icapm vech asian market

8/13/2019 ICAPM VECH Asian Market

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Looking for risk premium and contagion in

Asia-Pacific foreign exchange markets$

Chu-Sheng Tai*

Department of Economics and Finance, College of Business Administration,

Texas A&M University-Kingsville, MSC 186, 700 University Boulevard, Kingsville,TX 78363-8203, USA

Abstract

This article tests pure contagion effects among four Asian foreign exchange markets,

namely, Japan, Hong Kong, Singapore, and Taiwan during the 1997 Asian crisis. A conditional

version of international capital asset pricing model (ICAPM) in the absence of purchasing

power parity (PPP) is used to control for economic fundamentals or systematic risks. The

empirical results show strong contagion effects in both conditional means and volatilities of

those markets after systematic risks have been accounted for. Specifically, the contagion-in-mean effects are mainly driven by the past return shocks in Hong Kong, Singapore, and

Taiwan. As for contagion in volatility, the lead/lag relationships appear to be multidirectional

among Japan, Singapore, and Taiwan, but between Hong Kong and Singapore, and between

Hong Kong and Taiwan, they are unidirectional, with Hong Kong playing the dominant role in

generating negative volatility shocks. In addition, the conditional ICAPM with asymmetric

multivariate general autoregressive conditional heteroscedastic in mean (MGARCH(1,1)-M)

structure is able to explain/predict on average 17.28% of the return variations in those markets.

Therefore, this study provide a further evidence that the time-varying risk premium is a very

strong candidate in explaining the predictable excess return puzzle [Lewis, K. K. (1994).

Puzzles in international financial markets. NBER Working Paper No. 4951] since the risk

1057-5219/$ - see front matterD 2004 Elsevier Inc. All rights reserved.

doi:10.1016/j.irfa.2004.02.020

$ An earlier version of the article was presented at the 2002 National Taiwan University International

Conference on Finance in Taipei, Taiwan, ROC, the 2002 Financial Management Association International

Annual Meeting in San Antonio, TX, and the 2003 Midwest Finance Association Annual Meeting in St. Louis,

MO, and was awarded the Outstanding Paper in International Finance in 2003 by the Midwest Finance

Association. I would like to thank the conference participants for their comments and suggestions. Any remaining

errors are my own.

* Tel.: +1-361-593-2355; fax: +1-361-593-3912.

E-mail address:[email protected] (C.-S. Tai).

International Review of Financial Analysis

13 (2004) 381 409


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premia founded in this article are not only statistically significant but also economically

significant.

D 2004 Elsevier Inc. All rights reserved.

JEL classification:C32; F31; G12

Keywords:Contagion; Spillover; Time-varying risk premium; Multivariate GARCH-M

1. Introduction

Due to a series of financial crises in 1990s, the study of the transmission of financial

shocks/crisis across markets/countries has become one of the most intensive research

topics in international financial literature in recent years. Previous articles on this topic

have failed to take into account an important distinction between the two concepts of

interdependenceand contagion.Masson (1998)argues that there are three main channels

that financial 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 occur when affected countries have similar

economic fundamentals or face common external shocks. The second type of financial

market interlinkages arises from spillover effects, which may be due to trade linkages or

financial interdependence. The first two channels of financial crises can be categorized as

fundamental-driven crises since the affected countries share some macroeconomic

fundamentals, which implies that the transmission of financial crises is due to theinterdependence among those countries and not necessarily due to contagion. The third

transmission channel is the pure contagion effect. Contagion here refers to the cases where

crisis in one country triggers a crisis elsewhere for reasons unexplained by macroeconomic

fundamentals. For instance, a crisis in one country may lead creditors and investors to pull

out from other countries over which they have a poor understanding resulting from

information asymmetries.

The goal of this article is to test the pure contagion effects among four Asian foreign

exchange markets, namely, Japan, Hong Kong, Singapore, and Taiwan during the 1997

Asian crisis. Specifically, in this article, I define contagion as significant spillovers of

country-specific idiosyncratic shocks during the crisis after economic fundamentals orsystematic risks have been accounted for. In testing for contagion, its existence depends

on the economic fundamentals used. Unfortunately, there is disagreement on the

definitions of the fundamentals. To control for the economic fundamentals, most

empirical studies tend to choose those fundamentals arbitrarily, such as by using

macroeconomic variables, dummies for important events, and time trends. The problem

with these control variables is that contagion is not well defined without reference to a

theory. To overcome this problem, I rely on an international capital asset pricing model

(ICAPM) in the absence of purchasing power parity (PPP), which provides a theoretical

basis in selecting economic fundamentals. The economic fundamentals under ICAPM

are the world market and foreign exchange risks, so the evidence of contagion is basedon testing whether idiosyncratic risksthe part that cannot be explained by the world

market and foreign exchange risksare significant in describing the dynamics of

C.-S. Tai / International Review of Financial Analysis 13 (2004) 381409382


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conditional mean and volatility in Asian foreign exchange markets during the crisis.

The ICAPM used in this article also provides another avenue to test the existence of

risk premium in foreign exchange markets since previous empirical studies using

consumption-based asset pricing model to test the existence of risk premium in ex-plaining the predictable excess return puzzle (Lewis, 1994) have not been very

successful.1

In addition to the contribution in overcoming the drawback of arbitrarily choosing

economic fundamentals in testing contagion effects in previous studies, another

contribution of this article is methodology used to test those effects. In particular, I

utilize an asymmetric multivariate general autoregressive conditional heteroscedastic in

mean (MGARCH-M) approach to model the conditional mean and asymmetric

volatility spillovers during the crisis, in addition to capturing the time dependencies

in the second moments of asset returns, a stylized property found in most financial

time series, which has been ignored by most empirical studies on contagion.2

Furthermore, the ICAPM in the absence of PPP with MGARCH-M parameterization

adopted in this article also overcomes the drawbacks in previous studies in testing risk

premium hypothesis in explaining the predictable excess returns puzzle, and thus

provides a new inside on the test of risk premium hypothesis. For example, Mark

(1988) uses a single-beta CAPM to price forward foreign exchange contracts and

specifies the betas as ARCH-like process. He estimates the model jointly for four

currencies using a generalized method of moments (GMM) procedure. His results

show significant time variation for the betas, and tests of the overidentifying

restrictions are not rejected. However, as pointed out by Mark, the GMM estimatoris robust, but, in general, is not asymptotically efficient. Consequently, instead of

using GMM estimation, McCurdy and Morgan (1991) also apply the single-beta

CAPM with a bivariate GARCH parameterization to price deviations from UIP for

five major currencies. They estimate their model currency by currency, while Mark

2 According to Dornbusch, Park, and Claessens (1999), Forbes and Rigobon (1999), and Kaminsky and

Reinhart (in press), previous empirical studies on contagion can be categorized by methodology into four groups:

(1) the testing of significant increases in correlation(Baig & Goldfajn, 1999; Calvo & Reinhart, 1996; Forbes &

Rigobon, 1998, 1999; Park & Song, 1999); (2) the testing of significance in innovation correlation (Baig &

Goldfajn, 1999); (3) the testing of significant volatility spillover(Edwards, 1998; Edwards & Susmel, 1999); (4)

crisis prediction regression (Bae, Karolyi, & Stulz, 2000; Eichengreen, Ross, & Wyplosz, 1996; Kaminsky &

Reinhart, in press; Sachs, Tornell, & Velasco, 1996; Van Rijckeghem & Weder, 1999). None of the contagion

studies mentioned above explicitly takes the time dependencies in the second moment into account. A recent

paper byBekaert, Harvey, and Ng (2002)applies three-stage univariate GARCH model to study contagion in

equity markets by testing whether there is evidence of significant increase in cross market residual correlation

during the crisis. Although they model conditional second moments, they cannot answer whether return shocks

originated from one market will significantly affect the other markets during the crisis.

1 For example,Backus, Gregory, and Telmer (1993),Cumby (1988),Kaminsky and Peruga (1990),andMark

(1985) use an intertemporal asset pricing model to test the existence of a time-varying risk premium in foreign

exchange markets. In this model, the risk premium is due to consumption risk measured by the covariance between

returns and the marginal utility of money. The results from these studies are disappointing because the observableingredients in the risk premium models do not vary sufficiently to explain the high degree of variabilityin asset

returns without implausibly large estimates of the coefficientof relative risk aversion (seeEngelm 1996).

C.-S. Tai / International Review of Financial Analysis 13 (2004) 381409 383


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(1988) estimates his model jointly across currencies, so the efficiency might be

sacrificed in McCurdy and Morgans study because cross-asset correlations and

parameter restrictions are ignored. To maintain the efficiency, Tai (2001) applies

MGARCH-M to test risk premium hypothesis, but similar to Mark (1988) andMcCurdy and Morgan (1991), he assumes that PPP holds, and thus ignores foreign

exchange risk. Therefore, under the fully parameterized multivariate model adopted in

this article, not only is the maximum efficiency gain retained in controlling the

systematic risks when testing the contagion effects, but also some interesting statistics

are recovered, which are mostly ignored in previous studies.3 In addition, the test of

ICAPM in the absence of PPP provides a new insight on the sources of time-varying

risk premium in foreign exchange markets.

The empirical results show strong contagion effects in both the conditional means

and volatilities of foreign exchange returns after systematic risks have been accounted

for. Specifically, the contagion-in-mean effects are mainly driven by the past return

shocks in Hong Kong, Singapore, and Taiwan. As for contagion in volatility, the lead/

lag relationships appear to be multidirectional among Japan, Singapore, and Taiwan,

but between Hong Kong and Singapore, and between Hong Kong and Taiwan, they

are unidirectional, with Hong Kong playing the dominant role in generating negative

volatility shocks.

The remainder of the article is organized as follows. Section 2 presents the theoretical

asset pricing model used to control for systematic risks when testing pure contagion

effects. Section 3 describes the econometric methodology employed to estimate the model

and several test hypotheses are presented in Section 4. Section 5 describes the data andempirical results are reported in Section 6. Some conclusions are offered in Section 7.

2. The theoretical motivation

We know that the first-order condition of any consumerinvestors portfolio optimi-

zation problem can be written as:

EMtRi;tjXt1 1; bi 1 . . .N 1

where Mt is known as a stochastic discount factor or an intertemporal marginal rate of

substitution; Ri,t is the gross return of asset i at time t and Xt 1 is market information

known at timet 1. Without specifying the form ofMt, Eq. (1) has little empirical contentsince it is easy to find some random variable Mtfor which the equation holds. Thus, it is

the specific form of Mt implied by an asset pricing model that gives Eq. (1) further

3 Previous studies of finding time-varying risk premia in foreign exchange marketsusing GMM, which does

not require researchers to model conditional second moments of asset returns, includeDumas and Solnik (1995)

andTai (1999). Other studies using multivariate GARCH approach includeBaillie and Bollerslev (1990), De

Santis and Gerard (1998),Giovannini and Jorion (1989),andTai (2001).Among the four studies, onlyDe Santis

and Gerard (1998)and Tai (2001)are able to detect significant time-varying risk premia, but they do not exam

how a financial crisis would affect the dynamics of the risk premia.



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empirical content (e.g.,Ferson, 1995; Tai, 2000). Suppose Mtand Ri,thave the following

factor representations:

MtaX

K

k1

bkFk;t ut 2

ri;taiXKk1

bikFk;t ei;t bi 1 . . .N 3

where ri,t=Ri,tR0,t is the raw returns of asset i in excess of the risk-free rate, R0,t, attime t, and E[utFk,tjXt1] =E[utjXt 1] =E[ei,tFk,tjXt 1] =E[ei,tjXt 1] = 0 bi,k; Fk,t arecommon risk factors that capture systematic risk affecting all assets ri,t including Mt; bik

are the associated time-invariant factor loadings that measure the sensitivities of the assetto the common risk factors, while utis an innovation, and ei,tare idiosyncratic terms that

reflect unsystematic risk. The risk-free rate, R0,t 1, must also satisfy Eq. (1).

EMtR0;t1 jXt1 1 4

Subtracting Eq. (4) from Eq. (1), we obtain

EMtri;t jXt1 0 bi 1 . . .N 5

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

Eri;tjXt1 Covri;t; Mt jXt1

EMtjXt1 bi 1 . . .N 6

Substitute Eq. (2) into Eq. (6):

Eri;t jXt1 X

k

bkEMtjXt1

Covri;t;Fk;tjXt1 X

k

kk;t1Covri;t;Fk;tjXt1

7

where kk,t 1 is the time-varying price of factor risk. Eq. (7) is a general conditionalmultifactor asset pricing model derived from the intertemporal consumptioninvestment

optimization problem.

In empirical tests, the SDF is projected onto five factors: the world market portfolio

and four currency returns.4 The selection of those five factors is theoretically justified

based on either the intertemporal CAPM ofMerton (1973)or an international version of

CAPM in the absence of PPP developed by Adler and Dumas (1983). To extend

domestic CAPM into an international setting, previous researchers assume that either

4 In this article, I consider four Asian foreign exchange rates: Japanese yen (JP), Hong Kong dollar (HK),

Singapore dollar (SG), and New Taiwan dollar (TA), so there are four currency risks plus one world market

risk (WD).



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investors have logarithmic utility or PPP holds. However, many empirical studies have

documented that the violation of PPP is a norm although PPP at best tends to hold in the

long run. In the absence of PPP resulting from either different consumption tastes or

violation of the law of one price, investors from different countries face different priceswhen holding the same asset. In this situation, international asset pricing model will

contain risk premia, which are related to the covariances of asset returns with exchange

rates, besides the traditional market risk premium.5 Therefore, a conditional multifactor

asset pricing model containing world market and foreign exchange risks (Eq. (7)) seems

to be reasonable and will be used to control for systematic risks in testing contagion

(e.g., De Santis & Gerard, 1998; Dumas & Solnik, 1995; Ferson & Harvey, 1994; Tai,

1999, among others). I can now rewrite the conditional multifactor asset pricing model

in Eq. (7) as

ri;tkw;t1Covri;t; rw;t jXt1 X

c

kc;t1Covri;t; rc;t jXt1 ei;t bi 1 . . .N

8

where w denotes world market risk and c is the currency risk.6

3. Econometric methodology

The conditional ICAPM in Eq. (7) has to hold for every asset. However, the modeldoes not impose any restrictions on the dynamics of the conditional second moments.

Several MGARCH models have been proposed to model the conditional second

moments, such as the diagonal VECH model of Bollerslev, Engle, and Wooldridge

(1988), the constant correlation (CCORR) model of Bollerslev (1990), the factor

ARCH (FARCH) model of Engle, Ng, and Rothschild (1990), and the BEKK model

of Engle and Kroner (1995). Among these four popular MGARCH models, the BEKK

model is better suited for the purpose of this article because it not only guarantees that

the covariance matrices in the system are positive definite, but also allows the

conditional variances and covariances of different markets to influence each other,

which is very important for testing contagion in this article. Although it is easy tounderstand, the VECH model might not yield a positive definite covariance matrix.

FARCH assumes that the covariance matrix is driven by the conditional variance

process of one portfolio (the market portfolio), and this assumption does not hold in

this article since the conditional covariance matrix is assumed to be driven not only

by market portfolio but also by foreign exchange returns. As for the CCORR model,

it restricts the correlation between two assets returns to be constant over time, which

is unlikely to hold as suggested by Longin and Solnik (1995) and Karolyi and Stulz

6 In this article, the factors are market portfolio and short-term currency deposits, which are traded assets, so I

can replace Fk,twith rk,t.

5 SeeAdler and Dumas (1983),Solnik (1974),andStulz (1981, 1984).



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(1996). As a result, a BEKK structure with asymmetric volatility effects is selected

over the other MGARCH specifications to model the conditional second moments of

asset returns and to test contagion effects among Asian foreign exchange markets.7

Specifically, the dynamic process for the conditional variance covariance matrix ofasset returns is specified as:

HtCVCAVHt1 ABVet1et1V B D Vht1ht1V DGVwt1wt1V

GKVnt1nt1V KLVlt1lt1V LMVmt1mt1V MPV

1t11t1V P Q Vst1st1V QSVtt1tt1V SVVft1ft1V V 9

where Ht is 5 5 time-varying variance covariance matrix of asset returns, C isrestricted to be a 5 5 upper triangular matrix, and A, B, D, G, K, L, M, P, Q, S,and V are diagonal matrices whose general form, X, is given by:

X

xJP;j 0 0 0 0

0 xHK;j 0 0 0

0 0 xSG;j 0 0

0 0 0 xTA;j 0

0 0 0 0 xWD;j

26666666666664

37777777777775

10

The 5 1 vector, gt 1, captures the asymmetric impact that the vector of pastnegative shocks has on the conditional covariance matrix in a manner similar to that

of Glosten, Jagannathan, and Runkle (1993), and is defined as:

gt1

mineJP;t1;

0

mineHK;t1; 0

mineSG;t1; 0

mineTA;t1; 0

mineWD;t1;0

26666666666664

37777777777775

11

7 The asymmetric volatility effects in variances and covariances have been documented in recent articles by,

among others,Kroner and Ng (1998)andBekaert and Wu (2000).



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second set of innovation vectors (1t 1,st 1, tt 1, ft 1) is that the first set captures overall

volatility spillovers during the entire sample period, while the second set captures the

asymmetric volatility spillovers during the crisis period. By including vectors 1t 1,st 1,

tt 1, andft 1, I can then test the incremental influences of volatility shocks on the foreignexchange markets, which is a true test of contagion in volatility. In this model, for example,

the conditional variance of excess Japanese yen returns, hJP,t, depends on its past conditional

variance, hJP,t 1, through the parameter, aJP, its own past shocks, eJP,t 1, through the

parameter, bJP, and past shocks of the other markets through the parameters, gJP, kJP,lJP, and

mJP. This conditional variance also depends on its own past negative shocks through the

parameter, dJP, and on past negative shocks of the other markets through the parameters,pJP,

qJP,sJP, andvJP during the crisis. Here, these parameters measure the incremental amounts

by which bad news in one market at time t 1 affect the conditional variance of excessJapanese yen returns at time t.

The parameterization of the conditional covariance matrix can therefore be viewed as

an extension of the diagonal BEKK representation ofEngle and Kroner (1995)that allows

for past shocks from other markets to influence conditional variances and covariances, for

asymmetries in the impacts of these shocks.9 This representation of the conditional

covariance matrix differs from the most general BEKK form in that conditional variances

are not permitted to depend on cross-products of lagged shocks, lagged conditional

variances of other markets, and lagged conditional covariances with other markets.

Similarly, conditional covariances are not influenced by lagged squared shocks and lagged

conditional variances in other markets. The parameterization presented here facilitates

testing of the null hypothesis of no volatility spillover effects against the alternative thatconditional variances depend on other markets only through their past squared shocks.

Even with this diagonal BEKK parameterization, it still requires the estimation of 70

parameters in the conditional covariance matrix.

Under the assumption of conditional normality, the log-likelihood to be maximized can

be written as

lnLq TN

2 ln2p

1

2

XTt1

lnAHtqA 1

2

XTt1

etqVHtq1etq 14

whereqis the vector of unknown parameters in the model. Since the normality assumptionis often violated in financial time series, I use quasi-maximum likelihood estimation

(QML) proposed by Bollerslev and Wooldridge (1992), which allows inference in the

presence of departures from conditional normality. Under standard regularity conditions,

the QML estimator is consistent and asymptotically normal and statistical inferences can

be carried out by computing robust Wald statistics. The QML estimates can be obtained by

maximizing Eq. (14) and calculating a robust estimate of the covariance of the parameter

estimates using the matrix of second derivatives and the average of the period-by-period

9 Ebrahim (2000) also uses this diagonal BEKK model to test volatility spillover effects between foreign

exchange and money markets, but in this article, I not only test the usual volatility spillover effects withinforeign

exchange markets and between foreign exchange and world equity markets, but also test contagion in asymmetric

volatility spillover effects within and between those markets during a crisis.



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outer products of the gradient. Optimization is performed using the Broyden, Fletcher,

Goldfarb, and Shanno algorithm.

4. Hypothesis testing

4.1. 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 of risk is economically appealing in the sense that

investors use all available information to form their expectations about future economic

performance, and when the information changes over time, they will adjust their expect-

ations and thus their expected risk premia when holding different risky assets. Therefore,

to test time-varying risk premium hypothesis, I allow not only the conditional second

moments (covariance risks) to change over time, but also the prices of covariance risks to

be time varying (Eq. (8)).

The dynamics of prices of risks are chosen according to the theoretical international

asset pricing model developed by Adler and Dumas (1983). In their model, the price of

world market risk is a weighted average of the coefficients of risk aversion of all national

investors. Since the weights measure the relative wealth of each country and if all investors

are risk averse, the world price of market risk should be positive. Thus, similar toBekaert

and Harvey (1995) and De Santis and Gerard (1997, 1998), an exponential function isused to model the dynamic ofkw,t 1and for the dynamics ofkc,t 1, a linear specification

is adopted because the model does not restrict the price of currency risk to be positive. 10

kw;t1 expuwVZt1 15

kc;t1ucVZt1 16

where Zt 1 is a vector of information variables observed at the end of time t 1 and usare time-invariant vectors of weights. Thus, the price of each source of currency risk is

assumed to be a linear function of the information variables in Zt 1, and the price of

world market risk is assumed to be an exponential function of information variables in

Zt 1. Given the dynamics of prices of risks, I can then test the time-varying risk premium

hypothesis by testing whether the information variables in Zt 1are significant in addition

to significant GARCH parameters.

10 As pointed out byDe Santis and Gerad (1997),the conditional ICAPM is only a partial equilibrium model,

and the theory does not help identify the state variables that affect the prices of market and currency risks, so

inevitably any parameterization of the dynamics ofkw,t 1 andkc,t 1 can be criticized for being ad hoc.



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4.2. Testing contagion in mean and volatility

To test whether a countrys past idiosyncratic shocks have significant impact on the other

countries condition returns (contagion in mean) during the Asian crisis, I incorporate pastcountry-specific innovations into Eq. (8). Specifically, Eq. (8) can be modified as

ri;tkm;t1Covri;t; rm;t jXt1 X

c

kc;t1Covri;t; rc;tjXt1 X

i;j

/ijej;t1

crisis

Xi;j

xijej;t1

ei;t; bi;j 17

where crisis is a dummy variable, which is equal to 1 during the crisis and 0 otherwise. In

testing the contagion-in-mean effects, I allow the past country-specific innovations to affectcurrency returns in theentiresample period, and then test whether there are any incremental

influences of past innovations on currency returns during the crisis period. Thus, the

contagion-in-mean hypothesis can be examined by testing whether the parameters,xij(i p

j), are individually or jointly significant after the systematic risks have been accounted for.

To test contagion-in-volatility hypothesis, one can test whether the elements in matrices

P,Q,S, andVare individually or jointly significant. For example, a test of null hypothesis

that pJP,j i s 0 (H0: pJP,j= 0) means that there is no contagion-in-asymmetric volatility

shocks from country j to Japan. Similarly, a test of null hypothesis ofH0: pi,HK= qi,SG =

si,TA= vi,WD = 0; bi = JP implies that the conditional volatility of Japanese yen returns is

not affected by the other countries negative idiosyncratic shocks. Finally, one can test thesource of negative idiosyncratic shocks. For example, to test whether the negative shocks

originate from Japan, one can test the null hypothesis ofH0:vHK,j=sSG,j= qTA,j=pWD,j= 0;

bj= JP.

5. Data and summary statistics

Weekly observations on four Asian currency spot prices and 1-week interest rates (JP,

HK, SG, and TA) are used to construct a time-series of weekly deviations from UIP. 11 The

Datastream world total market return index (WD) is used to proxy world market risk.12

Seven-day eurodollar interest rate is used as conditionally risk-free rate to compute the

excess equity returns on WD and the four excess Asian currency returns (or the ex post

deviations from UIP). In particular, the excess world market return is computed as ri;tln pt

pt1

152 ln1i

US$t1, where pt is the Datastream world total return index (dividend

11 Ideally, it would be interesting to use currency and interest rate data from other Asia-Pacific countries,

such as Indonesia, the Philippines, South Korea, Thailand, Malaysia, etc., but the short-term interest rate data for

those countries are not available during the sample period considered in this study.12 I prefer to use the world total market return index complied by Datastream, which captures more than 75%

of the market, as opposed to the widely used Morgan Stanley Capital International index, which captures only

approximately 60% of the total market.



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included) at time t and it 1US$ is the annualized 7-day eurodollar interest rate known at

timet 1. The excess currency return is computed as ri;t 152

ln1it1* ln stst1

152 ln

1iUS$

t1, where stis the spot rate at time texpressed as domestic price (the U.S. dollar)of one unit of Asian currency and it 1* is the annualized short-term Asian currencyinterest rate known at time t 1.

I select a set of conditioning variables that have been widely used in the international asset

pricing literature (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 WD in excess of the 7-day

eurodollar interest rate (DIV), the change in the U.S. term premium, measured by the yield

difference between 10-year Treasury constant maturity rate and 7-day eurodollar rate

(DUSTP), the U.S. default premium, measured by the yield difference between Moodys

Table 1

Panel A: Summary statistics of foreign exchange returns and world equity return

Returns JP HK SG TA WD

Mean (%) 0.020 0.007 0.017 0.021 0.068S.D. (%) 1.683 0.093 0.773 0.723 1.900

Minimum (%) 6.174 0.603 4.851 4.319 13.755

Maximum (%) 14.500 0.457 8.292 5.875 7.608

Skewness 1.138** 0.971** 1.239** 0.242** 0.713**Excess kurtosis 7.972** 9.892** 23.411** 13.180** 5.375**

B J 2122.542** 3138.013** 17,111.99** 5371.034** 954.907**LB(20) 25.299 54.833** 124.861** 40.245** 20.448

LB2(20) 52.276** 195.194** 286.789** 56.706** 38.934**

Panel B: Unconditional correlation of conditioning variables

DIV DUSTP USDP WD

DIV 1

DUSTP .122 1

USDP .159 .038 1WD .052 .017 .034 1

The statistics are based on weekly data from January 16, 1987 to March 23, 2001 (741 observations). The interest

rates are 1-week Euroyen deposit rate (JP), 1-week Hong Kong deposit rate (HK), 1-week Singapore deposit rate(SG), and 10-day Taiwan money market rate (TA). WD is the Datastream world total market return index in

excess of the 7-day Eurodollar interest rate.

The BeraJarque (BJ) tests normality based on both skewness and excess kurtosis and is distributed v2 with

two degrees of freedom.

LB(20) and LB2(20) denote the LjungBox test statistics for up to the 20th-order autocorrelation of the raw and

squared returns, respectively.

The conditioning variables are the excess dividend yield, measured by the dividend yield on Datastream world

total market 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

and 7-day Eurodollar rate (DUSTP), the U.S. default premium, measured by the yield difference between

Moodys Baa- and Aaa-rated U.S. corporate bonds (USDP), and the lagged excess return on Datastream world

total market return index (WD).

*Statistical significance at the 5% level.

**Statistical significance at the 1% level.



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Baa- and Aaa-rated U.S. corporate bonds (USDP), the lagged excess return on Datastream

world total market return index (WD), and a constant (CONSTANT).13

The weekly data ranges from January 2, 1987, to March 23, 2001, which is a 743-data-

point series. However, I work with rates of return and use the first difference ofconditioning variables, and finally all the conditioning variables are used with a 1-week

lag, relative to the excess return series, which leaves 741 observations expanding from

January 16, 1987, to March 23, 2001. All the data are extracted from Datastream.

Table 1 presents summary statistics of the continuously compounded excess world

equity returns and currency returns. As can be seen from panel A, WD not only has the

highest weekly mean returns, 0.068%, but also the highest standard deviation, 1.900%.

Comparing the performance of four excess currency returns, TA is the best one with a

mean of 0.021% per week and a standard deviation of 0.723%, and JP, on the other hand,

performs worst with a return of 0.020% per week and a standard deviation of 1.683%.Table 1also reports skewness, excess kurtosis, BeraJarque, and LjungBox statistics.

In all cases, skewness and excess kurtosis are significantly higher than they should be

under normality, and hence BeraJarque test rejects normality for all excess return series.

The LjungBox test statistics for raw returns (LB(20)) are significant at the 1% level in

three excess currency returns, implying strong linear dependencies among those returns.

For squared returns, LB2(20) is significant at the 1% level for all the return series,

indicating strong nonlinear dependencies in both currency and equity returns. This is

consistent with the volatility clustering observed in most stock and foreign exchange

markets, suggesting that the use of a conditional heteroscedasticity model is advisable.

The unconditional correlation coefficients for the conditioning variables are reported inpanel B ofTable 1.The correlation coefficients are small, and all are below .5, indicating

that the selected conditioning variables contain sufficiently orthogonal information.

6. Empirical evidence

The QML estimation of the conditional ICAPM (Eq. (17)) is reported in Table 2.The

hypothesis tests regarding the prices of risks and the predictability of conditioning

variables are presented inTable 3.The hypothesis tests concerning the contagion in mean

and volatility are shown inTables 4 and 5,respectively. Finally, summary statistics aboutthe sources of risk premia and diagnostic test statistics for the standardized residuals are

reported inTable 6.

6.1. The evidence of time-varying risk premia

First, considering the test results for the existence of time-varying risk premium. The

results are very encouraging. For example, the joint hypothesis of zero prices of market and

currency risks is strong rejected by Wald statistic (Wald = 2300.169) with a Pvalue of 0.

13 The excess dividend yield (DIV) is highly correlated with the U.S. term premium (USTP), so similar to

De Santis and Gerard (1997, 1998), I use first difference of the U.S. term premium (DUSTP) as one of the

conditioning variables.



14/29

Table 2

Quasi-maximum likelihood estimation of the conditional ICAPMa

Conditional mean process

World prices of market and currency risks

CONSTANT DIV DUSTP USDP WD

uw 3.932(3.399)

1.807

(3.173)

4.137(3.415)

60.930

(10.862)**

24.863

(4.326)**

uJP 1.625

(4.403)

11.726

(5.055)*

176.896(42.429)**

66.220

(67.145)

150.697(71.683)*

uHK 412.099

(113.249)**

326.048

(108.925)**

1123.212(530.127)*

2450.446(1224.145)*

2140.210

(957.788)*

uSG 35.537

(11.663)**

87.034

(13.466)**

401.491(56.286)**

378.680

(165.597)*

431.662(86.084)**

uTA 30.215

(5.741)**

9.306

(5.105)

304.737

(41.050)**

300.213

(46.236)**

333.379

(43.048)**

Mean spillovers

j = JP j = HK j = SG j = TA WD

/JP,j 0.013 (0.031) 0.598 (0.499) 0.092 (0.073) 0.142 (0.077)

/HK,j 0.001 (0.002) 0.232 (0.043)** 0.003 (0.005) 0.010 (0.006)

/SG,j 0.008 (0.014) 0.347 (0.240) 0.018 (0.034) 0.049 (0.035)/TA,j 0.025 (0.011)* 0.415 (0.209)* 0.224 (0.041)** 0.076 (0.034)*

Contagion in mean

xJP,j 0.222 (0.082)** 3.604 (1.908) 0.573 (0.106)** 0.475 (0.134)**xHK,j 0.005 (0.004) 0.160 (0.064)* 0.017 (0.006)** 0.037 (0.006)**xSG,j 0.001 (0.040) 3.170 (1.073)** 0.115 (0.072) 0.207 (0.080)**xTA,j 0.042 (0.034) 0.100 (0.826) 0.172 (0.063)** 0.490 (0.101)**

Conditional variance process

JP HK SG TA WD

aj 0.924 (0.018)** 0.911 (0.059)** 0.797 (0.028)** 0.055 (0.041) 0.750 (0.067)**bj 0.183 (0.034)** 0.347 (0.089)** 0.213 (0.058)** 1.345 (0.162)** 0.234 (0.035)**dj 4.958 (1.974)* 2.626 (6.150) 3.224 (3.728) 2.302 (5.790) 12.641 (5.066)*

Volatility spilloversJP HK SG TA WD

j= JP 0.001 (0.001) 0.054 (0.018)** 0.006 (0.032) 0.178 (0.103)j= HK 0.141 (0.403) 0.499 (0.343) 2.126 (0.836)* 1.468 (1.189)j= SG 0.002 (0.049) 0.002 (0.003) 0.255 (0.053)** 0.024 (0.096)

j= TA 0.080 (0.062) 0.009 (0.008) 0.161 (0.048)* 0.043 (0.054)j= WD 0.091 (0.032)** 0.005 (0.003)* 0.046 (0.011)** 0.040 (0.055)

Contagion in asymmetric volatility

JP HK SG TA WD

j= JP 0.221 (0.193) 26.782 (3.904)** 32.096 (4.925)** 17.484 (7.656)*j= HK 1116.507

(1512.059)

7505.472(1667.680)**

7813.758

(2745.339)**

1607.466

(1669.696)



15/29

The joint hypothesis of constant prices of market and currency risks is also significantly

rejected (Wald = 1001.038). Next, the joint hypothesis of constant prices of currency risks is

strongly rejected by Wald statistic (Wald = 332.470), and the joint hypothesis of constant

price of market risk is also rejected (Wald = 151.039). These test results imply that both

market and currency risks are not only priced but also time varying. Finally, the hypothesis

of constant price of currency risk for each currency is tested individually, and Wald teststatistic rejects the null at the 1% level in every case, implying that all four currencies are

sources of the time-varying currency risk premium. These results are consistent with the

findings ofDe Santis and Gerard (1998)andDumas and Solnik (1995).14 The conditioning

variables selected in this article are all very useful in predicting the dynamics of the risk

prices as can be seen from the hypothesis tests (10 13) reported inTable 3.That is, the null

hypothesis of zero predictability of conditioning variable is strongly rejected by Wald

statistic at the 1% level in all cases. Although statistically significant time-varying risk

premia are found, an interesting question to ask is to what extent these predictable risk

premia are economically significant. In answering this question, I computed pseudo-R2

statistic calculated as the ratio between the explained sum of squares and the total sum of

squares. As can be seen from Table 6, the reported pseudo-R2s for four excess currency

returns range from 9.957% for HK to 24.361% for TA, with an average of 17.284%, which

is significant higher than those reported in similar studies.15 These relatively high pseudo-

Conditional variance process

Contagion in asymmetric volatility

JP HK SG TA WD

j= SG 15.325 (7.376)* 0.264 (0.275) 8.547 (6.641) 17.142 (5.645)**j= TA 4.601 (1.747)** 0.125 (0.150) 0.397 (1.774) 9.181 (4.435)*

j= WD 10.450 (2.118)** 0.328 (0.205) 0.885 (1.552) 0.145 (1.067)

Log-likelihood function: 17,376.527

The reported parameter estimates for both the volatility spillover and contagion in asymmetric volatility

coefficients can be interpreted as follows. For example, ifxij represents the volatility spillover coefficient from

marketjto marketi, then the volatility spillover coefficient estimate from HK to JP is .141, which correspondsto gJP,HK in matrix G in the variancecovariance matrix in Eq. (9). Similarly, the volatility spillover coefficient

estimate from SG to JP is .002, which corresponds to kJP,SGin matrixKin the variance covariance matrix in Eq.

(9), and so on. The reported parameter estimates for the contagion in asymmetric volatility coefficients have thesame interpretation as those for volatility spillover coefficients.aRobust standard errors are given in parentheses.* Statistical significance at the 5% level.** Statistical significance at the 1% level.

Table 2 (continued)

14 BothDe Santis and Gerard (1998)andDumas and Solnik (1995)use excess returns on 1-month European

currency deposit rates to proxy for currency risks; however, in this article, 1-week Asian currency deposit rates are

employed to test the existence of time-varying currency risk premia.15 Using bivariate GARCH model to price deviations from UIP for five major currencies, McCurdy and

Morgan (1991)find that their model on average can only explain 2.22% of the return variations in their sample.

Two possible explanations for their relatively low pseudo-R2s are that they assume PPP and thus ignore currency

risk as a potential source of risk premium, and they estimate the bivariate model for each currency instead of

estimating all currencies jointly with the world equity portfolio.



16/29

R2 s indicate that the model perform very well in explaining the deviations from UIP. Based

on these empirical results, one can safely conclude that the predictable excess return puzzle

is due to the existence of time-varying risk premia and the sources of the risk premia come

not only from market risk, but also from currency risk.

6.2. Evidence of mean spillover and contagion in mean

After controlling the systematic currency and world market risks, I can then test the

contagion-in-mean effects. However, before that I need to the overall mean spillovereffects in the entire sample period, so any incremental mean spillover effects can be tested

during the crisis period. It can be seen from Table 4that the joint hypothesis of no mean

Table 3

Hypothesis tests concerning prices of risks and predictability of conditioning variables

Null hypothesis Wald df Pvalue

1. Are the prices of market and currency risks equal to zero?H0: uw =uc = 0; bc 2300.169 25 .000

Zt 1={CONSTANT,DIV,DUSTP,USDP,WD}

2. Are the prices of market and currency risks constant?

H0: uw =uc = 0; bc 1001.038 20 .000

Zt 1={DIV,DUSTP,USDP,WD}

3. Are the prices of currency risks equal to zero?

H0: uc = 0; bc 1478.836 20 .000

Zt 1={CONSTANT,DIV,DUSTP,USDP,WD}

4. Are the prices of currency risks constant?

H0: uc = 0; bc 332.470 16 .000


5. Is the price of market risk constant?

H0: uw = 0 151.039 4 .000


6. Is the price of the Japanese yen risk constant?

H0: uJP= 0 51.563 4 .000

Zt 1 = DIV,DUSTP,USDP,WD

7. Is the price of the Hong Kong dollar risk constant?

H0: uHK= 0 26.712 4 .000


8. Is the price of the Singapore dollar risk constant?

H0: uSG = 0 91.051 4 .000

Zt 1={DIV,D

USTP,USDP,WD}9. Is the price of the New Taiwan dollar risk constant?

H0: uTA= 0 76.311 4 .000


10. Is there no predictability from excess dividend yield?

H0: um,k=uc,k= 0; bc; k= DIV 101.186 5 .000

11. Is there no predictability from the change in term premium?

H0: um,k=uc,k= 0; bc; k= DUSTP 110.935 5 .000

12. Is there no predictability from the U.S. default premium?

H0: um,k=uc,k= 0; bc; k= USDP 106.507 5 .000

13. Is there no predictability from the world market portfolio?

H0: um,k=uc,k= 0; bc; k= WD 169.883 5 .000



17/29

spillover (14) is rejected at the 1% level only for TA. To find out the sources of meanspillover for TA, one can check statistical significance of individual mean spillover

coefficient,/, reported inTable 2.Table 2indicates that the sources of mean spillover for

TA come from JP, HK, and SG, and SG appears to be the major market in generating

return shocks for the other three markets based on the hypothesis test (11) reported in

Table 4.

Now, I can test the contagion-in-mean effects. Table 4 shows that these effects are

statistically significant at the 1% level for three markets: JP, HK, and SG. For example, the

joint hypothesis of no contagion-in-return shocks for JP (H0:xJP,j= 0; bj = HK,SG,TA)

during the crisis is strongly rejected by Wald statistic (Wald = 40.589) at the 1% level. The

same rejection also applies to HK and SG. To find out the sources of contagion-in-returnshocks for JP, one can examine the individual significance of contagion-in-mean

coefficient, xJP,j, reported in Table 2 based on robust standard errors. Basically, the

Table 4

Hypothesis tests concerning contagion in mean


1. Is there no mean spillover for JP?H0: /JP,j= 0; bj= HK,SG,TA 5.608 3 .132

2. Is there no mean spillover for HK?

H0: /HK,j= 0; bj= JP,SG,TA 3.106 3 .375

3. Is there no mean spillover for SG?

H0: /SG,j= 0; bj= JP,HK,TA 3.744 3 .290

4. Is there no mean spillover for TA?

H0: /TA,j= 0; bj= JP,HK,SG 47.796 3 .000

5. Is there no contagion in return shocks for JP?

H0: xJP,j= 0; bj= HK,SG,TA 40.589 3 .000

6. Is there no contagion in return shocks for HK?

H0: xHK,j= 0; bj= JP,SG,TA 36.898 3 .000

7. Is there no contagion in return shocks for SG?

H0: xSG,j= 0; bj= JP,HK,TA 17.306 3 .000

8. Is there no contagion in return shocks for TA?

H0: xTA,j= 0; bj= JP,HK,SG 7.724 3 .052

9. Is there no mean spillover from JP?

H0: /i,JP= 0; bi = HK,SG,TA 5.551 3 .135

10. Is there no mean spillover from HK?

H0: /i,HK= 0; bi = JP,SG,TA 6.093 3 .107

11. Is there no mean spillover from SG?

H0: /i,SG= 0; bi = JP,HK,TA 31.310 3 .000

12. Is there no mean spillover from TA?

H0: /i,TA= 0;b

i = JP,HK,SG 5.217 3 .15613. Is there no contagion in return shocks from JP?

H0: xi,JP= 0; bi = HK,SG,TA 3.477 3 .323

14. Is there no contagion in return shocks from HK?

H0: xi,HK= 0; bi = JP,SG,TA 12.682 3 .005

15. Is there no contagion in return shocks from SG?

H0: xi,SG = 0; bi = JP,HK,TA 42.669 3 .000

16. Is there no contagion in return shocks from TA?

H0: xi,TA= 0; bi = JP,HK,SG 51.321 3 .000



18/29

current returns in JP are affected by past return shocks in SG (xJP,SG = 0.573) and TA(xJP,TA= 0.475), in addition to its own past return shocks (xJP,JP= 0.222). Similarly, thecurrent return shocks in HK are due to the past return shocks in SG (xHK,SG = 0.017)and TA (xHK,TA= 0.037), in addition to its own past return shocks (xHK,HK= 0.160).The current return shocks in SG are due to the past return shocks in HK (xSG,HK= 3.170)

and TA (xSG,TA= 0.207), and finally, the current return shocks in TA are due to the past

return shocks in SG (xTA,SG = 0.172). By examining the significance of those individual

contagion-in-mean coefficients, one can conclude that basically all the contagion-in-meaneffects originate from three markets: HK, SG, and TA and none from JP, and this

conclusion has been confirmed by the hypothesis tests (1316) reported inTable 4.

Table 5

Hypothesis tests concerning contagion in volatility


1. Is there no volatility spillover for JP?H0: gi,HK= ki,SG= li,TA= mi,WD= 0; bi = JP 10.008 4 .040

2. Is there no volatility spillover for HK?

H0: m i,JP=gi,SG= ki,TA= li,WD= 0; bi = HK 4.794 4 .309

3. Is there no volatility spillover for SG?

H0: li,JP= mi,HK=gi,TA= ki,WD= 0; bi = SG 43.629 4 .000

4. Is there no volatility spillover for TA?

H0: ki,JP= li,HK= mi,SG=gi,WD= 0; b = TA 30.587 4 .000

5. Is there no contagion in asymmetric volatility shocks for JP?

H0: p i,HK= qi,SG =si,TA= vi,WD= 0; bi = JP 32.508 4 .000

6. Is there no contagion in asymmetric volatility shocks for HK?

H0: vi,JP=pi,SG= qi,TA=si,WD= 0; bi = HK 5.632 4 .228

7. Is there no contagion in asymmetric volatility shocks for SG?

H0: s i,JP= vi,HK=pi,TA= qi,WD= 0; bi = SG 83.254 4 .000

8. Is there no contagion in asymmetric volatility shocks for TA?

H0: q i,JP=si,HK= vi,SG =pi,WD= 0; bi = TA 59.588 4 .000

9. Is there no volatility spillover from JP?

H0: mHK,j= lSG,j= kTA,j=gWD,j= 0; bj= JP 11.539 4 .021

10. Is there no volatility spillover from HK?

H0: gJP,j= mSG,j= lTA,j= kWD,j= 0; bj= HK 8.808 4 .066

11. Is there no volatility spillover from SG?

H0: kJP,j=gHK,j= mTA,j= lWD,j= 0; bj= SG 23.962 4 .000

12. Is there no volatility spillover from TA?

H0: lJP,j= kHK,j=gSG,j= mWD,j= 0;b

j= TA 14.385 4 .00613. Is there no volatility spillover from WD?

H0: mJP,j= lHK,j= kSG,j=gTA,j= 0; bj= WD 30.392 4 .000

14. Is there no contagion in asymmetric volatility shocks from JP?

H0: vHK,j=sSG,j= qTA,j=pWD,j= 0; bj= JP 71.069 4 .000

15. Is there no contagion in asymmetric volatility shocks from HK?

H0: pJP,j= vSG,j=sTA,j= qWD,j= 0; bj= HK 28.590 4 .000

16. Is there no contagion in asymmetric volatility shocks from SG?

H0: qJP,j=pHK,j= vTA,j=sWD,j= 0; bj= SG 20.485 4 .000

17. Is there no contagion in asymmetric volatility shocks from TA?

H0: sJP,j= qHK,j=pSG,j= vWD,j= 0; bj= TA 10.754 4 .029

18. Is there no contagion in asymmetric volatility shocks from WD?

H0: vJP,j=sHK,j= qSG,j=pTA,j= 0; bj= WD 27.150 4 .000



19/29

6.3. Evidence of volatility spillover and contagion in volatility

Turning to volatility spillovers and contagion effects on the conditional variance of

excess currency returns, it can be seen from Table 5 that the hypothesis of no volatilityspillover (14) is rejected in all cases except HK. In particular, by examining the robust

standard errors of volatility spillover parameters reported inTable 2,it can be seen that the

Table 6

Summary statistics and residual diagnostics

JP HK SG TA WD

Full sample periodPredicted total risk premium (%) 0.046 0.006 0.029 0.037 0.079S.D. 0.389 0.018 0.347 0.357 0.388

Market risk premium (%) 0.022 0.000 0.005 0.003 0.106

S.D. 0.057 0.002 0.020 0.036 0.335

Currency risk premium (%) 0.068 0.006 0.034 0.034 0.027S.D. 0.384 0.018 0.347 0.355 0.195

Conditional volatility (%) 1.579 0.081 0.611 0.791 1.941

S.D. 0.414 0.037 0.419 0.805 1.406

Price of risk 2.101 62.013 1.681 3.137 2.195S.D. 8.968 124.582 30.894 16.581 4.348

Crisis period

Predicted total risk premium (%) 0.199 0.005 0.214 0.012 0.019S.D. 0.747 0.011 1.007 0.882 0.448

Market risk premium (%) 0.024 0.000 0.013 0.012 0.127

S.D. 0.067 0.002 0.045 0.080 0.398

Currency risk premium (%) 0.222 0.006 0.226 0.000 0.108S.D. 0.761 0.011 1.008 0.895 0.327

Conditional volatility (%) 2.345 0.104 1.611 1.721 2.230

S.D. 0.742 0.029 0.704 1.397 0.659

Price of risk 2.972 63.730 9.037 1.084 2.052S.D. 7.296 56.320 19.391 11.348 5.172

Residual diagnostics

B J 61.243** 5425.881** 46.233** 1679.036** 395.827**

LB(20) 21.674 25.941 27.070 24.297 15.560

LB2(20) 17.300 68.825** 7.408 15.496 10.009

Pseudo-R2 (%) 12.087 9.957 22.732 24.361 4.371

Engle and Ng (1993) asymmetric tests

Sign bias test 0.904 1.551 0.258 0.101 0.049Negative size bias test 0.297 0.032 0.207 0.599 0.214Positive size bias test 0.321 5.532** 0.338 0.946 1.749

The BeraJarque (BJ) tests normality based on both skewness and excess kurtosis and is distributed v2 with

two degrees of freedom.

LB(20) and LB2(20) are the Ljung Box test statistics of order 20 for serial correlation in the standardized

residuals and standardized residuals squared.

Pseudo-R2 is computed as the ratio between the explained sum of squares and total sum of squares.

*Statistical significance at the 5% level.

**Statistical significance at the 1% level.



20/29


21/29

6.4. Residual diagnostics

To access the fit of the conditional ICAPM with MGARCH(1,1)-M specification,

Table 6 reports the Ljung Box statistics for 20th-order serial correlation in the level(LB(20)) and squared standardized residuals (LB2(20)) as well as the asymmetry test

developed by Engle and Ng (1993).Under the multivariate framework, the standardized

residuals at time t is computed as Zt=Ht1/2et, where Ht

1/2 is the inverse of the

Cholesky factor of the estimated variancecovariance matrix. The LjungBox statistics

show no serious linear and nonlinear dependencies for the standardized residuals of

excess currency returns, with one exception in which LB2(20) is significant at the 1%

level for HK. Thus, based on the LjungBox statistics, the volatility process is correctly

specified. However, as suggested by Engle and Ng, the LjungBox test may not have

much power in detecting misspecifications related to the asymmetric effects. For this

purpose, the set of diagnostics proposed by Engle and Ng are used.16 These tests are

based on the news impact curve implied by a particular ARCH-type model used. The

premise is that if the volatility process is correctly specified, then the squared

standardized residuals should not be predictable based on observed variables. The

results reported in Table 6 show no evidence of misspecification. As for B J test

statistics, they are all significant, indicating departures from normality, which justifies

the use of robust standard errors computed from using the QML method of Bollerslev

and Wooldridge (1992). Overall, the MGARCH(1,1)-M specification fits the data very

well.

6.5. Asian crisis and time-varying risk premia

One advantage of modeling the conditional second moments via MGARCH approach

is that it enables one to recover some interesting statistics, such as conditional volatility,

and, more importantly, the size of different risk premia. These interesting statistics will not

be available if one leaves the condition second moments unspecified, such as the pricing

kernel approach employed byDumas (1993),Dumas and Solnik (1995),andTai (1999).17

Table 6 reports those statistics. For example, the predicted weekly total risk premium is

measured by

TRPi;tkm;t1him;tX

c

kc;t1hic;t; i JP; HK; SG; TA 18

16 Engle and Ng (1993)asymmetric tests include the sign bias, the negative size bias, and the positive size

bias tests. The sign bias test examines the impact of positive and negative innovations on volatility not predicted

by the model. The squared standardized residuals are regressed against a constant and a dummy St that takes

the value of unity ifet 1 is negative and 0 otherwise. The test is based on the t statistic forSt. The negative

(positive) size bias test examines how well the model captures the impact of large and small negative (positive)

innovations, and it is based on the regression of the squared standardized residuals against a constant and

Stet 1((1 St

)et 1). The computed t statistic for St et 1 ((1 St

)et 1) is used in this test.17 See the comments provided by Campbell Harvey in Dumas (1993).



22/29

and ranges from 0.046% for JP to 0.079% for WD. The TRPi,tcan be decomposed intotwo components: currency risk premium (CRPi,t) and market risk premium (MRPi,t). The

currency risk premium is measured by

CRPi;tX

c

kc;t1hic;t; i JP; HK; SG; TA 19

and the market risk premium is measured by

MRPi;tkm;t1him;t; i JP; HK; SG; TA: 20

The predicted average total risk premium and its variability are basically dominated by

the currency risk premia. For instance, the currency risk premium (and its standard

deviation) is 0.068% (0.384%) for JP, 0.006% (0.018) for HK, 0.034% (0.347%)for SG, and 0.034% (0.355%) for TA. However, the predicted market risk premium and its

standard deviation are relatively small as compared to those of predicted currency risk

premium. This empirical evidence points out that an international asset pricing model

under PPP would not deliver economically significant risk premia in foreign exchange

markets.

In light of the result byFlood and Rose (1996) that the forward premium puzzle or

predictable excess return puzzle is less severe for countries with fixed exchange rates, it

will be interesting to examine whether the reported predicted risk premium confirm theirresult.18 If the exchange rate regime for a country is completely flexible (independent

float), we would expect a more severe predictable excess return puzzle in terms of grater

magnitudes in both the size and variability of the predicted risk premium (ex post

deviations from UIP). On the other hand, if the exchange rate regime is completely fixed

(hard peg), we should expect smaller magnitudes of the size and variability of the

predicted risk premium. However, if the exchange rate regime is between above two polar

regimes, such as managed float, we would expect that the magnitudes of the size and

variability of the predicted risk premium fall into the ranges of those for the two polar

regimes. In other words, the absolute size and the variability of predicted risk premium for

each country in general should positively related the degree of the flexibility of itsexchange rate regime. The predicted risk premium for each currency reported in Table 6

confirms our conjecture, and is consistent with the result by Flood and Rose. For example,

the exchange rate regimes for the countries for the period studied in this article range from

independent float (Japan), managed float (Taiwan and Singapore) to hard peg (Hong

Kong), and the size (variability) of their respective predicted total risk premium ranges

from 0.046% (0.389%), to 0.037% (0.357%), to 0.029% (0.347%), to 0.006%(0.018%).

18 If covered interest parity holds, the predictable excess return puzzle will be the same as forward premium

puzzle since the deviations from UIP can be expressed as the difference between expected future spot rates and

current forward rates (i.e., forward bias or forward forecast error).



23/29

Fig.

1.

Actualand

predictedriskpremia.



24/29

Fig.

2.

Currencyandmarketriskpremia.



25/29


26/29

To see if the dynamics of predicted excess currency returns behave differently during

the crisis, the same statistics are calculated for the crisis period. As can be seen from the

table, the averages of the estimated total risk premia and their standard deviations change

dramatically, especially for JP, SG, and TA. For these three markets, the average of thepredicted risk premium decreases from 0.046% to 0.199% for JP, from 0.029% to 0.214% for SG, and from 0.037% to 0.012% for TA, and theses decreases are mainlydue to the drops in their respective currency risk premium components. Since the

estimated model is fully parameterized, the impact of the dynamics of the prices of

currency risk can be separated from the estimated covariances in determining the estimated

currency risk premia. Because the estimated covariances are on average positive during the

entire sample and the average price of each currency risk is negative except TA, the

estimated currency risk premia are negative, implying that investors are willing to give up

some of the total risk premium when the hedging value of the assets in the portfolio

becomes predominant. By comparing the prices of currency risk in two different sample

periods, it is not surprised to see that the currency risk premium decreases since the prices

of currency risk are lower during the crisis period. Another observation worth mentioning

is that the predicted risk premium for excess currency returns is basically dominated by the

currency risk premium; however, the predicted risk premium for the world equity market is

dominated by the market risk premium, suggesting the importance of incorporating

currency risk in pricing the deviations from UIP.

A useful complement toTable 6is to display the time-series plots of those interesting

statistics. Fig. 1 contains the plots of actual risk premia (deviations from UIP) and

predicted risk premia. It can be seen that the dynamics of the predicted risk premia followvery closely to those of actual risk premia, especially during the period of Asian crisis.

These close resemblances have been confirmed by the relatively high pseudo-R2 statistics

reported inTable 6.Fig. 2displays the plots of time-varying currency risk and market risk

premia. Clearly, the currency risk premia are not only more volatile but also higher than

the market risk premia. Finally, Fig. 3 contains the plots of conditional volatility. The

conditional volatility for each currency shows significant time variation, especially during

the crisis period.

7. Summary and concluding remarks

This article tests whether there are pure contagion effects in both conditional means

and volatilities of Asian foreign exchange markets during the 1997 Asian crisis. Previous

studies on contagion have failed to take into account the important distinction between

the two concepts of interdependence and contagion. Specifically, in this article, I define

contagion as significant spillovers of country-specific idiosyncratic shocks during the

crisis after economic fundamentals or systematic risks have been accounted for. To

control for the economic fundamentals, I rely on an ICAPM in the absence of PPP, which

provides a theoretical basis in selecting economic fundamentals. The economic funda-

mentals under ICAPM are the world market and foreign exchange risks, so the evidenceof contagion is based on testing whether idiosyncratic risksthe part that cannot be

explained by the world market and foreign exchange risksare significant in describing



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Dornbusch, R., Park, Y. C., & Claessens, S. (1999). Contagion: How it spreads and how it can be stopped.

Mimeo, MIT.

Dumas, B. (1993). A test of the international CAPM using business cycles indicators as instrumental

variables. In J. Frankel (Ed.), The internationalization of equity markets (pp. 23 58). Chicago, IL:

University of Chicago Press.

Dumas, B., & Solnik, B. (1995). The world price of exchange rate risk. Journal of Finance, 50, 445 479.

Ebrahim S. (2000). Volatility transmission between foreign exchange and money markets. Bank of Canada

Working Paper No. 16.

Edwards, S. (1998). Interest rate volatility, capital controls and contagion. NBER Working Paper No. 6756.

Edwards, S., & Susmel, R. (1999). Interest rate volatility in emerging markets: Evidence from the 1990s. Mimeo,

UCLA and University of Houston.

Eichengreen, B., Rose, A. K., & Wyplosz, C. (1996). Contagious currency crises. NBER Working Paper

No. 5681.

Engel, C. (1996). The forward discount anomaly and the risk premium: A survey of recent evidence.Journal of

Empirical Finance, 3, 123 192.

Engle, R. F., & Kroner, K. (1995). Multivariate simultaneous GARCH. Econometric Theory, 11, 122 150.Engle, R. F., & Ng, V. K. (1993). Measuring and testing the impact of news on volatility. Journal of Finance,48,

17491778.

Engle, R. F., Ng, V. K., & Rothschild, M. (1990). Asset pricing with a FACTOR-ARCH covariances structure:

Empirical estimates for treasury bills. Journal of Econometrics, 45, 213 237.

Ferson, W. E. (1995). Theory and testing of asset pricing models. In R. A. Jarrow, V. Maksimovic, & W. T.

Ziemba (Eds.), Finance, handbooks in operation research and management science, vol. 9 ( pp. 145 200).

Amsterdam: North-Holland.

Ferson, W. E., & Harvey, C. R. (1993). The risk and predictability of international equity returns. Review of

Financial Studies, 6, 527 567.

Ferson, W. E., & Harvey, C. R. (1994). Sources of risk and expected returns in global equity markets.Journal of

Banking and Finance, 18, 775 803.

Flood, R. P., & Rose, A. K. (1996). Fixes: Of the forward discount puzzle. Review of Economics andStatistics, 78, 748752.

Forbes, K., & Rigobon, R. (1998). No contagion, only interdependence: Measuring stock market co-movements.

NBER Working Paper No. 7267.

Forbes, K., & Rigobon, R. (1999). Measuring contagion: Conceptual and empirical issues. Mimeo, MIT.

Giovannini, A., & Jorion, P. (1989). The time variation of risk and return in the foreign exchange and stock

markets.Journal of Finance, 44, 307 325.

Glosten, L. R., Jagannathan, R., & Runkle, D. (1993). On the relation between expected value and the volatility

of the nominal excess return on stocks. Journal of Finance, 48, 17791801.

Harvey, C. R. (1991). The world price of covariance risk. Journal of Finance, 46, 117157.

Kaminsky, G. L., & Peruga, R. (1990). Can time-varying risk premium explain excess returns in the forward

market for foreign exchange? Journal of International Economics, 28, 47 70.

Kaminsky, G. L., & Reinhart, C. M. (2000). On crises, contagion, and confusion. Journal of InternationalEconomics, 51, 145168.

Karolyi, G. A., & Stulz, R. (1996). Why do markets move together? An investigation of U.S. Japan stock return

comovements.Journal of Finance, 51, 951 986.

Kroner, K. F., & Ng, V. K. (1998). Modeling asymmetric comovements of asset returns. Review of Financial

Studies, 11, 817 844.

Lewis, K. K. (1994). Puzzles in international financial markets. NBER Working Paper No. 4951.

Longin, F., & Solnik, B. (1995). Is the correlation in international equity returns constant: 19701990? Journal

of International Money and Finance, 14, 3 26.

Mark, N. C. (1985). On time-varying risk premia in the foreign exchange market: An econometric analysis.

Journal of Monetary Economics, 16, 318.

Mark, N. C. (1988). Time-varying betas and risk premia in the pricing of forward foreign exchange contracts.

Journal of Financial Economics, 22, 318.

Masson, P. (1998). Contagion: Monsoonal effects, spillovers, and jumps between multiple equilibria. IMF

Working Paper WP/98/142.



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