looking for contagion in currency futures markets

LOOKING FOR CONTAGION

IN CURRENCY FUTURES

MARKETS

CHU-SHENG TAI

This article tests whether there are pure contagion effects in both condi-tional means and volatilities among British pound, Canadian dollar,Deutsche mark, and Swiss franc futures markets during the 1992 ERMcrisis. A conditional version of international capital asset pricing model(ICAPM) in the absence of purchasing power parity (PPP) is used to con-trol for economic fundamentals. The empirical results indicate that overallthere are no mean spillovers among those futures markets, but they aredetected during the crisis period. That is, past return shocks originating inany one of the four markets have no impact on the other three marketsduring the entire sample period, suggesting that these markets are weak-form efficient. However, this weak-form market efficiency fails to holdduring the market turmoil, especially for British pound and Swiss franc,and the sources of contagion-in-mean effects are mainly due to the returnshocks originating in three European currency futures markets. As for thecontagion-in-volatility, it is detected for British pound only because itsconditional volatility is influenced by the negative volatility shocks fromCanadian dollar, Deutsche mark, and Swiss franc, with Deutsche mark

For Correspondence, Chu-Sheng Tai, Department of Economics and Finance, College of BusinessAdministration, Texas A&M University-Kingsville, MSC 186, 700 University Blvd., Kingsville, TX78363-8203, e-mail: [email protected]

Received September 2002; Accepted January 2003

� Chu-Sheng Tai is an assistant professor of finance in the Department of Economics andFinance at the College of Business Administration of Texas A&M University-KingsvilleIn Kingsville, TX.

The Journal of Futures Markets, Vol. 23, No. 10, 957–988 (2003) © 2003 Wiley Periodicals, Inc.Published online in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/fut.10092

958 Tai

playing the dominant role in generating these shocks. JEL Classifications:C32; F31; G12. © 2003 Wiley Periodicals, Inc. Jrl Fut Mark 23:957–988,2003

INTRODUCTION

The 1997–1999 financial crises have brought about a renewed interest inthe study of the transmission of financial shocks/crisis across markets/countries. The existing literature on this study has primarily focused oneither stock markets or foreign exchange markets, and futures marketshave been scarcely discussed. Because futures prices contain informa-tion about investors’ expectations of the underlying assets, it will certainlybe interesting to examine if the dynamics of those prices change as theinvestors adjust their expectations during the financial crisis. In addition,previous research on this study has failed to take into account an impor-tant distinction between the two concepts of interdependence and conta-gion. Masson (1999) argues that there are three main channels thatfinancial markets turbulence can spread from one country to another.They are monsoonal effects, spillovers and pure contagion effects.“Monsoonal” effects, or “contagions from common causes” tend to occurwhen affected countries have similar economic fundamentals or facecommon external shocks. The second type of financial market interlink-ages arises from spillover effects, which may be due to trade linkagesor financial interdependence. The first two channels of financial crisescan be categorized as fundamentals-driven crises because the affectedcountries share some macroeconomic fundamentals, which imply thatthe transmission of financial crises is due to the interdependence amongthose countries and not necessarily due to contagion. The third transmis-sion channel is the pure contagion effect. Contagion here refers to thecases where crisis in one country triggers a crisis elsewhere for reasonsunexplained by macroeconomic fundamentals. For instance, a crisis inone country may lead creditors and investors to pull out from othercountries over which they have a poor understanding resulting frominformation asymmetries.

The purpose of this article is to test whether there were pure conta-gion effects among currency futures markets during the 1992 ERMcrisis. The European Monetary System (EMS) ran into trouble during1992. Britain was in severe recession with unemployment rates higherthan at any other time since the Great Depression of 1929–1933. Italyalso was also experiencing recession and high inflation. These conditions

Contagion in Currency Futures Markets 959

1For the details of the ERM crisis, please see Levi (1996).

in Britain and Italy occurred while Germany was experiencing its costlyreunification. High German interest rates due to the costs of reunifica-tion led Britain and Italy to raise interest rates during a recession tomaintain their currency’s value, and led speculators to bet that the lattertwo countries would devalue their currencies. Germany refused to makeany major concession by lowering interest rates, eventually forcingBritain and Italy to withdraw from the Exchange Rate Mechanism(ERM) of the EMS.1 The European currency crisis of 1992 culminatedas the French franc came under strong speculative pressure, followedby the virtual collapse of the ERM in August 1993. This 1992–1993currency crisis of ERM will certainly be an interesting episode to studycontagion. Specifically, in this article “contagion” is defined as significantspillovers of market-specific idiosyncratic shocks during the crisis aftereconomic fundamentals or systematic risks have been accounted for. Intesting for contagion, its existence depends on the economic fundamen-tals used. Unfortunately, there is disagreement on the definitions of thefundamentals. To control for the economic fundamentals, most empiri-cal studies tend to choose those fundamentals arbitrarily, such as byusing macroeconomic variables, dummies for important events, and timetrends. The problem with these control variables is that contagion is notwell defined without reference to a theory. To overcome this problem, aninternational capital asset pricing model (ICAPM) in the absence of pur-chasing power parity (PPP) is utilized to control the economic funda-mentals. The economic fundamentals under ICAPM are the worldmarket and foreign exchange risks, so the evidence of contagion isbased on testing whether idiosyncratic risks—the part that cannot beexplained by the world market and foreign exchange risks—are signifi-cant in describing the dynamics of conditional mean and volatility ofcurrency futures returns during the ERM crisis.

In addition to the contribution in overcoming the drawback ofarbitrarily choosing economic fundamentals in testing contagion effectsin previous studies, another contribution of this article is the method-ology used to test those effects. In particular, an asymmetric MultivariateGeneral Autoregressive Conditional Heteroscedastic in Mean(MGARCH-M) model is implemented to model the conditional meanand asymmetric volatility spillovers during the crisis, in addition to cap-turing the time dependencies in the second moments of asset returns, a

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2According to Forbes and Rigobon (2001), Dornbusch et al. (2000), and Kaminsky and Reinhart(2000), previous empirical studies on contagion can be categorized by methodology into fourgroups: (1) the testing of significant increases in correlation (Baig & Goldfajn, 1999; Calvo &Reinhart, 1996; Forbes & Rigobon, 1998, 1999; Park & Song, 2001); (2) the testing of significancein innovation correlation (Baig & Goldfajn, 1999); (3) the testing of significant volatility spillover(Edwards, 1998; Edwards & Susmel, 2000); (4) crisis prediction regression (Bae et al., Stulz, 2003;Eichengreen et al., 1996; Kaminsky & Reinhart, 2000; Sachs et al., 1996; Van Rijckeghem & Weder,1999). None of the contagion studies mentioned above explicitly takes the time dependencies in thesecond moment into account. A recent article by Bekaert et al. (2002) applies three-stage univariateGARCH model to study contagion in equity markets by testing whether there is evidence of signifi-cant increase in crossmarket residual correlation during the crisis. Although they model conditionalsecond moments, they cannot answer whether return shocks originating in one market will signifi-cantly affect the other markets during the crisis.

stylized property found in most financial time series, which has beenignored by most empirical studies on contagion.2 Furthermore, theMGARCH-M model adopted in this article also overcomes the draw-backs in previous studies in testing risk premium hypothesis in currencyfutures prices, and thus provides a new insight on the existence oftime-varying risk premium in those prices. For example, Kho (1996)applied single-beta CAPM with a bivariate GARCH parameterization toprice currency futures prices, and found significant time-varying marketrisk premium in those prices. He estimated his model currency by cur-rency, so the efficiency might be sacrificed in his study because crossas-set correlations and parameter restrictions are ignored. In addition, Kho(1996) implicitly assumed that PPP held, and thus ignored foreignexchange risk. Instead of using the single-beta CAPM, McCurdy andMorgan (1992) employed a two-factor model with a trivariate GARCHparameterization, and concluded that the risk premia contained in cur-rency futures prices were due to both market and consumption risks.However, similar to Kho (1996), McCurdy and Morgan (1992) estimatedtheir model currency by currency, so the efficiency might again be sacri-ficed in their study. Therefore, under the fully parameterized multivari-ate model adopted in this article, not only is the maximum efficiencygain retained in controlling the systematic risks when testing the conta-gion effects, but also some interesting statistics are recovered, which aremostly ignored in previous studies. In addition, the test of ICAPM in theabsence of PPP provides a new insight on the sources of time-varyingrisk premium in currency futures prices.

The empirical results show that overall there are no mean spilloversamong British pound, Canadian dollar, Deutsche mark, and Swiss francfutures prices, but they are detected during the crisis period. That is,past return shocks originating in any one of the four markets have noimpact on the other three markets during the entire sample period,


suggesting that these markets are weak-form efficient. However, thisweak-form market efficiency fails to hold during the crisis period, espe-cially for British pound and Swiss franc, and the sources of contagion-in-mean effects are mainly due to the return shocks originating in threeEuropean currency futures markets. As for the contagion-in-volatility, itis detected for British pound only because its conditional volatility isinfluenced by the negative volatility shocks from Canadian dollar,Deutsche mark, and Swiss franc, with Deutsche mark playing the domi-nant role in generating those shocks. Finally, the sources of time-varyingrisk premia come not only from the world market risk, but also from theforeign exchange risk, implying the important role of foreign exchangerisk in pricing currency futures prices. The empirical results from thisstudy provide useful insight to both investors and policy makers. Forexample, for crosshedging purposes, firms or investors should certainlyadjust their hedging portfolios in response to the changing dynamicsof their hedging instruments during the crisis. The dynamic link-ages among futures prices during the crisis should concern policymakers because these linkages have implications for regulatory policy infutures and spot markets.

The remainder of the article is organized as follows. The next sectionpresents the theoretical asset pricing model used to control for systematicrisks when testing pure contagion effects. Section 3 describes the econo-metric methodology employed to estimate the model and several testhypotheses are presented in Section 4. Section 5 describes the data andempirical results are reported in Section 6. Some conclusions are offeredin the final section.

THE THEORETICAL MOTIVATION

The first-order condition of any consumer-investor’s portfolio optimizationproblem can be written as:

(1)

where Mt is known as a stochastic discount factor (SDF) or an intertem-poral marginal rate of substitution (IMRS); Ri,t is the gross return ofasset i at time t, and �t�1 is market information known at time t � 1.Without specifying the form of Mt, Equation (1) has little empirical con-tent because it is easy to find some random variable Mt for which theequation holds. Thus, it is the specific form of Mt implied by an assetpricing model that gives Equation (1) further empirical content (e.g.,

E[MtRi,t 0 �t�1] � 1,�5i

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Ferson, 1995; Tai, 2000). Suppose Mt and Ri,t have the following factorrepresentations:

(2)

(3)

where ri,t � Ri,t � R0,t is the raw returns of asset i in excess of the risk-freerate, R0,t, at time t, and

are common risk factors that capture system-atic risk affecting all assets ri,t including Mt; bik are the associated time-invariant factor loadings that measure the sensitivities of the asset to thecommon risk factors, while ut is an innovation and ei,t are idiosyncraticterms that reflect unsystematic risk. The risk-free rate, R0,t�1, must alsosatisfy Equation (1).

(4)

Subtract Equation (4) from Equation (1):

(5)

Apply the definition of covariance to Equation (5), obtaining:

(6)

Substitute Equation (2) into Equation (6):

(7)

where lk,t�1 is the time-varying price of factor risk. Equation (7) is ageneral conditional multifactor asset pricing model derived from theintertemporal consumption-investment optimization problem.

In empirical tests, the SDF is projected onto two factors: the worldmarket and currency factors. The selection of those two factors is theo-retically justified based on the international version of CAPM in theabsence of PPP developed by Adler and Dumas (1983). To extend

� aklk,t�1Cov(ri,t, Fk,t 0 �t�1)

E[ri,t 0 �t�1] � ak

�bk

E[Mt 0 �t�1] Cov(ri,t, Fk,t 0 �t�1)

E[ri,t 0 �t�1] �Cov(ri,t, �Mt 0 �t�1)

E[Mt 0 �t�1]�5i

E[Mtri,t 0 �t�1] � 0�5i

E[MtR0,t�1 0 �t�1] � 1

E[ei,t 0 �t�1] � 0 5i, k; Fk,t

E[utFk,t 0 �t�1] � E[ut 0 �t�1] � E[ei,tFk,t 0 �t�1] �

ri,t � ai � aK

k�1 bikFk,t � ei,t�5i

Mt � a � aK

k�1 bkFk,t � ut


3Adler and Dumas (1983) present a model in which a combination of the world market and meas-ures of currency risk is mean variance efficient. Empirically, the foreign exchange risk can be brokendown into a separate factor for each currency, as in Dumas and Solnik (1995), De Santis and Gerard(1998), and Tai (1999), or can be approximated by a single aggregate variable, as in Jorion (1991),Ferson and Harvey (1994), Choi et al. (1998), and Tai (2000). Simplicity leads me to prefer the lat-ter approach. The choice of whether to include individual currencies or to aggregate currency riskis, nevertheless, a difficult one.

domestic CAPM into an international setting, previous researchersassume either that investors have logarithmic utility or that PPP holds.However, many empirical studies have documented that the violation ofPPP is a norm, although PPP at best tends to hold in the long run. In theabsence of PPP resulting from either different consumption tastes orviolation of the law of one price (LOP), investors from different coun-tries face different prices when holding the same asset. In this situation,international asset pricing model will contain risk premia that are relatedto the covariances of asset returns with exchange rates, besides the tradi-tional market risk premium.3 Therefore, a conditional multifactor assetpricing model containing world market and foreign exchange risks[Equation (7)] seems to be reasonable and will be used to control sys-tematic risks in testing contagion. Now the conditional multifactor assetpricing model in Equation (7) can be written as

(8)

where m denotes world market risk and c is the global currency risk.

ECONOMETRIC METHODOLOGY

The conditional ICAPM in Equation (8) has to hold for every asset.However, the model does not impose any restrictions on the dynamicsof the conditional second moments. Several multivariate GARCH(MGARCH) models have been proposed to model the conditional secondmoments, such as the diagonal VECH model of Bollerslev et al. (1988),the constant correlation (CCORR) model of Bollerslev (1990), the factorARCH (FARCH) model of Engle et al. (1990), and the BEKK model ofEngle and Kroner (1995). Among these four popular MGARCH models,the BEKK model is better suited for the purpose of this article because itnot only guarantees that the covariance matrices in the system are posi-tive definite, but also allows the conditional variances and covariances ofdifferent markets to influence each other, which is very important fortesting contagion. As a result, a BEKK structure with asymmetric volatil-ity effects is selected over the other MGARCH specifications to model

ri,t � lm,t�1 Cov(ri,t,rm,t 0 �t�1) � lc,t�1 Cov(ri,t;rc,t 0 �t�1) � ei,t�5i

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the conditional second moments of currency futures returns and to testcontagion effects among those returns.4 Specifically, the dynamic processfor the conditional covariance matrix of asset returns is specified as:

(9)

where Ht is 6 � 6 time-varying variance–covariance matrix of assetreturns; C is restricted to be a 6 � 6 upper triangular matrix, and A, B,D, G, K, L, M, N, P, Q, S, V, and Y are diagonal matrices whose generalform, X, is given by:

(10)

The 6 � 1 vector, ht�1, captures the asymmetric impact that the vec-tor of past negative shocks has on the conditional covariance matrix in amanner similar to that of Glosten et al. (1993), and is defined as:

(11)

The effects of past shocks of other markets on a market’s con-ditional variance or conditional covariances (volatility spillovers) arecaptured by the vectors ct�1, jt�1, mt�1, nt�1, and ut�1, which are asfollows:

ht�1 � Fmin(eBP,t�1, 0)min(eCD,t�1, 0)min(eDM,t�1, 0)min(eSF,t�1, 0)min(eTWFX,t�1, 0)min(eWorld,t�1, 0)

V

X � FxBP 0 0 0 0 00 xCD 0 0 0 00 0 xDM 0 0 00 0 0 xSF 0 00 0 0 0 xTWFX 00 0 0 0 0 xWorld

V

� Y� # rt�1r�t�1# Y

� Q� # tt�1t�t�1# Q � S� # yt�1y�t�1

# S � V� # zt�1z�t�1# V

� M� # nt�1n�t�1# M � N� # ut�1u� t�1

# N � P� # �t�1��t�1# P

� G� # ct�1c�t�1# G � K� # jt�1j�t�1

# K � L� # mt�1m�t�1L

Ht � C�C � A� # Ht�1# A � B� # et�1e�t�1

# B � D� # ht�1h�t�1# D

4The asymmetric volatility effects in variances and covariances have been documented in recentarticles by, among others, Kroner and Ng (1998) and Bekaert and Wu (2000).


(12)

Several articles in the literature show that volatility spilloversbetween markets are asymmetric in the sense that negative innovations ina market increase volatilities in other markets more than do positive inno-vations in that market. Consequently, it will be interesting to see whethersuch asymmetric volatility spillovers do occur during the crisis. The vectors�t�1, tt�1, yt�1, zt�1, and rt�1 capture this asymmetry and are defined as:

(13)rt�1 � Fcrisis[min(eWorld,t�1, 0)]crisis[min(eBP,t�1, 0)]crisis[min(eCD,t�1, 0)]crisis[min(eDM,t�1, 0)]crisis[min(eSF,t�1, 0)]crisis[min(eTWFX,t�1, 0)]

Vzt�1 � Fcrisis[min(eTWFX,t�1, 0)]

crisis[min(eWorld,t�1, 0)]crisis[min(eBP,t�1, 0)]crisis[min(eCD,t�1, 0)]crisis[min(eDM,t�1, 0)]crisis[min(eSF,t�1, 0)]

V;yt�1 � Fcrisis[min(eDM,t�1, 0)]crisis[min(eTWFX,t�1, 0)]crisis[min(eWorld,t�1, 0)]crisis[min(eBP,t�1, 0)]crisis[min(eCD,t�1, 0)]crisis[min(eDM,t�1, 0)]

V;tt�1 � Fcrisis[min(eDM,t�1, 0)]

crisis[min(eSF,t�1, 0)]crisis[min(eTWFX,t�1, 0)]crisis[min(eWorld,t�1, 0)]crisis[min(eBP,t�1, 0)]crisis[min(eCD,t�1, 0)]

V;�t�1 � Fcrisis[min(eCD,t�1, 0)]crisis[min(eDM,t�1, 0)]crisis[min(eSF,t�1, 0)]crisis[min(eTWFX,t�1, 0)]crisis[min(eWorld,t�1, 0)]crisis[min(eBP,t�1, 0)]

V;

nt�1 � FeTWFX,t�1

eWorld,t�1

eBP,t�1

eCD,t�1

eDM,t�1

eSF,t�1

V;�ut�1 � FeWorld,t�1

eBP,t�1

eCD,t�1

eDM,t�1

eSF,t�1

eTWFX,t�1

Vct�1 � FeCD,t�1

eDM,t�1

eSF,t�1

eTWFX,t�1

eWorld,t�1

eBP,t�1

V;�jt�1 � FeDM,t�1

eSF,t�1

eTWFX,t�1

eWorld,t�1

eBP,t�1

eCD,t�1

V;�mt�1 � FeSF,t�1

eTWFX,t�1

eWorld,t�1

eBP,t�1

eCD,t�1

eDM,t�1

V;

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5The ERM crisis period is assumed to be between 9/18/1992 and 08/27/1993.6Ebrahim (2000) also uses this diagonal BEKK model to test volatility spillover effects between for-eign exchange and money markets, but in this article not only are the usual volatility spillover effectstested within currency futures markets and between them and world equity market, but also conta-gion in asymmetric volatility spillover effects are tested within currency futures markets andbetween them and world equity market during a crisis.

where crisis is a dummy variable, which is equal to 1 during the crisis andzero otherwise.5 The difference between the first set of innovation vec-tors (ct�1, jt�1, mt�1, nt�1, ut�1) and the second set of innovation vectors(�t�1, tt�1, yt�1, zt�1, rt�1) is that the first set captures overall volatilityspillovers during the entire sample period, while the second set capturesthe asymmetric volatility spillovers during the crisis period. By includingvectors �t�1, tt�1, yt�1, zt�1, and ut�1, the incremental influences ofvolatility shocks on the currency futures returns can then be tested,which is a true test of contagion-in-volatility. In this model, for example,the conditional variance of British pound futures returns, hBP,t, dependson its past conditional variance, hBP,t�1, through the parameter, aBP, itsown past shocks, eBP,t�1 through the parameter, bBP, and past shocks ofthe other markets through the parameters, gBP, kBP, lBP, mBP, and nBP.This conditional variance also depends on its own past negative shocksthrough the parameter, dBP, and on past negative shocks of the othermarkets through the parameters, pBP, qBP, sBP, vBP, and yBP during the cri-sis. Here, these parameters measure the incremental amounts by whichbad news in one market at time t � 1 affect the conditional variance ofBritish pound futures returns at time t.

The parameterization of the conditional covariance matrix cantherefore be viewed as an extension of the diagonal BEKK representationof Engle and Kroner (1995), which allows for past shocks from othermarkets to influence conditional variances and covariances, for asymme-tries in the impacts of these shocks.6 This representation of the con-ditional covariance matrix differs from the most general BEKK form inthat conditional variances are not permitted to depend on crossproductsof lagged shocks, lagged conditional variances of other markets, andlagged conditional covariances with other markets. Similarly, conditionalcovariances are not influenced by lagged squared shocks and lagged con-ditional variances in other markets. The parameterization presented herefacilitates testing of the null hypothesis of no volatility spillover effectsagainst the alternative that conditional variances depend on other mar-kets, only through their past squared shocks. Even with this diagonalBEKK parameterization, it still requires the estimation of 78 parametersin the conditional covariance matrix.


Under the assumption of conditional normality, the log-likelihood tobe maximized can be written as:

(14)

where is the vector of unknown parameters in the model. Because thenormality assumption is often violated in financial time series, the quasi-maximum likelihood estimation (QML) proposed by Bollerslev andWooldridge (1992), which allows inference in the presence of departuresfrom conditional normality, is utilized. Under standard regularity condi-tions, the QML estimator is consistent and asymptotically normal andstatistical inferences can be carried out by computing robust Wald statis-tics. The QML estimates can be obtained by maximizing Equation (14),and calculating a robust estimate of the covariance of the parameterestimates using the matrix of second derivatives and the average of theperiod-by-period outer products of the gradient. Optimization is per-formed using the Broyden, Fletcher, Goldfarb, and Shanno (BFGS)algorithm.

HYPOTHESIS TESTING

Testing Time-Varying Risk Premium

Many empirical studies have shown that the prices of risks are time-varying (e.g., De Santis & Gerard, 1997, 1998; Dumas & Solnik, 1995;Harvey, 1991; Tai, 1999, 2001; among others). This time-varying price ofrisk is economically appealing in the sense that investors use all availableinformation to form their expectations about future economic perform-ance, and when the information changes over time, they will adjust theirexpectations and thus their expected risk premia when holding differentrisky assets. Therefore, in testing time-varying risk premium hypothesis,not only are the conditional second moments (covariance risks) allowedto change over time, but also the prices of covariance risks are permittedto be time-varying [Equation (8)].

The dynamics of prices of risks are chosen according to the theoret-ical international asset pricing model developed by Adler and Dumas(1983). In their model, the price of world market risk is a weighted aver-age of the coefficients of risk aversion of all national investors. Becausethe weights measure the relative wealth of each country and if allinvestors are risk averse, the world price of market risk should be posi-tive. Thus, similar to Bekaert and Harvey (1995) and De Santis and

�

ln L(�) � �TN2

ln 2p �12a

p

t�1ln 0Ht(�) 0 � 1

2 a

T

t�1et(�)�Ht(�)�1et(�)

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7As pointed out by De Santis and Gerad (1997), the conditional ICAPM is only a partial equilibriummodel, and the theory does not help identify the state variables that affect the prices of market andcurrency risks, so inevitably any parameterization of the dynamics of and can be criti-cized for being ad hoc.

lc,t�1lm,t�1

Gerard (1997, 1998) an exponential function is used to model thedynamic of and for the dynamics of lm,t�1 and for the dynamics of lc,t�1,a linear specification is adopted because the model does not restrict theprice of currency risk to be positive.7

(15)

(16)

where Zt�1 is a vector of information variables observed at the end oftime and t � 1 and w’s are time-invariant vectors of weights. Thus, theprice of currency risk is assumed to be a linear function of the informa-tion variables in Zt�1, and the price of world market risk is assumed to bean exponential function of information variables in Zt�1. Given thedynamics of prices of risks, I can then test the whether the world pricesof market and currency risks are significantly priced and change overtime by testing whether the information variables in Zt�1 are significantin addition to significant GARCH parameters.

Testing Contagion in Mean and Volatility

To test whether a market’s past idiosyncratic shocks have significantimpact on the other markets’ conditional returns (contagion-in-mean)during the ERM crisis, the past market-specific innovations are incorpo-rated into Equation (8). Specifically, Equation (8) can be modified as:

(17)

where crisis is a dummy variable, which is equal to 1 during the crisis andzero otherwise. In testing the contagion-in-mean effects, the pastmarket-specific innovations are allowed to affect currency futuresreturns in the entire sample period, and whether there are any incre-mental influences of past innovations on these returns during the crisisperiod are then tested. Thus, the contagion-in-mean hypothesis can be

� crisis aai, jvij ej,t�1b � ei,t;�5i, j

ri,t � lm,t�1Cov(ri,t, rm,t 0 �t�1) � lc,t�1Cov(ri,t; rc,t 0 �t�1) � ai, jfij ej,t�1

lc,t�1 � w�c zt�1

lm,t�1 � exp(w�m zt�1)


8For example, the British pound futures contract has a trading cycle with expiration in March, June,September, and December. During March prices from the June contract are taken for the futurestime series until the first business day of June, when the September contract takes over, even if theJune contract is still trading.9Between the world total market return index complied by Datastream and the widely used MorganStanley Capital International (MSCI) index, Datastream index is preferred because it captures morethan 75% of the market when compared to MSCI index, which only captures approximately 60% ofthe total market.

examined by testing whether the parameters, vij (i j), are individuallyor jointly significant after the systematic risks have been accounted for.

To test contagion-in-volatility hypothesis, one can test whether theelements in matrices P, Q, S, V, and Y are individually or jointly sig-nificant. For example, a test of null hypothesis that pBP,j is zero(H0 : pBP,j � 0) means that there is no contagion in asymmetric volatilityshocks from market j to British pound futures market. Similarly, a testof null hypothesis of H0 : pi,CD � qi,DM � si,SF � vi,TWFX � yi,World � 0;5i � BP or implies that the conditional volatility of British pound futuresreturns is not affected by the other markets’ negative idiosyncraticshocks. Finally, one can test the source of negative idiosyncratic shocks.For example, to test whether the negative shocks originate from Britishpound futures market, one can test the null hypothesis of H0 : yCD,j �

vDM,j � sSF,j � qTWFX,j � pWorld,j � 0; 5j � BP.

DATA AND SUMMARY STATISTICS

Futures prices for the British pound, Canadian dollar, Deutsche mark,and Swiss franc (BP, CD, DM, and SF, respectively) are taken fromDatastream. The futures prices are continuous settlement prices andcorrespond to the nearest (to expiry) contract month. They switch to thenext contract following the standard Datastream rollover procedure, andare labeled by the acronyms IBPCS00, ICDCS00, IDMCS00, andISFCS00.8 Datastream world total market return index (World) and thetrade-weighted U.S. dollar price of the currencies of major industrializedcountries (TWFX) are used to construct the world market risk and cur-rency risk, respectively.9 Seven-day Eurodollar interest rate is used asconditionally risk-free rate to compute the excess return on World.Weekly percentage currency returns are computed as:

where pt is either the currency futures price or TWFX at time t.

ri,t � ln a pt

pt�1b

970 Tai

10The excess dividend yield (DIV) is highly correlated with the U.S. term premium (USTP), so simi-lar to De Santis and Gerard (1997, 1998) the first difference of the U.S. term premium (�USTP) isused as one of the conditioning variables.

Several conditioning variables that have been widely used in theinternational asset pricing literature are selected (e.g., Bekaert & Harvey,1995; Bekaert & Hodrick, 1992; De Santis & Gerard, 1997, 1998;Ferson & Harvey, 1993; Harvey, 1991; Tai, 1999, 2000; among others).They are excess dividend yield measured by the dividend yield on Worldin excess of the 7-day Eurodollar interest rate (DIV), the change in theU.S. term premium, measured by the first difference of the yield differ-ence between 10-year Treasury constant maturity rate and 7-dayEurodollar rate (�USTP), the U.S. default premium, measured by theyield difference between Moody’s Baa-rated and Aaa-rated U.S. corpo-rate bonds (USDP), the lagged excess return on Datastream world totalmarket return index, and a constant (CONSTANT).10

The weekly data ranges from January 5, 1990, to March 23, 2001,which is a 586-data-point series. However, the rates of return and thefirst difference of conditioning variables are used, and finally all the con-ditioning variables are used with a 1-week lag, relative to the returnseries; that leaves 584 observations expanding from January 19, 1990, toMarch 23, 2001. All the data are extracted from Datastream.

Table I presents summary statistics of the continuously compoundedcurrency futures returns and excess world market returns. As can be seenfrom panel A, World not only has the highest weekly mean returns,0.036%, but also the highest standard deviation, 1.876%. Comparing theperformance of four currency futures returns, they are all negative, withSF being the best one with a mean of �0.023% per week but a high stan-dard deviation of 1.688%. CD, on the other hand, performs worst with anaverage return of �0.050% per week and a standard deviation of 0.698%.Figure 1 plots the futures price and returns for each currency. After look-ing at the plots, it is not surprising to find that the average currencyfutures returns are all negative because the futures prices are dropping,especially after 1995 in the sample period.

Table I also reports Bera-Jarque and Ljung-Box statistics. Bera-Jarque test rejects normality for all return series. The Ljung-Box test sta-tistics for raw returns [LB(24)] are not significant at any conventionallevel in all series, implying a weak form efficiency of currency futuresmarkets. However, for squared returns, LB2(24) is significant at the 1%level for all series except BP, indicating strong nonlinear dependenciesin the sample. This is consistent with the volatility clustering observed in


TABLE I

Summary Statistics of Currency Futures and World Stock Returnsa

Returns BP CD DM SF TWFX World

Mean (%) �0.025 �0.050 �0.045 �0.023 0.027 0.037Std. dev. (%) 1.394 0.698 1.511 1.688 0.861 1.876Minimum (%) �9.887 �2.361 �5.452 �6.457 �3.926 �9.127Maximum (%) 4.950 2.289 5.092 6.440 2.745 7.608B � J 575.270** 13.489** 8.550* 28.883** 41.517** 166.491**LB(24) 34.770 29.731 19.231 22.869 31.318 23.777LB2(24) 34.335 37.474* 81.019** 45.966** 64.051** 117.292**

Unconditional Correlation of Conditioning Variables

DIV �USTP USDP World

DIV 1�USTP 0.082** 1USDP �0.029 0.059 1World 0.055 �0.031 0.017 1

a(i) The statistics are based on weekly data from 01/19/90 to 03/23/01 (584 observations). The currency futuresreturns are British pound (BP ), Canadian dollar (CD), Deutsche mark (DM), and Swiss franc (SF ). The excessreturns on Datastream world total market return index (World ) is used to proxy the global market risk, and thelog first difference of the trade-weighted U.S. dollar price of the currencies of major industrialized countries(TWFX ) is used to proxy the currency risk. (ii) The Bera-Jarque (B � J ) tests normality based on both skewnessand excess kurtosis and is distributed x2 with two degrees of freedom. (iii) LB(24) and LB2(24) denote the Ljung-Box test statistics for up to the 24th order autocorrelation of the raw and squared returns, respectively. (iv) Theconditioning variables are the excess dividend yield, measured by the dividend yield on Datastream world totalmarket return index in excess of the 7-day Eurodollar deposit rate (DIV ), the change in the U.S. term premium,measured by the first difference of the yield difference between 10-year Treasury constant maturity rate and7-day Eurodollar rate (�USTP), the U.S. default premium, measured by the yield difference between Moody’sBaa-rated and Aaa-rated U.S. corporate bonds (USDP ), and the lagged excess return on Datastream worldtotal market return index (World ). (v) * and ** denote statistical significance at the 5 and 1% level, respectively.

most financial time series, suggesting that the use of a conditionalheteroscedasticity model is advisable.

The unconditional correlation coefficients for the conditioningvariables are reported in panel B of Table I. The correlation coefficientsare pretty small, and most of them are insignificant, indicating thatthe selected conditioning variables contain sufficiently orthogonalinformation.

EMPIRICAL EVIDENCE

The quasi-maximum likelihood estimation of the conditional ICAPM[Equation (17)] is reported in Table II. The hypothesis tests regardingthe prices of risks and the predictability of conditioning variables are

972 Tai

FIGURE 1Currency futures prices and returns.

2.01.91.81.71.61.51.4

1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001

1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001

1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001

1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001

1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001

1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001

a: Currency futures price: BP

b: Currency futures price: CD

c: Currency futures price: DM

d: Currency futures price: SF

e: U.S. Trade Weighted Exchange Index: TWFX

f: World market stock Index: World

0.900.850.800.750.700.650.60

0.750.700.650.600.550.500.450.40

0.900.850.800.750.700.650.600.55

1101051009590858075

3000

2500

2000

1500

1000

500


FIGURE 1Currency futures prices and returns (continued).

0.0500.0250.000

�0.025

0.0240.0160.004

0.000�0.004�0.016�0.024

�0.06

�0.075

�0.04

�0.10�0.08�0.06�0.04�0.02

0.000.020.040.060.08

�0.03�0.02�0.01

0.000.010.020.03

�0.050�0.025

0.0000.0250.0500.075

�0.04�0.02

0.000.020.040.06

�0.050�0.075�0.100

1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001

1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001

1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001

1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001

1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001

1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001

g: Currency futures return: BP

h: Currency futures return: CD

i: Currency futures return: DM

j: Currency futures return: SF

k: U.S. Trade Weighted Currency return: TWFX

l: World Market return: World

974 Tai

TABLE II

Quasi-Maximum Likelihood Estimation of the Conditional ICAPMa

Conditional Mean Process

CONSTANT DIV �USTP USDP World

World Prices of Market and Currency Risks

�0.105 1.993 0.789 30.155 �22.602(1.989) (0.942)* (1.549) (22.151) (16.373)

�25.342 5.974 198.823 374.510 162.099(10.003)* (7.177) (79.530)* (83.286)** (219.166)

j � BP j � CD j � DM j � SF

Mean Spillovers

�0.060 �0.062 0.060 �0.036(0.077) (0.082) (0.117) (0.109)

0.010 �0.068 0.072 �0.028(0.055) (0.052) (0.068) (0.059)

�0.030 �0.064 �0.056 0.005(0.050) (0.102) (0.066) (0.050)

�0.060 �0.077 0.034 �0.096(0.067) (0.137) (0.070) (0.067)

Contagion in Mean

�0.148 �0.031 �0.738 0.532(0.160) (0.541) (0.177)** (0.201)**

0.117 0.060 �0.098 �0.013(0.099) (0.143) (0.099) (0.098)

0.193 �0.247 �0.029 �0.164(0.103) (0.254) (0.084) (0.082)*

0.287 �0.413 �0.077 �0.287(0.095)** (0.319) (0.128) (0.114)*

Conditional Variance Process

i � BP i � CD i � DM i � SF i � TWFX i � World

ai 0.387 0.934 0.784 0.725 0.774 0.932(0.063)** (0.028)** (0.015)** (0.022)** (0.014)** (0.027)**

bi 0.147 0.156 0.180 0.199 0.251 0.297(0.068)* (0.081) (0.039)** (0.047)** (0.041)** (0.060)**

di 7.019 �1.622 1.698 2.232 5.322 �2.011(4.474) (3.780) (1.505) (1.588) (6.113) (2.614)

Volatility Spilloversb

j � BP �0.040 �0.121 �0.009 0.014 �0.027(0.047) (0.033)* (0.037) (0.024) (0.039)

j � CD �0.077 0.104 0.175 �0.136 �0.095(0.105) (0.093) (0.071)** (0.069)* (0.182)

vSF, j

vDM, j

vCD, j

vBP, j

fSF, j

fDM, j

fCD, j

fBP, j

�c

�m


TABLE II (Continued)

Conditional Variance Process

i � BP i � CD i � DM i � SF i � TWFX i � World

j � DM 0.006 0.026 0.000 0.036 0.027(0.063) (0.040) (0.041) (0.022) (0.063)

j � SF 0.142 �0.052 �0.016 0.018 �0.028(0.097) (0.040) (0.026) (0.028) (0.058)

j � TWFX 0.118 0.059 0.008 0.001 �0.163(0.123) (0.075) (0.046) (0.070) (0.164)

j � World �0.203 �0.044 �0.031 �0.026 0.085(0.027)** (0.034) (0.024) (0.022) (0.019)**

Contagion in Asymmetric Volatilityb

j � BP �0.002 �1.224 �2.159 �0.007 0.011(0.371) (1.245) (1.446) (0.353) (0.124)

j � CD 58.061 �0.642 �9.823 12.007 0.208(27.698)* (7.412) (10.634) (7.169) (11.386)

j � DM �25.846 �0.235 �0.282 1.546 2.047(8.206)** (0.965) (3.639) (1.435) (2.376)

j � SF �26.394 1.989 �0.058 0.057 �1.543(10.779)* (1.675) (1.689) (1.129) (2.233)

j � TWFX �58.548 10.619 7.962 1.005 �0.234(35.594) (23.401) (10.598) (3.055) (20.544)

j � World 0.359 2.214 �9.517 9.857 �0.567(13.180) (7.378) (8.886) (9.985) (3.441)

Log-Likelihood Function: 14926.771

aRobust standard errors are given in parentheses. * and ** denote statistical significance at the 5 and 1% level,respectively.bThe reported parameter estimates for both the volatility spillover and contagion-in-asymmetric-volatility coeffi-cients can be interpreted as follows. For example, if xij represents the volatility spillover coefficient from marketj to market i, then the volatility spillover coefficient estimate from CD to BP is �0.077, which corresponds togBP,CD in matrix G in the variance–covariance matrix in Equation (9). Similarly, the volatility spillover coefficientestimate from DM to BP is 0.006, which corresponds to kBP,DM in matrix K in the variance–covariance matrix inEquation (9), and so on. The reported parameter estimates for the contagion-in-asymmetric-volatility coeffi-cients have the same interpretation as those for volatility spillover coefficients.

presented in Table III. The hypothesis tests concerning the contagion inmean and volatility are shown in Tables IV and V, respectively. Finally,summary statistics about the sources of risk premia and diagnostic teststatistics for the standardized residuals are reported in Table VI.

The Evidence of Time-Varying Risk Premia

First, consider the test results for the existence of time-varying riskpremium. The results are very encouraging. For example, the joint

976 Tai

11Both Dumas and Solnik (1995) and De Santis and Gerard (1998) use excess returns on 1-monthEuropean currency deposit rates to proxy for currency risks; however, in this article weekly currencyfutures prices are employed to test the existence of time-varying currency risk premia.

TABLE III

Hypothesis Tests Concerning Prices of Risks and Predictabilityof Conditioning Variables

Null Hypothesis Wald d.f. P-Value

1. Are the prices of currency and market and risks equal to zero? 112.127 10 0.000H0 : wc � wm � 0; Zt�1 � {CONSTANT, DIV, �USTP, USDP, World }

2. Are the prices of currency and market risks constant? 41.086 8 0.000H0 : wc � wm � 0; Zt�1 � {DIV, �USTP, USDP, World }

3. Is the price of currency risk equal to zero? 37.167 5 0.000H0 : wc � 0; Zt�1 � {CONSTANT, DIV, �USTP, USDP, World }

4. Is the price of currency risk constant? 33.039 4 0.000H0 : wc � 0; Zt�1 � {DIV, �USTP, USDP, World }

5. Is the price of market risk equal to zero? 70.446 5 0.000H0 : wm � 0; Zt�1 � {CONSTANT, DIV, �USTP, USDP, World }

6. Is the price of market risk constant? 5.013 4 0.285H0 : wm � 0; Zt�1 � {DIV, �USTP, USDP, World }

7. Is there no predictability from excess dividend yield? 4.809 2 0.090H0 : wc,k � wm,k � 0; 5k � DIV

8. Is there no predictability from the change in term premium? 6.497 2 0.038H0 : wc,k � wm,k � 0; 5k � �USTP

9. Is there no predictability from the U.S. default premium? 20.810 2 0.000H0 : wc,k � wm,k � 0; 5k � USDP

10. Is there no predictability from the world market portfolio? 2.975 2 0.225H0 : wc,k � wm,k � 0; 5k � World

hypothesis of zero prices of market and currency risks is strong rejectedby Wald statistic (Wald � 112.127) with a p-value of zero. The jointhypothesis of constant prices of market and currency risks is also signifi-cantly rejected (Wald � 41.086). Next, the joint hypothesis of constantprice of currency risks is strongly rejected by the Wald test(Wald � 37.167), but the joint hypothesis of constant price of marketrisk can not be rejected with a p-value of 0.285. These test results implythat currency risk is not only priced but also time varying, which is con-sistent with the findings of Dumas and Solnik (1995) and De Santis andGerard (1998).11 For market risk, it is priced, but its price does notappear to change over time. The conditioning variables useful in predict-ing the dynamics of the risk prices include the change in the U.S. termpremium (�USTP) and default premium (USDP) as evidenced from thehypothesis tests (#8 and #9) reported in Table III.


Evidence of Mean Spilloverand Contagion in Mean

After controlling the systematic currency and market risks, the test ofcontagion-in-mean effects can be carried out. However, before that, theoverall mean spillover effects in the entire sample period need to be con-trolled, so any incremental mean spillover effects can be tested duringthe crisis period. It can be seen from Table II that none of the meanspillover parameters, f, is significant based on robust standard errors,

TABLE IV

Hypothesis Tests Concerning Mean Spillover and Contagion in Mean


1. Is there no mean spillover for BP? 1.165 3 0.761H0 : fBP,j � 0; 5j � CD, DM, SF

2. Is there no mean spillover for CD? 3.125 3 0.372H0 : fCD,j � 0; 5j � BP, DM, SF

3. Is there no mean spillover for DM? 0.819 3 0.844H0 : fDM,j � 0; 5j � BP, CD, SF

4. Is there no mean spillover for SF? 1.163 3 0.761H0 : fSF,j � 0; 5j � BP, CD, DM

5. Is there no contagion in return shocks for BP? 20.867 3 0.000H0 : vBP,j � 0; 5j � CD, DM, SF

6. Is there no contagion in return shocks for CD? 1.788 3 0.617H0 : vCD,j � 0; 5j � BP, DM, SF

7. Is there no contagion in return shocks for DM? 7.777 3 0.050H0 : vDM,j � 0; 5j � BP, CD, SF

8. Is there no contagion in return shocks for SF ? 10.509 3 0.014H0 : vSF,j � 0; 5j � BP, CD, DM

9. Is there no mean spillover for BP? 0.795 3 0.850H0 : fi,BP � 0; 5i � CD, DM, SF

10. Is there no mean spillover from CD? 0.656 3 0.883H0 : fi,CD � 0; 5i � BP, DM, SF

11. Is there no mean spillover from DM? 1.521 3 0.677H0 : fi,DM � 0; 5i � BP, CD, SF

12. Is there no mean spillover from SF? 0.297 3 0.960H0 : fi,SF � 0; 5i � BP, CD, DM

13. Is there no contagion in return shocks from BP? 13.023 3 0.004H0 : vi,BP � 0; 5i � CD, DM, SF

14. Is there no contagion in return shocks from CD? 1.699 3 0.637H0 : vi,CD � 0; 5i � BP, DM, SF

15. Is there no contagion in return shocks from DM? 18.695 3 0.003H0 : vi,DM � 0; 5i � BP, CD, SF

16. Is there no contagion in return shocks from SF? 12.840 3 0.004H0 : vi,SF � 0; 5i � BP, CD, DM

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TABLE V

Hypothesis Tests Concerning Volatility Spillover and Contagion in Volatility


1. Is there no volatility spillover for BP? 65.827 5 0.000H0 : gi,CD � ki,DM � li,SF � mi,TWFX � ni,World � 0; 5i � BP

2. Is there no volatility spillover for CD? 8.060 5 0.152H0 : ni,BP � gi,DM � ki,SF � li,TWFX � mi,World � 0; 5i � CD

3. Is there no volatility spillover for DM? 19.868 5 0.001H0 : mi,BP � ni,CD � gi,SF � ki,TWFX � li,World � 0; 5i � DM

4. Is there no volatility spillover for SF? 7.312 5 0.198H0 : li,BP � mi,CD � ni,DM � gi,TWFX � ki,World � 0; 5i � SF

5. Is there no contagion in asymmetric volatility shocks for BP? 54.916 5 0.000H0 : pi,CD � qi,DM � si,SF � vi,TWFX � yi,World � 0; 5i � BP

6. Is there no contagion in asymmetric volatility shocks for CD? 1.4254 5 0.921H0 : yi,BP � pi,DM � qi,SF � si,TWFX � vi,World � 0; 5i � CD

7. Is there no contagion in asymmetric volatility shocks for DM? 2.258 5 0.812H0 : vi,BP � yi,CD � pi,SF � qi,TWFX � si,World � 0; 5i � DM

8. Is there no contagion in asymmetric volatility shocks for SF? 5.046 5 0.410H0 : si,BP � vi,CD � yi,DM � pi,TWFX � qi,World � 0; 5i � SF

9. Is there no volatility spillover from BP? 14.891 5 0.010H0 : nCD,j � mDM,j � lSF,j � kTWFX,j � gWorld,j � 0; 5j � BP

10. Is there no volatility spillover from CD? 14.309 5 0.013H0 : gBP,j � nDM,j � mSF,j � lTWFX,j � kWorld,j � 0; 5j � CD

11. Is there no volatility spillover from DM? 2.983 5 0.702H0 : kBP,j � gCD,j � nSF,j � mTWFX,j � lWorld,j � 0; 5j � DM

12. Is there no volatility spillover from SF? 8.579 5 0.127H0 : lBP,j � kCD,j � gDM,j � nTWFX,j � mWorld,j � 0; 5j � SF

13. Is there no volatility spillover from TWFX? 2.987 5 0.701H0 : mBP,j � lCD,j � kDM,j � gSF,j � nWorld,j � 0; 5j � TWFX

14. Is there no volatility spillover from World? 75.252 5 0.000H0 : nBP,j � mCD,j � lDM,j � kSF,j � gTWFX,j � 0; 5j � World

15. Is there no contagion in asymmetric volatility shocks from BP? 3.151 5 0.676H0 : yCD,j � vDM,j � sSF,j � qTWFX,j � pWorld,j � 0; 5j � BP

16. Is there no contagion in asymmetric volatility shocks from CD? 7.154 5 0.209H0 : pBP,j � yDM,j � vSF,j � sTWFX,j � qWorld,j � 0; 5j � CD

17. Is there no contagion in asymmetric volatility shocks from DM? 13.141 5 0.022H0 : qBP,j � pCD,j � ySF,j � vTWFX,j � sWorld,j � 0; 5j � DM

18. Is there no contagion in asymmetric volatility shocks from SF? 9.423 5 0.093H0 : sBP,j � qCD,j � pDM,j � yTWFX,j � vWorld,j � 0; 5j � SF

19. Is there no contagion in asymmetric volatility shocks from TWFX? 3.219 5 0.666H0 : vBP,j � sCD,j � qDM,j � pSF,j � yWorld,j � 0; 5j � TWFX

20. Is there no contagion in asymmetric volatility shocks from World? 2.442 5 0.785H0 : yBP,j � vCD,j � sDM,j � qSF,j � pTWFX,j � 0; 5j � World

implying that currency futures markets are very efficient in processingavailable information. This conclusion has also been further confirmedby the hypothesis tests of no mean spillover (#1–#4) reported inTable IV.


TABLE VI

Summary Statistics and Residual Diagnosticsa

BP CD DM SF TWFX World

Full sample periodPredicted total returns (%) 0.016 �0.001 �0.001 �0.010 �0.001 0.134Std dev. 0.285 0.121 0.219 0.327 0.090 0.227

Predicted returns due to mean spillovers 0.018 �0.005 0.001 0.000and contagion-in-mean (%)

Std dev. 0.274 0.119 0.178 0.293

Predicted total risk premium (%) �0.002 0.004 �0.002 �0.010 �0.001 0.134Std dev. 0.075 0.018 0.116 0.126 0.090 0.227

Predicted market risk premium (%) 0.011 0.006 0.017 0.011 �0.017 0.143Std dev. 0.013 0.016 0.028 0.026 0.030 0.237

Predicted currency risk premium (%) �0.013 �0.002 �0.019 �0.021 0.016 �0.009Std dev. 0.077 0.010 0.118 0.127 0.091 0.066

Conditional volatility (%) 1.341 0.677 1.464 1.652 0.832 1.793Std dev. 0.536 0.083 0.118 0.129 0.098 0.502

Time-varying price of risk 3.719 1.871Std dev. 3.487 11.548

Crisis periodPredicted total returns (%) 0.203 �0.075 �0.028 �0.022 �0.007 0.187Std dev. 0.886 0.281 0.496 0.840 0.055 0.141

Predicted returns due to mean spillovers 0.224 �0.073 �0.016 0.007and contagion-in-mean (%)

Std dev. 0.881 0.282 0.496 0.825

Predicted total risk premium (%) �0.021 �0.002 �0.012 �0.028 �0.007 0.187Std dev. 0.052 0.010 0.082 0.082 0.055 0.141

Predicted market risk premium (%) 0.012 0.002 0.040 0.027 �0.043 0.211Std dev. 0.024 0.008 0.026 0.028 0.035 0.153

Predicted currency risk premium (%) �0.033 �0.003 �0.052 �0.056 0.035 �0.023Std dev. 0.048 0.006 0.079 0.077 0.052 0.036

Conditional volatility (%) 2.175 0.795 1.630 1.795 0.859 1.589Std dev. 1.558 0.093 0.302 0.345 0.104 0.230

Time-varying price of risk 7.614 4.789Std dev. 3.336 6.332

Pseudo R2(%) 4.194 3.005 2.090 3.759 1.090 1.977

Residual diagnosticsB � J 10.184** 6.234* 25.950** 7.010* 81.009** 20.606**LB(24) 35.112 25.993 26.823 15.945 26.469 30.666LB2(24) 27.185 31.440 42.277* 27.763 45.208** 18.889

Engle and Ng (1993) asymmetric testsSign bias test 0.577 0.456 �0.396 �1.263 �0.871 0.914Negative size bias test �0.541 �0.324 0.919 0.711 �0.690 0.326Positive size bias test 0.422 �0.271 �0.942 0.116 0.100 �1.527Joint test 0.412 0.544 0.639 0.909 0.357 2.108

a(i) The Bera-Jarque (B � J ) tests normality based on both skewness and excess kurtosis and is distributed x2 with twodegrees of freedom. (ii) LB(24) and LB2(24) are the Ljung-Box test statistics of order 24 for serial correlation in the stan-dardized residuals and standardized residuals squared. (iii) Pseudo R2 is computed as the ratio between the explained sumof squares and total sum of squares. (iv) * and ** denote statistical significance at the 5 and 1% level, respectively.

980 Tai

Now, it would be interesting to see if the weak-form market efficiencycontinues to hold during the 1992 ERM crisis. That is, the test of conta-gion in mean effects can be conducted. As shown in Table IV, these effectsare statistically significant at the 1% level in two markets: BP and SF. Forexample, the joint hypothesis of no contagion in return shocks for BP(H0 : vBP,j � 0; 5j � CD, DM, SF) during the crisis is strongly rejected bythe Wald statistic (Wald � 20.867) at the 1% level. The same rejectionalso applies to SF. To find out the sources of contagion in return shocksfor BP, one can again examine the individual significance of contagion-in-mean parameter, vBP,j, reported in Table II based on robust standarderrors. Basically, the current returns in BP are negatively affected by thepast return shocks in DM (vBP,DM � �0.738) and positively affected bythose in SF (vBP,SF � 0.532), while the current return shocks in SF aredue to the past return shocks in BP (vSF,BP � 0.287), in addition to its ownpast return shocks. By examining the significance of these individual con-tagion-in-mean parameters, one can conclude that basically the returnshocks originate from three markets: BP, DM, and SF, the hypothesistests (#13, #15, and #16) confirm this conclusion.

Evidence of Volatility Spilloverand Contagion in Volatility

Turning to volatility spillovers and contagion effects on the conditionalvariance of currency futures returns, it can be seen from Table V that thehypothesis of no volatility spillover (#1–#4) is rejected in two cases: BPand DM. By examining the robust standard errors of volatility spilloverparameters reported in Table II, it can be seen that the conditional vari-ance of depends negatively on lagged shocks in World (nBP,World �

�0.203). For DM, its conditional variance is negatively affected bythe lagged shocks in BP (mDM,BP � �0.121). Although the hypothesisof no volatility spillover for SF (H0 : lSF,BP � mSF,CD � nSF,DM � gSF,TWFX �

kSF,World � 0) cannot be rejected, the contagion-in-mean parameter is sig-nificant at the 1% level for mSF,CD, implying that the conditional varianceof SF is significantly affected by the past volatility shocks from CD.Overall, the sources of volatility spillovers originate from three markets:BP, CD, and World, as evidenced from the significant Wald test statisticsfor the hypotheses tests (#9, #10, and #14) reported in Table V.

It will be interesting to examine next where the dynamics of condi-tional variances of these currency futures returns behave differently dur-ing the crisis. In particular, the question of whether markets’ negativeidiosyncratic shocks become contagious during the crisis after controlling


the overall volatility spillovers can be answered. That is, the test ofcontagion-in-volatility hypothesis can be carried out. The results areagain reported in Tables II and V.

As shown in Table V, the joint hypothesis of no contagion in asym-metric volatility shocks during the crisis is strongly rejected by the Waldstatistic at the 1% level only for BP. To investigate the possible sources ofasymmetric volatility shocks, one can again test the individual signifi-cance of contagion-in-asymmetric-volatility parameters reported inTable II based on robust standard errors. As can be seen, the conditionalvariance of is affected by the past volatility shocks from three markets,namely CD, DM, and SF. Among these three markets, DM is the majormarket in generating negative volatility shocks for BP, because thehypothesis of no contagion in volatility shocks from each possible sourceis only rejected for DM with a p-value of 0.022.

Finally, in addition to the volatility spillover and contagion-in-volatilityparameter estimates shown in Table II, Table II also reports the estimatesfor GARCH and ARCH parameters (ai, bi) and own asymmetric volatilityshock parameters, di. The GARCH parameters are all significant at the 1%level, implying that all the conditional variance processes are highly per-sistence. However, none of the parameters, di, is significant, suggestingthat asymmetries do not present in the currency futures markets.

Residual Diagnostics

To access the fit of the conditional ICAPM with MGARCH(1,1)-M spec-ification, Table VI reports the Ljung-Box statistics for 24th-order serialcorrelation in the level [LB(24)] and squared standardized residuals[LB2(24)] as well as the asymmetry test developed by Engle and Ng(1993). Under the multivariate framework, the standardized residuals attime t is computed as where is the inverse of theCholesky factor of the estimated variance–covariance matrix. The Ljung-Box statistics show no serious linear and nonlinear dependencies for thestandardized residuals of currency futures returns with one exception.Thus, based on the Ljung-Box statistics, the volatility process is correctlyspecified. However, as suggested by Engle and Ng, the Ljung-Box testmay not have much power in detecting misspecifications related to theasymmetric effects. For this purpose, the set of diagnostics proposed byEngle and Ng (1993) are used.12 These tests are based on the news

H�1�2tZt � H�1�2

t et,

12Engle and Ng (1993) asymmetric tests include the sign bias, the negative size bias, and the posi-tive size bias tests. The sign bias test examines the impact of positive and negative innovations onvolatility not predicted by the model. The negative (positive) size bias test examines how well themodel captures the impact of large and small negative (positive) innovations.

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impact curve implied by a particular ARCH-type model used. The prem-ise is that if the volatility process is correctly specified, then the squaredstandardized residuals should not be predictable based on observedvariables. The results reported in Table VI show no evidence of misspec-ification. As for B � J test statistics, they are all significant, indicatingdepartures from normality, which justifies the use of robust standarderrors computed from using the quasi-maximum likelihood method ofBollerslev and Wooldridge (1992). Overall the MGARCH(1,1)-M speci-fication fits the data very well.

ERM Crisis and Time-Varying Risk Premia

One advantage of modeling the conditional second moments via multi-variate GARCH approach is that it enables one to recover some interest-ing statistics such as conditional volatility, and, more importantly, the sizeof different risk premia. These interesting statistics will not be available ifone leaves the condition second moments unspecified such as the pricingkernel approach employed by Dumas (1993), Dumas and Solnik (1995),and Tai (1999).13 Table VI reports those statistics. For example, the pre-dicted total returns can be decomposed into two components. The firstcomponent is predicted total risk premium, which is measured by

(18)

It ranges from �0.010% (SF) to 0.004% (CD). The second compo-nent is the returns due to mean spillovers in the entire sample periodand the contagion-in-mean during the crisis period, and it ranges from�0.005% (CD) to 0.018% (BP). To examine the importance of differentsystematic risk components in describing the dynamics of currencyfutures returns, one can further decompose the TRPi,t into two compo-nents: market risk premium (MRPi,t) and currency risk premium(CRPi,t). The market risk premium is measured by

(19)

and the currency risk premium is measured by

(20)

For instance, the predicted market risk premium (and its standarddeviation) ranges from 0.006% (0.016%) for CD to 0.017% (0.028%) forDM. On the other hand, the predicted currency risk premium (and its

CRPi,t � lc,t�1hic,t;�i � BP, CD, DM, SF

MRPi,t � lm,t�1him,t;�i � BP, CD, DM, SF

TRPi,t � lm,t�1him,t � lc,t�1hic,t;�i � BP, CD, DM, SF

13See the comments provided by Campbell Harvey in Dumas (1993).


standard deviation) ranges from �0.021% (0.127%) for SF to �0.002%(0.010%) for DM. The lower or even negative predicted total risk premi-um is basically dominated by the negative currency risk premium duringthe sample period. This finding further confirms the importance ofincorporating the currency risk factor when testing risk premia incurrency futures prices.

To see if the dynamics of predicted currency futures returns behavedifferently during the crisis, the same statistics are calculated for thecrisis period. As can be seen from the table, the averages of the estimatedtotal returns and their standard deviations change dramatically com-pared to those calculated for the entire sample period. In particular, theaverage of the predicted returns for BP increases from 0.016 to 0.203%,and this return increase is mainly due to the mean spillovers pluscontagion-in-mean component (0.018 versus 0.224%). On the otherhand, the averages of the estimated returns for the other three currencyfutures decrease. Specifically, for CD, this decrease is again due to themean spillovers plus contagion-in-mean component (�0.005 versus�0.073%). This result implies that the 1992 ERM crisis has differentimpacts on the return dynamics for BP and CD. For DM and SF, thedecrease is due to the drop in the currency risk premium component. Forexample, the predicted currency risk premium decreases from �0.019 to�0.052% for DM, and from �0.021 to �0.056% for SF. Because theestimated model is fully parameterized, the impact of the dynamics ofthe price of currency risk can be separated from the estimated covari-ances in determining the estimated currency risk premia. Because theestimated covariances are all negative during the entire sample and theaverage price of currency risk is positive, the estimated currency risk pre-mia are negative, implying that investors are willing to give up some ofthe total risk premium when the hedging value of the assets in the port-folio becomes predominant. By comparing the price of currency risk intwo different sample periods, it is not surprised to see that the currencyrisk premium decreases because the price of currency risk increasesfrom 3.719 for the entire sample to 7.614 for the crisis period. Anotherobservation worth mentioning is that the predicted returns for currencyfutures is basically dominated by the currency risk premium; however,the predicted returns for the world equity market are dominated by themarket risk premium, suggesting the importance of incorporatingcurrency risk in pricing currency futures.

A useful complement to Table VI is to display the time-series plotsof those interesting statistics. The predicted total returns, market riskpremium, currency risk premium, and conditional volatility for eachcurrency futures are plotted in Figure 2a–d, 2e–h, 2i–l, and 2m–p,

FIG

UR

E 2

Pre

dict

ed c

urre

ncy

futu

res

retu

rns,

mar

ket,

and

cur

renc

y ri

sk p

rem

ia, a

nd c

ondi

tion

al v

olat

ility

.


respectively. It can be seen that the dynamics of the predicted currencyfutures returns follow more closely to those of the predicted currencyrisk premia than to those of the predicted market risk premia, especiallyduring the period of ERM crisis. In addition, the conditional volatility foreach return series increases significant during the crisis period. Finally,Figure 3 displays the dynamics of time-varying risk prices. As can beseen, both the dynamics of the prices of market and currency risks showsignificant time variation, especially in the beginning and at the end of1990s, which correspond to the periods of the 1991 Gulf war, the 1992ERM crisis, the 1997 Asian crisis, the 1998 Russian crisis, and the 1999Brazilian crisis.

SUMMARY AND CONCLUDING REMARKS

This article tests whether there are pure contagion effects in both condi-tional means and volatilities of currency futures returns during the 1992ERM crisis. Previous studies on contagion have failed to take intoaccount the important distinction between the two concepts of interde-pendence and contagion. Specifically, “contagion” is defined as significantspillovers of asset-specific idiosyncratic shocks during the crisis aftereconomic fundamentals or systematic risks have been accounted for. Tocontrol for the economic fundamentals, an international capital asset

FIGURE 3Time-varying price of risk.

986 Tai

pricing model (ICAPM) in the absence of PPP is utilized. The economicfundamentals under ICAPM are the world market and foreign exchangerisks, so the evidence of contagion is based on testing whether idiosyn-cratic risks—the part that cannot be explained by the world market andforeign exchange risks—are significant in describing the dynamics of con-ditional mean and volatility of currency futures returns during the crisis.

The empirical results indicate that overall there are no meanspillovers among British pound, Canadian dollar, Deutsche mark, andSwiss franc futures prices, but they are detected during the crisis period.That is, past return shocks originating in any one of the four markets haveno impact on the other three markets during the entire sample period,suggesting that these markets are weak-form efficient. However, this weakform-market efficiency fails to hold during the crisis period, especially forBritish pound and Swiss franc, and the sources of contagion-in-meaneffects are mainly due to the return shocks originating in three Europeancurrency futures markets. As for the contagion-in-volatility, it is detectedfor British pound only because its conditional volatility is influenced bythe negative volatility shocks from Canadian dollar, Deutsche mark, andSwiss franc, with Deutsche mark playing the dominant role in generatingthose shocks. Finally, the sources of time-varying risk premia come notonly from the world market risk, but also from the foreign exchange risk,suggesting the important role of foreign exchange risk in pricing currencyfutures prices. The empirical results from this study have important impli-cations in dynamic currency hedging and policy making. A potential inter-esting future study from this article will be to develop a dynamic hedgingstrategy and evaluate its effectiveness given the possible changes in riskstructure that may occur during the market turmoil.

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