Time-Varying Risk Premium and Contagion in Foreign Exchange Markets: Evidence from the 1997 Asian Crisis

Chu-Sheng Tai* Department of Economics and Finance, College of Business Administration, Texas A&M

University, MSC 186, 1115 University Blvd., Kingsville, TX 78363-8203, USA

Abstract

In this paper, I examine simultaneously whether time-varying risk premium can explain the predictable excess return puzzle (Lewis (1994)), and whether there are contagion effects among foreign exchange markets during the 1997 Asian crisis. I use a conditional version of international CAPM (ICAPM) in the absence of purchasing power parity (PPP) to derive a measure of the risk premium. To incorporate time-varying feature of the risk premium into the model, I allow not only the second moments of asset returns to change over time by utilizing multivariate GARCH-in-mean (MGARCH-M) modeling strategy, but also the prices of risks to evolve through time based on some predetermined information variables. Estimation results show significant time-varying risk premia in deviations from uncovered interest parity (UIP), and these risk premia mainly compensate currency speculators for bearing not just market risk but currency risk. Overall, the conditional ICAPM with MGARCH-M structure is able to explain/predict on average more than 26% (26.138%) of the return variations in foreign exchange markets, a very high return predictability compared to previous studies. Therefore, I can conclude that the time-varying risk premium is a very strong candidate in explaining the predictable excess return puzzle since the risk premia detected in this paper are not only statistically significant but also economically significant. As for the tests of contagion, I find strong pure contagion effects in both conditional means and volatilities of foreign exchange markets after systematic risks have been accounted for. Specifically, the contagion-in-mean effects are mainly driven by the past innovations in Japan, Hong Kong, and Singapore. As for contagion in volatility, the lead/lag relationships appear to be multidirectional with Hong Kong playing the dominant role in generating contagion effects at volatility level since all the other three markets are significantly influenced by the past innovations in Hong Kong.

JEL Classifications: C32; F31; G12 Key Words: Predictable excess return puzzle; Contagion; Asset pricing; Time-varying risk

premium; Multivariate GARCH-M

* Corresponding author. Tel: +1 361 593 2355; fax: +1 361 593 3912; e-mail: ctai@tamuk.edu

1

Time-Varying Risk Premium and Contagion in Foreign Exchange Markets: Evidence from the 1997 Asian Crisis

Abstract

In this paper, I examine simultaneously whether time-varying risk premium can explain the predictable excess return puzzle (Lewis (1994)), and whether there are contagion effects among foreign exchange markets during the 1997 Asian crisis. I use a conditional version of international CAPM (ICAPM) in the absence of purchasing power parity (PPP) to derive a measure of the risk premium. To incorporate time-varying feature of the risk premium into the model, I allow not only the second moments of asset returns to change over time by utilizing multivariate GARCH-in-mean (MGARCH-M) modeling strategy, but also the prices of risks to evolve through time based on some predetermined information variables. Estimation results show significant time-varying risk premia in deviations from uncovered interest parity (UIP), and these risk premia mainly compensate currency speculators for bearing not just market risk but currency risk. Overall, the conditional ICAPM with MGARCH-M structure is able to explain/predict on average more than 26% (26.138%) of the return variations in foreign exchange markets, a very high return predictability compared to previous studies. Therefore, I can conclude that the time-varying risk premium is a very strong candidate in explaining the predictable excess return puzzle since the risk premia detected in this paper are not only statistically significant but also economically significant. As for the tests of contagion, I find strong pure contagion effects in both conditional means and volatilities of foreign exchange markets after systematic risks have been accounted for. Specifically, the contagion-in-mean effects are mainly driven by the past innovations in Japan, Hong Kong, and Singapore. As for contagion in volatility, the lead/lag relationships appear to be multidirectional with Hong Kong playing the dominant role in generating contagion effects at volatility level since all the other three markets are significantly influenced by the past innovations in Hong Kong.

JEL Classifications: C32; F31; G12 Key Words: Predictable excess return puzzle; Contagion; Asset pricing; Time-varying risk

premium; Multivariate GARCH-M

2

I. Introduction

The uncovered interest parity (UIP) hypothesis states that the domestic nominal

interest rate equals the foreign nominal rate on a comparable asset plus the expected

change in the exchange rate over the period to maturity of the asset. Under the standard

assumption of rational expectations, and risk neutral agents, the ex post excess returns of

holding foreign currency deposits just equal the market true expected excess returns plus a

forecast error that is unpredictable ex ante. Given this joint assumption, tests of UIP are

essentially tests of the efficiency of the forward market for exchange rates if covered

interest parity (CIP) holds.1 One important conclusion from this market efficiency study is

that there exist predictable components in excess returns from holding foreign currency

deposits.2 This predictable excess return is one of the puzzles in international finance

literature.3 Although the hypothesis that forward exchange rates are unbiased predictor of

future spot rates has usually been rejected, most researchers are still inconclusive as to

whether the forward bias is due to market inefficiency (irrationality) or to the presence of a

time varying risk premium.4

1 If CIP holds, 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).

2 Hodrick (1987) provides a detailed survey on the empirical studies of market efficiency of forward and

futures markets.

3 See Hodrick (1987), Cumby (1988), Korajczyk and Viallet (1992), Bekaert and Hodrick (1993) and Lewis

(1994).

4 See for example, Hansen and Hodrick (1980, 1983), Hodrick and Srivastava (1984), Korajczyk (1985),

Mark (1985, 1988), Hodrick (1987), Cumby (1988), and Kaminsjy and Peruga (1990).

3

Since the zero risk premium is hardly compatible with the existing applied finance

literature, this time-varying risk premium argument has led to an intensive search for

proper specification of the risk premium in foreign exchange markets. Theoretical

international finance models developed by Solnik (1974), Roll and Solnik (1977), Hodrick

(1981), Alder and Dumas (1983), and Stulz (1981, 1984) consider the pricing of foreign

currency deposits in much the same way as that of other financial assets. In these models,

the excess return from holding a foreign currency deposit results from a risk premium that

has to be paid to risk averse speculators for taking the risk of future changes in exchange

rates. If this foreign exchange risk can not be diversified when forming a well-diversified

portfolio, then standard portfolio theory tells us that this risk is systematic and should be

priced in an asset market in equilibrium. However, if the foreign exchange risk is

completely diversifiable, it should not command a risk premium. As a result, if currency

speculation involves systematic risk, speculative returns should be nonzero and are

predictable. In this case, UIP will be violated even if rational expectations hold.

Another line of research in the international financial literature which has drawn a

lot of attentions in recent years is the study of the transmission of financial shocks/crisis

across markets/countries, which has introduced an important distinction between the two

concepts of interdependence and 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. For instance, several Asian

countries shared common features such as a high reliance on foreign denominated debt

and a relatively stable exchange rate against the U.S. dollar. Thus, the occurrence of a

4

crisis across several countries may be due to an initial disturbance in other places, and not

due to the transmission of a shock from one country to another. The second type of

financial market inter-linkages arises from spillover effects, which may be due to trade

linkages or financial interdependence. For example, Asia countries tend to compete in the

same export markets in the West as well as in similar products, so a devaluation of one

currency has a negative impact on the international competitiveness of other countries. In

additional to trade links, spillovers may occur if different countries are financial

interdependent if they borrow from the same creditors. For example, a currency crisis in

country A reduces the ability of domestic borrowers to replay their loans to outside banks,

which forces the foreign banks to rebuild their capital by recalling some of their loans,

including loans made to borrowers in other countries. Borrowers from country B then

suffer from credit crunch caused by the impact of the currency crisis in country A on their

creditors. The first two channels of financial crises can be categorized as fundamentals-

driven crises since the affected countries share some macroeconomic fundamentals, which

implies that the transmission of financial crises is due to the interdependence 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 paper is to test simultaneously both the existence of time-varying

risk premium in explaining the predictable excess return puzzle and the pure contagion

5

effects among Asian foreign exchange markets during the 1997 Asian crisis 5 .

Specifically, in this paper I define ‘contagion’ as significant spillovers of country-specific

idiosyncratic shocks during the crisis after economic fundamentals or systematic risks

have been accounted for. In testing for contagion, its existence depends on the economic

fundamentals used. 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 me 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 based on testing whether

idiosyncratic risks- the part that cannot be explained by the world market and foreign

exchange risks, are significant in describing the dynamics of conditional mean and

volatility in foreign exchange markets during the crisis. The ICAPM used in this paper

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 explaining the predictable excess return puzzle have

not been very successful.6

5 To my knowledge, this is the first paper to use Asian foreign exchange data to investigate the predictable

excess return puzzle.

6 For example, Mark (1985), Cumby (1988), Kaminsky and Peruga (1990), Backus, Gregory and Telmer

(1993) use an intertemporal asset pricing model (IAPM) 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 observable ingredients in the risk premium models do not vary

6

In addition to overcoming the drawback of arbitrarily choosing economic

fundamentals in testing contagion effect in previous studies, in this paper I employ a

different methodology to test the existence of both time-varying risk premium and

contagion. Specifically, I use a Multivariate General Autoregressive Conditional

Heteroscedastic in Mean (MGARCH-M) model to capture the time dependencies in the

second moment, a stylized property found in most financial time-series, which has been

ignored by most empirical studies on contagion7. The MGARCH-M model adopted in this

paper also overcomes the drawbacks in previous studies in testing risk premium

hypothesis in explaining the predictable excess returns puzzle (e.g., Mark (1988),

McCurdy and Morgan (1991)). Mark (1988) uses a single-beta CAPM to price the

forward foreign exchange contracts from the point of view of a U.S. investor. He specifies

the betas as ARCH-like process and 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 (1988), the GMM estimator is 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

sufficiently to explain the high degree of variability in asset returns without implausibly large estimates of

the coefficient of relative risk aversion. (See Engel (1996))

7 Previous empirical studies on contagion can be categorized by methodology into four groups: (1) the

testing of significant increases in correlation (Calvo and Reinhart (1996), Baig and Goldfajn (1999), Forbes

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

correlation (Baig and Goldfajn (1999)); (3) the testing of significant volatility spillover (Edwards (1998),

Edwards and Susmel (1999)); (4) crisis prediction regression (Bae, Karolyi, and Stulz (2000), Eichengreen,

Ross, and Wyplosz (1996), Kaminsky and Reinhart (2000), Rijckeghem and Weder (1999), Sachs, Tornell,

7

parameterization to price deviations from UIP for five European currencies. They

estimate their model currency by currency, while Mark (1988) estimates his model jointly

across currencies, so the efficiency might be sacrificed in McCurdy and Morgan’s (1991)

study. Moreover, theses two studies all assume that PPP hold.

Therefore, under the fully parameterized multivariate model adopted in this paper,

not only is the maximum efficiency gain retained in testing the risk premium hypothesis in

explaining the predictable excess return puzzle, but also some interesting statistics are

recovered, which are mostly ignored in previous studies.8

II. The Theoretical Motivation

We know that the first-order condition of any consumer-investor’s portfolio

optimization problem can be written as:

1]|[ 1, =Ω −ttit RME , Ni ⋅⋅⋅⋅⋅⋅=∀ 1 (1)

where M t is known as a stochastic discount factor (SDF) or an intertemporal marginal

rate of substitution (IMRS); tiR , is the gross return of asset i at time t and 1−Ωt is market

and Velasco (1996)). None of the contagion studies mentioned above explicitly takes the time

dependencies in the second moment into account.

8 Previous papers that do not have much success in detecting time-varying risk premia in foreign exchange

markets using multivariate GARCH approach include Giovannini and Jorion (1989) and Baillie and

Bollerslev (1990).

8

information known at time 1−t . Without specifying the form of M t , equation (1) has

little empirical content since it is easy to find some random variable M t for which the

equation holds. Thus, it is the specific form of M t implied by an asset pricing model that

gives equation (1) further empirical content (e.g., Ferson (1995)). Suppose M t and tiR ,

have the following factor representations:

t

K

ktkkt uFaM ++= ∑

=1,β (2)

ti

K

ktkikiti Fr ,

1,, εβα ++= ∑

=

Ni ⋅⋅⋅⋅⋅⋅=∀ 1 (3)

where ttiti RRr ,0,, −= is the raw returns of asset i in excess of the risk-free rate, tR ,0 , at

time t , and 0]|[]|[]|[]|[ 1,1,,11, =Ω=Ω=Ω=Ω −−−− ttittktittttkt EFEuEFuE εε ki,∀ ; tkF ,

are common risk factors which capture systematic risk affecting all assets tir , including

M t ; ikβ are the associated time-invariant factor loadings which measure the sensitivities

of the asset to the common risk factors, while tu is an innovation and ti,ε are idiosyncratic

terms which reflect unsystematic risk. The risk-free rate, 1,0 −tR , must also satisfy equation

(1).

1]|[ 11,0 =Ω −− ttt RME (4)

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

9

0]|[ 1, =Ω −ttitrME Ni ⋅⋅⋅⋅⋅⋅=∀ 1 (5)

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

]|[

)|;(]|[

1

1,1,

−

−− Ω

Ω−=Ω

tt

tttitti ME

MrCovrE Ni ⋅⋅⋅⋅⋅⋅=∀ 1 (6)

Substitute equation (2) into equation (6):

)|;()|,(]|[

]|[ 1,,1,1,,1

1, −−−−

− Ω=ΩΩ

−=Ω ∑∑ ttkti

ktkttkti

k tt

ktti FrCovFrCov

MErE λ

β (7)

where 1, −tkλ is the time-varying price of factor risk. Equation (7) is a general conditional

multi-factor asset pricing model derived from the intertemporal consumption-investment

optimization problem.

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

portfolio and four currency returns.9 The selection of those five factors is theoretically

justified based on either the intertemporal CAPM of Merton (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 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

9 In this paper, I consider four Asian foreign exchange rates: Japanese yen, Hong Kong dollar, Singapore

dollar, and New Taiwan dollar, so there are four currency risks plus one world market risk.

10

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

violation of the law of one price (LOP), investors from different countries face different

prices when 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. 10 Therefore, a conditional

multi-factor asset pricing model containing world market and foreign exchange risks

(equation (7)) seems to be reasonable and will be used to test risk premium hypothesis in

foreign exchange markets. (e.g., Ferson and Harvey (1994), Dumas and Solnik (1995), and

De Santis and Gerard (1998), among others.) I can now rewrite the conditional multi-

factor asset pricing model in equation (7) as

tjttctjc

tcttmtjtmtj rrCovrrCovr ,1,,1,1,,1., )|;()|,( ελλ +Ω+Ω= −−−− ∑ Nj ⋅⋅⋅⋅⋅⋅=∀ 1 (8)

where “m ” denotes world market risk and c is the currency risk. 11

III. Econometric Methodology

The conditional ICAPM in equation (7) has to hold for every asset. However, the

model does not impose any restrictions on the dynamics of the conditional second

moments. Several multivariate GARCH (MGARCH) models have been proposed to

model the conditional second moments, such as the diagonal VECH model of Bollerslev,

10 See Solnik (1974), Stulz (1981, 1984) and Adler and Dumas (1983).

11 In this paper, the factors are market portfolio and short-term currency deposits, which are traded assets, so

we can replace “ tkF , ” with “ tkr , ”.

11

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 paper 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 paper. Although it is ease to

understand, 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 paper

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 (1996).12 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.13 Specifically, the dynamic

process for the conditional variance-covariance matrix of asset returns is specified as:

GGBBAHACCH tttttt ⋅⋅+⋅⋅+⋅⋅+= −−−−−'

11''

11'

1'' ηηεε (9)

12 Another multivariate GARCH model proposed recently by Kroner and Ng (1998) is General Dynamic

Covariance (GDC) model. The GDC model is a hybrid of the CCOOR model structure and the BEKK

model structure, so it also restricts the conditional correlation between asset returns to be a constant

although it is flexible enough to encompass the four multivariate GARCH models discussed above.

13 The asymmetric volatility effects in variances and covariances have been documented in recent papers by,

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

12

where tH is NN × time-varying variance-covariance matrix of asset returns; C is

restricted to be a NN × upper triangular matrix, and A , B , and G are NN × free

matrices of unknown parameters, with elements ijc , ija , ijb , and ijg . The 1×N vector,

1−tη , captures the asymmetric impact that the vector of past innovations has on the

conditional covariance matrix in a manner similar to that of Glosten et al. (1993), and is

defined as: 1,1, −− = titi εη if 01, <−tiε , 0 otherwise. In this model the conditional variance

and covariance of each asset return are related to past conditional variances and

covariances, past squared residuals and cross residuals, and past squared asymmetric

shocks and cross-asymmetric shocks. One drawback of the asymmetric BEKK model is

the larger number of parameters that must be estimated. For a system of N equations,

there are 2)7( 2 NN + parameters. For example, a system of 5 equations has 90 parameters.

To keep the size of the parameter space manageable, I impose three constraints. First, I

assume that A is a diagonal matrix since previous studies have shown that the off-

diagonal elements in A tend to be insignificant. Second, since the purpose of this paper is

to test contagion effects among foreign exchange markets, I assume that the contagion-in-

volatility effects only occur among foreign exchange markets themselves, and not with the

world market portfolio. That is, the off-diagonal elements in B will be zero only for the

last row and the last column if the world market portfolio is the last asset.14 Finally, I

assume that only the market asymmetric shocks affect the variance and covariance of asset

returns. Kroner and Ng (1998) show that the volatility asymmetry of both small and large

stock portfolios in the U.S. stems mostly from shocks in the large stock portfolio.

14 In estimation, I restrict B to be a diagonal matrix during ‘non-crisis’ period, so I can test whether there is

a significant contagion in volatility during the ‘crisis’ period.

13

Consequently, it will be interesting to see if the volatility asymmetry of market portfolio, a

‘large’ portfolio, has any effect on short-term currency deposit, a ‘small’ portfolio.

The parameter matrices A , B , and G now have the following forms:

=

55

44

33

22

11

00000000

00000000

0000

aa

aa

a

A ;

=

55

44434241

34333231

24232221

14131211

00000

00

0

bbbbb

bbbbbbbb

bbbb

B ;

=

5554535251

00000

0000000000

00000

ggggg

G

This reduces the parameter space considerably while maintaining flexibility in modeling

the dynamics of conditional second moments. For a system of 5 assets, there are 42

parameters including the parameters in matrix C instead of 90. Under the assumption of

conditional normality, the log-likelihood to be maximized can be written as:

)()()(21

|)(|ln21

2ln2

)(ln 1 '

11

θεθθεθπθ tt

T

tt

T

tt HH

TNL −

==∑∑ −−−= (10)

where θ is the vector of unknown parameters in the model. Since the normality

assumption is 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 equation (10), and calculating a robust estimate of the

covariance of the parameter estimates using the matrix of second derivatives and the

14

average of the period-by-period outer products of the gradient. Optimization is performed

using the Broyden, Fletcher, Goldfarb, and Shanno (BFGS) algorithm.

IV. Hypothesis Testing

Testing Time-varying Risk Premium

Many empirical studies have shown that the prices of risks are time-varying. (e.g.,

Harvey (1991), Dumas and Solnik (1995), and De Santis and Gerard (1997, 1998), 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

expectations 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 (equation (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 to Bekaert and Harvey (1995) and De Santis and Gerard (1997, 1998) an

exponential function is used to model the dynamic of 1, −tmλ and for the dynamics of 1, −tcλ ,

15

a linear specification is adopted because the model does not restrict the price of currency

risk to be positive.

)exp( 1'

1, −− = tmtm zϕλ (11)

1'

1, −− = tctc zϕλ (12)

where 1−tZ is a vector of information variables observed at the end of time 1−t and ϕ ’s

are 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 1−tZ , and the price of world

market risk is assumed to be an exponential function of informa tion variables in 1−tZ .

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

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

to significant GARCH parameters.

Testing Contagion in Mean and Volatility

To test whether a country’s past idiosyncratic shocks have significant impact on

the other countries’ condition returns (contagion in mean) during the crisis, I incorporate

country-specific past innovations into equation (8). Specifically, the equation (8) can be

modified as:

tjji

tiijttctjc

tcttmtjtmtj ddummyrrCovrrCovr ,1,1,,1,1,,1., )()|;()|,( εελλ ++Ω+Ω= ∑∑≠

−−−−− ; ji,∀ (13)

16

where ""dummy is a dummy variable, which is equal to one during Asian crisis and zero

otherwise.15 Thus, the contagion in mean hypothesis can be examined by testing whether

the coefficients, ijd , are individually or jointly significant after the systematic risks have

been accounted for.

To test contagion in volatility hypothesis, we can test whether the off-diagonal

elements in matrix B are individually or jointly significant. For example, a test of null

hypothesis that jib , is zero ( 0: ,0 =jibH ) means that there is no contagion in volatility from

country i to country j . Similarly, a test of null hypothesis that jib , is zero for all i

( ibH ji ∀= ;0: ,0 ) implies that the conditional volatility of country j is not affected by the

other countries’ idiosyncratic shocks.

IV. Data and Summary Statistics

I analyze four Asian currency deposit rates: one-week Euroyen deposit rate ( JP ),

one-week Hong Kong deposit rate ( HK ), one-week Singapore deposit rate (SG ), and 10-

day Taiwan money market rate ( TA ).16 The value-weighted Morgan Stanley Capital

International (MSCI) world index ( MSWRLD ) is proxied for world market risk. 7-day

Eurodollar deposit rate is used as conditionally risk-free rate to compute the excess returns

15 I assume Asian crisis began in the first week of July 1997 (July 4, 1997) and ended in the last week of

June 1998 (June 26, 1998).

16 Ideally I would like to use interest rate data from other Asia-Pacific countries such as Indonesia, the

Philippines, South Korea, Thailand, and Malaysia etc., but the short-term interest rate data for those

countries are not available from Datastream.

17

on the MSCI world index, and the four Asian currency deposit rates (or the deviations

from UIP). In particular, the excess equity returns are computed as:

)1ln()ln( $1

1,

ust

t

tti i

pp

r −−

+−= where tp is the MSCI world total return index (dividend

included) at time t , and $1

USti − is 7-day Eurodollar deposit rate known at time 1−t . The

excess currency returns (or the deviations from UIP) are computed as:

)1ln()ln()1ln( $1

1

*1,

USt

t

ttti i

ss

ir −−

− +−++= where ts is the spot rate at time t expressed as

domestic price (the U.S dollar) of one unit of Asian currency; *1−ti is the short-term Asian

currency deposit rate known at time 1−t .

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

international asset pricing literature (e.g., Harvey (1991), Bekaert and Hodrick (1992),

Ferson and Harvey (1993), Bekaert and Harvey (1995), and De Santis and Gerard (1997,

1998), among others). They are excess dividend yield measured by the dividend yield on

S&P 500 index in excess of the 7-day Eurodollar deposit rate ( DIV ), the change in 7-day

Eurodollar deposit rate ( EURO∆ ), 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 ( USTP∆ ), the U.S. default premium, measured by the yield difference between

Moody’s Baa-rated and Aaa-rated U.S. corporate bonds ( USDP ), and a constant

(CONSTANT ).17

17 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 ( USTP∆ ) as one of

the instruments.

18

Observations are sampled at weekly intervals. 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 of conditioning variables, and finally all the

conditioning variables are used with a one-week lag, relative to the excess return series;

that leaves 740 observations expanding from January 23, 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, the MSWRLD has the

highest mean returns (0.075%) and highest standard deviation (2.112%). Comparing the

performance of four currency returns, the TA is the best one with the mean return of

0.02%, and the JP is the worst one with a negative mean return of 0.024%.

Table 1 also reports skewness, excess kurtosis, Bera-Jarque and Ljung-Box

statistics. In most cases, the index of kurtosis and the Bera-Jarque test statistic strongly

reject the hypothesis of normally distributed returns. The Ljung-Box test statistics for raw

returns ( )20(LB ) are significant at the 1% level in three currencies, implying strong linear

dependencies among those returns. For squared returns, )20(2LB is significant at the 1%

level for all the 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: Large (small) changes in prices tend to be followed by large

(small) changes of either sign. The GARCH models used in this study are well known to

capture this property.

19

The unconditional correlation coefficients for the conditioning variables are

reported in Panel B of Table 1. All the correlation coefficients are below 0.5, indicating

that the selected variables contain sufficiently orthogonal information.

VI. Empirical Evidence

The quasi-maximum likelihood estimation of the conditional ICAPM (equation

(13)) is reported in Table 2. The hypothesis tests regarding the prices of risks and the

predictability of conditioning variables are presented in Table 3. The hypothesis tests

concerning the contagion in mean and volatility are shown in Table 4. Finally, summary

statistics concerning the sources of risk premia and diagnostic test statistics for the

standardized residuals are reported in Table 5.

Evidence of Time-varying Risk Premium

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

The results are very encouraging. For example, the joint null hypothesis of zero prices of

market and currency risks is strong rejected by Wald statistic (Wald = 10110.78) with a p-

value of zero. The joint null hypothesis of constant prices of market and currency risks is

also significantly rejected (Wald = 2555.52). Next, the joint null hypothesis of constant

prices of currency risks is strongly rejected by Wald test (Wald = 367.02), and the joint

null hypothesis of constant price of market risk is also rejected (Wald = 223.89). These

test results imply that both market and currency risks are not only priced but also time

20

varying. Finally, the null hypothesis of constant price of currency risk for each currency is

tested individually, and Wald test statistic rejects the null at the 1% level in every case,

implying that all four exchange rates are sources of the time-varying currency risk

premium. These results are consistent with the findings of Dumas and Solnik (1995) and

De Santis and Gerard (1998).18 The conditioning variables selected in this paper are all

very useful in predicting the dynamics of the risk prices as can be seen from the

hypothesis tests (#10 - #13) reported in Table 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 2R statistic calculated as the

ratio between the sum of squared fitted value of the risk premium and the sum of squared

actual risk premium (deviations from UIP). As can be seen from Table 5, the reported

pseudo 2R s range from 4.54% for JP to 61.407% for HK , with an average of 26.138%,

which is significant higher than those reported in similar studies.19 These relatively high

pseudo- sR2 indicate that the model perform very well in explaining the deviations from

UIP. Based on these empirical results, we 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.

18 Both Dumas and Solnik (1995) and De Santis and Gerard (1998) use excess returns on one-month

European currency deposit rates to proxy for currency risks; however, in this paper one-week Asian

currency deposit rates are employed to test the existence of time-varying currency risk premia.

19 The average pseudo- sR 2 in similar studies are only about 2.22% in McCurdy and Morgan (1991), and

4.06% in De Santis and Gerard (1998).

21

Evidence of Contagion in Mean and Volatility

Next, considering the test results of contagion effects on the first moment of

foreign exchange returns, it can be seen from Table 4 that these effects are statistically

significant for all four markets. For example, the joint null hypothesis of no contagion in

return shocks for JP ( TASGHKidH JPi ,,;0:0 , =∀= ) during the crisis is strongly rejected

by Wald statistic (Wald = 21.274) at the 1% level. The same rejection also applies to the

other three markets. To find out the sources of contagion in return shocks for JP , we can

examine the individual significance of contagion-in-mean parameter, JPid , , reported in

Table 2 based on robust standard errors. Basically, the current returns in JP are

negatively affected by past return shocks in the HK ( JPHKd , = -4.198). Similarly, the

current return shocks in HK are due to the past return shocks in JP ( HKJPd , = 0.012) and

SG ( HKSGd , = -0.023). For the case of SG , its current return shocks basically come from

the past return shocks in JP ( SGJPd , = -0.254). Finally, the current returns in TA are

influenced by HK ( TAHKd , = -8.654) and SG ( TASGd , = 0.234). By examining the

significance of those individual contagion-in-mean coefficients, we can see that basically

all the contagion-in-mean effects originate from three markets: JP , HK , and SG , and

none from TA . Although contagion-in-mean effects are statistically significant, a more

interesting question to ask is to what extent these effects are economically significant in

terms of generating abnormal profits after time-varying risk premia have been accounted

for. To answer this question, I compute percentage of variation in each one of the four

foreign exchange returns that can be explained on the basis of past information generated

by JP , HK , and SG . The percentages not reported here range from 1.115% for JP to

5.592% for TA , with an average of 3.059%. These percentages are very small, and if

22

transaction costs are taken into account, then we can safely conclude that the four markets

are weak-form efficient.

Turning to contagion effects on the conditional volatility of foreign exchange

returns, it can be seen from Table 4 that the joint null hypothesis of no contagion in

volatility shocks during the crisis is strongly rejected by Wald statistic in all cases. To

examine the possible sources of volatility shocks, we can examine the individual

significance of contagion-in-volatility parameter, jib , , reported in Table 2 based on robust

standard errors. Basically, the conditional variance of each market is affected positively

by its past innovations in all cases. That is, the diagonal elements in matrix B are all

significant at the 1% level. As for the off-diagonal elements, JP is affected by the past

innovations in HK ( JPHKb , = 0.010); HK is affected by past innovations in JP ( HKJPb , =

1.638) and TA ( HKTAb , = 8.593); SG is affected by the past innovations in JP ( SGJPb , =

0.170), HK ( SGHKb , = -0.032), and TA ( SGTAb , = -0.140) , and finally TA is influenced by

HK ( TAHKb , = 0.068), and SG ( TASGb , = 0.573). Overall, the contagion effects in

conditional second moments are very significant in Asian foreign exchange markets, and

they occur in a multidirectional way, with HK being the dominant one since it affects all

the other three markets. Table 2 also presents the parameter estimates ( jmg , ) of

asymmetric volatility shocks from the world equity market ( MSWRLD ). 20 The

parameters are all significant at the 1% level except TA , implying that market asymmetric

shocks have significant impact on the conditional volatility of Asian foreign exchange

20 To save space, Table 2 does not report the parameter estimates in matrices C and A of conditional

variance process since those estimates are not particularly interesting in this paper, but their results are

available upon request.

23

markets. 21 However, this market asymmetric volatility shocks affect each market

differently. For instance, they affect HK in a positive way ( HKmg , = 0.049), but in a

negative way for JP ( JPmg , = -0.406) and SG ( SGmg , = -0.496), implying that negative

world equity return shocks induce higher conditional volatility in HK than positive return

shocks, but they reduce the conditional volatility in JP and SG .

Economic Explanations

As discussed in introduction, the pure contagion effect may arise from information

asymmetries in financial markets. As pointed out by Calvo and Mendoza (2000), investor

may downplay national specificities and asymmetries, and consider several countries in a

region as substantially homogenous. A new piece of information concerning one country

can then be extrapolated and applied to the entire region. Calvo and Mendoza (2000) also

argue that as the number of countries in a portfolio increases, it is increasingly costly to

acquire country-specific information which forces the portfolio manager to follow the lead

of the investor most likely to be informed of the prospects of one particular country – a

phenomenon called herding behavior. For example, considering two portfolio managers

investing in assets issued by country A and B. Because of information processing costs,

the two managers choose to focus their analytical efforts on, respectively, country A and

country B. Due to her limited knowledge of country B, country A’s specialist determines

the shares of country B’s assets in her portfolio by replicating the behavior of country B’s

21 De Santis, Gerard, and Hillion (2000) finds that market asymmetric shocks are not very strong in

international equity markets, but they do not test whether they are significant for foreign exchange

markets.

24

specialist. The key aspect of such as strategy is that country A’s specialist observes the

action but not the ultimate motivation of country B’s specialist. For instance, a sale of

country B’s assets by country B’s specialist may be the result of bad news about country

B, or the liquidity demand from investors. If the sale is due to liquidity demand, then the

mimicking behavior of country A’s specialist will cause a generalized capital outflow

from country B, even though there is no deterioration in country B’s fundamentals. To

relate the herding behavior argument to the significant contagion found in this paper, we

can think of the portfolio manager as a money market mutual fund manager. When a

shock hits one country in Asia, fund manager would want to pull out of their positions

because the cost of underperforming the group average is much higher than the benefit of

outperforming the group, which leads to large excess co-movements within Asia.

Residual Diagnostics

To access the fit of the conditional ICAPM with MGARCH specification, Ljung-

Box tests are performed on standardized residuals ( LB ) and squared standardized

residuals ( 2LB ). Under the multivariate framework, the standardized residuals at time t is

computed as ttt HZ ε2/1−= , where 2/1−tH is the inverse of the Cholesky factor of the

estimated variance-covariance matrix. The results of tests for serial correlation up to 20

lags are reported in Table 5 along with Bera-Jarque ( JB − ) test statistics. LB and 2LB

statistics of order 20 show no serious linear and nonlinear dependencies for the

standardized residuals of foreign exchange returns, with one exception in which )20(2LB

is significant at the 1% level for HK . As for JB − test statistics, they are all significant,

indicating departures from normality, which justifies the use of robust standard errors

25

computed from using the quasi-maximum likelihood method of Bollerslev and

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

The Size of Risk Premia

One advantage of modeling the conditional second moments via multivariate

GARCH 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 by Dumas (1993) and Dumas

and Solnik (1995).22 Table 5 reports those statistics. For example, the predicted total risk

premium is measured by

tjcc

tctjmtmtj hhTRP ,1,,1,, ∑ −− += λλ ; TASGHKJPj ,,,= (14)

and ranges from -0.066% for JP , -0.025% for SG , -0.020% for HK , and -0.018% for

TA , to 0.033% for MSWRLD . The tjTRP , can be decomposed into two components:

currency risk premium ( tjCRP , ) and market risk premium ( tjMRP , ). The currency risk

premium is measured by

tjcc

tctj hCRP ,1,, ∑ −= λ ; TASGHKJPj ,,,= (15)

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

26

and the market risk premium is measured by

tjmtmtj hMRP ,1,, −= λ ; TASGHKJPj ,,,= (16)

The predicted total risk premia are basically dominated by the currency risk premia

except MSWRLD , which is dominated equally by both world market risk and currency

risk. For instance, the currency risk premium is -0.067% for JP , -0.020% for HK ,

-0.029% for SG , and -0.011% for TA . Furthermore, the dynamics of predicted time-

varying risk premium in foreign exchange markets are mainly driven by the time variation

of currency risk prices because both the sample means and standard deviations of time-

varying risk prices are greater than those of conditional volatilities. These statistics point

out the important role of time-varying price of risk relative to the conditional volatility in

describing the dynamics of asset returns.

A useful complement to Table 5 is to display the time-series plots of those

interesting statistics. Figure I contain plots of actual risk premia (deviations from UIP)

and predicted risk premia. It can be seen that the dynamics of the predicted risk premia

follow very 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- 2R

statistics reported in the last row of Table 5. Figure II present the plots of time-varying

prices of currency risks and conditional volatilities. As can be seen from the plots, the

prices of four currency risks fluctuate significantly between positive and negative values

and range from -57.965 to 68.610 for JP , -1269.701 to 279.506 for HK , -207.041 to

313.479 for SG , and -41.518 to 68.832 for TA . However, the variation of conditional

27

volatility for each market is relatively small compared to those of currency risk prices, but

it increases significant during the 1997 Asian crisis for all four markets.

VI. Summary and Concluding Remarks

In this paper, I study the time-varying prices of risks and conditional volatilities in

four Asian foreign exchange markets in an attempt to provide a new evidence of time-

varying risk premium in explaining the predictable excess return puzzle. I also attempt to

test whether there are contagion effects in both conditional means and volatilities of those

markets during the 1997 Asian crisis. To derive a measure of the risk premium, I apply a

conditional version of international CAPM (ICAPM) in the absence of PPP, and the model

is estimated and the parameter restrictions are tested based on the asset pricing theories.

To incorporate time-varying feature of the risk premium into the model, I allow not only

the second moments of asset returns to change over time by utilizing MGARCH-M

modeling strategy, but also the prices of risks to evolve through time based on some pre-

specified conditioning variables.

Estimation results show significant time-varying risk premia in the deviations from

UIP, and these risk premia mainly compensate currency speculators for bearing not just

market risk but currency risk. This empirical evidence implies that an international asset

pricing model under PPP would not deliver economically significant risk premia in foreign

exchange markets. The results also indicate that the dynamics of foreign exchange

returns are mainly due to the time-variations of currency risk prices, implying that

incorporating time-varying prices of risks into the asset pricing model is more important

28

than just modeling the conditional volatilities of asset returns. Overall, the conditional

ICAPM with MGARCH-M structure is able to explain/predict on average more than 26%

(26.138%) of the return variations in foreign exchange markets, a very high return

predictability compared to previous studies. Therefore, we can safely conclude that the

time-varying risk premium is a very strong candidate in explaining the predictable excess

return puzzle since the risk premia detected in this paper are not only statistically

significant but also economically significant.

As for the tests of contagion, I find strong pure contagion effects in both the

conditional means and volatilities of foreign exchange markets after systematic risks have

been accounted for. Specifically, the contagion-in-mean effects are mainly driven by the

past innovations in Japan, Hong Kong, and Singapore. As for contagion in volatility, the

lead/lag relationships appear to be multidirectional with Hong Kong playing the dominant

role in generating contagion effects at volatility level since all the other three markets are

significantly influenced by the past innovations in Hong Kong. Finally, market

asymmetric volatility shocks are also found to be significant for Japan, Hong Kong, and

Singapore.

29

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37

Table 1 Panel A: Summary statistics of foreign exchange returns and world equity return a

Returns JP HK SG TA MSWRLD Mean (%) -0.024 -0.007 -0.019 0.020 0.075

Std. Dev. (%) 1.680 0.092 0.772 0.723 2.112 Minimum (%) -6.174 -0.603 -4.851 -4.319 -18.716 Maximum (%) 14.500 0.457 8.292 5.875 11.016

Skewness 1.144** -1.074** 1.246** 0.244** -0.761** Excess Kurtosis 8.048** 10.065** 23.615** 13.170** 17.495**

JB− 2159.100** 3266.452** 17387.502** 5355.509** 9509.433**

)20(LB 24.886 65.601** 125.329** 40.169** 14.465

)20(2LB 52.422** 183.311** 286.973** 56.696** 54.582**

Panel B: Unconditional correlation of conditioning variables

DIV EURO∆ USTP∆ USDP DIV 1 EURO∆ 0.111 1 USTP∆ 0.126 0.440 1

USDP -0.165 -0.016 0.037 1 a

(i) The statistics are based on weekly data from 01/23/87 to 03/23/01 (740 observations). The interest rates are one-week Euroyen deposit rate ( JP ), one-week Hong Kong deposit rate ( HK ), one-week Singapore deposit rate (SG ), and 10-day Taiwan money

market rate ( TA). MSWRLD is the MSCI world total index return in excess of the 7-day Eurodollar interest rate. (ii) The Bera-

Jarque ( JB− ) tests normality based on both skewness and excess kurtosis and is distributed 2χ with two degrees of freedom.

(iii) )20(LB and )20(2LB denote the Ljung-Box test statistics for up to the 20th order autocorrelation of the raw and squared

returns, respectively. (iv) The conditioning variables are the excess dividend yield, measured by the dividend yield on S&P 500 index in excess of the 7-day Eurodollar deposit rate (DIV ), the change in 7-day Eurodollar deposit rate ( EURO∆ ), 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 ( USTP∆ ), and the U.S. default premium, measured by the yield difference between Moody’s Baa-rated and Aaa-rated U.S.

corporate bonds (USDP ). (v) * and ** denote statistical significance at the 5% and 1% level, respectively.

38

Table 2 Quasi-Maximum Likelihood estimation of the conditional ICAPM a

Conditional mean process

World prices of market and foreign exchange risks CONSTANT DIV EURO∆ USTP∆ USDP

123.571 6918.977 7093.682 181.508 -22508.470 mϕ

(15.745)** (803.442)** (893.164)** (107.911) (3034.259)** 0.620 375.049 1554.642 -238.495 1330.963

JPϕ (9.778) (149.338)* (851.222) (784.952) (914.432) 753.222 5577.715 1513.446 -17275.528 -95145.720

HKϕ (148.265)** (2651.516)* (2932.513) (2260.799)** (10354.912)**

3.291 -104.436 -5489.450 8395.413 -956.920 SGϕ

(2.347) (63.269) (1922.629)** (1583.324)** (444.727)*

-2.924 610.260 -281.752 -1528.281 3499.389 TAϕ

(11.239) (154.642)** (241.962) (513.505)** (1456.253)* Contagion in mean

JP HK SG TA MSWRLD

JPid , -4.198 (1.920)*

-0.125 (0.129)

-0.145 (0.138)

HKid , 0.012 (0.004)** -0.023

(0.005)** -0.011 (0.007)

SGid , -0.254 (0.069)**

0.270 (1.720) -0.115

(0.080)

TAid , -0.019 (0.043)

-8.645 (0.911)**

0.234 (0.040)**

Conditional variance process Contagion in volatility

JPib , 0.139 (0.034)**

0.010 (0.003)**

0.122 (0.083)

-0.050 (0.066)

HKib , 1.638 (0.825)*

0.698 (0.040)**

-1.905 (1.136)

8.593 (1.214)**

SGib , 0.170 (0.079)*

-0.032 (0.006)**

0.253 (0.037)**

-0.140 (0.053)**

TAib , 0.013 (0.057)

0.068 (0.008)**

0.573 (0.078)**

0.709 (0.116)**

Asymmetric market volatility shock

jmg , -0.406 (0.147)**

0.049 (0.009)**

-0.496 (0.130)**

0.144 (0.136)

-0.071 (0.142)

Log-Likelihood Function: 17197.823 a

Returns: tj

jitiij

ctjctctjmtmtj ddummyhhr ,1,,1,,1,, )( εελλ +++= ∑∑

≠−−−

; TASGHKJPji ,,,, =∀

tm

ctmctctmtmtm hhr ,,1,,1,, ελλ ∑ ++= −−

; ),0(~| 1 ttt HN−Ωε

where )exp( 1'

1, −− = tmtm zϕλ ; 1'

1, −− = tctc zϕλ ; TASGHKJPc ,,,=

,,,,1 USDPUSTPEURODIVCONSTANTz t ∆∆=−

GARCH: GGBHBAACCH tttttt ⋅⋅+⋅⋅+⋅⋅+= −−−−−'

11'

1''

11'' ηηεε

Standard errors are given in parentheses . )20(LB and )20(2LB are the Ljung-Box test statistics of order 20 for serial correlation in

the standardized residuals and standardized residuals squared. Pseudo 2R is computed as the ratio between the sum of squared fitted

value of the risk premia and the sum of squared actual returns. * and ** denote statistical significance at the 5% and 1% level, respectively.

39

Table 3 Hypothesis tests concerning prices of risks and predictability of conditioning variables

Null Hypothesis Wald d.f. P-Value 1. Are the prices of market and currency risks equal to zero?

,,,,;0:0

1 USDPUSTPEURODIVCONSTANTZcH

t

cm

∆∆=∀==

−

ϕϕ 10110.779 25 0.000

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

,,,;0:0

1 USDPUSTPEURODIVZcH

t

cm

∆∆=∀==

−

ϕϕ 2555.520 20 0.000

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

,,,,;0:0

1 USDPUSTPEURODIVCONSTANTZcH

t

c

∆∆=∀=

−

ϕ 1154.374 20 0.000

4. Are the prices of currency risks constant?

,,,;0:0

1 USDPUSTPEURODIVZcH

t

c

∆∆=∀=

−

ϕ 367.021 16 0.000

5. Is the price of market risk constant? ,,,;0:0 1 USDPUSTPEURODIVZH tm ∆∆== −ϕ 223.891 4 0.000

6. Is the price of the Japanese yen risk constant? ,,,;0:0 1 USDPUSTPEURODIVZH tJP ∆∆== −ϕ 15.325 4 0.004

7. Is the price of the Hong Kong dollar risk constant? ,,,;0:0 1 USDPUSTPEURODIVZH tHK ∆∆== −ϕ 148.191 4 0.000

8. Is the price of the Singapore dollar risk constant? ,,,;0:0 1 USDPUSTPEURODIVZH tSG ∆∆== −ϕ 36.882 4 0.000

9. Is the price of the New Taiwan dollar risk constant? ,,,;0:0 1 USDPUSTPEURODIVZH tTA ∆∆== −ϕ 20.999 4 0.000

10. Is there no predictability from excess dividend yield? DIVkcH kckm =∀== ;;0:0 ,, ϕϕ 411.934 5 0.000

11. Is there no predictability from the change in Eurodollar rate? EUROkcH kckm ∆=∀== ;;0:0 ,, ϕϕ 114.423 5 0.000

12. Is there no predictability from the change in term premium? USTPkcH kckm ∆=∀== ;;0:0 ,, ϕϕ 111.627 5 0.000

13. Is there no predictability from the U.S. default premium? USDPkcH kckm =∀== ;;0:0 ,, ϕϕ 643.023 5 0.000

40

Table 4 Hypothesis tests concerning contagion in mean and volatility

Null Hypothesis Wald d.f. P-Value 1. Is there no contagion in return shocks for JP ?

TASGHKidH JPi ,,;0:0 , =∀= 21.274 3 0.000

2. Is there no contagion in return shocks for HK ? TASGJPidH HKi ,,;0:0 , =∀= 64.538 3 0.000

3. Is there no contagion in return shocks for SG ? TAHKJPidH SGi ,,;0:0 , =∀= 20.003 3 0.000

4. Is there no contagion in return shocks for TA ? SGHKJPidH TAi ,,;0:0 , =∀= 90.236 3 0.000

5. Is there no contagion in volatility shocks for JP ? TASGHKibH JPi ,,;0:0 , =∀= 15.373 3 0.001

6. Is there no contagion in volatility shocks for HK ? TASGJPibH HKi ,,;0:0 , =∀= 169.859 3 0.000

7. Is there no contagion in volatility shocks for SG ? TAHKJPibH SGi ,,;0:0 , =∀= 40.690 3 0.000

8. Is there no contagion in volatility shocks for TA ? SGHKJPibH TAi ,,;0:0 , =∀= 105.058 3 0.000

9. Are the market asymmetric volatility shocks equal to zero? TASGHKJPjgH jm ,,,;0:0 , =∀= 84.428 4 0.000

41

Table 5 Summary statistics and residual diagnostics

JP HK SG TA MSWRLD

-0.066 -0.020 -0.025 -0.018 0.033 Predicted total risk premium (%) Std Dev. 0.352 0.069 0.361 0.295 0.322

0.000 0.000 0.000 0.000 0.017 Market risk premium (%) Std Dev. 0.003 0.001 0.001 0.000 0.321

-0.067 -0.020 -0.029 -0.011 0.017 Currency risk premium (%) Std Dev. 0.284 0.067 0.322 0.266 0.027

0.000 0.000 0.004 -0.007 Return shocks due to contagion (%) Std Dev. 0.177 0.013 0.145 0.171

Prices of currency and market Risks -1.040 -151.171 -0.794 4.643 0.383 Std Dev. 8.053 217.023 27.344 11.269 7.394

1.609 0.084 0.657 0.727 2.083 Conditional volatility (%) Std Dev. 0.401 0.049 0.535 0.521 0.001

JB− 179.039** 6549.642** 44.004** 2183.075** 9939.824** )20(LB 22.094 31.033 21.030 20.937 14.798 )20(2LB 18.696 40.764** 23.955 9.075 53.949**

Pseudo 2R (%) 4.540 61.407 21.955 16.651 2.348

42

Figure I: Actual and estimated risk premia

43

Figure II: Prices of currency risks and conditional volatilities