HIC are minimized for a lag length of one.


Crises

Werner Barthel

Introduction

The GeneralModel

Related Models


Data

Modelspecification

Estimation

Results

Conclusion

Conditional volatility structure

I Preliminary analysis of the volatility structure of theeleven return series

I GARCH(1,1) models for each of the series:

rt = µt + ut

ut =√

htzt

ht = α0 + α1u2t−1 + β1ht−1

ut ∼ N (0,ht)

zt ∼ i .i .d .(0,1)

I SIC is minimized for five out of eleven return seriesby the GARCH(1,1) model.


Crises

Werner Barthel

Introduction

The GeneralModel

Related Models


Data

Modelspecification

Estimation

Results

Conclusion

Model specification (1)I East Asian crisis is characterized as a cross market

crises.I Two asset markets (equity (q) and currency (x)) in

six countriesI Equity returns:

Ri,q,t = δi,qWt + λi,qMq,t + ωi,qCi,t + φi,qui,q,t+

θi,x ,1Mx ,t−1︸︷︷︸(∗)

+ γi,x ,0εx ,t︸︷︷︸(∗∗)

+ τiu0,q,t−1︸︷︷︸(∗∗∗)

i = 0,1, . . . ,5

I (*): Spillovers from the currency marketI (**): Contagion from currency marketI (***): Effect of an idiosyncratic shock in the US (lag

due to time zone differences)


Crises

Werner Barthel

Introduction

The GeneralModel

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Data

Modelspecification

Estimation

Results

Conclusion

Model specification (2)

I Empirical analogue for currency returns:

Ri,x ,t = δi,xWt + λi,xMx ,t + ωi,xCi,t + φi,xui,x ,t+

θi,q,1Mq,t−1︸︷︷︸(∗)

+ γi,q,0εq,t︸︷︷︸(∗∗)

+ω0,xC0,t︸︷︷︸(∗∗∗)

+φ0,xu0,x ,t︸︷︷︸(∗∗∗∗)

i = 0,1, . . . ,5

I (*): Spillovers from the equity marketI (**): Contagion from the equity marketI (***): US country factor included as the US are the

numeraire country.I (****): Effect of an idiosyncratic shock in the US (No

time lag as exchange rates are based on the NYclose.).


Crises

Werner Barthel

Introduction

The GeneralModel

Related Models


Data

Modelspecification

Estimation

Results

Conclusion

Factor dynamicsI Autocorrelation of world and common factors

Wt = ρW Wt−1 + νt

Mj,t = ρM,jMj,t−1 + εj,t j = q, x

I Conditional distributions of residuals

νt ∼ N (0,hW ,t)

εj,t ∼ N (0,hM,j,t)

I GARCH(1,1) structures of conditional variances

hW ,t = 1− αW − βW + αWν2t−1 + βW hW ,t−1

hM,j,t = 1− αM,j − βM,j + αM,jε2j,t−1 + βM,jhM,j,t−1

I Distribution of country and idiosyncratic factors

Ci,t ∼ N (0,1) i = 0,1, . . . ,5

ui,t ∼ N (0,1)


Crises

Werner Barthel

Introduction

The GeneralModel

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Data

Modelspecification

Estimation

Results

Conclusion

Unconditional volatility decomposition

Figure: Based on the specifications of Ri,q,t , Ri,x,t , and theirfactor dynamics


Crises

Werner Barthel

Introduction

The GeneralModel

Related Models


Data

Modelspecification

Estimation

Results

Conclusion

Estimation approach

I The unobserved factors in a latent factor model areusually extracted using a Kalman filter.

I However, the authors claim that the Kalman filter isinconsistent due to the nonlinearities arising from theGARCH structure of the model. Gourieroux andMonfort (1994)

I An Estimation through maximum likelihoodprocedures needs multidimensional integrals that arebeyond the scope of standard numerical methods.

I The authors thus propose a simulation estimator.


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Werner Barthel

Introduction

The GeneralModel

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Data

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Estimation

Results

Conclusion

Simulation estimator - basic idea

I Simulate the latent factor model for an initial set ofstarting parameters to generate a set of simulatedreturns.

I The simulated returns are then calibrated with theactual returns via a set of moment conditions.

I Moment conditions:I Represent an auxiliary modelI Should capture the empirical characteristics of the

data (contemporaneous correlations amongstreturns, autocorrelations in both the means and thevariances of returns)

I Used to identify the parameters of the underlyingmodel

I See Dungey and Martin (2004)


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Werner Barthel

Introduction

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Data

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Estimation

Results

Conclusion

Indirect parameter estimates (1)

Figure: Parameter estimates with standard errors inparentheses

I Standard errors are in general relatively large.I A joint test confirms a correct specification.


Crises

Werner Barthel

Introduction

The GeneralModel

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Data

Modelspecification

Estimation

Results

Conclusion

Indirect parameter estimates (2)

Figure: Overall, contemporaneous, autocorrelation, andvolatility consistency tests

I Consistency tests that compare the moments of theauxiliary model using the actual data with the samemoments based on the simulated data.

I Under H0 the model is correctly specified and thetest statistics are asymptotically χ2 distributed.

I Overall test can be broken down in terms ofmoments of the auxiliary model that are designed tocapture the respective features of the data.


Crises

Werner Barthel

Introduction

The GeneralModel

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Data

Modelspecification

Estimation

Results

Conclusion

Dynamics

I Strength and duration of the effects of shocksI Computation of impulse responses:

I Simulating the estimated model over the crisis period10,000 times and computing the mean of thesimulated values for each time horizon.

I Confidence intervals are calculated as 2 standarddeviations of the simulated data.


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Werner Barthel

Introduction

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Data

Modelspecification

Estimation

Results

Conclusion

Impulse responses (1)

Figure: Effects of a one unit shock in the global factor


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Werner Barthel

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Conclusion


Figure: Effects of a one unit shock in the currency market factor


Crises

Werner Barthel

Introduction

The GeneralModel

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Data

Modelspecification

Estimation

Results

Conclusion


Figure: Effects of a one unit shock in the equity market factor


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Werner Barthel

Introduction

The GeneralModel

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Data

Modelspecification

Estimation

Results

Conclusion

Tests of contagion and spillovers (1)

I The above impulse responses contain bothcontagion and spillover effects.

I The following tests are based on a likelihood ratiotest which compares the constrained andunconstrained values of the indirect estimator.

I Under H0 the test statistic is asymptotically χ2R

distributed where R is the number of restrictions.


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Werner Barthel

Introduction

The GeneralModel

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Data

Modelspecification

Estimation

Results

Conclusion

Tests of contagion and spillovers (2)

Figure: Likelihood ratio tests of statistical significance ofalternative models


Crises

Werner Barthel

Introduction

The GeneralModel

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Data

Modelspecification

Estimation

Results

Conclusion

Variance decompositions (1)

I How to get the relative size of the contribution ofspillovers and contagion to the volatility in assetreturns?

I → volatility decomposition


Crises

Werner Barthel

Introduction

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Data

Modelspecification

Estimation

Results

Conclusion

Variance decompositions (2)

Figure: Volatility decompositions of asset markets during thecrises period: expressed in percentages


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Werner Barthel

Introduction

The GeneralModel

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Data

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Estimation

Results

Conclusion

Comparison with pre-crises period (1)

I How to examine further the relative strength ofcontagion?

I Compare results to pre-crises period where therewas no contagion.

I A fixed exchange rate regime prevailed: →concentrate on equity markets

I Three factors are now no longer identifiableseparately.

I A one factor model is estimated over the period 1stJanuary 1996 to 31st March 1997.


Crises

Werner Barthel

Introduction

The GeneralModel

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Data

Modelspecification

Estimation

Results

Conclusion

Comparison with pre-crises period (2)

Figure: Contributions to the increase in equity returns volatilityfrom pre-crises to crisis period


Crises

Werner Barthel

Introduction

The GeneralModel

Related Models


Data

Modelspecification

Estimation

Results

Conclusion

Conclusion

I A dynamic latent factor framework is used to model arange of potential linkages that connect assetmarkets across countries during financial crises.

I Latent factors are identified by the comovements ofasset returns within and across classes of financialmarkets.

I Importance of cross-market linkages for both assetreturns

I Spillovers: cross-market linkages in t of shockswhich occurred in t − 1

I Contagion: residual shocks that arecontemporaneously transmitted

I Spillover effects between markets were relativelylarger than contagion effects.

I Both were statistically significant.


Crises

Werner Barthel

Introduction

The GeneralModel

Related Models


Data

Modelspecification

Estimation

Results

Conclusion

Thank you for your attention!

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