4 chu-sheng tai -- time-varying risk premia in foreign exchange and equity markets- evidence from...

7/23/2019 4 Chu-Sheng Tai -- Time-varying risk premia in foreign exchange and equity markets- evidence from AsiaPacific

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Journal of Multinational Financial Management

9 (1999) 291316

Time-varying risk premia in foreign exchangeand equity markets: evidence from AsiaPacific

countries

Chu-Sheng Tai *

Department of Economics, The Ohio State Uniersity, Columbus, OH 43210, USA

Received 15 July 1998; accepted 26 February 1999

Abstract

This paper examines the validity of the risk premia hypothesis in explaining deviations

from Uncovered Interest Parity (UIP) and the role of deviations from Purchasing Power

Parity (PPP) in the pricing of foreign exchange rates and equity securities in five AsiaPacific

countries and the US. Using weekly data from 1 January, 1988 to 27 February, 1998, I find

that conditional variances are not related to the deviations from UIP in any statistical sense

based on an univariate GARCH(1,1)-M model. As I consider both foreign exchange and

equity markets together and test a conditional international CAPM (ICAPM) in the absence

of PPP, I cannot reject the model based on the J-test by Hansen (Econometrica 50 (1982),

1029 1054) and find significant time-varying foreign exchange risk premia present in the

data. This empirical evidence supports the notion of time-varying risk premia in explainingthe deviations from UIP. It also supports the idea that the foreign exchange risk is not

diversifiable and hence should be priced in both markets. 1999 Elsevier Science B.V. All

rights reserved.

Keywords:International asset pricing; Uncovered interest parity; Foreign exchange risk premium

JEL classification: F31; G12; C32

www.elsevier.com/locate/econbase

* Corresponding author. Tel.: +1-614-2922639; fax: +1-614-2923906.

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

1042-444X/99/$ - see front matter 1999 Elsevier Science B.V. All rights reserved.

P I I : S 1 0 4 2 - 4 4 4 X ( 9 9 ) 0 0 0 0 4 - 3


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C.-S. Tai/J. of Multi. Fin. Manag. 9 (1999) 291316292

1. Introduction

One dimension that distinguishes domestic finance from international finance is

foreign exchange risk. The increasing globalization has promoted investors to

allocate a significant portion of their portfolio holdings in foreign assets in order to

earn significant benefits from international diversification. To manage the risk of

international portfolios, portfolio managers might want to know whether foreign

exchange risk is a priced factor, which has direct implication for hedging strategies.

Foreign exchange risk pricing is also important to corporate financial managers. Ifexchange risk is not priced in the equity markets, corporate hedging is not

justifiable since investors are not willing to pay a premium for firms with active

hedging policies, e.g. Dufey and Srinivasulu (1983), Smith and Stulz (1985) and

Jorion (1991). Utilizing Rosss arbitrage pricing theory (APT) (Ross, 1976), Jorion

(1991) fails to find significant foreign exchange risk premia in the US stock market.

However, Choi et al. (1998) find that foreign exchange risk is priced in the Japanese

stock market. In an international context, Ferson and Harvey (1994), Korajczyk

and Viallet (1992), Dumas and Solnik (1995) all find that foreign exchange risk is

a priced factor.

Another body of literature in international finance has focused on the efficiency

of foreign exchange market since the breakdown of the Bretton Woods system offixed exchange rates in 1973. One important building block to many models used in

testing market efficiency is the hypothesis of uncovered interest parity (UIP). This

hypothesis states that if interest rate differential is different from the expected rate

of change of the exchange rate, risk neutral agents tend to move their uncovered

funds across financial markets until equality is re-established. Thus, 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. One

important conclusion coming out of this research is that there exist predictable

components in excess returns of holding foreign currency deposits. This predictable

excess return is one of the puzzles in international finance literature. 1 Two possiblesources of explanations have been proposed to account for this puzzle. First, the

assumption of rational expectations is violated and hence agents make systematic

forecast errors.2 Second, agents are not risk neutral, and thus demand a risk

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

Lewis (1994).2 For example, Bilson (1981), Meese (1986), Frankel and Froot (1987) argue that agents systematically

make mistakes in predicting exchange rates, and reject rational expectations. Obstfeld (1986), Lewis

(1988), Kaminsky (1993) suggest that even if expectations are fully rational ex ante, exchange rate

forecast may appear biased and serially correlated in the ex post sample if there is the possibility of a

major policy change, which is the so called peso problem. McCallum (1994) argues that monetaryauthorities manage interest rates so as to smooth their movements, while also resisting changes in

exchange rates that creates a wedge between the nominal interest rate differentials and expected rate of

change in exchange rates.


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C.-S. Tai/J. of Multi. Fin. Manag. 9 (1999) 291316 293

premium when holding risky assets.3 For example, Fama (1984), Hansen

and Hodrick (1980, 1983), Hodrick and Srivastava (1984), Korajczyk (1985),

Cumby (1988), Mark (1985, 1988), Kaminsky and Peruga (1990) all conclude

that forward rates differ from expected future spot rates by a time-varying

risk premium.4 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

the foreign exchange market. However, empirical research has failed to demon-

strate a measure of foreign exchange risk that can account for observed pre-dictable components in foreign exchange, or which is even priced.5 Two possible

reasons may account for this failure. First, most empirical work seeking to

apply asset pricing models to foreign exchange has continued to focus on

models which assume purchasing power parity (PPP).6 However, many authors

have shown that the violation of PPP is a norm although PPP tends to hold in

the long run. In the absence of PPP resulting from either different consump-

tion tastes or violation of the law of one price (LOP), investors from different

countries face different prices of goods. 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.7

As a result, in order to seriously address the issue of pricing of foreign exchangerisk, an asset pricing model that incorporates deviations from PPP is required.

Second, previous empirical tests for foreign exchange risk premia have focused

mainly on foreign exchange markets and ignored international equity markets

except Giovannini and Jorion (1987, 1989), Bekaert and Hodrick (1992), Korajczyk

and Viallet (1992), Dumas and Solnik (1995). As mentioned earlier, the increasing

globalization has attracted domestic investors to hold foreign assets in order to

reduce systematic risk. Consequently, investors tend to hold different kinds of

assets in international financial markets rather than just foreign currencies. Thus,

one should not isolate foreign exchange markets from other asset markets when

testing international asset pricing models. As pointed out by Giovannini and Jorion

(1987) a joint test should be more powerful than the existing work that looks at twosets of assets separately.8

3 Of course, if the underlying risk is diversifiable, there will be no risk premium.4 If covered interest parity (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).5 Engel (1996) provides a detailed survey on this issue.6 Examples of papers examining pricing of forward contracts under PPP include Mark (1988), Cumby

(1988), Korajczyk and Viallet (1992).7 See Solnik (1974), Stulz (1981), Adler and Dumas (1983), Hodrick (1981).8

Examples that look at only equity market include Stehle (1977), Korajczyk and Viallet (1989),Cumby and Glen (1990), Harvey (1991), Chan et al. (1992), Ferson and Harvey (1993), etc. Examples

that look at foreign currency include Hansen and Hodrick (1983), Mark (1985, 1988), Cumby (1988),

Levine (1989), Baillie and Bollerslev (1990), McCurdy and Morgan (1991), Backus et al. (1993), etc.


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Because of the importance of foreign exchange risk pricing mentioned above

and its inconclusive empirical findings, the goal of this paper is to examine the

validity of the (time-varying) risk premia hypothesis and the role of deviations from

PPP in the pricing of foreign exchange rates and equity securities in five Asia

Pacific countries and the US. Specifically, I first apply an univariate GARCH(1,1)

in Mean (GARCH(1,1)-M) model to jointly test for time-varying risk premia and

rational expectations in those markets from the perspective of a representative

Japanese investor. Then, I apply generalized method of moments (GMM) method-

ology (Hansen, 1982) to empirically estimate and test international asset pricingmodels in the absence of PPP under both unconditional and conditional frame-

works.9 Using weekly data from 1 January, 1988 to 27 February, 1998, I find that

conditional variances are not related to deviations from UIP in any statistical sense

based on the univariate GARCH(1,1)-M model. As I consider both foreign

exchange and equity markets together and test a conditional international CAPM

in the absence of PPP, I can not reject the model based on the J-test by Hansen

(1982), and find significant time-varying foreign exchange risk premia present

in the data. This empirical evidence supports the notion of time-varying risk

premia in explaining the deviations from UIP. It also supports the idea that the

foreign exchange risk is not diversifiable and hence should be priced in both

markets.This paper is divided in the following manner. Section 2 exposes the GARCH

model for testing the joint hypothesis of risk premium and rational expectations.

Section 3 motivates the international CAPM (ICAPM) specification for the time-

varying risk premium and presents the econometric methodology used to test the

ICAPM. Section 4 discusses the data. Section 5 reports the empirical results. The

last section concludes.

2. The risk premium and rational expectations

The UIP hypothesis postulates an equilibrium relationship that can be expressedas

it it*=Et(st+1)stert+1=E(st+1)st+ it* it+t+1=Et(ert+1)+t+1(1)

where st is the (log of the) exchange rate, expressed as the dollar price of one unit

of foreign currency; it* is the (log of one plus) foreign interest rate; it is the (log of

one plus) domestic interest rate; ert+1 is the realized excess return on foreign

currency; t+1=st+1Et(st+1) is the statistical forecast error, and Et () is the

statistical expectations operator conditional on time t information. The UIP

hypothesis states that expected excess returns, Et(ert+1), to uncovered currency

9 I use unconditional to mean risk premia are time-invariant, whereas conditional means risk

premia are time varying.


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speculation are zero. If expected excess returns are zero, then in a large sample

realized excess returns should be unpredictable. In other words, under the assump-

tion of rational expectations, the forecast errors are assumed to be unpredictable

given information available at the time the forecast is made, so that t+1 is

orthogonal to any information available at time t. Under risk neutrality, a finding

of nonzero ex ante excess returns to currency speculation is consistent with market

inefficiency.10 However, under risk aversion, a finding of nonzero ex ante excess

returns does not necessarily imply market inefficiency since it is consistent with a

risk premium argument provided that rational expectations hold. Thus, due to thisjoint nature of tests for market efficiency and for the presence of a risk premium,

researchers often assume either that expectations are rational and test for the

presence of a risk premium, or assume no risk premium and test for rational

expectations.

To preserve the joint nature of the hypothesis testing, I consider following

GARCH(1,1)-in-Mean model, which was introduced by Bollerslev (1986) as a

generalized class of ARCH-in-Mean models.

ert+1=RPt+b1ert+b2ert1+b3ert2+b4ert3+t+1 (2)

RPt=a0+a1ht+1 (3)ht+1=c0+c1t

2+c2ht (4)

t+1tGED(0,ht+1, ) (5)In Eq. (2), the information variables available at time t are used to test for rational

expectations. If the null hypothesis, H0:b1=b2=b3=b4=0, is rejected, then the

rational expectation hypothesis is not justified in estimates of Eq. (2). The formula-

tion of the risk premium (RPt) follows Domowitz and Hakkio (1985) which is

defined in Eq. (3) where ht+1 is the conditional component of the variance of the

error term t+1. The conditional density function defined in Eq. (5) is modeled as

a Generalized Error Distribution (GED) to take the leptokurtosis found in most

financial data including exchange rates into account.11 Thus, the risk premium has

a constant component (a0) and a time varying component, which is the standarddeviation of the conditional variance (ht+1). If both a0 and a1 are insignificantlydifferent from zero, there is no risk premium. If a00 but a10, there is a

constant premium. If a10, this is evidence of a time-varying risk premium.

The GARCH(1,1)-M model has been chosen to incorporate heteroskedasticity

into the estimation procedure. To estimate Eqs. (2) (4) under conditional GED

with degrees of freedom, 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

10

This argument is based on the implicit assumption of a perfect capital market.11 The GED is a generalization of the normal distribution. It includes the normal distribution if the

parameter has a value of 2. is a measure of tail-thickness. If 2 a fat-tailed distribution results. The

lower limit for is 0. If 1, the unconditional variance does not exist.


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Expanding the cov(Ri,Rm), and rearranging terms:

E(Ri)=+E()(1)var() cov(Rm, )+(1)cov(Ri, )

+ cov(Ri,Rm) (10)

In Eq. (10), the first four terms of the right-hand side sum to nominally risk-free

rate of return, R, if it exists. Thus, we can rewrite Eq. (10) in the following form:

E(Ri)=R+(1)cov(Ri, )+ cov(Ri,Rm) (11)

Eq. (11) is a nominal CAPM which indicates that uncertain inflation produces a

separate premium in nominal returns even if investors were risk neutral (=0).

Next we want to extend this nominal CAPM in an international setting. We can

measure the rate of inflation over a period in any country in any currency. Suppose

we choose the US dollar ($) as numeraire, then the rate of inflation in country l in

terms of $ can be expressed as following:13

l$=(1+ l

l)(1+e l$)1 (12)

where l$ is the rate of inflation in country l in dollar units and e l

$ is the relative

change in the spot exchange rate (dollar price of one unit local currency) over the

period. Similarly, the rate of return, Ri, of all securities expressed in foreign

currency units can be translated into dollar using following formula:

Ri=(1+R il)(1+e l

$)1 (13)

whereR il is the rate of return on security iexpressed in the non-dollar currency and

e l$ is the rate of change of the spot exchange rate expressed in dollars per unit of

non-dollar currency. The international nominal CAPM, expressed in dollars, can

now be derived in the following way. For each country l, a domestic nominal

CAPM similar to Eq. (11) holds:

E(Ri)=R+(1l)cov(Ri, l

$)+ l cov(Ri,Rpl) (14)

whereR is the dollar, nominally risk-free interest rate and R pl=ix ilRi(x il being the

weight allocated by investors of country lto security i) is the dollar rate of returnon the optimal portfolio held by the investors of country l. In order to aggregate

Eq. (14) over all of the investor groups, we divide both sides of Eq. (14) by l,

multiply them by Wl (each countrys wealth), sum them over all national investor

groups, and finally divide them bylWl/ l, to get

E(Ri)=R+l

(1

l1)Wl

cov(Ri, l$)

W + cov(Ri,Rm) (15)

where

W=

lWl,

1

=

l

Wl/ l

W ,

13 In the empirical tests, I use Japanese yen as a base currency.


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l is the coefficient of relative risk aversion for investors from country l, and is

an average of the risk aversion coefficients for each national group, weighted by the

corresponding relative wealth Wl/W.

The international nominal CAPM (Eq. (15)), now contains as many in-

flation premia as there are national investor groups. Since the variability in

the exchange rate is much greater than the variability in the inflation rate, we

can assume that local inflation rate is nonrandom, which is the case of Solnik

(1974), then cov(Ri, l$)=cov(Ri,e l

$) because ll+e l

$= l$.14 Consequently, in the

international CAPM, the foreign exchange risk becomes one of the systematic risksunder which PPP does not hold and local inflation rates are nonstochastic.

Consider the dollar rate of return from a foreign currency deposit, Vl$, which is

given by:

Vl$=(1+Vl

l)(1+e l$)1 (16)

Then, cov(Ri,e l$)=cov(Ri,Vl

$Vll)=cov(Ri,Vl

$) since the foreign nominal cur-

rency deposit rate in local currency units,Vll, is known at the time when the deposit

was made, and hence is nonrandom. Thus, we can rewrite Eq. (15) as

E(Ri)=R+l

(1

l1)Wl

cov(Ri,Vl$)

W + cov(Ri,Rm) (17)

Suppose there are L+1 countries and a set of N=n+L+1 assetsother thanthe measurement-currency depositwhich is composed of n equities, L nonmea-

surement-currency deposits and the world portfolio of equities which is the Nth and

last asset. Since we are interested in the conditional tests of international CAPM,

we can rewrite Eq. (17) in its conditional form:

E[rit t1]= L

l=1

l, t1cov[rit,rn+ l,t t1]+m,t1cov[rit,rmt t1] (18)

where m,t1=t1= 1

Ll=1Wt1

l

Wt1

1

l

and l, t1=t1 1

l1Wt1l

Wt1and rit

is the nominal return on asset or portfolioi,i=1 N, from timet 1 tot, in excessof the rate of interest of the currency in which returns are measured; rn+ l, t is the

excess return on the nonmeasurement foreign currency deposit; rmt is the excess

return on the world market portfolio; l,t1, l=1 L, are the time-varying world

price of exchange rate risk; m, t1 is the time-varying world price of market risk,

and t1 is the information set that investors use in forming their portfolios. The

international CAPM, Eq. (18), is the conditional version of Eq. (14) in Adler and

Dumas (1983) which takes into account the fact that investors of different countries

have different views about asset returns.

14

The relative PPP is expressed as US$

=(1+ ll

)(1+e l$

)1. If relative PPP holds, then ll

+e l$

US

$ =0. If relative PPP does not hold, then ll+e l

$ US$ =u where u are the deviations from relative

PPP. If we assume local inflation is nonstochastic, then US$ = l

l=0. Thus,e l$=uwhich implies that the

rate of exchange rate change is equal to the deviations from relative PPP.


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3.2. Econometric methodology: The pricing kernel

The pricing kernel method, initiated by Hansen and Jagannathan (1991), was

generalized by Dumas and Solnik (1995) to test asset pricing models and will be

used in this paper. We know that the first-order condition of any consumerin-

vestors optimization problem can be written as:

E[Mt(1+rf, t1)t1]=1 (19)E[Mtrit t1]=0 i=1 N (20)

whereMt is the marginal rate of substitution between nominal return at date t and

at date t1 and rf, t1 is the conditionally riskfree rate of interest known at date

t1. Without specifying the form ofMt, Eq. (20) has little empirical content since

it is easy to find some random variable Mt for which the equation holds. Thus, it

is the specific form of Mt implied by an asset pricing model that gives Eq. (20)

further empirical content (see Ferson, 1995). The Mt for international CAPM in

Eq. (18) has the following form:

Mt=

10,t1 L

l=1

l, t1rn+ l, tm,t1rmtn/(1+rf,t1) (21)

where

0, t1= L

l=1

l, t1E[rn+ l,t t1]m, t1E[rm,t t1]

The new time varying term,0, t1, appears as a way of ensuring Eq. (19) holds.For

econometric purposes, following Dumas and Solnik (1995) two auxiliary assump-

tions are needed:

Assumption 1: the information set t1 is generated by a vector of instrumental

variables Zt1. Zt1 is a 1Kvector of predetermined instrumental variables that

reflect everything that is known to the investor at time t1.

Assumption 2:0, t1=Zt10, l, t1=Zt1l,m, t1=Zt1m,l=1 L. (22)

Here, the s are the time-invariant vectors of weights. Based on Eq. (19), we define

the innovation ut:

Mt(1+rf, t1)=1ut (23)

and given Assumption 2 and the definition of Mt in Eq. (21), we can write ut as:

ut=1Mt(1+rf,t1)=Zt10+ L

l=1

Zt1lrn+ l, t+Zt1mrmt (24)

with ut satisfying:

E[ut t1]=0 (25)Next, based on Eq. (20), we define the innovation hit:


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hit=ritritut (26)

with hit satisfying:

E[hit t1]=0 (27)One can form the 1+Nvector of residuals t=(ut,ht). Combining Eqs. (25) and

(27) under Assumption 1 yields:

E[tZt1]=0 (28)

It follows that

E[ft(0)]=E[Zt1 t]=0 for t=1, 2 T (29)

whereZt1 is a 1Kvector and t is a 1(1+N) vector and T is the number of

observations over time. Thus, there are K(1+N) moment conditions. One can

test these moment restrictions implied by the theory using Hansens test of the

orthogonality conditions used in the estimation (Hansen, 1982).

4. Data and summary statistics

Most of the empirical literature concerning the efficiency of foreign exchange

markets and international equity markets is based on exchange rate vis-a-vis the US

dollar. This implies that not all reported results are necessarily independent of each

other. Thus, it is interesting to investigate foreign exchange risk premia based on

some other base currencies and compare the results with previous findings using the

US dollar as a base currency. In addition, due to the facts that lots of the empirical

studies have been done in developed countries and that developing countries start

to play an important role in the international financial markets, this paper focuses

on five AsiaPacific capital markets: Japan, Hong Kong, Singapore, Taiwan, and

Malaysia and one major developed market: the US. Among theses five AsiaPacific

capital markets, Japan is the largest capital market in terms of its market capitaliza-tion. Thus, Japanese yen is chosen to be the base currency.

I consider 12 assets (N=12), seven equity indices (n+1=7) and five currency

deposits (L=5). The seven equity indices consist of six national indices (n=6;

Hong Kong, Singapore, Taiwan, Malaysia, Japan, and the US) and one world

equity index (the 12th and last asset). These total return indices of national equity

markets are from Morgan Stanley Capital International Perspective (MSCI). The

five currency deposits are Hong Kong 1-week deposit (HKDEP1W), Singapore

1-week deposit (SNGDP1W), Taiwan 10-day money market (TAMM10D),

Malaysia 1-month deposit (MYDEP1M), and Eurodollar 7-day deposit rate

(ECUDS1M).15 Thus, there are five exchange rate risk premia in the international

CAPM. Observations are sampled at weekly intervals. The excess return on an

15 The data on one-week currency deposit rates for Taiwan and Malaysia are not available, so a

10-day money market rate and one-month deposit rate are used for Taiwan and Malaysia, respectively.


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equity market is the log difference of total return index in excess of 7-day Euroyen

interest rate. The excess return on a currency holding (i.e. weekly deviations from

UIP) is the 7-day interest rate of that currency compounded by the rate of change

of the spot exchange rate in excess of the 7-day Euroyen interest rate.

The selection of instruments draws on previous studies. Harvey (1991) shows that

US information variables are useful in predicting foreign equity returns. Giovannini

and Jorion (1987), Bekaert and Hodrick (1992) find that nominal interest rates have

explanatory power for the time variation of currency returns. Thus, Five instru-

ments are chosen in this study. They are the lagged world excess equity return(WORLD), the dividend yield on S&P 500 index in excess of the 7-day Euroyen

deposit rate (DIV),16 the change in the US term premium, measured by the yield on

the 10-year US Treasury note in excess of the 7-day Euroyen deposit rate (USTP),

the change in 7-day Euroyen deposit (EUROY), and a constant. These variables

are linked to the business cycle and to changes in global uncertainty.17 The weekly

data ranges from January 1, 1988 to 27 February, 1998, which is a 531-data-point

series. However, I work with rates of return and use the first difference of

Table 1

Variable definitions and notations (weekly data: 01/22/8802/27/98: 528 observations)

NotationVariable

MSUSAMMSCI USA total return index

MSJPANMSCI Japan total return index

MSCI Hong Kong total return index MSHGKG

MSSINGMSCI Singapore total return index

MSCI Taiwan total return index MSTAIW

MSCI Malaysia total return index MSMALY

MSCI World total return index MSWRLD

Foreign currency deposit rates

EURO-currency (LDN) US$ 7 daymiddle rate ECUSD7D

EURO-Currency (LDN) Japan 7 daymiddle rate ECJAP7D

Hong Kong Deposit 1 week-middle rate HKDEP1WSingapore Deposit 1 week-middle rate SNGDP1W

Taiwan Money Market 10 day-middle rate TAMM10D

MYDEP1MMalaysia Deposit 1 month-middle rate

Information ariables

S&PCOMPS&P 500 COMPOSITEdividend yield

FRTCM10US Treasury Constant Maturities 10-year

S&P 500 dividend in excess of 7-day Euroyen rate: S&PCOMPECJAP7D DIV

EUROYThe change in the 7-day Euroyen deposit rate: ECJAP7D(t)ECJAP7D(t1)

USTPFirst difference of the change in US term premium:(FRTCM10ECJAP7D)

WORLDLagged Return on MSCI world total return index

16 The data on Japanese dividend yield is not available, so I use dividend yield on S&P500 and convert

it into Japanese yen using corresponding weekly yen/$ spot rate.17 See Fama and French (1989).


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information variables which have to be translated from US dollar into

Japanese yen, and finally all the instruments are used with a 1-week lag,

relative to the excess return series; that leaves 528 observations expanding

from 22 January, 1988 to 27 February, 1998. Table 1 describes the var-

iables and notations used in this paper. All the data are obtained from

DATASTREAM.

Panel A of Table 2 contains summary statistics for the data. Not surprisingly,

the excess returns on the equity indices have higher mean returns, but also

higher volatility than the excess returns on the currency deposits. In terms of

Sharpe ratio, the US has the highest ratio in equity return (0.1098), and Singapore

has the highest ratio in currency return (0.0319). Overall Asia Pacific financial

markets may be characterized as high-return and high-volatility markets. The

coefficients of skewness and excess kurtosis reveal nonnormality in the data.

This is consistent with previous findings that both stock and currency returns

are not normally distributed and have a comparatively fat tailed distri-

bution. GARCH model is developed for the purpose of capturing this non-

normal distribution and will be applied to test time-varying risk premium and

rational expectations jointly in the next section. The last two columns in Panel A of

Table 2 report the LjungBox portmanteau test statistics for independence in thereturn and squared return series up to 24 lags, denoted by Q(24) and Q 2(24)

respectively.18 The hypothesis of linear independence is not rejected at 10% level for

all equity returns, but is rejected for all currency returns at 5% level except for New

Taiwan dollar. Independence of the squared return series is rejected for all return

series at 5% level except for Singapore dollar and New Taiwan dollar. Clearly, the

nonlinear dependencies are much prevalent than the linear dependencies. Both these

linear and nonlinear dependencies will be taken into account by the GARCH

model.

Panel B reports the summary statistics for the instruments. The correl-

ation matrix of the instruments in Panel C shows that the selected variables

contain sufficiently orthogonal information.19

To insure all the return seriesand instrumental variables are stationary, I conduct two unit root tests: aug-

mented Dickey Fuller (ADF) and Phillips Perron (PP). All the test results

reject the null hypothesis of unit root nonstationarity, and hence all the var-

iables used in this study are considered as stationary satisfying the GMM assump-

tion.20

18 The formula for the LjungBox statistic is, LB(k)=T(T+2)kj=1j2/Tjwhere j is the jth lagautocorrelation, kis the number of autocorrelations, and T is the sample size (Ljung and Box (1978)).19 The instruments used by Dumas and Solnik (1995) are highly correlated thus may not contain

enough orthogonal information in their study.20 The results of unit root tests are not reported here, but are available upon request.


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Table 2

Summary statistics for excess returns and instrumentsa

Mean Maximum Skewness SD SHP Minimum

Panel A: Excess equity and currency returns

0.1154 0.1069 0.6861***0.00259MSUSAM 0.0238 0.1098

0.3351***0.22120.1940MSJPAN NA0.03580.00111

0.3452***MSHGKG 0.00262 0.0409 0.0645 0.3490 0.2492

0.0230 0.22070.00123MSSING 0.03660.0341 0.2201

0.00173 0.3877 0.1481 0.0636 0.0272MSTAIW 0.4300

0.00065 0.3976 0.0922 0.0444 0.0152MSMALY 0.3356

0.4824***0.0429 0.05310.03160.01460.00049ECUSD7D

0.0513 0.0457 0.4691***HKDEP1W 0.01460.00031 0.0232

0.6097***0.0496SNGDP1W 0.04120.03190.01330.00039

0.00035 0.0714 0.23585**0.0155 0.0226TAMM10D 0.0519

1.2055***MYDEP1M 0.00032 0.0188 NA 0.1532 0.1039

0.3220***0.11770.0231 0.0621 0.1090MSWRLD 0.00141

Panel B: Instruments

MaximumSD MinimumMean

0.044250.051900.01464DIV 0.00015

1.1E06 0.00007 0.00043EUROY 0.00044

0.08123USTP 0.00007 0.02094 0.08330


14/26

Table 2 (Continued)

Panel C: Unconditional correlation

DIV EUROY USTP WORLD

1DIV

0.0295 1EUROY

USTP 0.7046 0.0551 1

WORLD 0.0515 0.0227 0.3691 1

a SHP is the Sharpe ratio. Q(24) and Q 2(24) are the LjungBox test statistics for serial correlation in th

respectively.

* Statistically significant at the 10% level.

** Statistically significant at the 5% level.

*** Statistically significant at the 1% level.


15/26


5. Empirical results

5.1. Distinguish rational expectations from (time -arying)risk premia:

GARCH(1,1)-M

The presence of linear dependencies suggests that the conditional mean of the

distribution of returns is a function of either past residuals or past returns. Based

on the rational expectations assumption, all information available at time when

forecast is made should be uncorrelated with forecast errors.21 Thus, if lagged andcurrent forecast errors and/or public available information can help in predicting

future forecast errors, this is evidence of irrationality or market inefficiency under

risk neutrality. However, most investors are risk averse and hence demand a risk

premium when holding uncovered foreign currency.22 The presence of second-mo-

ment dependencies suggests that the conditional variance of returns is time-depen-

dent and heteroskedastic. Following Bollerslev (1986), I specify the conditional

variance of returns as a GARCH(p,q ) process and assume that the possible

time-varying risk premia is due to this time-varying volatility in the second moment

of the distribution of excess returns. In my empirical tests, the GARCH(1,1)-M

model is chosen to fit the data.23 As indicated in Section 2, rational expectations

will be rejected if the null hypothesis, H0:b1=b2=b3=b4=0, is rejected. On theother hand, a significant a1 coefficient indicates the presence of time-varying risk

premium, and a significant a0 coefficient provides the evidence of constant risk

premium in foreign exchange markets. The results are shown in Table 3. Based on

the robust Wald statistics, the rational expectations hypotheses are rejected for

Singapore dollar, New Taiwan dollar and Malaysian Ringgit at 1% level and are

not rejected for the US dollar and Hong Kong dollar. This implies that the foreign

exchange markets for Singapore, Taiwan and Malaysia do not appear to be efficient

in a rational sense since the coefficients on the past forecast errors are statistically

significant. As far as the risk premium is concerned, I only find weak evidence of

time-varying risk premium for the New Taiwan dollar at 10% level, and there is no

evidence supporting the presence of constant and time-varying risk premia for theother four currencies. These results are consistent with Domowitz and Hakkio

(1985) where they can not reject the null hypothesis of no risk premium for

currencies of five industrial countries based on an ARCH-in-Mean model, and with

Baillie and Bollerslev (1990) where they utilize a multivariate GARCH approach to

model the time-varying risk premia and fail to find significant time-varying risk

premia for four European currencies. Based on their findings, Baillie and Bollerslev

21 Under CIP and UIP, the forward forecast error is equivalent to the deviation from UIP, which is

the excess return from foreign currency speculation.22

If foreign exchange risk is diversifiable, then there will be no risk premium even investors are riskaverse.23 Eqs. (2) (4) were estimated jointly with different specifications for p and q. No lags exceedingp=1

and q=1 were found to be significant.


16/26


Table 3

Estimation of GARCH(1,1)-M modela,b

Parameter SNGDP1WECUSD7D TAMM10D MYDEP1MHKDEP1W

0.0151 0.00350.0003 0.00160.0040a0(0.2990)(0.0233) (0.7887) (0.4439) (0.5239)

1.2577 0.14880.3549 0.15530.0067a1(0.8595) (0.2825) (0.8081)(0.0066) (0.3789)

0.0081 0.05140.0076 0.0325b1

0.0329

(0.0840) (1.0588) (0.5836)(0.5325) (0.1331)

0.1251 0.06190.1089 0.13070.0797b2(1.8848)*(1.6348) (2.9370)*** (1.3534) (3.7823)***

0.10290.0893 0.1123 0.1102 0.0995b3(1.8791)* (2.9231)***(2.1754)** (2.6308)***(1.9099)*

0.02560.0349 0.0233 0.0541 0.0237b4(0.5900) (1.4207)(0.6153) (0.6713)(0.6723)

0.0000 0.0002c0 0.00000.0001 0.0001

(1.4687) (2.2583)**(1.4221) (1.1237)(0.9710)

0.16790.1782 0.0866 0.1753 0.1123c1(1.3951) (2.7803)***(1.9084)* (4.4911)(2.7664)***

0.33210.2156 0.7029 0.1091 0.8611c2(0.8211)(0.3298) (3.8979)*** (0.3673) (16.4341)***

1.1803 1.35721.3575 1.2036 1.3227(9.9912)***(10.1587)*** (7.1493)*** (10.4949)*** (14.2836)***

0.7895 0.28440.5000 0.97340.3937c1+c22.9324 0.5513HL 25.67240.7436 1.0001

1556.5834 1464.57701498.4396 1465.9631LIK 1500.4516

WALD1 4.0042 2.6158 4.7900* 1.48440.3957

22.5627*** 14.9456***7.7348 19.5350***WALD2 7.6648

97.7892*** 68.5185***JB 243.1383***74.9357*** 66.8170***

19.2743 17.087325.7880 20.8932Q(24) 28.1112

12.3079 20.2327Q 2(24) 18.772819.1097 18.4634

a

ert+1=RPt+b1ert+b2ert1+b3ert2+b4ert3+t+1

RPt=a0+a1ht+1ht+1=c0+c1t

2+c2ht

t+1tGED(0,ht+1, ).

b Robust t-statistics are given in parentheses. LIK is the maximum log-likelihood value. WALD1 is

the Wald statistics for H0:a0=a1=0, WALD2 is the Wald test statistics for H0:b1=b2=b3=b4=0.

HL is the half-life of a shock measured in weeks. Q (24) and Q 2(24) are the LjungBox test statistics for

serial correlation in the standardized residuals and their squared values. Jarque-Bera test (JB) tests them

on normality.





17/26


(1990) argue that the forward market efficiency is possibly violated either due to

inefficient processing of information by market participants, so that marked

deviations from rationality occur, or alternatively that other theoretical models to

explain time-varying risk premia are required. The results for the conditional

variance equations indicate significant ARCH effects for the US dollar, Hong Kong

dollar and New Taiwan dollar and GARCH effect for Singapore dollar and

Malaysian Ringgit according to the coefficient estimates of c s. Volatility persis-

tence, measured by the sum ofc1and c2, is greater than 0.5 except for the US dollar

and New Taiwan dollar indicating a high degree of volatility persistence. A moreintuitive way of measuring volatility persistence is the half-life (HL) of a shock

calculated as HL= log(0.5)/log(c1+c2). The HLs for Hong Kong dollar, Singa-

pore dollar, and Malaysian Ringgit are greater than one week, but they are less

than 1 week for the US dollar and New Taiwan dollar. This implies that most

shocks last more than one week for most of AsiaPacific foreign exchange markets.

To assess the robustness of the results and the adequacy of the model, I conduct

diagnostic tests based on the standardized residuals of the model. The LjungBox

portmanteau test statistics for independence in the standardized residuals are

calculated using autocorrelations up to 24 lags. None of Q(24) and Q 2(24) test

statistics is significant at conventional significance levels, so the univariate

GARCH(1,1)-M seems to be an adequate model in capturing the linear andnonlinear dependencies found in the data. The Jarque-Bera tests reject the hypoth-

esis of normality for all series of standardized residuals. This evidence against

normality warrants the use of QML inferential procedures in the analysis.

In summary, the GARCH(1,1)-M model with a conditional GED distribution

does not provide any evidence of time-varying risk premia rather it points to a

violation of rational expectations hypothesis for some foreign exchange markets.

However, the insignificant risk premium coefficients found in all markets may result

from either a poor measure of risk or the misspecification of the model. In other

words, the conditional standard deviation may not be the proper measure of risk or

the univariate GARCH(1,1)-M is not a proper econometric model in modeling the

risk premium.

24

Therefore, before all possible empirical models have been explored,it is premature to abandon the risk premium interpretation of the unbiased forward

rate hypothesis or the deviations from UIP. As a result, I turn to the theoretical

international capital asset pricing model (ICAPM) derived in Section 3 and

empirically test it for the presence of time-varying risk premia.

5.2. Estimation and tests of ICAPM

5.2.1. Unconditional tests of ICAPM

In this section, I estimate the unconditional versions of the two contending

ICAPMs by setting Z=1 in Eq. (22). The results of these two separate estimations

24

Although no GARCH in mean effect is found in a purely time-series model, namely univariateGARCH(1,1)-M, several studies have successfully found significant time-varying risk premia in both

equity and foreign exchange markets when applying multivariate GARCH(1,1)-M model with asset

pricing restrictions. (De Santis and Gerard (1997, 1998), Tai (1998)).


18/26


Table 4

Unconditional one-factor ICAPMa,b,c,d

Coefficient t-statisticPrice of risk

0.0037 0.682001.37600.0254m

a E[rit t1]=mcov[rit,rmtt1].b The GMM test is based on the moment condition in Eq. (29) with the instrumental variables reduced

to Z=1.c The new term, 0, appears as a way of ensuring that Eq. (19) holds.d Test of overidentifying restrictions: J=156.4121 2 with 11 d.f. (critical value: (0.05, 11)

2 =19.675).

are shown in Tables 4 and 5. In Table 4, the unconditional ICAPM in which the

market risk proxied by MSCI world equity index is the only systematic risk is

rejected ( 112 =156.41) by the J-test with a P-value of zero. This result is different

from previous studies of Cumby and Glen (1990), Harvey (1991), Ferson and

Harvey (1994), Dumas and Solnik (1995) where they find that the MSCI world

equity index is mean-variance efficient using monthly equity returns denominated in

Table 5

Unconditional six-factor ICAPMa,b,c,d,e,f

Price of risk t-statisticCoefficient

Panel A: Parameter estimates

0 0.44 (5.6123)***

(7.8256)***5.2687USHK 5.0304 (7.4625)***

SI (1.6055)0.2043

0.1111 (1.6110)TAMA 0.0949 (2.4182)**

(1.5522)m 0.0464

Panel B: Hypothesis tests

d.f.Null hypothesis P-valueWald

69.2517 0Are the prices of market and currency risk equal to 6

zero?

H0: US=HK=SI=TA=MA=m=0

Are the prices of currency risk equal to zero?

068.8688H0: US=HK=SI=TA=MA=0 5

a E[rit t1]=5l=1lcov[rit,r6+l,t t1]+mcov[rit,rmt t1].b The GMM test is based on the moment condition in Eq. (29) with the instrumental variables reduced

to Z=1.c The new term, 0 appears as a way of ensuring that Eq. (19) holds.d US, US dollar; HK, Hong Kong dollar; SI, Singapore dollar; TA, New Taiwan dollar; MA,

Malaysian Ringgit.e

t-statistics are given in parenthesesf Test of Overidentifying restrictions: J=8.0983 2 with 6 d.f. (critical value: (0.05,6)2 =12.592).




19/26


the US dollar for developed countries. Panel B of Table 5 displays the uncondi-

tional test of ICAPM with five foreign exchange risk premia in addition to the

market risk premium. The J-test ( 62=8.09 with a P-value of 0.23) fails to

reject the model. The point estimate of the world price of market risk, which

approximates the constant relative risk aversion, is equal to 4.64 but its

robust t-statistic is not significant25. Since the goal of this study is to examine

the validity of risk premium hypothesis and the role of deviations from PPP

in the pricing of foreign exchange and equity markets, I test zero prices of

six risk factors considered in this paper (i.e. five exchange rate risks plus one marketrisk). First, the joint null hypothesis of zero prices of foreign exchange risk and

market risk is significantly rejected with a P-value of zero based on the Wald test.

Second, the joint null hypothesis of zero prices of foreign exchange risk is also

significantly rejected with a P -value of zero. To provide further evidence of foreign

exchange risk pricing, I apply Newey West D-test (Newey and West, 1987) to

discriminate between the unconditional one-factor and six-factor ICAPMs since

they are nested. This test involves two steps. I first estimate the unconditional

six-factor ICAPM, which is the unrestricted model, and save the final weighting

matrix. I then use this weighting matrix to re-estimate the model under the

restriction of zero prices of foreign exchange risk, which is the null hypothesis. The

difference of the minimized objective functions from the two estimations is 2

distributed with degrees of freedom equal to the number of restrictions that the

restricted model imposes on the unrestricted one. As can be seen from Table 7, the

null hypothesis of zero foreign exchange risk pricing is rejected with a P-value of

zero.

Based on above tests, one can conclude that the risk premium hypothesis is

supported, and the foreign exchange risk is priced in these five Asia

Pacific countries and the US In short, the unconditional tests indicate that

simply extending the domestic CAPM to an international setting is not

warranted and point out that researchers should consider other risk factors

such as the foreign exchange risk when testing international asset pricing

models.

5.2.2. Conditional tests of ICAPM

Tables 6 and 8 report the estimation results of the conditional ICAPMs. In Table

6, the conditional ICAPM with one-factor is rejected at 5% level by the J-test

( 552 =221.8 with a P -value of zero) Table 7. However, the J-test fails to reject the

conditional six-factor ICAPM ( 302 =28.96 with a P-value of 0.52) as shown in

Panel A of Table 8. The joint null hypothesis of zero prices on foreign exchange

aerisk and market risk is significantly rejected at 1% level based on the Wald test.

In addition, the joint null hypothesis of zero prices on foreign exchange risk is also

significantly rejected at 1% level. Moreover, the null hypothesis of constant prices

of foreign exchange risk is rejected with a P-value of 0.0006. These test results

25 The number reported in the table is equal to 0.0464 because we use percentage returns during the

estimation.


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Table 6

Conditional one-factor ICAPMa,b,c,d

Instruments (Z) m0

CONSTANT 0.0037 0.01557

(0.7887) (0.8182)

EUROY 33.1423 68.9460

(0.5648) (0.3710)

DIV 0.4318 0.7800

(1.0171) (0.4658)

0.70450.0513USTP

(0.6825)(0.2251)

0.0048 0.0101WORLD

(1.4015) (1.0504)

a E[rit t1]=m, t1cov[rit,rmt t1] and 0,t1=Zt10, m, t1=Zt1m.b The GMM test is based on the moment condition in Eq. (29) with the instrumental variables

including the lagged world excess equity return (WORLD), the S&P 500 dividend yield in excess of

7-day Euroyen deposit rate (DIV), the change in the US default premium (USTP), the change in 7-day

Euroyen deposit rate (EUROY), and a CONSTANT. The new time varying term, 0, t1 appears as

a way of ensuring that Eq. (19) holds.c t-statistics are given in parentheses.d

Test of overidentifying restrictions: J=221.8724. 2

with 55 d.f. (critical value: (0.05, 55)2

=73.312).

simply that the foreign exchange risk is not only priced but also time-varying. To

find out which currency contributes to this time-varying foreign exchange risk

premia, I also conduct the Wald tests on the hypothesis of zero price on individual

currencies. As can be seen in the Panel B, the US dollar and the Hong Kong dollar

are the two major currencies that contribute to this time-varying characteristic of

foreign exchange risk premia.26 The instruments useful in predicting these time-

varying risk prices are the DIV and USTP. To discriminate between these two

conditional ICAPMs, I again apply the NeweyWest D-test to test null hypothesis

of zero prices on foreign exchange risk. Table 7 shows that the D-statistics is

108.884 with a P-value of zero. Thus, the foreign exchange risk is priced in theconditional ICAPM. Next I test the null hypothesis of time-invariant prices of

foreign exchange risk and it is also rejected by the D-test with a P-value of 0.0007.

These reinforce the test results based on the Wald tests that foreign exchange risk

is indeed time varying. Unlike Dumas and Solnik (1995) where they are able to

discriminate between the unconditional six-factor ICAPM and the conditional

counterpart based on the J-tests, I can not reject both models. To discriminate

between these two ICAPMs, I also conduct the D-test because they are nested.

Table 7 indicates that the null hypothesis of unconditional six-factor ICAPM is

26 As pointed out by the referee that Hong Kong dollar is pegged to the US dollar, so it is not

surprising to find similar behavior between these two currency returns. However, because the focus ofthis paper is to see if the ICAPMs in the absence of PPP hold using AsiaPacific equity and currency

data, to incorporate the nature of different exchange rate arrangements into the model is beyond the

scope of this paper.


21/26

Table 7

Diagnosticsa,b,c

2 DIFFERENCE NULL HYPOTHESIS (RESTRICTED ALTERNATIVE HYPOTHESIS (UN-

MODEL) STATISTICS)RESTRICTED MODEL)

1. Unconditional one-factor ICAPM 76.96578.0983=6Unconditional six-factor ICAPM

Unconditional one-factor ICAPM Conditional six-factor ICAPM 145.153328.9636=2.

Unconditional six-factor ICAPM Conditional six-factor ICAPM 79.858328.9636=3.

137.848128.9636=Conditional six-factor ICAPM4. Conditional one-factor ICAPM

Time-invariant world price of market Conditional six-factor ICAPM 32.261628.9636=5.

risk6. Time-invariant world prices of foreign Conditional six-factor ICAPM 75.516228.9636=

exchange risk

a NeweyWest D-test (Newey and West, 1987) involves two steps. We first estimate the unrestricted model,

use this weighting matrix to re-estimate the model under the restriction, which is the null hypothesis. The dif

from the two estimations is 2 distributed with degrees of freedom equal to the number of restrictions that the

one.b One-factor, world market risk; six-factor, five foreign exchange risks plus world market risk; unco

conditional, time-varying prices of risks.c NeweyWest D-statistics report on the 2 for the difference of the minimized objective function from the e

models.


22/26

Table 8

Conditional six-factor ICAPMa,b,c,d,e

Instruments (Z) US

HK

SI

Panel A: Parameter estimates

5.4485 5.24310.52CONSTANT 0.243

(6.44)** (8.35)** (7.84)** (1.65

287.98 278.88EUROY 1913198.08

(0.37) (0.04) (0.42) (1.2

11.DIV 26.55 190.86 208.48

(0.(2.86)**(2.84)** (3.16)**

115.87111.07 0.3USTP 16.20

(3.24)** (2.76)** (2.85) (0.0

0.0WORLD 0.0002 0.1580 0.1396

(0.0045) (0.45) (0.37) (0.0


d.f. P-valueWaldNull hypothesis

30Are the prices of market and currency risk equal to zero? 0110.55

H0: USk = HK

k = SIk = TA

k = MAk =0

k=CONSTANT, DIV, EUROY, USTP, WORLD

108.88 25 0Are the prices of currency risk equal to zero?

H0: USk = HK

k = SIk = TA

k = MAk =0

k=CONSTANT, DIV, EUROY, USTP, WORLD

46.55 20 0.0006Are the prices of currency risk constant?

H0: USk = HK

k = SIk = TA

k = MAk =0

k=DIV, EUROY, USTP, WORLD

Is the price of the US dollar risk constant? 10.55 4 0.0321

H0: USk =0; k=DIV, EUROY, USTP, WORLD

0.01214Is the price of the Hong Kong dollar risk constant? 12.82H0: HK

k =0; k=DIV, EUROY, USTP, WORLD

Is the price of the Singapore dollar risk constant? 3.87 4 0.4235

H0: SIk =0; k=DIV, EUROY, USTP, WORLD

Is the price of the New Taiwan dollar risk constant? 47.25 0.1230

H0: TAk =0; k=DIV, EUROY, USTP, WORLD


23/26

Table 8

Conditional six-factor ICAPMa,b,c,d,e


Null hypothesis Wald d.f. P-value

0.661542.41Is the price of the Malaysian Ringgit risk constant?

H0: MAk =0; k=DIV, EUROY, USTP, WORLD

3.29 0.50944Is the price of market risk constant?

H0: mk=0; k=DIV, EUROY, USTP, WORLD

a

E[rit t1]=5

l=1

l,t1cov[rit,r6+l,t t1]+m,t1cov[rit,rmtt1] and 0, t1=Zt10,l, t1=Zt1l,m

b The GMM test is based on the moment condition in Eq. (29) with the instrumental variables including the l

the S&P 500 dividend yield in excess of 7-day Euroyen deposit rate (DIV), the change in the US default prem

deposit rate (EUROY), and a CONSTANT. The new time varying term, 0,t1, appears as a way of ensurc US, the US dollar; HK, Hong Kong dollar; SI, Singapore dollar; TA, New Taiwan dollar; MA, Malaysid t-statistics are given in parentheses.e Test of overidentifying restrictions: J=28.9636. 2 with 30 d.f. (critical value: (0.05, 30)

2 =43.773).




24/26


rejected with a P-value of 0.0051 implying that the conditional ICAPM in the

absence of PPP outperforms the unconditional counterpart.

6. Summary and conclusions

This paper examines the validity of the risk premia hypothesis in explaining

deviations from UIP and the role of deviations from PPP in the pricing of foreignexchange rates and equity securities in five Asia Pacific countries and the US.

Using weekly data from 1 January, 1988 to 27 February, 1998, I find that

conditional variances are not related to deviations from UIP in any statistical sense

based on an univariate GARCH(1,1)-M model. As I consider both foreign ex-

change and equity markets together and test a conditional international CAPM in

the absence of PPP, I can not reject the model based on the J-test by Hansen

(1982), and find significant time-varying foreign exchange risk premia present in the

data.

Overall the findings in this paper support the idea that the predictable component

in deviations from UIP is due to a time-varying foreign exchange risk premium, and

not to irrationality among market participants. The evidence of significant foreign

exchange risk pricing supports the idea that foreign exchange risk is not diver-

sifiable and hence investors should be compensated for bearing this risk. It also

supports the role of deviations from PPP in pricing foreign exchange rates and

equity securities since foreign exchange risks are modeled as covariances between

excess returns and deviations from PPP in this paper. Furthermore, the empirical

results found in this paper suggest that a multi-factor asset pricing model outper-

forms a single-factor asset pricing model, and especially in its conditional form.

Acknowledgements

This paper is part of my doctoral thesis at the Ohio State University. I wish to

thank my advisor, Nelson C. Mark, for his guidance, and Paul Evans, Zhiwu Chen,

J. Huston McCulloch and seminar participants at the 1999 EFA Annual Meeting in

Miami Beach, FL, the 5th TCFA Annual Meeting in Boston, MS, the 7th SFM

Conference in Kaohsiung, Taiwan, ROC, and the 11th AFBC in Sydney, Australia

for their helpful comments and suggestions.

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