International Review of Financial Analysis 18 (2009) 250–259

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International Review of Financial Analysis

The estimation and determinants of emerging market country risk and the dynamicconditional correlation GARCH model

Andrew Marshall ⁎, Tubagus Maulana, Leilei TangDepartment of Accounting and Finance, University of Strathclyde, UK

⁎ Corresponding author. Department of AccountingUniversity of Strathclyde 100 Cathedral Street, Glasgow141 548 3894; fax: +44 141 552 3547.

E-mail address: a.marshall@strath.ac.uk (A. Marshal1 EM are attractive to investors as they exhibit high ex

volatility (Aggarwal et al., 1999). They also offer divercorrelation with developed markets making it possible t(Harvey, 1995).

1057-5219/$ – see front matter © 2009 Elsevier Inc. Aldoi:10.1016/j.irfa.2009.07.004

a b s t r a c t

a r t i c l e i n f o

Article history:Received 25 November 2008Received in revised form 29 July 2009Accepted 29 July 2009Available online 7 August 2009

Keywords:Country riskEmerging marketsTime-varying beta

Country risk assessment is central to the international investment, which recently has increasingly focusedon emerging markets (EM). In this paper we proxy for country risk in EM by using time-varying beta. Weextend existing literature by applying a dynamic conditional correlation GARCH model. After confirming betais time varying in twenty EM over the period January 1995 to December 2008 we investigate the GARCH(1,1) model and find the t-distribution generates the lowest forecast errors compared to the normal errordistribution and a generalised error distribution. In a comparison of previous modelling techniques theresults of our modified Diebold–Mariano test statistics suggest that the Kalman Filter model outperforms theGARCH model and the Schwert and Seguin (1990) model. Using a DCC-GARCH model our evidence suggeststhat considering dynamic betas can improve beta out-of-sample predicting ability and therefore offerspotential gains for investors. Finally, we find dynamic betas across EM are strongly associated with eachnation's interest rates, US interest rates and the Consumer Price Index (CPI) and to a lesser extent theexchange rates. Our results have some similarities to those in previous studies of developed markets in theeconomic determinants of time-varying beta but differences exist in the results on best model to forecasttime-varying beta. These findings have implications for estimating country risk for investment and riskmanagement purposes in EM.

© 2009 Elsevier Inc. All rights reserved.

1. Introduction

For international investors country risk assessment is an essentialfactor in the investment process. Country risk is the potential volatilityand default in financial assets due to political and/or financial eventsin the given country. Emerging markets (EM) have grown inimportance as a destination for international investment and therehas been a huge increase in volume of investments in Asia, EasternEurope and Latin America by funds and individuals.1 Understandingthe relations between international stock markets and how theselinkages vary through time is of great importance for country riskdiversification. An obvious source for assessing country risk is theglobal country risk rating provided by rating agencies such asInternational Country Risk Guide and the Economist Intelligence

and Finance, Curran Building,G4 0LN Scotland, UK. Tel.: +44

l).pected returns as well as highsification benefits due to lowo construct low risk portfolios

l rights reserved.

Unit (see Erb et al., 1996 and Oetzel et al., 2001). The alternativeapproach, which is the focus of this paper, addresses country risk froma portfolio investment perspective based on the capital asset pricingmodel (CAPM) (Bouchet et al., 2003). According to Erb et al (1996), byusing international version of the CAPM one can infer the beta value asindicator of country risk. Brooks, Faff and McKenzie (2002) relatetime-varying betawith country risk. Time-varying systematic risk is ofinterest to both institutional and individual investors and it is alsoimportant to investigate the link between time-varying variances,correlations, and betas in both developed and EM (see Andersen et al.,2005).

The overall finding from a review of the literature on betaestimation supports the notion that beta is time varying for developedmarkets. Given the instability and high volatility in EM it would beexpected that betas in thesemarketswould be time varying. However,little research has been conducted on the best model to forecast time-varying beta and its determinants in EM and therefore the implica-tions for investors in these markets. One of the research objectives inthis paper, following the approaches proposed by Brooks et al. (2002),is to find the best country risk model for EM. Brooks et al. (2002)examined the time-varying beta coefficient within the framework ofcountry risk by using bivariate GARCH models to calculate betas forseventeen developed countries. In particular they focused on threemodels, the multivariate generalised ARCH (M-GARCH) model

251A. Marshall et al. / International Review of Financial Analysis 18 (2009) 250–259

(Bollerslev, 1990), the Schwert and Seguin (1990) (hereafter S and S)model and the random walk Kalman Filter model.2

There are five empirical research questions in this paper: (i) are EMcountry betas time varying?, (ii) which distribution of GARCH (1,1)model is the best formodelling time-varying beta (country risk) in EM?,(iii) whichmodel is best for modelling time-varying beta (country risk)in EM?, (iv) does taking time variation in betas into account improveout-of-sample predictability compared to constant beta in a hedgingstrategy?, and (v) what are the potential economic determinants thatcause beta to be time varying in EM? We extend existing literature onmodelling techniques by applying dynamic conditional correlation(DCC) GARCHmodels (Engle, 2002). A particularly appealing feature ofthe DCC-GARCH model is that it preserves the simple interpretation ofthe univariate GARCHmodels but also provides a consistent estimate ofthe dynamic correlation matrix.

We find for our sample of EM counties that beta is time varyingwhen using a number of approaches, including the DCC-GARCHmodel. Based on the in-sample forecast, in an evaluation ofdistributions of the GARCH (1,1) model we find that the GARCH(1,1) under a t-distribution generates the lowest forecast errors. In acomparison of country risk models our modified Diebold–Marianotest statistics suggest that the Kalman Filter model outperforms thealternative models tested. Our evidence suggests that by consideringdynamic betas in a hedging strategy can improve beta out-of-samplepredicting ability and therefore offers potential gains for investors.We also find common determinants of dynamic betas across countriesas time-varying betas are strongly associated with each nation'sinterest rates, Consumer Price Index, US interest rates and to a lesserextent with foreign exchange rates. This result is consistent withstudies of developed markets and single country and regional studiesof EM. Our results have some similarities to those in previous studiesof developed markets in the economic determinants of time-varyingbeta but some differences exist in the best model to forecast time-varying beta. Overall our results have practical implications forinvestors who focus on investing in EM, for example calculating theappropriate cost of capital. Allowing for variation over time is not onlyessential for understanding the dynamic process among the riskyassets in the portfolio but also for finding appropriate weightallocation for the portfolio. Our results have some similarities tothose in previous studies of developed markets in the economicdeterminants of time-varying beta but differences exist in the resultson the best model to forecast time-varying beta.

This paper is organized as follows. In Section 2 we specify theestimation models. We follow this in Section 3 with a description ofthe data used in this study. Section 4 presents the empirical results ontime-varying beta estimation, a comparison of the estimation models,an evaluation of the predicting abilities between dynamic andconstant betas and our investigation of the economic determinantsof time-varying beta values. Conclusions are provided at the end.

2. Model specifications

2.1. Beta estimation

The standard approach to estimate beta (or unconditional beta) isthe market model regression:

Ri;t = αi + βiRw;t + �i;t for t = 1;Λ; T 1

where: Ri,t is the return on country i for period t; Rw,t is the return onthe world index for period t; and ɛi,t is the disturbance vector. The

2 They find the GARCH model produces similar results to Kalman Filter estimationand S and S (1990) query stochastic factor. Also, focusing on developed marketsBrooks et al. (1998) and Faff et al. (2000) find that the random walk model is the mostappropriate model in Australian industry indices and UK industry sectors respectively.

slope coefficient βi is a measure of the relative systematic risk ofcountry i. To classify a country according to its systematic risk wehave to compare its international beta value with the beta value of theworld market index, which has the value of unity. We can define acountry that has an international beta greater (less) than unity hasgreater (less) systematic risk than that of the benchmark globalmarket index. In this model the relation between the explanatory andexplained variables remains constant through the estimation period.When this assumption is an unreasonable other models need to beconsidered to estimate the parameters.

2.2. GARCH (1,1) model

Standard univariate GARCH models have successfully modelledconditional time-varying stock return variance. The time-varyingvariance is partly due to the volatility of national stockmarket evolvingover time and partly due to the interdependence across national stockmarket changing though time (Longin and Solnik, 1995). Theimportance of incorporating the interdependence of across nationalmarket has lead to equal empirical success of multivariate GARCHmodels (Bollerslev et al., 1988; Bollerslev, 1990; Engle and Kroner,1995; Alexander 2000). To generate the multivariate generalisedARCH (M-GARCH) model we use the same method as outlined inBrooks et al., (2002) but add twomore distributions under the GARCH(1,1) model namely the t-distribution and the GED distribution (seeAppendix A for the research method for the GARCH (1,1) model).

2.3. Schwert and Seguin (1990) model

A significant contribution onmodelling “marketmodel” regressionwith time-varying beta is proposed by S and S (1990). The conditionalcovariance of returns in stock markets i and j, given information setΩt−1, is specified as σi;j;t≡ðRi;t ;Rj;t jΩt−1Þ = c0;i;j + c1;i;jσ2

w;t , where σw,

t2 is the conditional variance of returns for the world market portfolio.The time-varying coefficient βi,t is equal to:

βi;t = covðRi;t ;Rj;t jΩt−1Þ = σ2w;t

= ∑N

j=1Xjσi;j;t = σ

2w;t

= ∑N

j=1Xjc0;i;j = σ

2w;t + ∑

N

j=1Xjc1;i;j

= βi + δi = σ2w;t

2

where: X is the world portfolio weight for the jth market. According toEq. (2), the time-varying beta consists of a constant term βi and atime-varying term δi/σ2

w,t. A positive δi implies that systematic riskfor country i varies inversely with the world stock market indexvolatility, and a negative δi implies that systematic risk and the worldstock market index volatility are positively related. If we substituteequation of the time-varying coefficient beta into the standardmarketmodel, we get the S and S (1990) model:

Ri;t = αi + βiRw;t + δiRw;t = σ2w;t + �i;t for t = 1;Λ; T: 3

The conditional variance of the market index in this estimationprocedure is obtained from the bivariate GARCH (1,1) model.

2.4. Kalman Filter model

The Kalman Filter model has been increasingly used in finance (seeMcKenzie et al., 2000). The structural times seriesmodels are regressionmodels with time dependent explanatory variables and time-varyingparameters. The state space representation is the form to deal with thiskind of model while the Kalman Filter is a recursive procedure for

3 ˆRi;t = αi + βi;tRw;t where: βi,t=beta coefficient generated from three differenttechniques and Rw,t=the return on the world market index. We estimate a conditionalintercept coefficient series for each technique. In order to obtain the αi coefficient, werun the following equation αi = Ri;t− βi;t Rw;t where: αi is equal to the meancountry return less than the mean conditional beta times of the mean world marketindex.

252 A. Marshall et al. / International Review of Financial Analysis 18 (2009) 250–259

estimating theoptimal state vector. The state space formulation assumesthat the forecast variable yt can be expressed as a linear function ofunobserved state variables and exogenous variables. It also assumed thatthe state variables depend on the previous state and the most commondynamic extension of the error term in the conventional model states:

yt = A′xt + H′zt + wtzt = Fzt−1 + vt

4

where: yt is the observable variable and zt is the unobservablevariables, xt is a vector of exogenous (or predetermined) variables andrandom errors wt and vt are i.i.d. and assumed to be uncorrelated atall lags. Formally this states: E(wt,vt′)=0; E(wt, wt′)=var (wt)=R;and E(vt, vt′)=var (vt)=Q. Together the two equations (yt and zt inEq. (4)) will form a state space model. We estimate three differentmodels of time-varying beta for the Kalman Filter: random walkβRW=βI,t−1+vit−1, random coefficient βRC=average β+vi,t−1, andautoregressive βAR=Ø (βi,t−1−average β)+average β+vi,t−1.

2.5. Dynamic condition correlation GARCH model

Themainproblemwith themultivariateGARCHmodelshas been theconstraints of the substantial computing restrictions. Most studiesrespond to these constraints by assuming constant correlation orreplying on unconditional variance–covariance matrices, which makesthe estimation a large model feasible. However, these approaches haveproblems in interpreting the coefficients on the univariate GARCHmodels and the poor performance for less correlated stock markets(Engle and Sheppard, 2001). Engle and Sheppard (2001) and Engle(2002) implement and evaluate dynamic condition correlation forportfolio assets allocation (avoiding the problems of relying solely onunconditional variance–covariance matrix). This study uses Engle's(2002) DCC-GARCH framework to estimate the parameters and thetime-varying correlations in order to improve the beta estimation. TheDCC-GARCH approach is well suited for the situation where the changeof correlation over time has impacts on beta estimation and prediction.We use the DCC (1,1) approach based within the family of generalisedARCH models (Engle, 1982; Bollerslev, 1990) and is being increasingused to model time-varying correlation. Adopting Engle (2002), weestimate the following set of equations:

rt jΩt−1∼Nð0;DtρtDtÞ 5

hi;t = ωi + αir2i;t−1 + βihi;t−1; i = 1;Λ; k 6

ɛt = D−1t rt eNð0;ρtÞ 7

ρt = diagðQtÞ−12QtdiagðQtÞ−

12 8

Qt = ð1−a−bÞ Q−

+ aɛt−1ɛ′t−1 + bQt−1 9

with rt=[r1t,Λ, rkt]′ as the k-dimensional vector of zero mean excessrisky return, Dt as a k×k diagonal matrix of conditional standarddeviations, i.e., Dt = diag½ ffiffiffiffiffiffiffiffi

h1;tq

; ⋯;ffiffiffiffiffiffiffihk;t

q �, Rt as the k×k time-varyingcorrelation matrix, Qt as the positive definite matrix defining thestructure of the dynamics, and

−Q = Eðɛtɛ′tÞ as the unconditional

covariance matrix of standardized variables. Eq. (6) is the normalconditional variance obtained from univariate GARCH model. Eq. (7)generates time-varying and standardized residuals. Eq. (8) decomposesthe correlation matrix ρt in order to ensure that ρt is positive definite.Eq. (9) is thekeypoints that capture thedynamic conditional correlationdata generating process. If a=b=0, Qt is conditional constantcorrelation data generating process. If a+bb1, Qt is mean revertingprocess. This specification takes into account both the simplicityinterpretation of the univariate GARCHmodels and consistent estimate

of the correlation matrix. The DCC parameters are estimated using atwo-stage procedure through maximizing the following log-likelihoodfunction:

L = −0:5∑T

t=1ð2 logð jDt j Þ + logð jρt j Þ + ɛ

′tρ

−1t ɛÞ: 10

Eq. (10) includes two varying components and requires a two-stage procedure. In the first stage, we only estimate the univariateGARCH coefficients in Eq. (6). In the second stage, we maximize thecorrelation component to estimate the DCC parameters in Eq. (9),conditional on the estimated coefficients from the first stage. Based onall the estimates of DCC-GARCH model we propose a time-varyingbeta specified as:

betat =Qt

ffiffiffiffiffiffihit

p ffiffiffiffiffiffiffihwt

phwt

=Qt

ffiffiffiffiffiffihit

pffiffiffiffiffiffiffihwt

p : 11

Engle and Sheppard (2001) propose the least biased multi-stepahead forecast the covariance matrix of the DCC-GARCH model. Then-step ahead forecast of dynamic conditional standard deviation Dt

and correlation ρt can be generated separately. The n-step aheadforecast of Dt is given by univariate GARCH:

ht + r j t−1 =ω

1−α−β+ ðα + βÞn−1 hh−

ω1−α−β

� �: 12

The forecast of ρt n-step ahead is:

ρt + r j t−1 = ∑n−2

i=0ð1−a−bÞ ρ

−ða + bÞi + ða + bÞn−1ρt : 13

From the DCC model we estimate the conditional correlationsbetween each individual country and world index. Then we calculatethe dynamic beta values for each country.

2.6. Assessing the relative performance of the models

To determine the performance of the models of alternative time-varying beta techniques we obtain in-sample forecast of stock marketindex return on each country.3 The difference between the actual andthe forecast values is defined as the forecast error as ɛt = ðyt− ytÞ.The accuracy of the forecast ρi;t generated from each of theconditional beta series can be assessed using the mean absoluteforecasting error (MAE) where:

MAE =∑n

t=1j�t j

n: 14

The MAE is defined by first making each error positive by taking itsabsolute value and then averaging the results. Alternatively, the forecastaccuracy can be evaluated using the mean square forecasting error(MSE):

MSE =∑n

t=1�2t

n: 15

6 In our initial investigation we used weekly US dollar value weighted indices fromthe Morgan and Stanley Capital International (MSCI) price index ranging from 12January 1995 to 28 April 2005 covering twenty-two EM countries and weekly

253A. Marshall et al. / International Review of Financial Analysis 18 (2009) 250–259

The best model to explain the time variant beta we select the onethat yields the smallest MAE andMSE. The formal testing procedure inorder to determine whether the differences between two forecastedseries are significant is the modified Diebold–Mariano statistic asproposed by Harvey et al. (1997).4

2.7. Hedging strategy

The typical hedging strategy of removing market risk is for oneunit of capital invested in country i at time t, the fundmanager hedgesthe country market risk by short selling betai,t+1|t units of worldmarket portfolio. betai,t+1|t is the optimal one-period-ahead forecastof country beta calculated by Eqs. (11), (12) and (13). Specifically, ourempirical comparison of dynamic and constant betas consists in usingthe DCC-GARCH (1,1) specification to produce one-period-aheadforecasts for the dynamic betas betai,t+1|t. In this case, we recursivelyestimate the DCC-GARCH (1,1) model using overlap windows of sixyears of daily data training sample (from 01/01/1995–29/12/2000;total of 1565 observations). At each point in time t+1, we generateone-period-ahead forecast of hedge ratio beta value betai,t+1|t until31/12/2008 and the error of this hedged position is calculated by:

ηi;t + 1 = ri;t + 1−betai;t + 1 j trw;t + 1: 16

Since the parameters of GARCH models change little on a dailybasis, the conditional volatility parameters are re-estimated everymonth. A month is defined as 22 consecutive trading days. The secondr-step ahead conditional correlation and variance forecasts are thesame as the first step but the GARCH parameters are re-estimated bycombining the training sample and the first r-step ahead 22observations to take into account the expanding information troughtime. We repeat this process in an increasing window setup until thelast observation for the holdout sample. Thus, the one-day-aheadforecast horizon is about eight years, about 2088 trading days.Therefore, there are 2088 one-period-ahead hedging errors ηi,t+1

over the last 8 years in our holdout sample for country i. The constantbetas are calculated based on the whole sample data. We assess theeffectiveness of dynamic and constant hedging strategies by consid-ering MAE and root mean squared error (RMSE) for the holdoutsample. The more effective hedging strategy should produce smallervalues of MAE and RMSE.

2.8. Economic determinants of time-varying beta

According to Bos and Newbold (1984) the variation in the stock'sbeta may be due to the influence of macroeconomic factors. Existingstudies of the relation between financial activity and economicactivity have shown that the change of monetary policy level andprice level (inflation rate) can lead to financial instability (Lucas, 1972,1973; Schwartz, 1995). Prior literature has focused on the impact ofmacroeconomic variables on developed markets. For EM Bilson,Brailsford and Hooper (2001) show that domestic money supply,goods prices and foreign exchange rates are significantly correlatedwith stock market returns. Verma and Soydemir (2006) considereconomic determinants time-varying beta in Latin America.5 Thispaper focuses on a wider sample of EM and unlike prior studies ondeterminants of dynamic beta values we apply panel-data regressionanalysis which has major advantages over traditional time-seriesregressions in term of improving the efficiency of relevant estimates.To examine the explanatory power of economic variables with regardto time-varying betas we collect five monetary and real economic

4 The modified Diebold–Mariano statistic tests of the following hypothesis andalternative: H0: MSE0=MSEP and H1: MSE0NMSEP.

5 Wdowinski (2004) and Andrade and Teles (2006) are single country studies ofPoland and Brazil respectively.

variables for each country (domestic interest rates, domestic moneysupply, Consumer Price Index, foreign exchange rates and industrialproduction) and an influential global economic variable (US interestrates). These economic variables have commonly been used to explaincountry risk in prior literature on developed (Abell and Krueger, 1989;Oetzel et al., 2001; Groenewold and Fraser, 1997) and developingmarkets (Wdowinski, 2004; Andrade and Teles, 2006; Verma andSoydemir, 2006). These economic variables are potentially non-stationary and therefore the augmented Dickey–Fuller (ADF) unit roottest is applied to examine the order of integration of each economicvariable. In ADF tests, the initial lag length is set at six, then testingdown to the first significant lag. Unlike Verma and Soydemir's (2006)time-series regression for each country, we test the determinants ofdynamic beta by running the following fixed effect of panel-dataregression:

betait = αi + θ′Xit + μit i = 1;Λ; k; t = 1;Λ; T 17

where: betait is the estimated dynamic beta from Eq. (11) then weaverage the estimated daily beta values for eachmonth to getmonthlybeta values, the αi are country specific constants, Xit is the vector ofthe error term μit represents the effects of the omitted variables thatare peculiar to both the individual country and time periods with E(μit)=0 and var(μit)=σ2

iμ.

3. Sample and data description

We use daily closing market indexes for twenty EM countries from1st January 1995 to 31st December 2008 collected from DataStream.These counties provide a very broad representation of EM.6 We alsouse US dollar value weighted index from the Morgan and StanleyCapital International (MSCI) price index to represent the world index.We compute continuously returns for all countries and MSCI index.The economic variable sample period spans from January 1995 toDecember 2008 in monthly intervals. The FX rates are the nominalvalues expressed as local currency per US dollar. The proxy for thenational interest rate is the rates for 30 days certificate of deposits(INT). Money supply (M1) is measured as the narrow stock of money.The price of goods (inflation) is the domestic CPI. Real activity ismeasured by the index for industrial production (IIP). Finally, weconsider an influential global variable and use US 3-month interestrate (USINT).7

4. Results

4.1. Tests of time-varying beta

Table 1 reports basic statistics of the mean and standard deviationof daily returns for each country and the unconditional correlation ofdaily national returns with MSCI returns for the whole sample period.The average daily returns vary from −0.035% for Pakistan to 0.048%for Egypt. The standard deviations vary from 1.35% for Chile to 3.25%for Russia. Both Russia and Egypt have the lowest unconditionalcorrelation with MSCI and Latin American countries have the highestunconditional correlation with MSCI.

The results of the market model specified in Eq. (1) for each of thecountries in our sample are presented in Table 2. All the beta

Datastream data for six further countries (Mexico, Indonesia, Malaysia, Philippines,Thailand and Greece). The results for this period using weekly data generally do notdiffer significantly from the results reported in this paper.

7 Further detailed description of these economic variables can be found in Abell andKrueger (1989), Andrade and Teles (2006) and Verma and Soydemir (2006).

Fig. 1. Average rolling window unconditional correlations. Average unconditionalcorrelation of all twenty counties. The correlations are calculated over a fixed windowlength of 3 years with a rolling window length of 3 months.

Table 1Summary statistics for weekly raw returns data for country indices and the worldmarket portfolio covering the period from 3 January 1995 to 31 December 2008.

Country Mean Standarddeviation

Skewness Kurtosis Jarque–Bera Beta estimate(std. error)

Argentina 0.0000 0.0247 −1.1513 21.2722 51,611.2 1.059a (0.038)Brazil 0.0002 0.0249 −0.0889 10.4757 8508.9 1.438ab (0.035)Chile 0.0000 0.0135 −0.0748 15.7281 24,655.2 0.729ab (0.020)Colombia 0.0003 0.0166 −0.1221 14.2405 19,235.1 0.482ab (0.027)Mexico 0.0003 0.0202 0.0228 15.4858 23,722.4 1.237ab (0.028)Peru 0.0004 0.0177 −0.1884 11.4319 10,840.1 0.785ab (0.027)Czech 0.0004 0.0174 −0.2666 15.9706 25,643.4 0.744ab (0.027)Egypt 0.0005 0.0161 −0.3662 10.9381 9670.2 0.120ab (0.027)Hungary 0.0004 0.0213 −0.4067 15.7428 24,809.5 0.988a (0.033)Israel 0.0002 0.0148 −0.3485 7.9130 3746.8 0.666ab (0.023)Poland 0.0001 0.0201 −0.1946 6.9457 2392.0 0.839ab (0.031)Russia 0.0004 0.0325 −0.3906 13.3554 16,410.3 1.208ab (0.052)Turkey 0.0003 0.0321 −0.1417 9.1880 5839.0 0.943a (0.053)China −0.0002 0.0212 0.0416 8.5503 4688.6 0.641ab (0.035)India 0.0001 0.0176 −0.3920 7.2323 2819.2 0.460ab (0.029)Korea 0.0000 0.0260 0.2550 16.1230 26,244.7 0.717ab (0.043)Malaysia −0.0001 0.0195 −0.8429 66.5907 615,760.6 0.308ab (0.033)Pakistan −0.0003 0.0200 −0.4919 9.0635 5741.9 0.051b (0.034)Philippines −0.0004 0.0182 0.5561 15.7329 24,858.4 0.351ab (0.031)Taiwan −0.0002 0.0176 −0.0696 5.5898 1023.6 0.374ab (0.029)World 0.0001 0.0096 −0.3947 13.1515 15,776.1

Note: aSignificantly different from zero. bSignificantly different from unity. Daily closingmarket indexes for twenty EM from 1 January 1995 to 31 December 2008 collectedfrom DataStream. US dollar value weighted index from the Morgan and Stanley CapitalInternational (MSCI) price index to represent the world index. Continuously returns forall countries and MSCI index. The return series for each market between period t−1and t is defined by Ri,t=ln(Pi,t/Pi,t−1)], where: Pi,t denotes the level of the stock marketindex for each country at time t and ln is the natural logarithm.

254 A. Marshall et al. / International Review of Financial Analysis 18 (2009) 250–259

coefficients are positive and significantly different from zero (exceptfor Pakistan). The highest (lowest) betas are 1.438 and 0.051 for Braziland Pakistan respectively and most of the countries (eighty percent)have beta values less than unity. Thus it implies the systematic risk ofthe majority of EM is less than that of the benchmark-world index.Interestingly, three of the four countries that have a beta value greater

Table 2Estimates of EM point betas.

Country Beta estimate(std. error)

R2 LagrangeMultiplier testc

White testc

Argentina 1.059a (0.038) 0.1718 68.18 (0.00) 38.97 (0.00)Brazil 1.438ab (0.035) 0.3110 583.55 (0.00) 120.54 (0.00)Chile 0.729ab (0.020) 0.2719 593.19 (0.00) 479.00 (0.00)Colombia 0.482ab (0.027) 0.0784 667.29 (0.00) 92.73 (0.00)Mexico 1.237ab (0.028) 0.3483 298.21 (0.00) 27.01 (0.00)Peru 0.785ab (0.027) 0.1839 249.53 (0.00) 297.88 (0.00)Czech 0.744ab (0.027) 0.1709 451.50 (0.00) 237.34 (0.00)Egypt 0.120ab (0.027) 0.0051 224.40 (0.00) 71.15 (0.00)Hungary 0.988a (0.033) 0.2005 239.39 (0.00) 158.87 (0.00)Israel 0.666ab (0.023) 0.1885 265.56 (0.00) 189.51 (0.00)Poland 0.839ab (0.031) 0.1626 335.47 (0.00) 126.80 (0.00)Russia 1.208ab (0.052) 0.1285 497.35 (0.00) 126.17 (0.00)Turkey 0.943a (0.053) 0.0804 501.82 (0.00) 30.85 (0.00)China 0.641ab (0.035) 0.0850 441.33 (0.00) 120.76 (0.00)India 0.460ab (0.029) 0.0639 423.45 (0.00) 62.68 (0.00)Korea 0.717ab (0.043) 0.0707 606.43 (0.00) 24.64 (0.00)Malaysia 0.308ab (0.033) 0.0233 135.45 (0.00) 8.29 (0.02)Pakistan 0.051b (0.034) 0.0006 333.72 (0.00) 2.28 (0.32)Philippines 0.351ab (0.031) 0.0346 141.36 (0.00) 15.27 (0.00)Taiwan 0.374ab (0.029) 0.0421 203.85 (0.00) 60.17 (0.00)

Note: aSignificantly different from zero. bSignificantly different from unity. cp-Values arein parenthesis. The standard approach to estimate beta (or unconditional beta) is themarket model regression which is defined as: Ri,t=αi+βiRw,t+εi,t for t=1,…, T,where: Ri,t is the return on country i for period t, Rw,t is the return on the world indexfor period t, and εi,t is the disturbance vector. The value of R-squared of the marketmodel together with the value of Lagrange Multiplier test and the value of White testare presented in the third, fourth and fifth column respectively.

than one are in Latin America. However we cannot make a generalconclusion about the use of unconditional country beta risk to explainthe risk-return in EM. By examining the mean return (Table 2) withthe value of the beta coefficient in Table 1 we find mixed results(supported by relatively low R-squared values of the market model).In general the ability of the world market return to explain thevariability of return in a particular market is weak. Since we areconsidering EM there could be a time lag in the adjustment to globalreturns in themarket model. We investigate this in further tests of themarket model with lags (of one and three months) in the globalreturns. Although this did change the beta estimates for a number ofcountries these differences were generally not significant and wereport beta values with contemporaneous values of the global marketreturn.

Having generated the international beta values we test the validityof the assumption that the beta value for each country is constant overtime. We initially use two different tests to examine a time invariantbehaviour of the beta values.8 We ran rolling windows of size fifty-two weeks so that each beta point reflects annualised figure. Wefound that all countries exhibited time variation in their betacoefficients and most of countries exhibited an increase in theircountry risk in 1997 (reflecting the Asian crisis) and in 2008(reflecting the credit crisis). The second test using the cumulativesum of the recursive residuals square (CUSUMSQ) shows that foreighteen of the twenty countries the parameters of the market modelare not stable over time.9 Following Longin and Solnik (1995), we alsoprovide a visual impression of the instability of the unconditionalcorrelation across countries. Fig. 1 provides average unconditionalcorrelation of all twenty counties.10 The correlations are calculatedover a fixed window length of 3 years with a rolling window length of3 months. Fig. 1 clearly shows that correlations change over time.11

We extend these tests with the DCC-GARCH approach to considerthe dynamic nature of the beta values. The key advantage of the DCC-GARCH model is that it allows conditional volatility and correlationsto vary over time, which in turn accounts for dynamic beta values.Table 3 displays the results of DCC-GARCH (1,1) for the whole sample.

8 The research method is described in Appendix B and the results for all these testare available from the author(s) on request.

9 Using a LM test the results are consistent with the CUSUMSQ results is thatheteroscedasticity is found for eighteen of twenty countries (based on the White testwe found nine countries that have heteroscedasticity).10 Figures for individual country are available from the author(s) on request.11 The rolling window correlation results for each individual country can be providedon request.

Table 3Maximum likelihood estimation of the DCC-GARCH (1,1) specification.

Country GARCH parameters DCC parameters LogL

ωi αi βi w αw βw a b

Argentina 0.00** (0.00) 0.11** (0.03) 0.86** (0.04) 0.00** (0.00) 0.08** (0.01) 0.91** (0.01) 0.02** (0.00) 0.96** (0.01) −22080Brazil 0.00** (0.00) 0.12** (0.02) 0.84** (0.03) 0.00** (0.00) 0.08** (0.01) 0.91** (0.01) 0.01** (0.00) 0.97** (0.01) −22315Chile 0.00** (0.00) 0.12** (0.02) 0.84** (0.04) 0.00** (0.00) 0.08** (0.01) 0.91** (0.01) 0.02** (0.01) 0.96** (0.01) −24280Colombia 0.00** (0.00) 0.24** (0.03) 0.72** (0.03) 0.00** (0.00) 0.08** (0.01) 0.91** (0.01) 0.00** (0.00) 0.99** (0.00) −23391Mexico 0.00** (0.00) 0.14** (0.04) 0.82** (0.04) 0.00** (0.00) 0.08** (0.01) 0.91** (0.01) 0.02** (0.01) 0.96** (0.01) −23237Peru 0.00** (0.00) 0.10** (0.02) 0.87** (0.02) 0.00** (0.00) 0.08** (0.01) 0.91** (0.01) 0.02** (0.01) 0.96** (0.01) −23139Czech 0.00** (0.00) 0.11** (0.01) 0.86** (0.02) 0.00** (0.00) 0.08** (0.01) 0.91** (0.01) 0.02** (0.01) 0.96** (0.01) −23108Egypt 0.00** (0.00) 0.11** (0.03) 0.86** (0.04) 0.00** (0.00) 0.08** (0.01) 0.91** (0.01) 0.02** (0.01) 0.96** (0.01) −23037Hungary 0.00** (0.00) 0.05** (0.01) 0.94** (0.04) 0.00** (0.00) 0.08** (0.01) 0.91** (0.01) 0.00 (0.02) 0.00 (0.23) −22367Israel 0.00** (0.00) 0.14** (0.04) 0.80** (0.05) 0.00** (0.00) 0.08** (0.01) 0.91** (0.01) 0.01** (0.01) 0.97** (0.02) −23590Poland 0.00** (0.00) 0.06** (0.02) 0.91** (0.03) 0.00** (0.00) 0.08** (0.01) 0.91** (0.01) 0.01 (0.01) 0.98** (0.02) −22338Russia 0.00** (0.00) 0.09** (0.02) 0.86** (0.03) 0.00** (0.00) 0.08** (0.01) 0.91** (0.01) 0.00** (0.00) 0.98** (0.00) −21047Turkey 0.00** (0.00) 0.14** (0.03) 0.84** (0.03) 0.00** (0.00) 0.08** (0.01) 0.91** (0.01) 0.01** (0.00) 0.98** (0.01) −20615China 0.00** (0.00) 0.10** (0.02) 0.88** (0.03) 0.00** (0.00) 0.08** (0.01) 0.91** (0.01) 0.01** (0.00) 0.98** (0.00) −22321India 0.00** (0.00) 0.11** (0.02) 0.87** (0.02) 0.00** (0.00) 0.08** (0.01) 0.91** (0.01) 0.00** (0.00) 0.99** (0.01) −22788Korea 0.00** (0.00) 0.12** (0.02) 0.84** (0.03) .000** (0.00) 0.08** (0.01) 0.91** (0.01) 0.00** (0.00) 0.99** (0.00) −21840Malaysia 0.00** (0.00) 0.07** (0.01) 0.92** (0.01) 0.00** (0.00) 0.08** (0.01) 0.91** (0.01) 0.00** (0.00) 0.99** (0.00) −23645Pakistan 0.00** (0.00) 0.08** (0.01) 0.91** (0.01) 0.00** (0.00) 0.08** (0.01) 0.91** (0.01) 0.01** (0.00) 0.98** (0.01) −22238Philippines 0.00** (0.00) 0.13** (0.02) 0.83** (0.03) 0.00** (0.00) 0.08** (0.01) 0.91** (0.01) 0.00** (0.00) 0.98** (0.01) −22629Taiwan 0.00** (0.00) 0.06** (0.01) 0.92** (0.01) 0.00** (0.00) 0.08** (0.01) 0.91** (0.01) 0.00** (0.00) 0.99** (0.00) −22549

Notes: Values in parenthesis are standard deviations. ** denotes significant at 0.05 level. Subscript i denotes country; subscript w denotes world index. DCC-GARCH (1,1) for thewhole sample of twenty EM. From the DCC model we estimate the conditional correlations between each individual country and world index. Then we calculate the dynamic betavalues for each country. The DCC parameters are estimated using a two-stage procedure through maximizing the following log-likelihood function:

L = −0:5∑T

t=1ð2 logðjDt j Þ + logð jρt j Þ + ɛ′tR

−1t ɛÞ. Based on all the estimates of DCC-GARCH model we propose a time-varying beta specified as: betat =

Qt

ffiffiffiffihit

p ffiffiffiffiffiffihwt

phwt

= Qt

ffiffiffiffihit

pffiffiffiffiffiffihwt

p . The

r-step ahead forecast of dynamic conditional standard deviation Dt and correlation ρt can be generated separately. The r-step ahead forecast of Dt is given by univariate GARCH:

ht + r j t−1 = ω1−α−β + ðα + βÞn−1 hh− ω

1−α−β

� �. And the forecast of ρt n-step ahead is: ρt + r j t−1 = ∑

n−2

i=0ð1−a−bÞ Rða + bÞi + ða + bÞn−1Rt where R is the unconditional

correlation matrix.

255A. Marshall et al. / International Review of Financial Analysis 18 (2009) 250–259

The estimated DCC parameters, â and b , are both statisticallysignificant, suggesting a good deal of persistence in the conditionalcorrelation process.12 Our findings are consistent with the literatureand are in line with our earlier results that EM betas fluctuate overtime. To get a visual impression of the dynamic beta values across thewhole countries, we plot the average dynamic values of the samplecountries in Fig. 2. This shows that the average value of betas varyfrom 0.2 to over 1.2.13

14 We find that the point estimates of conditional betas of the three approaches areall of reasonable magnitude.15 It should be noted here that when the performance of GARCH and S and S (1990)query model are compared using the Ashley et al. (1980) query testing procedure, theresults are not statistically significant different.16 We also consider the results of the modified Diebold and Mariano test statistic todetermine whether the difference in forecast errors are statistically significant,specifically it provides information on the proportion of countries that rejected thenull hypothesis of equal MSE. Only the Kalman Filter class models are significantly

4.2. Estimation of time-varying beta — GARCH (1,1)

We initially compare the performance of GARCH (1,1) model with anormal distribution, with a t-distribution and a generalised errordistribution (GED).Wefind that the estimated coefficients for every EMare significantly different from zero. All three estimated coefficients inthe variance equation are positive for each country under eachdistribution and thus the coefficient restrictions to ensure that thevariance is positive are satisfied.We found different results for volatilitypersistence (measuring the stability of the GARCH (1,1) model underthe three different distributions). The beta values derived from theGARCH (1,1) models under the three distributions do not deviate fromthe point of estimates of the market model (correlation coefficientbetween beta series generated from the market model and beta seriesgenerated from the GARCH (1,1) under the three different distributionsis high). The values of beta for each country vary significantly. Thisfinding supports research on time-varying beta in other markets (e.g.Brooks et al., 2002). Within the GARCH (1,1) model the t-distributionprovided the lowestMSE (in twelve of the twenty cases) as compared tothe GARCH (1,1) with normal distribution and GED. The in-sampleassessment of the relative performance of the three models suggests

12 Due to the potential importance of the credit crisis on our data we redo theestimation without 2008 and find that the DCC-GARCH estimation results do notchange significantly.13 Dynamic beta figures for individual country are available from the author(s) onrequest.

that the multivariate GARCH with t-distribution produces the lowestforecasting errors measured byMSE. These findings are in line with thetheory underpinning the fat tails behaviour of asset returns, which isusually indicated by kurtosis (these unreported results are availablefrom the authors on request).

4.3. Estimation of time-varying beta — model comparison

Table 4 compares three commonly applied models for conditionalbeta14 and summarizes the results of MSE of all models for each EM.The results show that the Kalman Filter technique dominates theother two techniques. Within the class of Kalman Filter model there isvariation in the best performing distribution as the autoregressivetechnique produced the lowest MSE in nine of the twenty cases,followed by random walk (eight cases) and random coefficient (fivecases). Our results are consistent with Brooks, Faff and McKenzie(1998) and Faff, Hillier and Hillier (2000). However, using MSCIdatabase and for developed countries, Brooks et al. (2002) foundGARCH model was superior.15 The results in Table 4 provide anevidence of superior forecasting performance of Kalman Filter modelsand hence the justification of their usage as the optimal technique togenerate estimates of country risk from among those models tested.16

different from the other models. In particular, the Kalman Filter random walk leads todifferent return forecasts from other models in over 90% of the countries tested. Thisfinding supports the previous argument to favour Kalman Filter as the best model topredict country risk in EM. However, we thank our referee for pointing out that thepossible reason for GARCH being inferior to Kalman Filter is due to simplicity ofGARCH (1,1) model in comparison to models with an optimal GARCH lag length.

Fig. 2. Average dynamic beta values for all countries. The average dynamic values of thewhole sample of twenty EM countries.

256 A. Marshall et al. / International Review of Financial Analysis 18 (2009) 250–259

However, Kalman Filter does not directly model the time-varyingcorrelation between each country against the world index.

4.4. Comparison of DCC dynamic and constant betas

The above tests are based on in sample to investigate dynamicbeta. We further provide economic benefits analysis to compareconstant beta and dynamic beta estimated from DCC model. Weconduct economic benefits analysis from the portfolio perspective toexamine the characterization of dynamic and constant beta values. To

Table 4Mean square errors of in-sample forecasts (×10−5).

Country GARCH S and S (1990) Kalman Filter

Normal t-Dist GED Normal t-Dist GED RW AR (1) R coeff

Argentina 5.27 5.28 5.28 5.03 5.03 5.03 4.30 4.47 4.60Brazil 4.38 4.37 4.38 4.26 4.26 4.26 3.58 3.96 4.07Chile 1.33 1.33 1.33 1.32 1.32 1.32 1.04 0.78 1.04Colombia 2.45 2.44 2.44 2.54 2.54 2.54 2.00 1.81 2.12China 2.78 2.79 2.78 2.66 2.66 2.66 2.26 2.17 1.77Mexico 2.48 2.47 2.47 2.54 2.54 2.54 1.98 2.03 2.36Peru 2.51 2.50 2.50 2.49 2.49 2.49 2.06 1.77 2.03Korea 2.59 2.65 2.59 2.58 2.58 2.58 2.34 2.02 2.24Malaysia 3.66 3.65 3.65 3.60 3.60 3.60 3.13 3.22 2.56Philippines 1.73 1.72 1.72 1.78 1.78 1.78 1.45 0.95 1.36Taiwan 3.42 3.42 3.42 3.38 3.38 3.38 3.04 3.16 2.57Czech 9.29 9.30 9.29 9.18 9.18 9.18 7.97 8.96 8.02Hungary 9.59 9.58 9.58 9.46 9.46 9.46 8.35 9.24 9.04Poland 4.19 4.19 4.19 4.11 4.11 4.11 3.71 3.49 3.68Turkey 2.92 2.91 2.91 2.87 2.88 2.87 2.56 2.12 2.51Egypt 6.34 6.34 6.34 6.27 6.27 6.27 5.67 5.96 5.98India 3.65 3.65 3.65 3.70 3.70 3.70 3.22 2.83 0.63Israel 4.01 4.01 4.01 4.01 4.01 4.01 3.75 3.70 3.61Pakistan 3.19 3.19 3.19 3.21 3.21 3.21 2.89 2.69 2.75Russia 2.97 2.97 2.97 2.96 2.96 2.96 2.67 2.27 2.51

Mean square error (MSE) estimates between the observed country returns series andthe in-sample forecast country returns series. The beta representations are GARCH (1,1)normal beta, GARCH (1,1) t-distribution beta, GARCH (1,1) GED beta, Schwert andSeguin (S and S 1990) normal beta, S and S (1990) t-distribution beta, S and S (1990)GED beta, Kalman Filter RandomWalk beta, Kalman Filter AutoRegressive (AR)(1) beta,and Kalman Filter Random Coefficient beta. The difference between the actual and theforecast values is defined as the forecast error as follows: �t = ðyt− ytÞ where yt is theobservable variable. The accuracy of the forecast ˆRi;t generated from each of theconditional beta series can be assessed using the following statistical measure:

MSE =∑n

t=1�2t

n where: MSE stands for the mean square forecasting error. In order todetermine the best model to explain the time variant beta we select the one that yieldsthe smallest MSE. Lowest MSE in bold.

assess the economic values of dynamic and constant beta, we applyand compare dynamic and constant hedging strategies. Dynamichedging strategy is that a portfolio manager hedges the time-varyingmarket risk of a nation equity market against the world marketportfolio using dynamic betas while the constant hedging strategy isthat a portfolio manager hedges the time-varying market risk of anation equity market against the world market portfolio usingconstant betas. Table 5 presents the MAE and RMSE results for fulltwenty countries for the holdout sample. It can be seen that althoughthe improvement of predicting the hedging errors from constant betasto dynamic betas is relatively small, there are consistent reductionvalues of both MAE and RMSE of almost all countries for dynamicbetas. This comparison results confirm that models take dynamic betainto account can improve the effectiveness of the overall hedgingstrategy.

4.5. Determinants of dynamic beta

The results of ADF unit root tests for all economic variablesexamined in the determinants of the dynamic betas are presented inTable 6. The results show that the null hypothesis of a unit root formost country economic variables cannot be rejected. Therefore, thoseun-stationary economic series are transformed to achieve stationaryby taking the first difference of the natural logarithm.

Table 7 contains estimates of panel regression (Eq. (17)) for theentire sample period. The estimation indicates that INT, CPI and USINThave a strong combined explanatory power to the change of betavalues (significant at 5% level) and to a lesser extent FX rates have aninfluence (significant at the 10% level). The adjusted R2 value is 50.2%for the entire period. The significant positive INT coefficient suggeststhat a nation increasing interest rates will increase the beta value(consistent with Erb et al., 1996; Gangemi et al., 2000 amongstothers). An increase in interest rates reflects anticipation of inflationgrowth and in EM economies inflation is generally negativelyperceived by financial markets as a risk for stable and sustainedgrowth. This illustrates the importance of domestic monetary policieson country risk. Consistent with this we find the coefficient of CPI ispositively significant, suggesting that the change of CPI has strongimpact on betas (consistent with Abell and Krueger, 1989 and Oetzelet al., 2001). However, our other monetary policy variable (M1) is notsignificant in the model.17 We find some weak support for the impactof FX rates on betas (consistent with previous research on the impactof foreign exchange exposure on firm level stock returns, Jorion, 1990;Choi et al., 1992 and the mixed results for Verma and Soydemir,2006).18 It is evident that USINT has an important determinant of betavalues for each country (see also Verma and Soydemir, 2006 on thesignificant impact of global factors on Latin American country betas).The result show that if US federal increase its 3-month interest rates,the beta values for each country significantly increase. We found thatthe one real economic variable examined (IIP) is an unlikelydeterminant of time-varying country risk (consistent Verma andSoydemir, 2006 and Wdowinski, 2004) suggesting that in general agreater influence of monetary variables than real variables on countryrisk. These results are generally consistent with prior work ondeveloped markets and single and regional studies of EM (see Abelland Krueger, 1989; Andrade and Teles, 2006, Verma and Soydemir,2006) and therefore highlight the variables that impact time-varyingcountry betas for investment and government policy purposes.

17 This is not consistent with Verma and Soydemir (2006) although they did findvariation on the influence on money supply in four Latin American countries.18 They found significance impact for exchange rates in Mexico and Brazil but noeffect on Argentina and Chile. However, Oetzel et al. (2001) do report that they findcurrency risk as an important determinant of country risk.

Table 5Comparison of dynamic and constant betas using hedging strategy.

Country MAE (%) RMSE (%)

Dynamic beta Constant beta Dynamic beta Constant beta

Argentina 1.58 1.66 0.063 0.069Brazil 1.41 1.61 0.039 0.054Chile 0.83 0.83 0.013 0.014Colombia 1.12 1.15 0.028 0.031Mexico 0.93 1.05 0.016 0.023Peru 1.07 1.20 0.023 0.032Czech 1.18 1.19 0.029 0.031Egypt 1.10 1.10 0.031 0.031Hungary 1.26 1.32 0.032 0.039Israel 0.86 0.89 0.015 0.017Poland 1.25 1.31 0.029 0.033Russia 1.55 1.61 0.055 0.063Turkey 2.12 2.24 0.097 0.107China 1.29 1.32 0.036 0.039India 1.16 1.19 0.028 0.030Korea 1.39 1.41 0.043 0.045Malaysia 0.68 0.69 0.011 0.011Pakistan 1.22 1.24 0.032 0.033Philippines 1.14 1.14 0.027 0.027Taiwan 1.19 1.20 0.027 0.028

The effectiveness of hedging strategy is evaluated by mean absolute error (MAE) androot mean squared error (RMSE). The more effective hedging strategy should producesmaller values of MAE and RMSE. This table presents the MAE and RMSE results for thetwenty EM in the sample.

Table 7Maximum likelihood estimation of the fixed effects panel regression.

Variable Coefficients Std

FX rates 0.9435* (0.55)INT 0.2789** (0.05)M1 −0.5086 (0.53)CPI 1.6226** (0.46)IIP −0.0466 (0.28)USINT 0.6208** (0.12)Adjusted R2 0.502LogL −1134

Notes: Standard errors are in the parentheses. ** denotes significant at 0.05 level. *denotes significant at 0.10 level. We run a panel regression to examine what economicvariables that affect the change values of beta for all countries. For each country, itsbeta value at time t is decided by local economic variables such as FX rates, INT,M1, CPI, IIP and a global economic variable, USINT: betait = αi + θ′Xit + μiti = 1;Λ; k; t = 1;Λ; T where betait is the estimated dynamic beta, αi are countryspecific constants, Xit is the vector of the error term μit represents the effects of theomitted variables that are peculiar to both the individual country and time periods withE(μit)=0 and var(μit)=σ2

iμ. Robust estimation of the corrected covariance matrix iscomputed by using the White estimator for unspecified heteroscedasticity. The fiveeconomic variables for each country and the global economic variable are fromDataStream. The economic variable sample period spans from January 1995 toDecember 2008 in monthly intervals. The foreign exchange rates (FX) are thenominal values expressed as local currency per US dollar. The proxy for nationalinterest rates (INT) is the rates for 30 days certificate of deposits. Money supply (M1) ismeasure as the narrow stock of money. Goods price (CPI) is the domestic ConsumerPrice Index. Real activity (IIP) is the index for industrial production. US interest rate(USINT) is the US 3-month interest rate.

257A. Marshall et al. / International Review of Financial Analysis 18 (2009) 250–259

5. Conclusions

Assessing country risk in EM is vital for investment and riskassessment purposes. The primary focus of this paper is modellingcountry risk using time-varying beta. Country risk assessment iscentral to the international investment, which recently has increas-ingly focused on EM.We extend existing literature by applying a DCC-

Table 6Augmented Dickey–Fuller (ADF) unit root test for economic variables.

FX rates INT M1 CPI IIP

Argentina −1.40 −2.45 4.32 0.98 −1.66Brazil −1.74 −1.53 1.42 0.23 −2.46Chile −1.60 −2.57 2.64 1.11 −1.00Colombia −1.81 −2.05 1.39 −1.06 −1.46Mexico −0.93 −2.90* 1.43 −3.65** −1.76Peru −2.53 −0.99 5.87 −2.25 0.09Czech −0.70 −1.82 3.76 −1.86 −1.84Egypt −0.98 −1.85 4.63 3.69 −1.94Hungary −1.86 −3.12* 1.07 −1.76 −0.78Israel −2.01 −1.41 4.17 −2.83 −1.23Poland −1.58 −1.95 3.63 −4.50** −0.90Russia −2.04 −5.55** 3.50 1.42 1.23Turkey −1.31 −3.15* 3.43 1.24 −0.54China 1.17 −2.75 4.35 −4.53** −2.74India −1.68 −1.67 3.47 1.00 0.88Korea −2.54 −2.39 −1.07 −0.03 −0.21Malaysia −2.63 −1.57 2.25 0.91 −0.44Pakistan −1.01 −1.82 2.25 5.04 −2.24Philippines −2.25 −2.33 1.84 0.85 −2.24Taiwan −2.62 −3.69** 0.29 −0.20 −1.08

Notes: ADF tests are conducted using up to two lags of the variables; a maximum of twolagged values is sufficient to render residuals white noise. Critical value is −2.88,**significant at 5%, *significant at 10%. Five economic variables for each country fromDataStream. The economic variable sample period spans from January 1995 toDecember 2008 in monthly intervals. The foreign exchange rates (FX) are thenominal values expressed as local currency per US dollar. The proxy for interest rateis the rates for 30 days certificate of deposits. Money supply (M1) is measure as thenarrow stock of money. Goods price (CPI) is the domestic Consumer Price Index. Realactivity (IIP) is the index for industrial production. The augmented Dickey–Fuller (ADF)unit root test is applied to examine the order of integration of each economic variable.In ADF tests, the initial lag length is set at 6, then testing down to the first significant lag.

GARCH model. After confirming the existing evidence in developedmarkets that beta is time varying in twenty EM the models we testGARCH (1,1), the S and S (1990) model and the Kalman Filter model.We find that in the GARCH (1,1) model the t-distribution generatesthe lowest forecast errors when compared to a normal errordistribution and a generalised error distribution. In a comparison ofprevious modelling techniques the results of the modified Diebold–Mariano test statistics suggest that the Kalman Filter model outper-forms the GARCHmodel, the Schwert and Seguin (1990)model. Theseresults are consistent with earlier studies on developed markets butlater studies have shown the GARCH model was superior. Ourevidence suggests that by considering dynamic betas can improvebeta out-of-sample predicting ability in a hedging strategy evidencesuggests that considering dynamic betas can improve beta out-of-sample predicting ability and therefore offers potential gains forinvestors. These results have practical implications for investors whofocus on investing in EM. Allowing for variation over time is not onlyfor more understanding the dynamic process among the risky assetsin the portfolio but also for finding appropriate weight allocation forthe portfolio. Finally, we also find common determinants of dynamicbetas across countries as the time-varying betas are stronglyassociated with each nation's interest rates, US interest rates andthe CPI and to a lesser extent with foreign exchange rates. This resultis consistent with studies of developed markets and single countryand regional studies of EM and therefore highlights the variables thatimpact time-varying country betas for investment and governmentpolicy purposes.

Appendix A. GARCH model

A general multivariate GARCH model for the k-dimensionalprocess εt=(ε1t,…, εkt) is given by:

�t = ztH1 = 2t A1

where: zt is a k-dimensional i.i.d. process with mean zero andcovariance matrix equal to the identity matrix Ik. From theseproperties of zt and �t=ztHt

1/2, it follows that E[�t|Ωt−1]=0andE½�t�′t jΩt�1� = Ht . To complete the model, a parameterization for the

258 A. Marshall et al. / International Review of Financial Analysis 18 (2009) 250–259

conditional covariance matrix Ht needs to be specified. We need todetermine the order on lagged shocks (q) and the order on laggedconditional covariance matrices (p). In this study we use bivariateGARCH (1,1). We specify the functional form of the conditional mean

as:R′i;t = ɛ′i;t , for i=1, 2 where: R′

it =R1tR2t

� �and �′it =

�1t�2t

� �which can

be described as �i,t|Ωt−1~N (0,Ht) and �i,t is conditioned by thecomplete information set at time t−1, Ωt−1, is normally distributedwith zero mean and a conditional covariance matrix Ht, which can be

described as ht =h11;th12;th21;th22;t

� �. We choose a bivariate GARCH (1,1)

model to specify the function of conditional variance matrix Ht.Therefore the conditional variance equations take the form in vectoras follows:

h11;th12;th22;t

24

35 =

ω11ω12ω22

24

35 +

α11α12α13α21α22α23α31α32α33

24

35 ×

�21;t�1

�1;t�1�2;t�1

�22;t�1

2664

3775 +

β11β12β13β21β22β23β31β32β33

24

35

×h11;t−1h12;t−1h22;t−1

24

35 A2

or

ðvechÞHt = W + Aɛ + BHt−1

where: Ht,W, A and B represent their respective matrices in the aboveequation. We use the approach proposed by Bollerslev (1990) andBollerslev et al. (1994) by setting the off-diagonals in the coefficientmatrices (i.e. matrices A and B) equal to zero. The general form of thediagonal model is given by:

hii;t = ωii + αii�2i;t�1 + βiihii;t−1 for i = 1;…; k

hij;t = ρijffiffiffiffiffiffiffiffihii;t

q ffiffiffiffiffiffiffiffihii;t

qfor all i≠j

: A3

Thus the conditional variance and covariance for bivariate GARCH(1,1) can be specified as:

h11;t = ω11 + α11�21;t�1 + β11h11;t−1

h22;t = ω22 + α33�22;t�1 + β33h22;t−1

h12;t = ρ12ffiffiffiffiffiffiffiffiffiffih11;t

q ffiffiffiffiffiffiffiffiffiffih22;t

q : A4

To ensure a positive conditional variances, the values of α, β, andω are restricted to zero or greater. In order to estimate the a timeseries of conditional betas under bivariate GARCH (1,1) model, weneed to assume that there is a constant correlation between the returnof a country stock market index with the return of the world stockmarket index. The time series of conditional beta is then obtained byusing the standard formula to estimate the beta, which is based on theformula to calculate the slope coefficient of a simple regression asfollows:

β = covðRi;t ;Rw;tÞ= ðRw;tÞ A5

where: Ri,t and Rw,t represent the return of country i and return of theworld stock index respectively. The variance series of the world stockindex is directly obtained from the Eq. (4) and the covariance seriesbetween country i and the world stock index is provided in the formof h12,t.

Appendix B. Tests for varying parameter of beta

We carry out three different tests to examine a time invariantbehaviour of the beta values.

i. Rolling regression

The rolling linear regression model is expressed as:

ytðnÞ = XtðnÞβtðnÞ + ɛtðnÞ; t = n;…; T: B1

where: yt(n) is an (n×1) vector of observations on the response, Xt(n)is an (n×k) matrix of explanatory variables, βt(n) is an (k×1) vectorof regression parameters and εt(n) is an (n×1) vector of error terms.The n observations in yt(n) and Xt(n) are the n most recent valuesfrom times t−n+1 to t.

ii. Cumulative sum of the recursive residuals square (CUSUMSQ) test

The CUSUMSQ test (Brown et al., 1975) is based on the teststatistic:

Sr =∑r

t=k + 1w2

t

∑n

t=k + 1w2

t

; r = k + 1;…;n B2

where: the sumof the squared recursive residuals to period r divided bythe total sum of squared recursive residuals. The values run from Sk=0(for r=k) to Sn=1 (for r=n) for the expected value of S under thehypothesis of parameter constancy which is: E[St]=(r−k)/(n−k).

iii. Heteroscedasticity-based tests of beta stability

For the Lagrange Multiplier (LM) test for an ARCH (p) process weretrieve the residual value (εi,t) from the estimated unconditionalmarket model and run the following regression model: ɛ2t = α0 +

∑p

s=1αsɛ

2t−s + υ. We test the null hypothesis of homoskedasticity H0:

α1 = α2 = α3 = … = αp = 0 against the alternative hypothesisthat at least one αs≠0 by using (n−p)R2 as test statistic where R2 isthe coefficient determination of the regression model. If the LMstatistic evaluated under the null hypothesis is greater than χα,(p−1)

2,the null hypothesis is rejected at level α≠0.

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