Time-varying risk premia in foreign exchange and equity markets: evidence from Asia–Pacific countries

Journal of Multinational Financial Management 9 (1999) 291 – 316 www.elsevier.com/locate/econbase

Time-varying risk premia in foreign exchange and equity markets: evidence from Asia–Pacific countries Chu-Sheng Tai * Department of Economics, The Ohio State Uni6ersity, 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 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 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 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. © 1999 Elsevier Science B.V. All rights reserved. Keywords: International asset pricing; Uncovered interest parity; Foreign exchange risk premium JEL classification: F31; G12; C32

* 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. PII: S 1 0 4 2 - 4 4 4 X ( 9 9 ) 0 0 0 0 4 - 3

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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. If exchange 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 Ross’s 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 of fixed 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 possible sources 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 monetary authorities 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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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 demonstrate a measure of foreign exchange risk that can account for observed predictable 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 consumption 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 exchange risk, 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 two sets of assets separately.8

3

Of course, if the underlying risk is diversifiable, there will be no risk premium. 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. 4

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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) methodology (Hansen, 1982) to empirically estimate and test international asset pricing models in the absence of PPP under both unconditional and conditional frameworks.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 timevarying 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 expressed as it −i*t = Et (st + 1) − st [ ert + 1 = E(st + 1)− st + i*− it + ot + 1 = Et (ert + 1)+ ot + 1 t (1) where st is the (log of the) exchange rate, expressed as the dollar price of one unit of foreign currency; i *t 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; ot + 1 =st + 1 −Et (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 assumption of rational expectations, the forecast errors are assumed to be unpredictable given information available at the time the forecast is made, so that ot + 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 this joint 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 +b2ert − 1 + b3ert − 2 + b4ert − 3 + ot + 1

(2)

RPt =a0 +a1 ht + 1

(3)

ht + 1 =c0 +c o +c2ht

(4)

ot + 1 Ft GED(0,ht + 1, 6)

(5)

2 1 t

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 formulation 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 ot + 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 standard deviation of the conditional variance ( ht + 1). If both a0 and a1 are insignificantly different from zero, there is no risk premium. If a0 " 0 but a1 " 0, there is a constant premium. If a1 "0, 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 n 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. The GED is a generalization of the normal distribution. It includes the normal distribution if the parameter 6 has a value of 2. 6 is a measure of tail-thickness. If 6 B 2 a fat-tailed distribution results. The lower limit for 6 is 0. If 6 B 1, the unconditional variance does not exist. 11

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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 likelihood function, and calculating a robust estimate of the covariance of the parameter estimates using the matrix of second derivatives and the average of the period-by-period outer products of the gradient. Optimization is performed using BFGS algorithm.

3. International capital asset pricing model (ICAPM)

3.1. The conditional ICAPM In deriving the ICAPM of Adler and Dumas (1983), we begin with the classic CAPM. The classic CAPM says that, in equilibrium, there must exist two numbers, h and u, such that, for all securities i 12: E(ri ) =h +ucov(ri, rm )

(6)

where ri is the real rate of return on security i; rm is the real rate of return on the market portfolio; h is the real rate of return on a zero–beta portfolio, and u is the market average degree of risk aversion. Since the real rate of return is unobservable, we can transform it into a nominal rate of return. The real rate of return, ri, is given by: ri =

1 + Ri −1 1+p

(7)

where Ri is the nominal rate of return and p is the rate of inflation. Suppose both security prices and general price indices follow stationary Ito processes (i.e. geometric Brownian motion): Ri dt = pi dt =

dPi =E(Ri ) dt + si dwi pi

(8)

dIi =E(pi ) dt +sp dzp Ii

where pi is the price of security i; E(Ri ) is the instantaneous nominal expected rate of return on security i; si is the instantaneous standard deviation of the nominal return on security i; wi is a standard Wiener process and dwi is the associated white noise; Ii is the general price index; E(pi ) is the expected value of the instantaneous rate of inflation; sp is the standard deviation of the instantaneous rate of inflation; zp is a standard Wiener process, and dzp is the associated white noise. We can substitute Eqs. (7) – (9) into Eq. (6) and apply Ito’s lemma to obtain E(Ri ) − E(p) +var(p) −cov(Ri, p)= h+ u cov(Ri − p, Rm − p)

(9)

12 The derivation of the ICAPM is based on Dumas (1994). For more details of deriving the ICAPM, see Adler and Dumas (1983).

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Expanding the cov(Ri −p, Rm −p), and rearranging terms: E(Ri ) = h+E(p) −(1 −u)var(p)− u cov(Rm, p)+ (1− u)cov(Ri, p) + u 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 − u)cov(Ri, p)+ u 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 (u= 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 p $l =(1 +p ll)(1 +e $l ) − 1

(12)

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

$ l

Ri =(1 +R li)(1 +e $l ) − 1

(13)

where R li is the rate of return on security i expressed 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 +(1 − u l)cov(Ri, p $l )+ u l cov(Ri, R lp)

(14)

where R is the dollar, nominally risk-free interest rate and R lp = i x liRi (x li being the weight allocated by investors of country l to security i ) is the dollar rate of return on 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 u l, multiply them by W l (each country’s wealth), sum them over all national investor groups, and finally divide them by l W l/u l, to get cov(Ri, p $l ) 1 + u cov(Ri, Rm ) E(Ri ) = R +u % ( l −1)W l u W l where W= % W l, l

13

1 = u

%W l/u l l , W

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

(15)

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u l is the coefficient of relative risk aversion for investors from country l, and u is an average of the risk aversion coefficients for each national group, weighted by the corresponding relative wealth W l/W. The international nominal CAPM (Eq. (15)), now contains as many inflation 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, p $l ) =cov(Ri, e $l ) because p ll + e $l = p $l .14 Consequently, in the international CAPM, the foreign exchange risk becomes one of the systematic risks under which PPP does not hold and local inflation rates are nonstochastic. Consider the dollar rate of return from a foreign currency deposit, V $l , which is given by: V $l =(1 +V ll)(1 +e $l ) −1

(16)

Then, cov(Ri, e $l ) = cov(Ri, V $l −V ll)= cov(Ri, V $l ) since the foreign nominal currency deposit rate in local currency units,V ll, is known at the time when the deposit was made, and hence is nonrandom. Thus, we can rewrite Eq. (15) as 1 cov(Ri, V $l ) E(Ri ) = R +u % ( l −1)W l + u cov(Ri, Rm) W l u

(17)

Suppose there are L +1 countries and a set of N= n+ L+1 assets—other than the measurement-currency deposit—which is composed of n equities, L nonmeasurement-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: L

E[rit Vt − 1]= % ll, t − 1cov[rit, rn + l, t Vt − 1]+ lm, t − 1cov[rit, rmt Vt − 1] l=1

where lm, t − 1 =ut − 1 =

1

and

 

ll, t − 1 = ut − 1

(18)

1 W lt − 1 − 1 and rit ul Wt − 1

Wl 1 Ll= 1 t − 1 × l Wt − 1 u is the nominal return on asset or portfolio i, i= 1 … N, from time t–1 to t, in excess of 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; ll, t − 1, l =1 …L, are the time-varying world price of exchange rate risk; lm, t − 1 is the time-varying world price of market risk, and Vt − 1 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 p $US =(1 + p ll)(1 +e $l ) −1. If relative PPP holds, then p ll +e $l − p $US = 0. If relative PPP does not hold, then p ll +e $l −p $US =u where u are the deviations from relative PPP. If we assume local inflation is nonstochastic, then p $US =p ll =0. Thus, e $l =u which 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 consumer–investor’s optimization problem can be written as: E[Mt (1 + rf, t − 1) Vt − 1]= 1

(19)

E[Mtrit Vt − 1]= 0

(20)

i =1 … N

where Mt is the marginal rate of substitution between nominal return at date t and at date t − 1 and rf, t − 1 is the conditionally riskfree rate of interest known at date t−1. Without specifying the form of Mt, 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:



n

L

Mt = 1 − l0, t − 1 − % ll, t − 1rn + l, t − lm, t − 1rmt /(1+ rf, t − 1) l=1

(21)

where L

l0, t − 1 = − % ll, t − 1E[rn + l,t Vt − 1]− lm, t − 1E[rm,t Vt − 1] l=1

The new time varying term, l0, t − 1, appears as a way of ensuring Eq. (19) holds.For econometric purposes, following Dumas and Solnik (1995) two auxiliary assumptions are needed: Assumption 1: the information set Vt − 1 is generated by a vector of instrumental variables Zt − 1. Zt − 1 is a 1× K vector of predetermined instrumental variables that reflect everything that is known to the investor at time t− 1. Assumption

2: l0, t − 1 = −Zt − 180, ll, t − 1 = Zt − 18l, lm, t − 1 = Zt − 18m,

l= 1 …L.

(22)

Here, the 8’s are the time-invariant vectors of weights. Based on Eq. (19), we define the innovation ut : Mt (1 + rf, t − 1) =1 − ut

(23)

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

ut =1 − Mt (1 + rf, t − 1) = −Zt − 180 + % Zt − 18lrn + l, t + Zt − 18mrmt

(24)

l=1

with ut satisfying: E[ut Vt − 1]= 0 Next, based on Eq. (20), we define the innovation hit :

(25)

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(26)

hit =rit −ritut with hit satisfying: E[hit Vt − 1]= 0

(27)

One can form the 1 +N vector of residuals ot = (ut, ht ). Combining Eqs. (25) and (27) under Assumption 1 yields: E[ot Zt − 1]= 0

(28)

It follows that E[ ft (b0)] =E[Z ’t − 1ot ]= 0

for

t= 1, 2 …T

(29)

where Zt − 1 is a 1× K vector and ot 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 Hansen’s 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 Asia – Pacific capital markets: Japan, Hong Kong, Singapore, Taiwan, and Malaysia and one major developed market: the US. Among theses five Asia–Pacific capital markets, Japan is the largest capital market in terms of its market capitalization. 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 instruments 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 (DUSTP), the change in 7-day Euroyen deposit (DEUROY), 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: 01/22/88–02/27/98: 528 observations) Variable

Notation

MSCI MSCI MSCI MSCI MSCI MSCI MSCI

MSUSAM MSJPAN MSHGKG MSSING MSTAIW MSMALY MSWRLD

USA total return index Japan total return index Hong Kong total return index Singapore total return index Taiwan total return index Malaysia total return index World total return index

Foreign currency deposit rates EURO-currency (LDN) US$ 7 day–middle rate EURO-Currency (LDN) Japan 7 day–middle rate Hong Kong Deposit 1 week-middle rate Singapore Deposit 1 week-middle rate Taiwan Money Market 10 day-middle rate Malaysia Deposit 1 month-middle rate

ECUSD7D ECJAP7D HKDEP1W SNGDP1W TAMM10D MYDEP1M

Information 6ariables S&P 500 COMPOSITE–dividend yield US Treasury Constant Maturities 10-year S&P 500 dividend in excess of 7-day Euroyen rate: S&PCOMP–ECJAP7D The change in the 7-day Euroyen deposit rate: ECJAP7D(t)–ECJAP7D(t−1) First difference of the change in US term premium:D(FRTCM10–ECJAP7D) Lagged Return on MSCI world total return index

S&PCOMP FRTCM10 DIV DEUROY DUSTP WORLD

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 variables 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 distribution. GARCH model is developed for the purpose of capturing this nonnormal 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 Ljung – Box portmanteau test statistics for independence in the return 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 correlation matrix of the instruments in Panel C shows that the selected variables contain sufficiently orthogonal information.19 To insure all the return series and instrumental variables are stationary, I conduct two unit root tests: augmented Dickey – Fuller (ADF) and Phillips–Perron (PP). All the test results reject the null hypothesis of unit root nonstationarity, and hence all the variables used in this study are considered as stationary satisfying the GMM assumption.20

The formula for the Ljung–Box statistic is, LB(k) =T(T+ 2)kj= 1r 2j /T− j where rj is the jth lag autocorrelation, k is 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. 18

Table 2 Summary statistics for excess returns and instrumentsa Mean

SD

SHP

Q(24)

Q 2(24)

3.9100***

25.0579

169.5870***

0.3351***

9.6692***

8.8004

140.2499***

Minimum

Maximum

Skewness

−0.1154

0.1069

0.6861***

−0.1940

0.2212

Kurtosis

Panel A: Excess equity and currency returns MSUSAM

0.0238

−0.00111

0.0358

MSHGKG

0.00262

0.0409

0.0645

−0.3490

0.2492

−0.3452***

16.2434***

16.5821

78.9340***

MSSING

0.00123

0.0341

0.0366

−0.2207

0.2201

−0.0230

13.8414***

20.9733

176.7243***

MSTAIW

0.00173

0.0636

0.0272

−0.4300

0.3877

0.1481

13.4483***

17.7231

196.0677***

MSMALY

0.00065

0.0444

0.0152

−0.3356

0.3976

0.0922

23.1050***

28.6745

112.3876***

ECUSD7D HKDEP1W

0.00049 0.00031

0.0146 0.0146

0.0316 0.0232

−0.0429 −0.0513

0.0531 0.0457

0.4824*** −0.4691***

1.1005*** 0.9774***

45.2884*** 45.4548***

40.2305** 43.9899***

SNGDP1W TAMM10D MYDEP1M

0.00039 0.00035 −0.00032

0.0133 0.0155 0.0188

0.0319 0.0226 NA

−0.0496 −0.0519 −0.1532

0.0412 0.0714 0.1039

−0.6097*** −0.23585** −1.2055***

1.4686*** 1.2603*** 13.8179***

39.1617** 28.8318 70.9687***

35.8026* 27.9724 331.6159***

0.00141

0.0231

0.0621

−0.1177

0.1090

0.3220***

4.9618***

16.6046

146.2610***

MSJPAN

MSWRLD

Panel B: Instruments Mean DIV DEUROY DUSTP

−0.00015 −1.1E−06 −0.00007

SD 0.01464 0.00007 0.02094

0.1098 NA

Minimum

Maximum

−0.05190 −0.00043 −0.08330

0.04425 0.00044 0.08123

C.-S. Tai / J. of Multi. Fin. Manag. 9 (1999) 291–316

0.00259

303

304

Panel C: Unconditional correlation DIV DEUROY

DUSTP

DIV DEUROY DUSTP WORLD

1 −0.3691

1 −0.0295 0.7046 0.0515

1 −0.0551 0.0227

WORLD

1

a SHP is the Sharpe ratio. Q(24) and Q 2(24) are the Ljung–Box test statistics for serial correlation in the excess returns and excess returns squared, respectively. * Statistically significant at the 10% level. ** Statistically significant at the 5% level. *** Statistically significant at the 1% level.

C.-S. Tai / J. of Multi. Fin. Manag. 9 (1999) 291–316

Table 2 (Continued)

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305

5. Empirical results

5.1. Distinguish rational expectations from (time-6arying) 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 and current 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-moment dependencies suggests that the conditional variance of returns is time-dependent 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 the other 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 the other 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 risk averse. 23 Eqs. (2)–(4) were estimated jointly with different specifications for p and q. No lag’s exceeding p =1 and q= 1 were found to be significant.

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306

Table 3 Estimation of GARCH(1,1)-M modela,b Parameter

ECUSD7D

HKDEP1W

SNGDP1W

TAMM10D

MYDEP1M

a0

−0.0003 (−0.0233) −0.0067 (−0.0066) −0.0329 (−0.5325) 0.0797 (1.6348) 0.0893 (1.9099)* −0.0349 (−0.6723) 0.0001 (0.9710) 0.1782 (2.7664)*** 0.2156 (0.3298) 1.3227 (10.1587)*** 0.3937 0.7436 1500.4516 0.3957 7.6648 74.9357*** 28.1112 19.1097

−0.0040 (−0.2990) 0.3549 (0.3789) 0.0076 (0.1331) 0.1089 (1.8848)* 0.1029 (2.1754)** −0.0256 (−0.6153) 0.0001 (1.4221) 0.1679 (1.9084)* 0.3321 (0.8211) 1.3575 (9.9912)*** 0.5000 1.0001 1498.4396 4.0042 7.7348 66.8170*** 25.7880 18.4634

−0.0151 (−0.7887) 1.2577 (0.8595) 0.0081 (0.0840) 0.1251 (2.9370)*** 0.1123 (1.8791)* −0.0233 (−0.5900) 0.0000 (1.4687) 0.0866 (1.3951) 0.7029 (3.8979)*** 1.1803 (7.1493)*** 0.7895 2.9324 1556.5834 2.6158 22.5627*** 97.7892*** 19.2743 12.3079

0.0035 (0.4439) −0.1488 (−0.2825) −0.0514 (−1.0588) 0.0619 (1.3534) 0.1102 (2.9231)*** −0.0541 (−1.4207) 0.0002 (2.2583)** 0.1753 (2.7803)*** 0.1091 (0.3673) 1.3572 (10.4949)*** 0.2844 0.5513 1464.5770 4.7900* 14.9456*** 68.5185*** 17.0873 20.2327

−0.0016 (−0.5239) 0.1553 (0.8081) −0.0325 (−0.5836) 0.1307 (3.7823)*** 0.0995 (2.6308)*** −0.0237 (−0.6713) 0.0000 (1.1237) 0.1123 (4.4911) 0.8611 (16.4341)*** 1.2036 (14.2836)*** 0.9734 25.6724 1465.9631 1.4844 19.5350*** 243.1383*** 20.8932 18.7728

a1 b1 b2 b3 b4 c0 c1 c2 n c1+c2 HL LIK WALD1 WALD2 JB Q(24) Q 2(24) a

ert+1 = RPt+b1ert+b2ert−1+b3ert−2+b4ert−3+ot+1 RPt =a0+a1 ht+1 ht+1 = c0+c1o 2t +c2ht ot+1 FtGED(0,ht+1, n). 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 Ljung–Box test statistics for serial correlation in the standardized residuals and their squared values. Jarque-Bera test (JB) tests them on normality. * Statistically significant at the 10% level. ** Statistically significant at the 5% level. *** Statistically significant at the 1% level.

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307

(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 persistence, measured by the sum of c1 and c2, is greater than 0.5 except for the US dollar and New Taiwan dollar indicating a high degree of volatility persistence. A more intuitive way of measuring volatility persistence is the half-life (HL) of a shock calculated as HL=log(0.5)/log(c1 + c2). The HL’s for Hong Kong dollar, Singapore 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 Asia–Pacific 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 Ljung–Box 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 and nonlinear dependencies found in the data. The Jarque-Bera tests reject the hypothesis 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 univariate GARCH(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)).

308

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Table 4 Unconditional one-factor ICAPMa,b,c,d Price of risk

Coefficient

t-statistic

l0 lm

0.0037 0.0254

0.6820 1.3760

E[rit Vt−1] = lm cov[rit, rmt Vt−1]. The GMM test is based on the moment condition in Eq. (29) with the instrumental variables reduced to Z= 1. c The new term, l0, appears as a way of ensuring that Eq. (19) holds. d Test of overidentifying restrictions: J = 156.4121 x2 with 11 d.f. (critical value: x 2(0.05, 11) =19.675). a

b

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 (x 211 =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

Coefficient

t-statistic

Panel A: Parameter estimates l0 lUS lHK lSI lTA lMA lm

0.44 5.2687 5.0304 0.2043 0.1111 −0.0949 0.0464

(5.6123)*** (7.8256)*** (7.4625)*** (1.6055) (1.6110) (−2.4182)** (1.5522)

Wald 69.2517

d.f. 6

P-value 0

68.8688

5

0

Panel B: Hypothesis tests Null hypothesis Are the prices of market and currency risk equal to zero? H0: lUS = lHK = lSI = lTA = lMA = lm =0 Are the prices of currency risk equal to zero? H0: lUS = lHK = lSI = lTA = lMA = 0

E[rit Vt−1] = 5l = 1ll cov[rit,r6+l,t Vt−1]+lm cov[rit,rmt Vt−1]. The GMM test is based on the moment condition in Eq. (29) with the instrumental variables reduced to Z= 1. c The new term, l0 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 parentheses f Test of Overidentifying restrictions: J =8.0983 x 2 with 6 d.f. (critical value: x 2(0.05,6) =12.592). *** Statistically significant at the 1% level. ** Statistically significant at the 5% level. a

b

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309

the US dollar for developed countries. Panel B of Table 5 displays the unconditional test of ICAPM with five foreign exchange risk premia in addition to the market risk premium. The J-test (x 26 = 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 market risk). 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 x 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 (x 255 =221.8 with a P-value of zero) Table 7. However, the J-test fails to reject the conditional six-factor ICAPM (x 230 = 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)

80

8m

CONSTANT

0.0037 (0.7887) −33.1423 (−0.5648) 0.4318 (1.0171) 0.0513 (0.2251) −0.0048 (−1.4015)

0.01557 (0.8182) 68.9460 (0.3710) −0.7800 (−0.4658) −0.7045 (−0.6825) 0.0101 (1.0504)

DEUROY DIV DUSTP WORLD

E[rit Vt−1] = lm, t−1cov[rit, rmt Vt−1] and l0, t−1 =−Zt−180, lm, t−1 =Zt−18m. 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 (DUSTP), the change in 7-day Euroyen deposit rate (DEUROY), and a CONSTANT. The new time varying term, l0, t−1 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. x 2 with 55 d.f. (critical value: x 2(0.05, 55) =73.312). a

b

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 timevarying risk prices are the DIV and DUSTP. To discriminate between these two conditional ICAPMs, I again apply the Newey–West 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 the conditional 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 of this paper is to see if the ICAPMs in the absence of PPP hold using ‘Asia – Pacific’ equity and currency data, to incorporate the nature of different exchange rate arrangements into the model is beyond the scope of this paper.

Table 7 Diagnosticsa,b,c

6.

ALTERNATIVE HYPOTHESIS (UNRESTRICTED MODEL)

x 2 DIFFERENCE (NEWEY–WEST D D.F. STATISTICS)

P-VALUE

Unconditional one-factor ICAPM Unconditional one-factor ICAPM Unconditional six-factor ICAPM Conditional one-factor ICAPM Time-invariant world price of market risk Time-invariant world prices of foreign exchange risk

Unconditional six-factor ICAPM Conditional six-factor ICAPM Conditional six-factor ICAPM Conditional six-factor ICAPM Conditional six-factor ICAPM

76.9657−8.0983= 68.8674 145.1533−28.9636=116.19 79.8583−28.9636= 50.8947 137.8481−28.9636=108.884 32.2616−28.9636=3.2980

11 33 28 25 4

0 0 0.0051 0 0.5092

Conditional six-factor ICAPM

75.5162−28.9636= 46.5526

20

0.0007

a Newey–West D-test (Newey and West, 1987) involves two steps. We first estimate the unrestricted model, and save the final weighting matrix. We then use this weighting matrix to re-estimate the model under the restriction, which is the null hypothesis. The difference of the minimized objective functions from the two estimations is x 2 distributed with degrees of freedom equal to the number of restrictions that the restricted model imposes on the unrestricted one. b ‘One-factor’, world market risk; ‘six-factor’, five foreign exchange risks plus world market risk; ‘unconditional’, prices of risk are time-invariant; ‘conditional’, time-varying prices of risks. c Newey–West D-statistics report on the x 2 for the difference of the minimized objective function from the estimations of both restricted and unrestricted models.

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1. 2. 3. 4. 5.

NULL HYPOTHESIS (RESTRICTED MODEL)

311

312

Table 8 Conditional six-factor ICAPMa,b,c,d,e Instruments (Z) Panel A: Parameter estimates CONSTANT

DIV DUSTP WORLD Panel B: Hypothesis tests Null hypothesis Are the prices of market and currency risk equal to zero? H0: 8 kUS = 8 kHK =8 kSI =8 kTA =8 kMA =0 Ök= CONSTANT, DIV, DEUROY, DUSTP, WORLD Are the prices of currency risk equal to zero? H0: 8 kUS = 8 kHK =8 kSI =8 kTA =8 kMA =0 Ök= CONSTANT, DIV, DEUROY, DUSTP, WORLD Are the prices of currency risk constant? H0: 8 kUS = 8 kHK =8 kSI =8 kTA =8 kMA =0 Ök= DIV, DEUROY, DUSTP, WORLD Is the price of the US dollar risk constant? H0: 8 kUS = 0; Ök=DIV, DEUROY, DUSTP, WORLD Is the price of the Hong Kong dollar risk constant? H0: 8 kHK = 0; Ök =DIV, DEUROY, DUSTP, WORLD Is the price of the Singapore dollar risk constant? H0: 8 kSI = 0; Ök =DIV, DEUROY, DUSTP, WORLD Is the price of the New Taiwan dollar risk constant? H0: 8 kTA = 0; Ök=DIV, DEUROY, DUSTP, WORLD

8US

8HK

8SI

8TA

8MA

8m

0.52 (6.44)** −287.98 (−0.37) 26.55 (2.84)** −16.20 (−3.24)** 0.0002 (0.0045)

5.4485 (8.35)** 278.88 (0.04) 190.86 (2.86)** −111.07 (−2.76)** −0.1580 (−0.45)

5.2431 (7.84)** 3198.08 (0.42) 208.48 (3.16)** −115.87 (−2.85) −0.1396 (−0.37)

0.2434 (1.65)* −1913.24 (−1.28) −11.67 (−0.82) −0.3264 (−0.03) −0.0041 (−0.05)

0.0461 (0.51) −585.51 (−0.28) −13.32 (−1.85)* −0.9775 (−0.20) 0.0474 (1.07)

−0.1267 (−1.86)* 178.86 (0.20) −4.6143 (−0.93) 4.7962 (1.08) 0.0054 (0.21)

0.0440 (1.24) −363.13 (−0.99) 7.3221 (0.62) 1.0769 (0.65) −0.0571 (−0.48)

Wald

d.f.

P-value

110.55

30

0

108.88

25

0

46.55

20

0.0006

10.55

4

0.0321

12.82

4

0.0121

3.87

4

0.4235

7.25

4

0.1230

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DEUROY

8

Table 8 Conditional six-factor ICAPMa,b,c,d,e

Is the price of the Malaysian Ringgit risk constant? H0: 8 kMA = 0; Ök =DIV, DEUROY, DUSTP, WORLD Is the price of market risk constant? H0: 8 km = 0; Ök = DIV, DEUROY, DUSTP, WORLD

Wald

d.f.

P-value

2.41

4

0.6615

3.29

4

0.5094

a 5

E[rit Vt−1] = % ll,t−1cov[rit,r6+l,t Vt−1]+lm,t−1cov[rit,rmt Vt−1]

and l0, t−1 =−Zt−180, ll, t−1 = Zt−18l, lm, t−1 = Zt−18m,

l= 1 …5.

l=1

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 (DUSTP), the change in 7-day Euroyen deposit rate (DEUROY), and a CONSTANT. The new time varying term, l0, t−1, appears as a way of ensuring that Eq. (19) holds. c US, the US dollar; HK, Hong Kong dollar; SI, Singapore dollar; TA, New Taiwan dollar; MA, Malaysian Ringgit. d t-statistics are given in parentheses. e Test of overidentifying restrictions: J = 28.9636. x 2 with 30 d.f. (critical value: x 2(0.05, 30) = 43.773). ** Statistically significant at the 10% level. * Statistically significant at the 5% level.

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Panel B: Hypothesis tests Null hypothesis

313

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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 foreign exchange 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 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. 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 diversifiable 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 outperforms 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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