time-varying market, interest rate, and exchange rate risk premia in the us commercial bank stock...

Journal of Multinational Financial Management

10 (2000) 397–420

Time-varying market, interest rate, andexchange rate risk premia in the US

commercial bank stock returns

Chu-Sheng TaiDepartment of Economics and Finance, College of Business Administration,

Texas A&M Uni6ersity – Kings6ille, Campus box 186, Kings6ille, TX 78363-8203, USA

Received 15 July 1999; accepted 18 February 2000

Abstract

This paper examines the role of market, interest rate, and exchange rate risks in pricing asample of the US Commercial Bank stocks by developing and estimating a multi-factormodel under both unconditional and conditional frameworks. Three different econometricmethodologies are used to conduct the estimations and testing. Estimations based onnonlinear seemingly unrelated regression (NLSUR) via GMM approach indicate that interestrate risk is the only priced factor in the unconditional three-factor model. However, based on‘pricing kernel’ approach by Dumas and Solnik [(1995). J. Finance 50, 445–479], strongevidence of exchange rate risk is found in both large bank and regional bank stocks in theconditional three-factor model with time-varying risk prices. Finally, estimations based onthe multivariate GARCH in mean (MGARCH-M) approach where both conditional firstand second moments of bank portfolio returns and risk factors are estimated simultaneouslyshow strong evidence of time-varying interest rate and exchange rate risk premia and weakevidence of time-varying world market risk premium for all three bank portfolios, namelythose of Money Center bank, Large bank, and Regional bank. © 2000 Elsevier Science B.V.All rights reserved.

JEL classification: C32; G12; G21

Keywords: Bank stock returns; Multivariate GARCH-M; Time-varying risk premium

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1042-444X/00/$ - see front matter © 2000 Elsevier Science B.V. All rights reserved.

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C.-S. Tai / J. of Multi. Fin. Manag. 10 (2000) 397–420398

1. Introduction

Merton (1973) argues that if market factor can not totally characterize theintertemporal changes in a risk-averse investor’s investment opportunity set, thenhe/she will demand a higher risk premium for exposure to extra-market factorswhich are correlated with the intertemporal changes in his/her investment opportu-nity set. Merton further argues that the level of market interest rates may providea single instrumental variable representing the shifts in the investment opportunityset. This suggests that researchers might want to incorporate the interest rate riskas one possible extra-market factor when testing intertemporal capital asset pricingmodels (ICAPM). For example, employing different estimation methodologies,Sweeney and Wagra (1986), Choi et al. (1992), Turtle et al. (1994), Song (1994), andElyasiani and Mansur (1998) all suggest that interest rate risk is one of the pricedfactors in the US stock market. However, Flannery et al. (1997) find that interestrate risk is priced for the overall US stock portfolios, but not for bank stockportfolios. This is particular puzzling given the fact that the returns and costs offinancial institutions are directed affected by the movements of market interestrates. Thus, it is interesting to re-examine whether the interest rate risk is thepotential determinant of bank stock returns.

The increasing volatility of exchange rates after the advent of the flexibleexchange rate system in the 1970s and the increasing globalization of the economy,including the banking sector, have created an additional source of uncertainty andrisk for firms operating in an international environment. Because fluctuations inexchange rates may result in translation gains or losses depending on banks’ netforeign positions, the exchange rate risk could be another potential determinant ofbank stock returns. Empirical studies concerning the pricing of exchange rate riskare inconclusive. For example, in a domestic context, Jorion (1991) finds thatexchange rate risk is not priced in the US stock market based on unconditional testsof multi-factor arbitrage pricing models. However, using same unconditional tests,Prasad and Rajan (1995) find that exchange rate risk is priced in the US, Japanese,and the UK stock markets. However, based on conditional tests, this inconclusiveresult seems to disappear. For example, both Choi et al. (1998) and Tai (2000) findthat exchange rate risk is priced in the Japanese stock market when testingconditional multi-factor asset pricing models. In an international context, theevidence of exchange rate risk pricing is overwhelming. For instance, Ferson andHarvey (1993, 1994), Korajczyk and Viallet (1989, 1993), Dumas and Solnik (1995)and Tai (1999a,b) all find that foreign exchange risk is one of the priced factors inglobal stock markets. Moreover, Tai (1998, 1999c) concludes that foreign exchangerisk is also priced in foreign exchange markets for both European and Asia-Pacificcountries. Thus, in the domestic context, it is interesting to examine whetherexchange rate risk is priced in the US bank stock returns.

Since most empirical studies concerning the pricing of bank stock returns mainlyfocus on the pricing of interest rate risk and very few published papers explicitlyinvestigate the joint interaction of exchange rates and interest rates on bank stockpricing except for Choi et al. (1992) and Wetmore and Brick (1994, 1998), the

C.-S. Tai / J. of Multi. Fin. Manag. 10 (2000) 397–420 399

purpose of this study is to examine the role of market, interest rate, and exchangerate risks in pricing the US Commercial Bank stock returns by estimating andtesting a three-factor model under both unconditional and conditional frameworks.This paper differs from previous studies in several ways. First, it conducts anin-depth investigation regarding the pricing of market, interest rate and exchangerate risks in the US commercial bank stock returns by utilizing three differenteconometric approaches: Nonlinear seemingly unrelated regression (NLSUR) viaHansen’s (1982) generalized method of moment (GMM), Dumas and Solnik’s(1995) ‘pricing kernel’ approach, and a multivariate GARCH in mean approach(MGARCH-M). In doing so, a more reliable conclusion regarding the pricing ofbank stock returns can be drawn, which has been inconclusive in previous papers.Another contribution of this paper is the utilization of the MGARCH-M approachwhich overcomes the problems of two-step procedure usually employed by re-searchers when estimating factor GARCH models (see Engle et al. (1990), Ng et al.(1992), and Flannery et al. (1997)). The MGARCH-M approach also complementsthe pricing kernel approach where the conditional second moments of asset returnsare left unspecified.1 Second, both unconditional and conditional version of multi-factor models are estimated and tested, given the inconclusive results found inprevious studies where both versions are tested separately. Finally, to obtain moreconvincing results, both individual bank stock returns and bank portfolio returnsare considered.

The empirical results can be summarized as follows. Estimations based onNLSUR via GMM indicate that interest rate risk is the only priced factor in theunconditional three-factor model. However, based on the pricing kernel approach,strong evidence of exchange rate risk is found in both large bank and regional bankstocks, and strong evidence of world market risk is found for the regional bankstocks in the conditional three-factor model with time-varying risk prices. However,no evidence of significant interest rate risk is detected, which is particularly puzzlingfor the bank stocks. Finally, estimations based on the MGARCH-M approachwhere both conditional first and second moments of bank portfolio returns and riskfactors are estimated simultaneously show strong evidence of time-varying interestrate and exchange rate risk premia and weak evidence of time-varying market riskpremium for all three bank portfolios, namely those of Money Center bank, Largebank, and Regional bank. Furthermore, among the three time-varying risk premia,the interest rate risk premium is the major one in describing the dynamics of the USbank stock returns. These empirical results provide new evidence on the role ofmarket, interest rate and exchange rate risks in pricing the US Commercial Bankstock returns and have important implications for banking, regulatory, and aca-demic communities.

The remainder of the paper is organized as follows. Section 2 contains literaturereview. Section 3 motivates the theoretical multi-factor asset pricing model. Section

1 Dumas and Solnik (1995) and Tai (1999a) both employ the ‘pricing kernel’ approach to testinternational CAPM. Since this approach does not require them to model the conditional covariances ofasset returns, some interesting questions can not be addressed in their studies.


4 presents the econometric methodologies used to test the multi-factor model.Section 5 discusses the data. Section 6 reports the empirical results. Concludingcomments are offered in Section 7.

2. Literature review

Previous studies on interest rate and exchange rate sensitivities in bank stockreturns include the works of Choi et al. (1992) and Wetmore and Brick (1994,1998). These authors apply a three-index model (market, interest rate, and exchangerate factors) to the bank stock returns under the assumption of constant varianceerror terms. Consequently, a simple regression technique such as OLS or GLS canbe employed to test whether the slope coefficients are significant different from zeroand that allows them to answer whether the bank stock returns are sensitive tothose risk factors. To test the stabalities of estimated slope coefficients, they dividethe full sample into several sub-samples based on pre-specified structure breaks.Then, they run separate regressions within the sub-samples and conduct the tests.What they find in their studies is that the coefficients of market risk, interest raterisk, and exchange rate risk are time dependent and differ by bank type. Thesestudies mainly focus on the sensitivities of beta risks and do not consider assetpricing tests.

Many studies have provided strong evidence against constancy of the conditionalvariance of asset returns and in favor of time-varying risk premia when ARCH-typemodel is employed. Thus, it is unwise if researchers continue to assume constantvolatility. Song (1994) is the first study to use the ARCH-type model in banking.He finds that ARCH-type modeling is the appropriate framework in analyzingbank stock returns based on Hansen’s (1982) test of overidentifying restrictions.According to his results, both market and interest rate risk measures (i.e., betas) ofbanks do change significantly over time and they are also priced in bank stocks.However, he does not consider the exchange rate risk. In addition, although GMMestimator is robust but, in general, it is not efficient. Flannery et al. (1997) isanother study applying ARCH-type modeling strategy in banking. Specifically theyapply a two-factor GARCH model originally developed by Engle et al. (1990) toprice both US bank and non-bank stock portfolios. They find that both market andinterest rate risks are time-varying and significantly priced in the non-bank stockportfolio, but only the market risk is priced in the bank stock portfolios. Onedrawback in their study is the two-step procedure used in estimating and testing atwo-factor GARCH model. As pointed out by Ng et al. (1992), the two-stepestimation procedure maintains consistency of the parameters of interest but itsacrifices the efficiency. Also, they do not consider exchange rate risk. Given thelack of study of exchange rate risk pricing and the previous inconclusive results ofinterest rate risk pricing in bank stock returns, it is the purpose of this paper tryingto provide more convincing evidence concerning the pricing of bank stock returnsby estimating and testing both unconditional and conditional three-factor assetpricing models utilizing three different econometric methodologies, namely NLSURvia GMM, pricing kernel, and MGARCH-M.


3. The theoretical motivation

We know that the first-order condition of any consumer-investor’s optimizationproblem can be written as:

E [MtRi,t � Vt−1]=1, Öi=1 ······N (1)

where Mt is known as a stochastic discount factor or an intertemporal marginalrate of substitution; Ri,t is the gross return of asset i at time t and Vt−1 is marketinformation known at time t−1.

Without specifying the form of Mt, Eq. (1) has little empirical content since it iseasy to find some random variable Mt for which the equation holds. Thus, it is thespecific form of Mt implied by an asset pricing model that gives Eq. (1) furtherempirical content (Ferson, 1995). Since this paper focuses on the pricing of market,interest rate and exchange rate risks on the commercial bank stock returns, itassumes that Mt and Ri,t have the following factor representations:

Mt=a+bWFW,t+bINTFINT,t+bFXFFX,t+ut (2)

ri,t=ai+biWFW,t+biINTFINT,t+biFXFFX,t+oi,t Öi=1 ······ N (3)

where ri,t=Ri,t−R0,t is the raw returns of asset i in excess of the risk-free rate, R0,t,at time t, E [utFk,t � Vt−1]=E [ut � Vt−1]=E [oi,tFk,t � Vt−1]=E [oi,t � Vt−1]=0Öi.k,Fk,t

(k=W, INT, FX) are three common risk factors (world market, interest rate, andexchange rate) which capture systematic risk affecting all assets ri,t including Mt, bik

(k=W, INT, FX) are the associated time-invariant factor loadings which measurethe sensitivities of the asset to the three common factors, while ut is an innovationand oi,t ’s are idiosyncratic terms which reflect unsystematic risk.2

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

E [MtR0,t−1 � Vt−1]=1 (4)

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

E [Mtri,t � Vt−1]=0 Öi=1 ······ N (5)

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

E [ri,t � Vt−1]=Co6(ri,t,−Mt � Vt−1)

E [Mt � Vt−1]Öi=1 ······ N (6)

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

E [ri,t � Vt−1]=%k

−bk

E [Mt � Vt−1]Co6(ri,t,Fk,t � Vt−1)

=%k

dk,t−1Co6(ri,t,Fk,t � Vt−1) Ök=W, INT, FX (7)

2 The empirical studies of Ferson and Harvey (1993) and Ferson and Korajczyk (1995) consistentlyshow that movements in factor exposures/betas account for only a small fraction of the predictablechange in expected returns, in both the domestic and the international context. Thus, to simplify themodel, a time-invariant factor beta seems to be reasonable.


where dk,t−1 is the time-varying price of factor risk.Eq. (7) is the conditional three-factor asset pricing model derived from the

intertemporal consumption-investment optimization problem which will be esti-mated and tested via pricing kernel approach in Section 6.

Alternatively the conditional three-factor asset pricing model can also be derivedbased on arbitrage arguments, such as Arbitrage Pricing Theory (APT) by Ross(1976). Substituting the factor model (Eq. (3)) into the right hand side of Eq. (6)and assuming that Co6(oi,t ; Mt+1)=0 implies

E [ri,t � Vt−1]=%k

bik

�Co6(Fk,t−Mt � Vt−1)E [Mt � Vt−1]

n=%

k

biklk,t−1 Ök

=W, INT, FX (8)

where lk,t−1 is the time-varying risk premium per unit of beta risk.Assuming Fk,t=E [Fk,t � Vt−1]+ok,t, where ok,t is the factor innovation with

E [ok,t � Vt−1]=0, and E [ok,toj,t � Vt−1] Ök" j, then Eq. (3) can be rewritten as:

ri,t=ai+%k

bikE [Fk,t � Vt−1]+%k

bikok,t+oi,t Öi=1 ······ N ; Ök=W, INT, FX

(9)

Taking conditional expectation on both sides of Eq. (9) and compare it with Eq.(8), then under the null hypothesis of ai=0 obtaining:

E [Fk,t � Vt−1]=lk,t−1 Ök=W, INT, FX (10)

Substituting Eq. (10) into Eq. (9), and assuming ai=0, Eq. (9) becomes

ri,t=%k

bik(lk,t−1+ok,t)+oi,t Öi=1 ······N ; Ök=W, INT, FX (11)

Eq. (11) is the conditional three-factor asset pricing model based on the arbitragearguments which will be estimated and tested using MGRACH-M methodology inSection 6.

To compare with previous studies in testing an unconditional multi-factor model,the unconditional version of Eq. (11) where expected factor risk premia, lk,t−1’s arerestricted to be time invariant will also be estimated and tested in Section 6.

4. Econometric methodologies

4.1. Pricing kernel approach

The ‘‘Pricing Kernel’’ approach, initiated by Hansen and Jagannathan (1991),was generalized by Dumas and Solnik (1995), and Tai (1999a) to test asset pricingmodels and will be used in this paper. The Mt for conditional three-factor assetpricing model in Eq. (7) has the following form:


Mt=�

1−d0,t−1−%k

dk,t−1Fk,tn,

(1+r0,t−1) Ök=W, INT, FX (12)

where d0,t−1= −�k

dl,t−1E [Fk,t � Vt−1] and R0,t−1=1+r0,t−1 is the risk-freereturn.

The new time varying term, d0,t−1, appears as a way of ensuring Eq. (4) holds.For econometric purposes, following Dumas and Solnik (1995) two auxiliaryassumptions are needed:

Assumption 1: the information set Vt−1 is generated by a vector of instrumentalvariables Zt−1.Zt−1 is a 1× l vector of predetermined instrumental variables that reflect every-thing that is known to investors at time t−1.

Assumption 2:

d0,t−1= −Zt−180

dk,t−1=Zt−18k, Ök=W, INT, FX

Here the 80 and 8k ’s are the time-invariant row vectors of weights for theinstruments for each of the risk factors.

Based on Eq. (4), defining the innovation ut :

Mt(1+r0,t−1)=1−ut (13)

and given assumption 2 and the definition of Mt in Eq. (13), ut can be written as:

ut=1−Mt(1+r0,t−1)= −Zt−180+%k

Zt−18kF,t Ök=W, INT, FX (14)

with ut satisfying:

E [ut � Vt−1]=0 (15)

Next, based on Eq. (5) defining the innovation hit :

E [Mtrit � Vt−1]=E� 1−ut

1+ro,t−1

rit � Vt−1n

=0 [ hit=rit−ritut Öi

=1 ······ N (16)

with hit satisfying:

E [hit � Vt−1]=0 (17)

One can form the 1+N vector of residuals et= (ut, ht). Combining Eq. (15) andEq. (17) and using Assumption 1 yields:

E [et � Zt−1]=0 (18)

It implies the following unconditional condition:

E [mt(b0)]=E [etZt−1]=0 Öt=1,2 ··· T (19)


The sample version of this population moment restriction is the momentcondition:

Ze=0 (20)

where Z is a T× l matrix and e is a T× (1+N) matrix, with T being the numberof observations over time. We test restrictions implied by the theory using Hansen’stest of the orthogonality conditions used in estimation (Hansen, 1982). He showsthat the minimizer quadratic criterion function is asymptotically (central) chi-square distributed with (N−3)× l degrees of freedom under the null hypothesisthat the model is correctly specified.3

4.2. Multi6ariate GARCH in mean (MGARCH-M) approach

Theoretical work by Merton (1973) relate the expected risk premium of factor k,lk,t−1, in Eq. (11) to its volatility and a constant proportionality factor. Insupporting these theoretical results, Merton (1980) tested a single-beta marketmodel and found that the expected risk premium on the stock market is positivelycorrelated with the predictable volatility of stock returns. As a result, the followingrelationship is postulated for lk,t−1 Ök=W, INT, FX :

lW,t−1=E(FW,t � Vt−1)=w0+w1hw,t (21)

lINT,t−1=E(FINT,t � Vt−1)= l0+ l1hINT,t (22)

lFX,t−1=E(FFX,t � Vt−1)=c0+c1hFX,t (23)

where hk,t (Ök=W, INT, FX) is factor k ’s conditional volatility. To complete theconditional three-factor model with time-varying risk premia, Eq. (11) can berewritten as:

ri,t= (w0+w1hw,t+oW,t)biW+ (l0+ l1hINT,t+oINT,t)biINT

+ (c0+c1hFX,t+oFX,t)biFX+oi,t Öi=1 ······ N (24)

Eq. (24) is the expanded three-factor asset pricing system, which can be used totest whether the predictable volatilities of the market-wide risk factors are signifi-cant sources of risk. This model allows for a test of the null hypothesis of theexistence of one or more significant risk premia, and for a test of the hypothesisthat the risk premia are jointly time-varying. Similarly the null hypothesis of theexistence of one or more significant factor sensitivities can also be tested based onEq. (24).

To estimate and test dynamic factor models similar to Eq. (24), Engle et al.(1990), Ng et al. (1992), and Flannery et al. (1997) utilize a factor (G)ARCH modelbecause it provides a plausible and parsimonious parameterization of time-varyingvariance-covariance structure of asset returns. However, they employ a two-step

3 There are l parameters 80, and l×3 parameters 8k ’s so the total number of parameters is 4× l.From Eq. (20) the number of moment conditions is l× (1+N). Thus, we have (N−3)× l degrees offreedom.


procedure to estimate the model.4 In the first step, the time-varying factor riskpremia are estimated via an univariate (G)ARCH-M model; in the second step, theestimated premia and conditional variance are then taken as the data series in theestimation of the conditional means and variances of each individual asset returnseries (Engle et al., 1990 and Ng et al., 1992) or of the conditional means butconstant variances of a set of portfolio returns (Flannery et al., 1997). The obviousadvantage of this procedure is that an arbitrarily large system can be estimatedwithout much difficulty. The disadvantage is that cross-asset correlations andparameter restrictions are ignored so that efficiency is sacrificed.

Given the computational difficulties in estimating a larger system of asset returns,parsimony becomes an important factor in choosing different parameterizations. Apopular parameterization of the dynamics of the conditional second moments isBEKK, proposed by Engle and Kroner (1995). The major feature of this parame-terization is that it guarantees that the covariance matrices in the system arepositive definite. However, it still requires researchers to estimate a larger numberof parameters. Instead of using BEKK specification, this paper employs a parsimo-nious GARCH process proposed by Ding and Engle (1994) to parameterize theconditional variance-covariance structure of asset returns. This specification allowsone to reduce the number of parameters to be estimated significantly if theconditional second moments are assumed to follow a diagonal process and thesystem is covariance stationary.5 Consequently, the process for the conditionalvariance-covariance matrix of asset returns can be written as:

Ht=H0*(ii−aa %−bb %)+aa %*ot−1o %t−1+bb %*Ht−1 (25)

where Ht is (N+3)× (N+3) time-varying variance-covariance matrix of assetreturns and risk factors. N+3 is the number of equations where the first Nequations are those for the bank portfolios, the (N+1)th equation is for theinterest rate risk factor; the (N+2)th equation is for the exchange rate risk factor,and the (N+3)th equation is for the world market risk factor. The elements on thediagonal of Ht are given by Eq. (24) for the individual bank portfolios, and by Eq.(21), Eq. (22) and Eq. (23) for three risk factors. H0 is the unconditional variance-covariance matrix of innovations, ot ·i is a (N+3)×1 vector of ones, a and b are(N+3)×1 vectors of unknown parameters, and * denotes element by elementmatrix product. The H0 is unobservable and has to be estimated. As suggested byDe Santis and Gerard (1997, 1998), it can be consistently estimated using iterativeprocedure. In particular, H0 is set equal to the sample covariance matrix of theexcess return in the first iteration, and then it is updated using the covariancematrix of the estimated residual at the end of each iteration. Under the assumptionof conditional normality, the log-likelihood to be maximized can be written as:

4 Koutmos (1997) applies a multivariate factor GARCH model to test if market portfolio is a dynamicfactor, but he only considers market risk.

5 In a diagonal system with N assets, the number of unknown parameters in the conditional varianceequation is reduced from 2N2+N(N+1)/2 under BEKK specification to 2N under the Ding-Englespecification.


ln L(u)= −TN2

ln 2p−12

%T

t=1

ln �Ht(u)�−12

% ot(u)%Ht(u)−1ot(u) (26)

where u is the vector of unknown parameters in the model and T is the numberof observations over time. Since the normality assumption is often violated infinancial time series, a quasi-maximum likelihood estimation (QML) proposed byBollerslev and Wooldridge (1992) which allows inference in the presence of depar-tures from conditional normality is used. Under standard regularity conditions, theQML estimator is consistent and asymptotically normal and statistical inferencescan be carried out by computing robust Wald statistics. The QML estimates can beobtained by maximizing Eq. (26), and calculating a robust estimate of the covari-ance of the parameter estimates using the matrix of second derivatives and theaverage of the period-by-period outer products of the gradient. Optimization isperformed using the Broyden, Fletcher, Goldfarb and Shanno (BFGS) algorithm,and the robust variance-covariance matrix of the estimated parameters is computedfrom the last BFGS iteration.

Given the computational complexity of the multivariate approach, its applicationis restricted to three bank portfolios, which are simultaneously modeled with thethree risk factors. Thus, the dimension of ot is 6 and that of the variance-covariancematrix is 6×6. Even with this low dimensional system the number of parametersto be estimated is 27.

5. The data and summary statistics

The sample consists of 31 commercial bank stocks traded on the New York andAmerican stock exchanges. The excess return on a bank stock is the log firstdifference of total return index in excess of 7-day Eurodollar deposit rate. Thesample is disaggerated by size into three equally weighted bank portfolios-themoney center bank portfolio (seven banks), the large bank portfolio (11 banks) andthe regional bank portfolio (13 banks).

Three economic risk variables are a world market risk (FW) measured as the USdollar return of the Morgan Stanley Capital International (MSCI) world equitymarket in excess of 7-day Eurodollar deposit rate, an interest rate risk (FINT)measured as the log first difference in the 10-year US Treasury Composite yield,and an exchange rate risk (FFX) measured as the log first difference in thetrade-weighted US dollar price of the currencies of 10 industrialized countries. Apositive change (FFX\0) indicates a depreciation of the dollar.

The instruments used in the GMM estimations include the world excess equityreturn (FW,t−1), a dividend yield on S&P 500 index in excess of the 7-dayEurodollar deposit rate (SPDIV), a change in the US term premium, measured bythe yield on the 10-year US treasury note in excess of the 7-day Eurodollar depositrate (DUSTP), a change in the US default premium, measured by the differencebetween Moody’s Baa-rated and Aaa-rated US corporate bond yields (DUSDP),and a constant.


Observations are sampled at weekly intervals. The weekly data ranges fromNovember 6, 1987 to August 28, 1998, which is a 565-data-point series. However,this paper works with rates of return and use the first difference of informationvariables, and finally all the instruments are used with a one-week lag, relative tothe excess return series; that leaves 562 observations expanding from November 27,1987 to August 28, 1998. Table 1 describes the variables and their symbols used inthis paper. All the data are extracted from DATASTREAM.

Summary statistics for bank stock returns, risk factors, and instruments used inthis paper are presented in Table 2. The mean excess returns for three bank stockportfolios are 0.2551% for Money Center bank, 0.2372% for Large bank, and0.2452% for Regional bank. These mean excess returns are all greater than0.1065%, the mean excess return for MSCI world equity index. However, theirstandard deviations are also greater than that of MSCI world equity index,indicating that investors are compensated for a higher risk premium when holdingbank stocks. The positive change in the exchange rate reflects the depreciation ofthe US dollar against the currencies of ten industrialized countries. The coefficientsof skewness and excess kurtosis reveal nonnormality in the data. The last twocolumns in Table 2 report the Ljung-Box portmanteau test statistics for indepen-dence in the return and squared return series up to 24 lags, denoted by Q(24) andQ2(24) respectively. The Ljung-Box portmanteau test statistics for independence inthe standardized residuals are calculated using autocorrelations up to 24 lags, andthey follow a x2 distribution with 24 degrees of freedom.6 The hypothesis of linearindependence is rejected at 5% level for Money Center bank and 1% level forRegional bank. Independence of the squared return series is rejected at 1% level forall three bank portfolio returns, MSCI world equity returns, and the exchange ratechanges. Clearly, the nonlinear dependencies are much prevalent than the lineardependencies found in the data and it is consistent with the volatility clusteringobserved in most financial data: Large (small) changes in prices tend to be followedby large (small) changes of either sign. The GARCH model used in this study iswell known to capture this property.

6. Empirical results

6.1. Unconditional test of three-factor model: NLSUR 6ia GMM

Following Ferson and Harvey (1994), this paper first estimates and tests theunconditional three-factor asset pricing model (Eq. (11)) where the expected factorrisk premia are assumed to be time-invariant as a restricted nonlinear seeminglyunrelated regression model (NLSUR). The NLSUR via Hansen’s (1982) generalizedmethod of moments (GMM), which is valid under weak statistical assumptions, isimplemented. To apply the GMM technique, the data used in the estimation must

6 The formula for the Ljung-Box statistic is LB(k)=T(T+2) �kj=1

r j2/(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)


Table 1Variable definitions and symbols

Name Symbols

Money centerBank America New BAC

CMBChase ManhattanCHM. Banking (LN) CHNYCitigroup CCIFirst Chicago NBD FCNMorgan (JP) & CO.PF.A MORGBank of New York BK

Larger bankWells Fargo WFCFirst Union FTU

FLTFleet Finl.GPMellon Bank MEL

NCBMNat.City Bancorp.NCCNat.CityNOBNorwest

PNC Bank PNCRNBRepublic NY.WBWachovia Corp.

Amsouth Banc. ASO

Regional bankComerica CMA

CFCrestar Finl.First Security FSCOFirstar FSR

KEYKeycorpMerc.Bancorp MTLNthn.Trust NTRSRiggs Natl RIGSSignet Banking SBKStar Banc STBUS Bancorp Del USBValley Nat.Bk. VLYUnion Planters UPC

Information 6ariablesEuro-currency (LDN) US$ 7 day ECUSD7DS&P 500 composite-dividend yield S&PDY

FRTCM10US treasury constant maturities 10 yearUS corporate bond moody’s S’ND AAA FRCBAAA

FRCBBAAUS corporate bond moody’s S’ND BAA

Risk factorsMSWRLDMSCI world US$

US treasury constant maturities 10 year FRTCM10US$TRDWUS $ Index (FED)-trade weighted


Table 2Summary statistics of bank stock returns, risk factors and instrumentsa

Mean (%) S.D.(%) Skewness Kurtosis Q(24) Q2(24)

Indi6idual banksMoney center

−0.1377 2.6666**BAC 28.25400.2961 95.7098**4.2006CMB 4.6039 −0.1748 1.9237** 49.5169** 281.8171**0.2347

3.87180.1329 17.1957** 365.9468** 51.3717** 0.6023CHNY0.1498 3.2391** 25.19674.4007 14.0356CCI 0.3874

3.42080.2565 0.07445 0.6309** 39.0412* 107.7093**FCNMORG −1.2863**0.0555 10.9677** 20.4297 13.91331.5067

0.02055 1.1759** 37.2687* 142.5659**4.1628WFC 0.3206

Large−0.1884 2.1950**BK 32.62330.3053 126.8239**4.05670.1976 1.1985** 30.98913.6531 93.3796**0.2745FTU

3.98440.1719 0.8171** 6.0529** 33.8288 105.9370**FLT−0.0135 0.8889** 26.3407MEL 12.65560.2654 3.6839−0.4992** 26.0323** 47.1987**4.4375 128.7636**0.2022NCBM

2.96740.2334 −0.1610 0.9782** 22.4665 107.1514**NCCNOB 0.03590.3616 0.6903** 35.5935 76.8951**3.4668

−0.01301 1.8859** 45.6492**3.6239 230.4390**PNC 0.13402.87500.1368 −0.5059** 4.0154** 21.0266 43.9046**RNB

WB −0.09610.2614 0.8838** 22.0680 54.9341**2.91990.5742** 1.74571** 25.4122 23.61112.8732ASO 0.2627

Regional−0.0038 1.8839**CMA 25.95420.2998 22.82033.02930.2584* 2.4376** 19.48343.9932 264.9610**CF 0.2469

3.81880.2806 −0.2368* 1.8083** 56.9787** 63.9084**FSCO1.5854** 14.8356** 34.5842FSR 5.63080.3341 3.32724.8841** 35.9988** 21.01473.2253 11.51720.2000KEY

3.48660.2626 −0.0276 1.4890** 13.3112 16.0097MTL1.3848** 11.3948** 35.6350NTRS 68.2217**0.3322 3.1791−0.1265 1.6827** 65.7222**5.7595 237.0455**RIGS −0.0468

5.52200.2323 −2.3421** 39.8593** 40.1195** 0.7907SBK0.6384** 5.5347** 13.1720STB 55.6055**0.3611 3.5700−0.0826 2.2598** 18.85913.5886 97.2846**0.2687USB

3.63150.2046 0.4646** 4.5719** 26.2556 25.5229VLYUPC 3.8087 0.3365** 1.6575** 25.5378 41.6411*0.2114

Bank portfolios−0.2883**Money center 1.1116**0.2551 41.3042* 166.5553**2.9465

0.2372 2.3308 −0.0938 0.7425** 30.9497 108.1141**Large2.28280.2452 −0.1537 1.5120** 42.7845** 139.8178**Regional

Risk factors0.5084**FW 11.2245**0.1065 15.5908 259.7811**1.8389

FINT 0.1480−0.00012 0.20301 31.5452 26.61120.002480.1401 0.8599** 21.8488 54.8806**1.17250.0175FFX

Instruments0.2343* −0.6946** 11938** 10325**SPDIV −0.0551 0.0305−1.0056** 63.6573** 115.3779**0.00747 135.3716**−0.00008DUSTP


Table 2 (Continued)

Q2(24)Skewness Kurtosis Q(24)Mean (%) S.D.(%)

−0.000018 0.000667 −0.2520** 44.1744* 182.2403**2.9766**DUSDP

a ‘Money Center’ is the equally weighted average of excess returns on 7 individual money centerbanks. ‘Large’ is the equally weighted average of excess returns on 11 individual large banks. ‘Regional’is the equally weighted average of excess returns on 13 individual regional banks. FW is the excess returnon the Morgan Stanley world stock total return index in US $. FINT is the log first difference ofFRTCM10. FFX is the log first difference of US$TRDW. SPDIV is the first difference of S&P500dividend yield in excess of ECUSD7D. DUSTP is the first difference of FRTCM10 in excess ofECUSD7D. DUSDP is the first difference of FRCBBAA in excess of FRCBAAA. Q(24) and Q2(24) arethe Ljung-Box test statistics of order 24 for serial correlation in the standardized residuals andstandardized residuals squared.

* Denotes statistically significant at the 5% level.** Denotes statistically significant at the 1% level.

be stationary. As a result, unit root tests are conducted to check if the variablesused in the estimation are stationary. The test results not shown here indicate thatthe null hypothesis of unit root nonstationarity is strongly rejected. The GMMestimator is robust in the sense that one can avoid the usual assumption ofhomoskedasticity and normality, which are unlikely to hold in these data.7 Theadvantage of this approach over the traditional Fama-McBeth approach is that theparameters (l, b) can be estimated jointly and it explicitly allows for contempora-neous correlations across the N assets, and thus is more efficient. A vector of onesand the contemporaneous values of the factor risk s, Fk,t, are used as theinstruments in the GMM. The orthogonality conditions therefore imply E(oitFk,t)=0 and E(oit)=0, for all i=1, ······ ,N and k=1, ······ ,K. The estimation results arepresented in Table 3. The unconditional three-factor model is not rejected at 5%level based on the test of overidentifying restrictions (x28

2 =11.1657 with a P-valueof 0.99)8. The estimates of factor loadings (b ’s) indicates that almost all banks (27out of 31) have significant negative factor loadings on interest rate risk at 1% level,14 banks are sensitive to exchange rate risk, and 20 banks are sensitive to the worldmarket risk. The negative factor loadings on interest rate risk indicate that banksare hurt by unexpected increases in the interest rates. As far as the factor riskpremia are concerned, the interest rate risk premium is the only significant factorpremium at 5% level with a point estimate of −0.0006%. This negative interest raterisk premium is consistent with previous work of Sweeney and Wagra (1986) andChoi et al. (1992) who use similar approach.

7 An alternative approach used by previous researchers (see, e.g., Gibbons, 1982; McElory andBurmeister, 1988; Jorion, 1991; Prasad and Rajan, 1995; Choi and Rajan, 1997; and Choi et al., 1998)is the iterated non-linear seemingly unrelated regression method, which is asymptotically equivalent tomaximum-likelihood estimation under the assumption of normality.

8 The total number of moments is 31×4=124 and the total number of parameters to be estimatedis 31×3+3=96; therefore we have 28 degree of freedoms for testing overidentifying restrictions.


Table 3Unconditional three-factor asset pricing model: NLSUR via GMM estimationa

bi,Wbi,INT bI,FXRit

−355.2634 (−4.8714)** 0.4171 (2.8459)** 0.3219 (3.4618)**BAC0.3518 (2.1863)* 0.2257(−5.1180)** (2.2131)*CMB −408.70900.2947CHNY (2.1192)*−59.6767 −0.0020 (−0.0233)(−0.8671)0.1044 (0.6772) 0.2182(−6.1226)** (2.2324)*CCI −469.1484

(−6.2034)**−366.6609 0.2587 (2.1773)* 0.2274 (3.0163)**FCN(−5.5951)**−145.5067 0.0826 (1.5770) 0.1032 (3.1078)**MORG

0.3258 (2.2371)* 0.3475(−5.0166)** (3.7614)**WFC −363.2796−392.0966 (−5.5666)** 0.1305 (0.9198) 0.2478 (2.7552)**BK

0.2225 (1.7362) 0.1764(−5.1118)** (2.1723)*−324.9226FTU(−4.7744)**−329.8369 0.2923 (2.1000)* 0.2565 (2.9069)**FLT(−5.7802)**−369.6595 0.3316 (2.5809)** 0.1069 (1.3117)MEL

0.0526 (0.3305) 0.1926(−0.3427) (1.9128)NCBM −26.9364(−5.4521)**−280.3459 0.2181 (2.1119)* 0.2778 (4.2394)**NCC

0.1140 (0.9584) 0.2660(−7.0917)** (3.5202)**−421.0542NOB0.2746 (2.1681)* 0.0421PNC (0.5235)−363.9035 (−5.7714)**0.0954 (0.9517) 0.1874(−5.4671)** (2.9483)**RNB −272.1622

WB (−6.9453)** 0.2434 (2.4114)* 0.1136 (1.7723)−349.70960.1204 (1.1895) 0.0661(−5.1460)** (1.0294)ASO −258.4112

(−7.0990)**−367.5825 0.2752 (2.6534)** 0.2420 (3.6723)**CMA(−4.7606)**−330.9412 0.1855 (1.3220) 0.2136 (2.4033)*CF

0.1604 (1.1729) 0.0499(−3.0319)** (0.5763)FSCO −204.9110(−5.1625)**−300.0107 0.1967 (1.6786) 0.1525 (2.0539)*FSR

0.3588 (3.2112)** 0.1685(−5.7198)** (2.3753)*−318.4414KEY0.2195 (1.7654) 0.1230MTL (1.5621)−210.9960 (−3.4297)**0.1989 (1.7876) 0.2227(−5.2820)** (3.1571)**NTRS −291.84160.3830 (1.8568) 0.1025 (0.7853)RIGS −107.4418 (−1.0537)0.3359 (1.7327) 0.2709(−4.7713)** (2.2056)*−458.4274SBK

(−2.9444)**−185.6498 0.0957 (0.7500) 0.1651 (2.0438)*STB(−3.8584)**−241.6937 0.2475 (1.9601)* 0.2691 (3.3624)**USB

0.1800 (1.3786) 0.0000(−1.5709) (0.0004)VLY −101.2892UPC 0.3995−239.7226 (2.9676)** 0.1230 (1.4411)(−3.5856)**

−0.000024 (−0.0107) 0.0024(−2.1346)* (0.8381)−0.000006Test of overidentifying restrictions (J-test): x25

2 =11.1657 [P-value=0.9980].

a rit=bi,INT(oINT,t+lINT)+bi,FX(oFX,t+lFX)+bi,W(oW,T+lW)+oit Öi where rit represents the excessbank stock returns, ok,t ’s are the de-meaned values of risk factors, l ’s are the risk premia associated withthe risk factors, and b ’s are the banks’ sensitivities to the risk factors. The instruments in the GMMestimations are a constant and the risk measures. The x2 test is the minimized values of the GMMcriterion function for the system. Robust t-statistics are given in parentheses.

* Indicate statistically significant at the 5% level.** Indicate statistically significant at the 1% level.

6.2. Conditional tests of three-factor model: pricing kernel approach

Since only the interest rate risk premium is detected in unconditional three-factormodel and previous studies have found strong evidence of time-varying risk premia,it is interesting to see if any evidence of time-varying risk premia with respect to the


assumed three risk factors can be found, in particular, the world market andexchange rate risks. The conditional three-factor model (Eq. (7)) for each of thethree bank types is estimated based on the pricing kernel approach. The empiricalresults are presented in Table 4.9

As can be seen from the table, the model applied to all three different bank typescan not be rejected at any conventional levels based on the J-test of overidentifyingrestrictions. Consequently, the hypothesis testing concerning the pricing of riskfactors can be conducted. Specifically, a Wald statistic is computed to test the nullhypothesis that all 8 ’s coefficients of instrumental variables are zero with respect toa particular risk factor. First, none of the Wald statistics is significant for MoneyCenter bank, indicating that the selected instruments are not useful in predictingrisk premia for Money Center bank. However, in contrary to the evidence found

Table 4Conditional three-factor asset pricing model: GMM estimationa

d.f.Null hypothesis Wald

Money center Large Regional

49.8133 [0.0002]1. H0: 80j=8W

j =8 INTj =8FX

j =0; 47.4026 [0.0005]22.4233 [0.3180]20Öj=CONSTANT, SPDIV,DUSTP, DUSDP, FW

19.6381 [0.1863]152. H0: 8Wj =8 INT

j =8FXj =0; 41.0977 [0.0003] 44.2926 [0.0001]

Öj=SPDIV, DUSTP, DUSDP,FW

2.8174 [0.7281]3. H0: 8Wj =0; Öj=CONSTANT, 12.4625 [0.0290]5 8.4402 [0.1336]

SPDIV, DUSTP, DUSDP, FW

4 9.8988 [0.0422]5.9154 [0.2056]0.9424 [0.8428]4. H0: 8Wj =0; Öj=SPDIV,

DUSTP, DUSDP, FW

5. H0: 8 INTj =0; Öj=CONSTANT, 5 3.7484 [0.9184] 5.8297 [0.3231] 11.6315 [0.0402]


3.2053 [0.5862] 6.1020 [0.1917]46. H0: 8 INTj =0; Öj=SPDIV, 2.2828 [0.6839]

DUSTP, DUSDP, FW

6.3888 [0.5241] 22.3676 [0.0004]7. H0: 8FXj =0; Öj=CONSTANT, 5 21.4304 [0.0007]


4 2.5891 [0.2702] 20.8759 [0.0003] 21.4631 [0.0003]8. H0: 8FXj =0; Öj=SPDIV,

DUSTP, DUSDP, FW

x452 =24.9728x25

2 =17.9905 x552 =37.6710Test of Overidentifying Restrictions

[0.9642].(J-test) [0.9933][0.6287]

a E [rit � Zt−1]�k dk,t−1Co6(ri,t ; Fk,t � Zt−1) Ök=W, INT, FXd0,t−1=−Zt−180

dk,t−1=Zt−18k, Zt−1={CONSTAMT,SPDIV,DUSTP,DUSDP,FW}t−1

P-values are in the brackets.

9 Since the pricing of three risk factors is the main focus in this paper, only the hypothesis testingresults are reported and parameter estimates based on the pricing kernel approach are not shown, butare available upon on request.


with respect to Money Center bank, significant pricing of time-varying risk factoris detected for Large bank. That is, the joint null hypothesis of constant risk pricesis strongly rejected at 1% level based on the Wald test. In particular, the time-vary-ing risk price basically comes from the exchange rate risk because the nullhypothesis of constant price of exchange rate risk is rejected at 1% level with aP-value of 0.0003. Finally, for Regional bank, the joint null hypothesis of constantrisk prices is strongly rejected at 1% level with a P-value of 0.0001 based on theWald test. The time-varying risk prices come from two sources: exchange rate riskand world market risk because the null hypotheses of constant price of exchangerate risk and world market risk is rejected at 1% and 5% level, respectively. Inadditional, significant price of interest rate risk is detected at 5% level although itis not time varying.

Overall the empirical evidence based on the pricing kernel approach indicatesthat exchange rate risk is an important risk factor in describing the dynamics of riskpremia found in the US bank stock returns, especially for the Large and Regionalbanks. This evidence of time-varying price of exchange risk is consistent withprevious work of Choi et al. (1998) in a domestic context, and of Ferson andHarvey (1993), Dumas and Solnik (1995) and Tai (1999a) in an internationalcontext. It may explain why previous researchers are not able to detect significantpricing of exchange rate risk when restricting themselves in an unconditionalframework.10

Although the pricing kernel estimation is parsimonious in the sense that re-searchers do not need to specify the dynamics of the conditional second moments,this parsimony also comes with cost. That is its inability to answer questions like‘‘What does the fitted risk premium look like?’’ and ‘‘What do the fitted conditionalcovariances look like?’’ To answer these interesting questions, the conditionalsecond moments in the asset pricing models should be explicitly modeled.11 Inaddition, one would expect the interest rate risk to receive a non-zero price for bankstock returns. Therefore, in the next section a parsimonious parameterization ofmultivariate GARCH in mean model is employed to explicitly deal with theseproblems.

6.3. Conditional tests of three-factor model: MGARCH-M

Given the computational complexity of estimating a multivariate system underthe GARCH framework, three equally weighted bank stock portfolios are studied,namely those of Money Center bank, Large Bank, and Regional bank. The

10 For example, Jorion (1991) tests unconditional multi-factor asset pricing models and fail to findsignificant evidence of exchange risk pricing in the US stock market. Hamao (1988) also can not find anyevidence of exchange risk pricing in the Japanese stock market.

11 Turtle et al. (1994), De Santis and Gerard (1997, 1998), Tai (1998, 1999b), and among others aregood examples on how to apply a multivariate GARCH process to model the dynamics of the secondmoments of asset returns in testing asset pricing models.


estimation results of conditional three-factor asset pricing model (Eq. (25)) usingMGARCH-M approach are presented in Table 5. Panel A reports QML estimatesof the parameters for the model. Regarding the factor betas, significant interest ratebetas are found for all three bank portfolios at 1% significance level. Consistentwith conventional wisdom, bank stock returns are very sensitive to the changes ininterest rates, and thus expose to interest rate risk. Exchange rate beta is significantfor Money Center bank at 5% level, and for Large bank at 10% level. Worldmarket beta is significant for Large bank at 5% level. Finding significant factorbetas does not necessarily imply that market participants care about those factorrisks because they may be diversifiable, and thus are not priced. To examinewhether the chosen three risk factors are priced by the market participants, we testwhether the estimated pricing parameters are statistically significant. As can be seenin Panel A, strong evidence of GARCH in mean effects are found for the dynamicsof interest rate and exchange rate risk factors since the parameters (l1, c1)are allsignificant at 1% level, and thus it has significant impact on the dynamics of riskpremia for the bank portfolio returns. However, the GARCH in mean effect ismarginally significant at 10% level for the MSCI world equity index, implying thatafter accounting for the time-varying interest rate and exchange rate risk premia inasset returns, the world market risk does not play a major role in explaining thedynamics of bank portfolio returns. To further examine the factor risk pricing, weconduct several hypothesis testing in Panel C. For example, the null hypotheses ofconstant risk premia with respect to interest rate and exchange rate risk factors arestrongly rejected at 1% level, and it is rejected at 10% level for the world marketrisk. The significant evidence of time-varying interest rate, and exchange rate riskpremia found in the US bank data points out the advantage of MGARCH-Mapproach over the previous two approaches. This advantage comes directly fromthe explicit modeling of conditional volatilities in both asset returns and riskfactors, which is ignored in the other two approaches.

Next, consider the estimated parameters for the conditional variance processes.With the exception of parameter a for MSCI world equity index, all the elementsin the vectors a and b are statistically significant at 1% level, implying that strongGARCH effect is present for all the return series. In addition, the estimates satisfythe stationarity conditions for all the variance and covariance processes.12

Panel B contains some diagnostic statistics on the standardized residuals (oth t−1/2)

and the standardized residuals squared (o t2ht

−1). With the exception of MoneyCenter bank, the null hypothesis of linear independency can not be rejected for allthe series, as evidenced by the insignificant Ljung Box statistics of order 24 for thestandardized residuals (Q(24)). Similarly, the null hypothesis of nonlinear indepen-dency can not be rejected based on the insignificant Ljung Box statistics of order 24for the standardized residuals squared (Q2(24)) except for the MSCI world equityindex. Overall, the conditional factor asset pricing model with MGARCH-Mparameterization effectively eliminates most of the linear and nonlinear dependen-

12 For the process in Ht to be covariance stationary, the condition aiaj+bibjB1 Öi,j has to be satisfied.(Bollerslev, 1986; De Santis and Gerard, 1997, 1998)

C.-S

.T

ai/J.

ofM

ulti.F

in.M

anag.10

(2000)397

–420

415

Table 5Quasi-maximum likelihood estimation of conditional three-factor asset pricing model: multivariate GARCH(1,1)-Ma

Panel A: parameter estimates

w0 w1c0l0 c1l10.01770.0009 (0.0008)−0.0002 (0.0005)−3E-06 (1.1E-06)** −0.40280.9691

(0.0879)**(0.2619)** (0.0100)*

FWFINT FFXRegionalLargeMoney center

−667.4991 −464.5774bINT,t −570.1476(88.8139)** (67.5516)** (62.2521)**

0.1012 (0.0532)FFX,t 0.1658 (0.0672)* 0.0832 (0.0669)0.0510 (0.0226)*bW,t 0.0445 (0.0340)0.0394 (0.0431)

0.20370.1842 0.1905 (0.0204)** 0.39660.1724 (0.0168)** −0.0001 (0.0247)A(0.0219)** (0.0490)**(0.0243)**

0.62690.9711 0.8694 (0.0046)**0.9662 (0.0063)**B 0.9736 (0.0056)** 0.9290(0.0167)**(0.0057)** (0.0667)**

Panel B: residual diagnostics

11.2759**1.4823** 1.2474** 1.8012**Kurtosis 0.1226 0.33832.8664 2.7552 3012.58**48.0432**B–J 94.3194**69.7296**

Q(24) 15.712443.3158** 26.8584 33.5961 32.1376 19.1102260.7326**26.8329 18.9065 22.977812.1728 22.0359Q2(24)

Likelihood function: 16040.46

Panel C: hypothesis testing concerning risk premia

WaldNull hypothesis d.f. P-value

0.00006262.34561. H0:w0=w1= l0= l1=c0=c1=0

212.0988 3 0.00002. H0: w1= l1=c1=03. H0: w0=w1=0 3.8815 2 0.1436

C.-S

.T

ai/J.

ofM

ulti.F

in.M

anag.10

(2000)397

–420

416

Table 5 (Continued)

Panel C: hypothesis testing concerning risk premia

Wald d.f. P-valueNull hypothesis

0.077313.12144. H0: w1=05. H0: l0= l1=0 15.0429 2 0.00056. H0: l1=0 0.000213.6927 1

21.0820 2 0.00007. H0: c0=c1=018. H0: c1=0 0.000020.9928

Panel D: predicted weekly time-varying risk premium and conditional volatility

Money center Large Regional

0.1997 0.1733 0.1415Avg. risk premium (%)0.0035 0.0045 0.0040Avg. world Mkt risk premium (%)

−0.0025Avg. FX risk premium (%) −0.0030−0.00490.2012 0.1718 0.1400Avg. interest rate risk premium (%)

Avg. conditional STD. (%) 2.2588 2.21702.8527

a ri,t= (w0+w1hw,t+oW,t)biW+(l0+l1hINT,t+oINT,t)biINT+(c0+c1hFX,t+oFX,t)biFX+oi,t

i=Money Center, Large, RegionalFW,t=w0+w1hw,t+ow,t lW,t=E(FW,t �Vt−1)=w0+w1hw,t

FINT,t= l0+l1hINT,t+oINT,t lINT,t=E(FINT,t � Vt−1)= l0+l1hINT,t

FFX,t=c0+c1hFXT,t+oFX,t lFX,t=E(FFX,t � Vt−1)=c0+c1hFX,t

ot � Vt−1�N(0, Ht)Ht=H0*(ii %−aa %−bb %)+aa %*ot−1o %t−1+bb %*Ht−1

where Ht is a 6×6 conditional covariance matrix of three bank portfolio returns and three risk factors. Q(24) and Q2(24) are the Ljung-Box test statisticsof order 24 for serial correlation in the standardized residuals and standardized residuals squared. B–J is the Bera-Jarque test statistic for normality. Robuststandard errors are given in parentheses.

* Denote statistical significance at the 5% level.** Denote statistical significance at the 1% level.


cies found in the raw data. However, the conditional normality assumption isrejected for most cases according to the index of excess Kurtosis and Bera-Jarquetest statistics, and that is why QML testing procedures are used.

Because the three-factor asset pricing model with MGARCH-M process is fullyparameterized, some interesting statistics can be recovered in this study. Panel Dcontains those statistics for the estimated time-varying risk premia and conditionalvolatility. For example, the estimated weekly total time-varying risk premium is0.1997% for Money Center bank, 0.1733% for Large Bank, and 0.1415% forRegional Bank. We can further decompose the estimated total time-varying riskpremium into three components: world market risk premium, foreign exchange riskpremium, and interest rate risk premium. For example, the estimated weekly worldmarket risk premium is 0.0035% for Money Center bank, 0.0045% for Large Bank,and 0.004% for Regional Bank. The estimated weekly foreign exchange riskpremium is −0.0049% for Money Center Bank, −0.0030% for Large Bank, and−0.0025% for Regional Bank. Finally, the estimated weekly interest rate riskpremium is 0.2012% for Money Center bank, 0.1718% for Large Bank, and 0.14%for Regional Bank. Clearly, the interest rate risk premium is the major componentin describing the dynamics of the US bank portfolio returns. Panel D also reportsthe estimated conditional volatility for each bank portfolio. The estimated weeklyconditional volatilities are 2.8527, 2.2587, and 2.2170% for Money Center Bank,Large Bank, and Regional Bank, respectively.

7. Conclusion

Most existing published work on the pricing of the US bank stock returnsgenerally focuses on the interest rate risk in addition to the market risk. However,the increasing volatility of exchange rates after the advent of the flexible exchangerate system in the 1970s and the increasing globalization of the internationalfinancial markets have created an additional source of uncertainty and risk forfirms operating in an international environment. Because fluctuations in exchangerates may result in translation gains or losses depending on banks’ net foreignpositions, the exchange rate risk could be another potential determinant of bankstock returns. This paper attempts to fill this gap by addressing the issue of pricingof market, interest rate, and exchange rate risks on the US bank stock returns. Itdiffers from previous studies concerning the pricing of bank stock returns in severalways. First, empirical estimations and testing are carried out by using threedifferent econometrics methodologies, namely NLSUR via Hansen’s (1982) GMM,Dumas and Solnik’s (1995) ‘pricing kernel’ approach, and the MGARCH-Mmodel. In particular, the use of MGARCH-M model is one of the contributions ofthis study because it overcomes the problem associated with the two-step procedureusually employed by previous researchers. Second, both the unconditional andconditional version of multi-factor models are estimated and tested, given theinconclusive results found in previous studies where both versions are testedseparately. Finally, to obtain more convincing results, both individual bank stock


returns and bank portfolio returns are considered. The empirical evidence found inthis paper can be summarized as follows.

Estimations based on NLSUR via GMM indicate that interest rate risk is theonly priced factor in the unconditional three-factor model. However, based on thepricing kernel approach, strong evidence of exchange rate risk is found in bothlarge bank and regional bank stocks, and strong evidence of world market risk isfound for the regional bank stocks in the conditional three-factor model withtime-varying risk prices. However, no evidence of significant interest rate risk isdetected, which is particularly puzzling for the bank stocks. Finally, estimationsbased on the MGARCH-M approach where both conditional first and secondmoments of bank portfolio returns and risk factors are estimated simultaneouslyshow strong evidence of time-varying interest rate and exchange rate risk premiaand weak evidence of time-varying market risk premium for all three bankportfolios, namely those of Money Center bank, Large bank, and Regional bank.The significant evidence of time-varying interest rate, and exchange rate risk premiafound in the US bank data points out the advantage of MGARCH-M approachover the previous two approaches. This advantage comes directly from the explicitmodeling of conditional volatilities in both asset returns and risk factors, which isignored in the other two approaches. Moreover, among the three time-varying riskpremia, interest rate risk premium is found to be the major one in describing thedynamics of the US bank portfolio returns.

Acknowledgements

For useful comments and suggestions on earlier drafts, I thank Nelson C. Mark,Paul Evans, G. Andrew Karolyi, Zhiwu Chen, J. Huston McCulloch, Peter Howitt,as well as workshop participants at The Ohio State University and seminarparticipants at the 1999 FMA Annual Meeting in Orlando, Florida, the 7thConference on Pacific Basin Finance, Economics and Accounting in Taipei, Tai-wan, ROC, and the 11th Annual PACAP/FMA Finance Conference in Singapore.I also thank the editor, I. Mathur, and an anonymous referee, for their professionalcritique and suggestions. Any remaining errors are, of course, my responsibility.

References

Bollerslev, T., 1986. Generalized autoregressive conditional heteroskedasticity. J. Econom. 31, 307–327.Bollerslev, T., Wooldridge, J.M., 1992. Quasi-maximum likelihood estimation and inference in dynamic

models with time-varying covariances. Econom. Rev. 11, 143–172.Choi, J.J., Elyasiani, E., Kopecky, K.J., 1992. The sensitivity of bank stock returns to market, interest

and exchange rate risks. J. Banking Finance 16, 983–1004.Choi, J.J., Hiraki, T., Takezawa, N., 1998. Is foreign exchange risk priced in the Japanese stock market?

J. Financial Quant. Anal. 33, 361–382.Choi, J.J., Rajan, M., 1997. A joint test of market segmentation and exchange risk factor in

international capital markets. J. Int. Business Stud. 28, 29–49.


De Santis, G., Gerard, B., 1997. International asset pricing and portfolio diversification with time-vary-ing risk. J. Finance 52, 1881–1912.

De Santis, G., Gerard, B., 1998. How big is the premium for currency risk? J. Financial Econ. 49,375–412.

Ding, Z., Engle, R.F., 1994. Large scale conditional covariance matrix modeling, estimation and testing.UCSD Discussion Paper.

Dumas, B., Solnik, B., 1995. The world price of exchange rate risk. J. Finance 50, 445–479.Elyasiani, E., Mansur, I., 1998. Sensitivity of the bank stock returns distribution to changes in the level

and volatility of interest rate: A GARCH-M model. J. Banking Finance 22, 535–563.Engle, R.F., Kroner, K.F., 1995. Multivariate simultaneous generalized ARCH. Econometric Theory 11,

122–150.Engle, R.F., Ng, V.K., Rothschild, M., 1990. Asset pricing with a FACTOR-ARCH covariances

structure: Empirical Estimates for Treasury bills. J. Econom. 45, 213–237.Ferson, W.E., 1995. Theory and testing of asset pricing models. In: Jarrow, R.A., Maksimovic, V.,

Ziemba, W.T. (Eds.), Finance, Handbooks in Operation Research and Management Science, Vol. 9.North Holland, Amsterdam.

Ferson, W.E., Harvey, C.R., 1993. The risk and predictability of international equity returns. Rev.Financial Stud. 6, 527–567.

Ferson, W.E., Harvey, C.R., 1994. Sources of risk and expected returns in global equity markets. J.Banking Finance 18, 775–803.

Ferson, W.E., Korajczyk, R.A., 1995. Do arbitrage pricing models explain the predictability of stockreturns? J. Business 68, 309–349.

Flannery, M.J., Hameed, A.S., Harjes, R., 1997. Asset pricing, time-varying risk premia and interest raterisk. J. Banking Finance 21, 315–335.

Gibbons, M.R., 1982. Multivariate tests of financial models. J. Financial Econ. 10, 3–27.Hamao, Y., 1988. An empirical examination of the arbitrage pricing theory. Jpn. World Economy 1,

45–62.Hansen, L.P., 1982. Large sample properties of the generalized method of moments estimators.

Econometrica 50, 1029–1054.Hansen, L.P., Jagannathan, R., 1991. Implications of security market data for models of dynamic

economies. J. Political Economy 99, 225–262.Jorion, P., 1991. The pricing of exchange risk in the stock market. J. Financial Quant. Anal. 26,

362–376.Korajczyk, R.A., Viallet, C.J., 1989. An empirical investigation of international asset pricing. Rev.

Financial Stud. 2, 553–585.Korajczyk, R.A., Viallet, C.J., 1993. Equity risk premia and the pricing of foreign exchange risk. J. Int.

Econ. 33, 199–228.Koutmos, G., 1997. Is the market portfolio a dynamic factor? Evidence from individual stock returns.

Financial Rev. 32, 411–430.Ljung, G.M., Box, G.E.P., 1978. On a measure of lack of fit in time series models. Biometrika 66,

297–303.McElory, M.B., Burmeister, E., 1988. Arbitrage pricing theory as a restricted non-linear multivariate

regression model. J. Business Econ. Stat. 6, 29–42.Merton, R.C., 1973. An intertemporal capital asset pricing model. Econometrica 41, 867–888.Merton, R.C., 1980. On estimating the expected return on the market: An exploratory investigation. J.

Financial Econ. 20, 323–361.Ng, V.K., Engle, R.F., Rothschild, M., 1992. A multi-dynamic-factor model for stock returns. J.

Econom. 52, 245–266.Prasad, A.M., Rajan, M., 1995. The role of exchange and interest risk in equity valuation: A

comparative study of international stock markets. J. Econ. Business 47, 457–472.Ross, S.A., 1976. The arbitrage pricing theory of capital asset pricing. J. Econ. Theory 13, 341–360.Song, F., 1994. A two-factor ARCH model for deposit-institution stock returns. J. Money Credit

Banking 26, 323–340.


Sweeney, R.J., Wagra, A.D., 1986. The pricing of interest-rate risk: evidence from the stock market. J.Finance 41, 393–410.

Tai, C.S., 1998. A multivariate GARCH in mean approach to testing uncovered interest parity: Evidencefrom Asia-Pacific foreign exchange markets. Unpublished Manuscript, The Ohio State University.

Tai, C.S., 1999a. Time-varying risk premia in foreign exchange and equity markets: Evidence fromAsia-Pacific countries. J. Multinational Financial Manage. 9, 291–316.

Tai, C.S., 1999b. Market integration, liberalization, and foreign exchange risk in Asia-Pacific emergingmarkets. Unpublished Manuscript, The Ohio State University.

Tai, C.S., 1999c. Can time-varying price of risk and volatility explain the predictable excess return puzzlein foreign exchange markets. Unpublished Manuscript, The Ohio State University.

Tai, C.S., 2000. On the pricing of foreign exchange risk and risk Exposure in the Japanese stock market.Unpublished Manuscript, The Ohio State University.

Turtle, H., Buse, A., Korkie, B., 1994. Tests of conditional asset pricing with time-varying moments andrisk prices. J. Financial Quant. Anal. 29, 15–29.

Wetmore, J.L., Brick, J.R., 1994. Commercial bank risk: market, interest rate, and foreign exchange. J.Financial Res. 17, 585–596.

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