Contagion: An Empirical Test

Board of Governors of the Federal Reserve System International Finance Discussion Papers Number 775 September 2003 Contagion: An Empirical Test Jon Wongswan NOTE: International Finance Discussion Papers are preliminary materials circulated to stimulate discussion and critical comment. References to International Finance Discussion Papers (other than anacknowledgmentthatthewriterhashadaccesstounpublishedmaterial)shouldbeclearedwiththe author or authors. Recent IFDPs are available on the Web at www.federalreserve.gov/pubs/ifdp/.

Contagion: An Empirical Test ∗ Jon Wongswan Abstract: Using the conditional Capital Asset Pricing Model (CAPM), this paper tests for the existence and pattern of contagion and capital market integration in global equity markets. Contagion is defined as significant excess conditional correlation among different countries’ asset returns above what could be explained by economic fundamentals (systematic risks). Capital market integration is defined as the situation in which only systematic risks are priced. The paper uses a panel of sixteen countries, divided into three blocs: Asia, Latin America, and Germany-U.K.-U.S., for the period from 1990 through 1999. The results show evidence of contagion and capital market integration. In addition, contagion is found to be a regional phenomenon. Keywords: contagion, CAPM, excess correlation JEL classification: G12, G14, G15, F30 ∗DivisionofInternationalFinance,BoardofGovernorsoftheFederalReserveSystem. Thepreviousversion of the paper was circulated under my previous name as Jon W. Tang. I would like to thank Ravi Bansal for his support, encouragement, and for his many insightful ideas that have been so helpful in preparing this paper. I also thank Tim Bollerslev, Campbell Harvey, Ranil Salgado, George Tauchen, Haibin Zhu, studentsintheDukeEconometricsandFinanceLunchGroup, participantsatthe2001AsiaPacificFinance Association Conference (Bangkok), and participants at the Bank for International Settlements workshop for their suggestions. Of course, I take responsibility for anyandall errors. For questions andcomments, please contactJonWongswan. Email: Jon.Wongswan@frb.gov. Theviewsinthispaperaresolelytheresponsibility of the author and should not be interpreted as reflecting the views of the Board of Governors of the Federal Reserve System or of any other person associated with the Federal Reserve System.

1 Introduction Theoccurrenceofseveralmajorfinancialcrisesinthelate1990shadlargeeffectsoneconomic performance, asset valuation, and the efficiency of the global financial markets in sharing risk. As a result policy makers, the media, and academics have increasingly focused their attentiononthespreadofcrises(shocks)fromcountrytocountry. Thisphenomenonisoften called (sometimes somewhat loosely) contagion. Although interest in contagion has never been higher, there is still no generally accepted definitionofcontagion1,letaloneunderstandingofthephenomenon. Contagionissometimes referred to as co-movements among countries that cannot be explained by economic fundamentals (Masson (1998)). This concept is similar to the notion of excess co-movements in Pindyck and Rotemberg (1990). In this paper I follow this definition, and more specifically, define contagion as significant excess conditional correlations among countries asset returns beyond what could be explained by economic fundamentals or systematic risks. With this definition, I test both for the existence and pattern of contagion in global equity markets. Empiricalstudiesofcontagionhaveexplodedinthepastfewyears, witheachstudyusing different testing methodologies and data samples.2 Despite the differences in methodologies, most studies have two controversial features in common. The first feature is that the proxies foreconomicfundamentalsarenotdefinedwithreferencetoatheory. Fromthewaywedefine contagion, its existence depends on the economic fundamentals used. Most empirical studies tend to choose fundamentals somewhat arbitrarily, using macroeconomic variables, dummies for important events, and time trends (e.g., Valdes (1997) and Baig and Goldfajn (1999)). Thecostofnotappropriatelycontrollingforeconomicfundamentalsisthatwemightpickup 1See Masson (1998) and Rigobon (2002) for detail discussion. Calvo and Reinhart (1996), Park and Song (2001), and Forbes and Rigobon (2002) refer to contagion as significant increases in asset returns comovements,whileValdes(1997),BaigandGoldfajn(1999),ConnollyandWang(2002),andBekaert,Harvey, andNg(2003)refertoitinanarrowerdefinitionassignificantincreasesinassetco-movementthatcannotbe explainedbyeconomicfundamentals. EdwardsandSusmel(2001,2003)refertocontagionasassetvolatility co-movements. In addition, Sachs, Tornell, and Velasco (1996), Eichengreen, Rose, and Wyplosz (1996), Gregorio and Valdes (2001), and Kaminsky and Reinhart (2000) define contagion as a situation in which a crisis in one country lead to a higher probability of a crisis occurring in another country. 2See Claessens, Dornbusch, and Park (2001) for a comprehensive review of the literature. 1

spurious relationships that are thought to be evidence of contagion. For example, a change in the U.S. monetary policy may induce equity markets in other countries to react in the same way. Masson (1998) provides detail discussion on this issue. Toprovideaframeworktocontrolforeconomicfundamentals, IrelyontheCapitalAsset Pricing Model (CAPM). The economic fundamental under the CAPM is the world market portfolio. Evidence of contagion is the significance conditional correlations of idiosyncratic risk–the part that cannot be explained by the world market portfolio. The second feature of these studies relates to the modeling of economic time-series. It is well known that most economic time-series exhibit time dependencies in the second moment (Mandelbrot (1963); Fama (1965)). As an illustration of time dependency, Figure 1 shows plotsofrollingcrosscountrycorrelationsinequitymarkets. Itisevidentfromthefigurethat equity returns exhibit time-varying correlations. Therefore, in order to make sense of the empirical results, it is important that we properly take this property into account.3 In this paper I use a multivariate General Autoregressive Conditional Heteroscedastic (GARCH) model, an extension of work developed by Engle (1982) and Bollerslev (1986), to model the conditional covariance matrix of idiosyncratic risks jointly with a univariate GARCH model for the market portfolio volatility. With a complete statistical model of the conditional covariance matrix of asset returns–the world market portfolio and idiosyncratic parts, I test for contagion jointly among different countries.4 AnotherpossibleproblemrelatingtotheuseoftheCAPMtopriceassetsforallcountries is the assumption of capital market integration. Capital market integration is defined as a situation in which only systematic risks are priced (King, Sentana, and Wadwani (1994); 3Inempiricalstudiesofcontagion,Boyer,Gibson,andLoretan(1999),ForbesandRigobon(2002),Rigobon (2002), Edwards and Susmel (2001, 2003), and Bekaert, Harvey, and Ng (2003) recognize heteroscedasticity in economic time-series and take this property into account when they perform the test. 4To my knowledge, this is the first paper to attempt to test for contagion jointly for a large number of countries (16). The multivariate GARCH model that I estimate has 313 parameters. The estimation is performed in Fortran 90 with NPSOL optimizer (Gill, Murray, Saunders, and White (1983)). A closely related, contemporaneous, paper is Bekaert, Harvey, and Ng (2003). They extend the world CAPM by decomposing the world market portfolio into the U.S. and regional returns. Unlike this paper, they do not modeltheconditionalcorrelationofidiosyncraticrisksdirectlyandtheyperformthetestintwosteps,which is less efficient than the one-step test performed in this paper. 2

Bekaert and Harvey (1995)). I implicitly assume that capital markets are fully integrated. Figure 2 illustrates the relationship between contagion and capital market integration concepts. Under the CAPM, evidence of capital market integration is the significance of only theworldmarketportfolioriskintheassetreturnequation. Totestthishypothesis,Itestfor thesignificanceofconstanttermsandidiosyncraticvolatilitiesinthereturnequation. Under the null hypothesis of capital market integration, all those terms should be insignificant. Using the conditional CAPM and properly modeling the time-series dependencies of equityreturns,Itestfortheexistenceandpatternofcontagionforsixteencountries,covering three country blocs for the period from 1990 through 1999. I find evidence for contagion and capital market integration. In addition, contagion is found to be a regional phenomenal. The results on capital market integration are robust to several specification tests. The remainder of the paper is organized as follows. Section 2 describes the setup and methodology of the tests. Empirical results are discussed in Section 3. Diagnostic tests of the model are presented in Section 4. Finally, Section 5 presents conclusions. 2 Model Setup and Methodology 2.1 Asset Excess Return From the Capital Asset Pricing Model (CAPM) of Sharpe (1964), Lintner (1965), and Black (1972), asset risk premium is proportional to the covariance of asset return and the market portfolio return. This framework is appropriated to analyze cross-sectional asset returns at any given point in time. Since we live in a dynamic world, it would be more realistic to assume that the CAPM holds conditionally period by period (Jagannathan and Wang (1996)). Under this framework, asset excess returns can be postulated as Zt = Bt−1 Et−1 (z t m )+Bt−1 {z t m−Et−1 (z t m )}+(cid:1)t, (1) Et−1 ((cid:1)t) = 0, m Et−1 ((cid:1)tz t ) = 0, 3

where Zt is an N ×1 vector of asset excess returns (asset return minus risk free rate), Bt−1 is an N×1 vector of asset conditional beta given the information at time t−1, z m is market t portfolio excess return, (cid:1)t is an N×1 vector of idiosyncratic risks, N is the number of assets, and Et−1 (·) denotes the mathematical expectation conditional on the information available at time t−1. It should be noted that the CAPM does not impose any restriction on the secondmomentoftheidiosyncraticrisks((cid:1)t). Theyareallowedtobecorrelatedacrossassets. The time-variation of asset conditional beta (Bt−1 ) is modeled as Bt−1 = b 0 +b 1 Jt−1 , (2) whereb 0 isanN×1vectorofconstants,b 1 isanN×K matrixofcoefficients,Jt−1 isanK×1 vector of information variables known at time t−1, and K is the number of information variables. This specification includes the usual static CAPM when b = 0. In general, the 1 time-variation of Bt−1 can be modeled as any function of information variables known at time t−1, but for simplicity I assume the function to be linear. Given the CAPM specification in (1) and (2), the conditional covariance matrix of asset excess returns is Vt−1 (Zt) = Bt−1 σ m 2 ,t B t (cid:2) −1 +Ωt, (3) whereVt−1 (Zt)denotesanN×N matrixoftheconditionalcovarianceofassetexcessreturns at time t given the information at time t−1, σ2 denotes the conditional variance of market m,t portfolioexcessreturnattimetgiventheinformationattimet−1, andΩt denotesanN×N matrix of the conditional covariance of the idiosyncratic risks at timet given the information at time t−1. The above setup shares many similarities with the Arbitrage Pricing Theory (APT) of Ross(1976)andChamberlainandRothschild(1983),forthecaseinwhichmarketportfoliois theonlyfactor. Theextensionofthisideatoestimatetheassetconditionalcovariancematrix is the Factor-Autoregressive Conditional Heteroscedastic (Factor-ARCH) model.5 There are 5Themajorworksinthisliteratureare DieboldandNerlove(1989),Engle,Ng,andRothschild(1990),Ng, Engle, and Rothschild (1992), Engle and Kozicki (1993), Engle and Susmel (1993), King, Sentana, and Wadwani (1994), and Demos and Sentana (1998). 4

two key differences between the model in this paper and the Factor-ARCH model. The first issue is the theoretical restriction on the idiosyncratic risks ((cid:1)t). The Factor- ARCH model is derived from the APT, which implies that the conditional covariance matrix of the idiosyncratic risks (Ωt) cannot have all off-diagonal elements be non-zero. However, from the derivation of the CAPM, the only restriction on the idiosyncratic risks is that they are orthogonal to the market portfolio. Therefore, in this paper I do not impose any restriction on the idiosyncratic risks conditional covariance matrix. This implication will be of interest in testing for contagion. However, how can I interpret a non-diagonal covariance matrix? From the standpoint of the APT, a non-diagonal covariance matrix means that I do not have enough relevant factors. On the contrary, since I rely on the maintain hypothesis, this result is interpreted as evidence of contagion based on the CAPM model. The second issue relates to the implementation issue. In most of the APT and Factor- ARCH studies, factors are often obtained from statistical methods–factor analysis or principal component analysis–which have no economic interpretation. However, in this paper I rely on the CAPM; therefore, the economic fundamental in this case is the market portfolio. 2.2 Market Portfolio Expected Return and Volatility From the CAPM, the market portfolio expected return has a linear relationship with its volatility. ImodelthetimevaryingmarketportfolioexcessreturnvolatilitywithaGARCH(1,1)in-mean as in Bollerslev, Engle, and Wooldridge (1988), z t m = α 1 σ m 2 ,t +ηt, (4) where ηt is the innovation of the market portfolio excess return. The conditional variance of the market portfolio return is defined as σ2 = γ +γ η2 +γ σ2 , (5) m,t 0 1 t−1 2 m,t−1 where γ , γ , and γ are parameters. 0 1 2 5

2.3 Idiosyncratic Risks Covariance Matrix In modeling the conditional covariance matrix, many methodologies can be employed. The conditional covariance matrix can be modeled as parametric functions, such as with the GARCH model (Bollerslev, Engle, and Wooldridge (1988)) and with some functions of information variables (Harvey (1991)). I model the conditional covariance matrix with a multivariate GARCH model. However, within the GARCH framework, there are many specifications that I can employ such as the DiagonalVECHmodelofBollerslev,Engle,andWooldridge(1988),theFactor-ARCHmodel of Engle, Ng, and Rothschild (1990), the Constant Conditional Correlation (CCORR) model ofBollerslev(1990),theBEKKmodelofEngleandKroner(1995),theGeneralizedDynamics Covariances (GDC) model of Kroner and Ng (1998), the R-GARCH model of Gallant and Tauchen (1998), the decentralized estimation of Ledoit, Santa-Clara, and Wolf (2002), the time-varying conditional correlation of Tse and Tsui (2002), and the Dynamic Conditional Correlation (DCC) model of Engle (2002). In selecting an appropriate model for this paper, the necessary conditions are as follows. First, the conditional covariance matrix should be positive semi-definite. Second, the matrix should be symmetric. Third, the matrix should be suitable for parameterizing the covariance to be zero while maintaining the variance to be positive. Under these requirements, the candidate models are the Diagonal VECH, the GDC, and the R-GARCH models. The Factor-ARCH and BEKK models cannot parameterize the covariances to be zero while maintaining positive variances.6 The CCORR restricts the conditionalcorrelationtobeconstantovertime. Thedecentralizedestimation,theDCC,and the time-varying conditional correlation model are nice ways to estimate a large conditional covariance matrix; however, they do not have a clean way to impose parametric restrictions so that conditional covariance equals zero. IchoosetheR-GARCH(1,1)modelforthefollowingreasons: first,theR-GARCH(1,1)allowsforricherdynamicsascomparedtotheDiagonalVECHandsecond,theR-GARCH(1,1) 6The Factor-ARCH is a special case of the BEKK model. 6

requiresasmallernumberofparametersascomparedtotheGDC.TheR-GARCH(1,1)specification is (cid:2) Ωt = RtR t , (6) vech(Rt) = ρ+P|(cid:1)t−1 |+diag(G)vech(Rt−1 ), (7) where Rt is an N×N upper triangular matrix, ρ is an N(N+1)/2×1 vector of constants, P isanN(N+1)/2×N matrixofcoefficients, GisadiagonalN(N+1)/2×N(N+1)/2matrix of the coefficients, and diag represents the diagonal part of a matrix. The R-GARCH(1,1) is similar to the GARCH(1,1) model, but instead of parameterizing the variance, R-GARCH parameterizes the standard deviation. One drawback of the R-GARCH model, also with other multivariate GARCH models in general, is the large number of parameters that need to be estimated. For R-GARCH(1,1) of N assets, there are N(N +1)(N +2)/2 parameters. For example, a system with 16 assets requires 2,448 parameters. To make the estimation feasible, I impose some restrictions on the P matrix. These restrictions are shown in the Appendix. The number of parameters under the restricted R-GARCH(1,1) of N assets is 2N(N +1)−N. In the case of 16 assets, this reduces the number of parameters to 528. A drawback to this specification is that it is sensitive to the ordering of assets.7 2.4 Estimation Method TheestimationisconductedbyQuasi-MaximumLikelihoodEstimation(QMLE).Therobust standard errors are calculated from H −1SH −1, where H is the Hessian and S is the outer productofthegradients(BollerslevandWooldridge(1992)). Thelog-likelihoodofthesample is (cid:1)T (cid:1)T L = − NT ln(2π)− 1 ln|Σt |− 1 Υ (cid:2) t Σ − t 1Υt, (8) 2 2 2 t=1 t=1 where L is the log-likelihood, T is the number of observations per asset,    Zt −C −Bt−1 Et−1 (z t m )  Υt =  , (9) z m−α −α σ2 t 0 1 m,t 7In Section 4, I test this sensitivity by estimating the model by changing the order of country returns. 7

and     (cid:8) (cid:9) Σt =   Bt−1   σ m 2 ,t B t (cid:2) −1 1 +   Ωt 0  . (10) 1 0 0 It should be noted that I also estimate the intercept terms in the mean equation, C and α . 0 Theoretically, the intercept terms should be zero. Alternatively, I can jointly model market portfolio and asset idiosyncratic risks conditional covariance matrix as one multivariate GARCH model, Σt (Bollerslev, Engle, and Wooldridge (1988)), as opposed to modeling Ωt and σ m 2 ,t separately. However, if I model Σt jointly, restriction of the zero idiosyncratic risk covariance will be non-parametric. The results would rely on the assumption of a distribution of Υt, which is hard to justify in a multivariate setting. In the contrast, the parameterization I use in this paper does not rely on the distributional assumption on Υt. 2.5 Hypothesis Testing The contagion hypothesis tests the significance of the conditional correlations among asset excessreturnsafteraccountingfortheCAPMsystematicrisk,marketportfolioexcessreturn. This hypothesis is equivalent to testing the significance of the conditional covariances of the idiosyncratic risks (Ωt). However, in testing for contagion, we are implicitly assuming that the capital market in each country is fully integrated.8 In other words, we are assuming that the world CAPM can price all assets. Therefore, to make sense of the result of the contagion test, I first test for capital market integration. I then proceed to test for contagion. The hypothesis for capital market integration is that if the capital market is fully integrated, then only systematic risk (market portfolio excess return) is priced. This implies a joint test on all intercepts in each country’s mean equation (C). The evidence for capital market integration is the insignificance of C. The test is performed by a robust Wald (W) test. Later in Section 4, I also use different parametric test by testing whether the idiosyncratic risk volatility is priced or not. 8See Figure 2 for a conceptual relationship between contagion and capital market integration. 8

The hypothesis for contagion is to test for the significance of the conditional covariances in the idiosyncratic risks (Ωt). I pursue the test by using a robust Lagrange Multiplier (LM) test. The parametric restrictions on the general model is in the Appendix. The test starts from the most restricted model. If that model is rejected, the model is then expanded, and this process repeats until the model cannot be rejected. The test for contagion begins from the null hypothesis of no contagion. I restrict the idiosyncratic conditional covariance matrix to be diagonal    ω 11,t 0 ... 0        0 ω 22,t ... 0   Ωt =    . . . . . . ... . . .    ,   0 0 ... ωNN,t where ωij,t is the idiosyncratic conditional covariance at time t between country i and j. Under this null hypothesis, the co-movements among countries can all be explained by systematic risk. If the model is rejected, I then test for contagion within a specific group. The grouping criteria are, for example, economic similarity, trading partners, common lenders, and geographic region. With this hypothesis, there is contagion within a group but not across groups. To illustrate the restrictions, consider contagion within the group for two groups of countries. The idiosyncratic covariance would be restricted to have the following structure:    ω 11,t ω 12,t 0 ... 0        ω 21,t ω 22,t 0 ... 0       Ωt =   0 0 ω 33,t ... ω 3N,t   .    . . . . . . . . . ... . . .      0 0 ωN3,t ... ωNN,t I then test for the restrictions. If the model is rejected, I relax more restrictions on the covariance matrix until it cannot be rejected. Specifically, I allow for more non-zero covariance terms. Once the model fails to reject, the structure from the grouping criterion is the pattern of contagion. It is worth mentioning that the most general model is the one that has contagion across all countries–which allows all covariance terms to be non-zero. 9

3 Empirical Results 3.1 Data Description The data series for equity market indices (total market return in U.S. dollars) are from Datastream Global Indices, except in the cases of Argentina and Brazil, for which the data series are from International Finance Corporation (IFC) Global indices.9 The series are mid-week (Wednesdays) on a weekly frequency from April 11, 1990 through September 15, 1999–a total of 493 observations. The sample includes four groups of countries as follows: South EastAsia(Indonesia, Malaysia, The Philippines, Singapore, andThailand), East Asia (Hong Kong, Japan, South Korea, and Taiwan), Latin America (Argentina, Brazil, Mexico, and Chile), and Germany, the U.K., and the U.S. Equity excess returns are computed as ex-post gross return minus ex-post one-month Euro dollar interest rate. Information variables to capture the time variation of beta (matrix J from equation(2)) include the world market dividend yield in excess of the risk free interest rate (DY), the change in the term structure spread (U.S. 10-year bond yield minus U.S. 3-month treasury bill: TERM), and the default spread (Moody’s Baa minus Aaa bond yields: DEF).10 Table 1 shows summary statistics on excess return for each country. The last three columns report Ljung-Box statistics, Q12, QAR(3)12, and QSAR(3)12, for excess returns, innovations of excess returns from an autoregressive model with three lags (AR(3)), and squared innovations of excess returns from an AR(3), respectively. The test statistic (Q12) indicates that returns are highly serially correlated. In order to identify the ARCH effect, I take out the effect of autocorrelation in excess returns by using an AR(3) model. The innovation from the AR(3) shows no indication of autocorrelation, while the squared innovation indicates a strong degree of autocorrelation, providing evidence of an ARCH effect. Therefore, itisappropriatetomodelthedependencyofthesecondmomentsofassetreturns. 9Datastream does not cover Brazil and their data for Argentina starts in August 1993. Morgan Stanley Capital International (MSCI) is another major alternative data source for equity market indices. I choose DatastreamoverMSCIbecauseMSCIonlyhasmarkettotalreturnonamonthlybasis. IFCdataonlycover emerging markets. 10Bekaert and Harvey (1995), Jagannathan and Wang (1996), and Ferson and Harvey (1999) advocated using these information variables to capture the world business cycle. 10

Tables2and3showtheunconditionalcorrelationandcovariancematrix. Itisinteresting tonotethatthecorrelationswithineachregionaremuchstrongerthanthecorrelationsacross the regions. Also, the Philippines and Taiwan have very low correlations with the rest of the world and have negative correlations with the world market portfolio. 3.2 Capital Market Integration and Contagion Hypotheses In this section, I test for capital market integration and contagion in equity markets under the assumption that beta is time-varying (Bollerslev, Engle, and Wooldridge (1988); Harvey (1989); Ferson and Harvey (1991)). The time-variation of beta is assumed to be a linear function of lagged information variables (equation 2). Ibeginbytestingthehypothesisofnocontagion,whichimpliesthattheconditionalcorrelationsafteraccountingfortheworldmarketportfolioexcessreturnarezero. Inotherwords, it implies that all co-movements can be explained by economic fundamentals, represented by the world market portfolio. This approach is equivalent to testing for the diagonality of the idiosyncratic risk conditional covariance matrix. As discussed in the previous section, this test implicitly assumes that capital markets are fully integrated. Therefore, I start with the test for capital market integration under the restricted model of no contagion. Figures 3 and 4 show the structure of and restrictions on the Ωt and Rt matrices. I call this hypothesis No Contagion. Table4showsresultsforthetestofcapitalmarketintegration. TherobustWaldstatistic is 19.24. The statistic fails to reject the null hypothesis of capital market integration, given the 95% critical value of 26.30 for χ2 . This result is not surprising, as it is well known 16 that, during the 1990’s, most countries liberalized their capital accounts. This finding is consistent with the results in Bekaert and Harvey (1995), Bekaert, Harvey, and Lumsdaine (2002), Bekaert and Harvey (2000), and Henry (2000), which all test for capital market integration in emerging markets. The test of contagion is performed with the robust LM statistic. (See the Appendix for the benchmark model.) The robust LM statistic is 1085.35 whichrejectsthenullhypothesisofnocontagionatthe95%confidencelevelgiventhecritical value of 532.08 for χ2 . 480 11

Given that the No Contagion hypothesis is rejected, I then test for contagion within a group of countries. I group countries by geographic regions. The rationale for using this criterion is, as shown in Kaminsky and Reinhart (2000), that grouping countries by geographic region (Gregorio and Valdes (2001)), economic similarities (Sachs, Tornell, and Velasco (1996)), trade with common third parties (Glick and Rose (1999)), and common lenders (Rijckeghem and Weder (2001, 2003)) all yield a similar set of countries. I divide the countries into four groups: South East Asia, East Asia, Latin America, and Germany-U.K.- U.S. This hypothesis is called Regional Contagion I. Figures 5 and 6 illustrate the grouping of countries and parametric restrictions on Ωt and Rt. Table 4 shows that the hypothesis of capital market integration can not be rejected at the 95% confidence level. The contagion hypothesis is also rejected at 95% confidence level. Inthenextstep,ItestforcontagionwithinaregionbytreatingSouthEastAsiaandEast Asia as one block, which I refer to as Asia. This hypothesis is termed Regional Contagion II. Figures 7 and 8 illustrate the grouping of countries and parametric restrictions on Ωt and Rt. The result for capital market integration is similar to that of the previous case, as shown in Table 4. As for the contagion hypothesis, the result shows that the hypothesis cannot be rejected. In other words, I find evidence for contagion within a group of countries but not across groups. The results show that from the standpoint of the CAPM model there is evidence of capital market integration and contagion within a geographic region. This result is similar to the findings in Bekaert, Harvey, and Ng (2003). To test the evidence of time-varying beta, I employ a robust Wald test on b for the 1 Regional Contagion II model. The robust Wald statistic is 75.26. The test statistic is distributed as χ2 and the critical value at the 95% confidence level is 65.17. The test 48 rejected the null hypothesis for time-invariant beta. The ability of the Regional Contagion II model to capture properties of returns series are shown in Table 5. I employ a test on the standardized residuals (U t −1Υt). The stan- (cid:2) dardization is based on a Cholesky decomposition (UtU t = Σt). If the model is correctly specified, the standardized residuals should be independently identically distributed (i.i.d). Table 5 shows test statistics for skewness, kurtosis, and 12th-order serial correlation (Ljung- 12

Box statistics: QZ12) and for squared 12th-order serial correlation (QZS12). The result indicates some degrees of dependency in the first moment. However, the Regional Contagion II model appears to capture dependencies in the second moment fairly well for all countries except Germany and the U.S. 3.3 Contribution of Market Portfolio to the Conditional Correlation The main objective of this paper is to test for contagion. Under the CAPM, contagion is definedassignificantconditionalcorrelationsafteraccountingfortheworldmarketportfolio. The results from time-varying beta indicates that there is evidence of regional contagion. Therefore it is of interest to investigate the extent to which the market portfolio can explain intra-regional conditional correlations. Figure9comparestheconditionalcorrelationsimpliedfromtheCAPMwithtime-varying beta under the Regional Contagion II model (solid line) and the conditional correlation computed from a rolling window (dashed line). This comparison offers evidence that conditional correlations implied from the model are smoother than the rolling correlation. The contribution of the world market portfolio (solid line) to the total conditional correlation (dashed line)isshown inFigure10. Itisinterestingtonotethatthe marketportfoliocancapturethe variation but fails to capture the level of correlation. However, in the case of Latin America, market portfolio can capture neither the variation nor the level. 4 Diagnostic Test 4.1 Market Portfolio Volatility Itisoftennotedthatequityreturnshavethicktaildistribution,whichthenormaldistribution cannot be able to capture. In testing for contagion in this paper, the estimates of the conditional volatility of the market portfolio play an important part. Although this paper uses QMLE and robust standard errors, which should give consistent estimates for both the parameters and standard errors, in practice the estimates could be different under different error distributions. 13

Thus, I estimate market portfolio volatility under the alternative t-distribution. Table 6 shows parameter estimates of the market portfolio volatility. The second and third columns show the estimates from the Regional Contagion II model with time-invariant and timevarying beta, respectively. The fourth column shows the parameter estimates of market volatility under the assumption of t-distribution with 5 degrees of freedom. The parameter estimates on the volatility equation are very close. Figure 11 shows the plot of the market portfolio volatility. It is evident that the estimates of volatility are almost the same. It is interesting to see that the volatility from the Regional Contagion II model is always of the same magnitude as that under the t-distribution. 4.2 Idiosyncratic Covariance Matrix Asmentionedintheprevioussection,onedrawbackoftherestrictedR-GARCHspecification is the sensitivity of the estimates to the ordering of assets. To check for the robustness, I estimate the Regional Contagion II model again by changing the orders of countries within each group. It turns out that the LM test of the model under the null hypothesis of regional contagion cannot be rejected at the 95% confidence interval. 4.3 Asymmetric Variance and Covariance In modeling the volatility of equity returns, many authors, including Nelson (1991), Glosten, Jagannathan, and Runkle (1993), Bekaert and Wu (2000), find evidence of asymmetric volatility. However, the evidence of asymmetric volatility in the emerging markets is mixed, asshowninBekaertandHarvey(1997)andLundblad(2000). Thefindingsareverypuzzling, because most people attribute asymmetric volatility to the leverage effect (Christie (1982)), which of course is a wide-spread phenomenon in the emerging markets. IemployanLMtestforasymmetricvolatility. Toaccountforasymmetry, theR-GARCH is modified to include ζt−1 which is to capture an addition impact of negative innovation beyond the same size positive innovation on returns conditional variance-covariance matrix. The modified R-GARCH specification is (cid:2) Ωt = RtR t , (11) 14

vech(Rt) = ρ+P|(cid:1)t−1 |+diag(G)vech(Rt−1 )+D|ζt−1 |, (12) where D and P are N(N +1)/2×N matrix of coefficients and ζt−1 is defined as        (cid:1) 1,t−1     ζ 1,t−1     .   .  (cid:1)i,t−1 if (cid:1)i,t−1 < 0 (cid:1)t−1 =   . .   , ζt−1 =   . .   , ζi,t−1 =  ∀i.     0 otherwise (cid:1)N,t−1 ζN,t−1 The restrictions on the D matrix are the same as those for the P matrix. It is interesting to note that under the modified R-GARCH, this specification can capture the asymmetry both in variance and covariance. The null hypothesis of no asymmetry in both the variance and covariance of idiosyncratic risks implies the parametric restriction D = 0 (under the three-block diagonal, Regional Contagion II model). The robust LM test statistic for equity markets under the Regional Contagion II model is 120.78. The test statistic is distributed as χ2 and the critical value at the 95% confidence level is 131.03. The result indicates that 106 we fail to reject the null hypothesis of no asymmetry at 95%. 4.4 Capital Market Integration From the test of contagion, I implicitly assume that capital markets are fully integrated. The test for capital market integration is to test whether only systematic risk is priced. I implemented the test in the previous section by testing the significance of the intercept in the mean equations (C). This test is only one of various tests under the definition of capital market integration. To check for the robustness of the result, I test whether idiosyncratic volatility is priced. The model specification is Zt = C +Bt−1 Et−1 (z t m )+Bt−1 {z t m−Et−1 (z t m )}+(cid:1)t+diag(A)diag(Ωt), (13) where A is a diagonal N ×N matrix of coefficients and diag represents the diagonal terms of a matrix. The null hypothesis of capital market integration implies parametric restriction C = 0 and A = 0. Due to the computational time, I use the estimates from the Regional Contagion II model, which also includes C, and apply an LM test for the significance of A. The robust LM test statistic is 24.25. The test statistic is distributed as χ2 and the critical value at the 16 15

95% confidence level is 26.30. The result indicates that we fail to reject the null hypothesis of capital market integration at 95%. 5 Conclusions This paper tests for contagion and capital market integration in equity markets using the conditionalCAPM.Thepaperoffersasystematicwaytotestforcontagionbyusingeconomic theory as a guide for which economic fundamentals belong in the empirical model and by recognizing and modeling the properties of economic time-series. The paper finds evidence of regional contagion and capital market integration in equity markets. The findings have several important implications. First, regulators should pay more attention to developments in both domestic and world financial markets since there might becontagionacrossmarkets. Second,theevidenceofregionalcontagionmightimplyregional factors that are not priced in world equity markets but that systematically affect all equity markets in the region. Therefore, if we can identify these regional factors, we might be able to hedge these risks. An extension of this work would be to explain regional contagion. This can be pursued in several directions. For example, it would be interesting to investigate whether currency markets can explain regional contagion. Another issue worth investigating is to study the effect of information asymmetry on contagion (e.g., Calvo and Mendoza (2000); Kyle and Xiong (2001); Kodres and Pritsker (2002)). 16

Appendix A Restrictions on the R-GARCH specification The idiosyncratic conditional covariance matrix is modeled as R-GARCH(1,1). The model is (cid:2) Ωt = RtR t , vech(Rt) = ρ+P|(cid:1)t−1 |+diag(G)vech(Rt−1 ), whereΩt isanN×N conditionalcovariancematrix, Rt isanN×N uppertriangularmatrix, ρ is an N(N +1)/2×1 vector of constants, P is an N(N +1)/2×N matrix of coefficients, G is a diagonal N(N +1)/2×N(N +1)/2 matrix of the coefficients, and N is the number of countries. The number of parameters for this covariance matrix is N(N +1)(N +2)/2. When N = 16, the number of parameters is 2,448. Under the restricted model (Regional Contagion II), the number of parameters is 585, which is a large number of parameters as compared to the data. The ratio of data per parameter is 13. To overcome this over parameterizing problem, I impose restrictions on the structure of the P matrix. The diagonal element of R is assumed to only depend on its own innovation and the off-diagonal is assumed to depend on its covariate. To illustrate the restrictions, consider a case in which N = 4. The R matrix is    r11,t r12,t r13,t r14,t       0 r22,t r23,t r24,t  Rt = .    0 0 r33,t r34,t  0 0 0 r44,t The variance-covariance matrix can be written in term of r’s as    r1 2 1,t+r1 2 2,t+r1 2 3,t+r1 2 4,t r12,tr22,t+r13,tr23,t+r14,tr24,t r13,tr33,t+r14,tr34,t r14,tr44,t      r12,tr22,t+r13,tr23,t+r14,tr24,t r2 2 2,t+r2 2 3,t+r2 2 4 r23,tr33,t+r24r34 r24,tr44,t   Ωt =    r13,tr33,t+r14,tr34,t r23,tr33,t+r24r34 r3 2 3,t+r3 2 4,t r34,tr44,t   r14,tr44,t r24,tr44,t r34,tr44,t r4 2 4,t 17

       r11,t   ρ11   p11 p12 p13 p14          r12,t     ρ12     p21 p22 p23 p24           r22,t     ρ22     p31 p32 p33 p34          vech(Rt)≡         r r r 1 2 3 3 3 3 , , , t t t         =         ρ ρ ρ 1 2 3 3 3 3         +         p p p 4 5 6 1 1 1 p p p 4 5 6 2 2 2 p p p 4 5 6 3 3 3 p p p 4 5 6 4 4 4                | | | (cid:2) (cid:2) (cid:2)1 2 3 , , , t t t − − − 1 1 1 | | |        +        r14,t   ρ14   p71 p72 p73 p74  |(cid:2)4,t−1 |              r24,t   ρ24   p81 p82 p83 p84               r34,t   ρ34   p91 p92 p93 p94  r44,t ρ44 p101 p102 p103 p104     g11 0 0 0 0 0 0 0 0 0  r11,t−1       0 g22 0 0 0 0 0 0 0 0     r12,t−1        0 0 g33 0 0 0 0 0 0 0     r22,t−1       0 0 0 g44 0 0 0 0 0 0  r13,t−1         0 0 0 0 g55 0 0 0 0 0  r23,t−1    .     0 0 0 0 0 g66 0 0 0 0  r33,t−1         0 0 0 0 0 0 g77 0 0 0  r14,t−1         0 0 0 0 0 0 0 g88 0 0  r24,t−1         0 0 0 0 0 0 0 0 g99 0  r34,t−1  0 0 0 0 0 0 0 0 0 g1010 r44,t−1 ItcanbeseenthatthediagonaltermsintheRt matrixonlyenterthediagonalpartofΩt. With that observation, I restricted the diagonal terms in the Rt to only depend on its own innovation, e.g., p 12 = p 13 = p 14 = 0. As for the covariance term, consider that r 12,t enters in ω 11,t and ω 12,t. I restricted r 12,t to only depend on the innovation of the first and second countries ((cid:1) 1,t−1 and (cid:1) 2,t−1 ). With the same logic, the P matrix for N = 4 is restricted to be 18

   p11 0 0 0      p21 p22 0 0       0 p32 0 0      p41 0 p43 0       0 p52 p53 0  P = .    0 0 p63 0       p71 0 0 p74       0 p82 0 p84       p91 0 p93 p94  0 0 0 p104 ThenumberofparametersundertherestrictedR-GARCH(1,1)ofNassetsis2N(N+1)−N. In the case of 16 assets, this reduces the number of parameters to 528. One drawback to this specification is that it is sensitive to the ordering of assets. 19

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scitsitatS yrammuS :1 elbaT 21)3(RASQ 21)3(RAQ 21Q sisotruK ssenwekS .veD .dtS naeM +,∗0080.363 +0114.91 ∗0409.62 ‡8410.01 4051.0 4451.6 1231.0aisenodnI ∗0019.531 0141.61 ∗0565.03 ‡1928.31 8911.0 7690.5 3811.0 aisyalaM ∗0114.93 0720.41 ∗0261.92 ‡2871.7 3120.0 9653.4 2371.0 senippilihP ehT ∗0048.461 0169.02 ∗0221.72 ‡3366.5 8532.0- 9639.2 3770.0 eropagniS ∗0076.161 0591.21 ∗0752.22 ‡8414.5 3634.0 4156.5 9360.0 dnaliahT ∗0119.08 0668.51 ∗0196.12 ‡0734.4 †7544.0- 5106.3 0523.0 gnoK gnoH ∗0769.84 0332.21 0860.61 ‡1868.4 †6294.0 8612.3 2200.0 napaJ ∗0025.623 0720.21 ∗0007.63 ‡4309.7 7100.0- 0443.5 0401.0 aeroK htuoS ∗0056.181 6728.7 ∗0598.12 ‡8274.7 8465.0 9333.5 9200.0nawiaT ∗0569.25 0883.01 0730.02 ‡0243.7 7756.0 0008.5 8184.0 anitnegrA ∗0987.87 9618.9 3018.9 ‡8708.3 4672.0 3961.7 8685.0 lizarB ∗0430.85 8068.9 ∗0945.63 ‡7629.4 6172.0 8402.3 6613.0 elihC ∗0379.88 5747.9 ∗0085.12 ‡2057.5 5663.0- 0225.4 1983.0 ocixeM ∗0007.551 0208.41 ∗0994.03 ‡1863.4 †7744.0- 0733.2 1201.0 ynamreG ∗0500.82 4315.7 0958.31 7062.4 1190.0 3590.2 2702.0 .K.U ehT ∗0018.411 0522.11 ∗0343.92 ‡1967.4 †4864.0- 3139.1 8162.0 .S.U ehT ∗0097.741 0780.02 ∗0784.62 ‡3054.4 8192.0- 9347.1 7831.0 dlroW 5068.4 8873.1 6300.0 7410.0 tluafeD 3180.4 6982.0 5200.0 0000.0 mreT 6686.2 6432.0 9520.0 6950.0dnediviD ,lizarBdna anitnegrAtpecxe ,secidnI labolG maertsataDmorf eraatadehT .)segatnecrep ylkeewni(snruter ssecxeylkeewrof scitsitats yrammusswohs elbatehT )1( yb detaluclac si nruter ssecxE .srallod .S.U ni era secidni nruteR tekraM latoT .secidni labolG )CFI( noitaroproC ecnaniF lanoitanretnI eht morf era hcihw eerhttsalehT .nrutertekramehtmorfetartseretnirallodoruEhtnom-enoehtgnitcartbus)2(dnaxednikcotss’yrtnuochcaerofnrutercitemhtiraehtgnitaluclac segnahcehtfogalsimreT .aaAdnaaaBgnitardnobs’ydooMneewtebsnruterdaerpsecivreSrotsevnIs’ydooMfogalehtsitluafeD .selbairavnoitamrofniwohsswor tseretnirallodoruEhtnom-enofossecxenidleiydnedividtekramdlrowfogalsidnediviD .seirutamhtnom-3dnaraey-01neewtebdleiyllibyrusaertfodaerpsehtni ,sisotruk dna ssenweks eht wohs snmuloc htffi dna htruof ehT .snoitavresbo 394 fo latot a rof 9991 rebmetpeS 51 hguorht 0991 lirpA 11 morf era seires llA .etar tnereffidyltnacfiingissisisotrukehtsetacidni‡ .lavretniecnedfinoc%59ehttanoitubirtsidlamronmorftnereffidyltnacfiingississenweksehtsetacidni† .ylevitcepser dradnats )7891( tseW dna yeweN htiw snoitidnoc tnemom MMG morf detupmoc era scitsitats owt esehT .lavretni ecnedfinoc %59 eht ta noitubirtsid lamron morf fo ledom )3(RA na morf laudiser ,)21Q( snruter ssecxe ylkeew eht fo noitalerroc laires redro-ht21 rof scitsitats tset xoB-gnujL wohs snmuloc eerht tsal ehT .srorre 1620.12,)%01(3945.81eraseulavlacitirc)21(2χehT .)21)3(RASQ(nruterssecxeylkeewfo)3(RAnamorfderauqslaudiserdna,)21)3(RAQ(nruterssecxeylkeew .ledom)6(RAnamorfscitsitatsehtsetacidni+ .lavretniecnedfinoc%59ehttatnacfiingissitneicffieocehtsetacidni ∗ .)%1(0712.62dna,)%5( 24

xirtaM noitalerroC :2 elbaT DW SU KU DB XM LC RB RA AT OK PJ KH HT GS HP YM DI 32.0 41.0 01.0 61.0 10.0- 31.0 21.0 90.0 20.0 12.0 61.0 83.0 54.0 14.0 50.0 34.0 00.1 DI 13.0 12.0 32.0 42.0 00.0 41.0 10.0 60.0 00.0 32.0 91.0 54.0 84.0 06.0 20.0 00.1 YM 11.0- 11.0- 70.0- 20.0 10.0- 80.0- 30.0 20.0 20.0 50.0- 70.0- 60.0- 10.0- 70.0- 00.1 HP 74.0 13.0 63.0 33.0 30.0 81.0 20.0 90.0 00.0 72.0 13.0 65.0 75.0 00.1 GS 43.0 62.0 62.0 92.0 10.0- 02.0 21.0 41.0 10.0- 23.0 71.0 64.0 00.1 HT 84.0 83.0 14.0 63.0 20.0- 72.0 20.0 11.0 30.0 13.0 32.0 00.1 KH 07.0 32.0 63.0 73.0 30.0 70.0 20.0- 40.0- 20.0 62.0 00.1 PJ 33.0 22.0 12.0 02.0 60.0- 51.0 40.0- 40.0- 40.0 00.1 OK 20.0- 20.0- 70.0- 31.0- 11.0- 40.0- 00.0 30.0 00.1 AT 20.0 80.0 00.0 60.0- 90.0- 42.0 03.0 00.1 RA 50.0 60.0 70.0 30.0 80.0- 81.0 00.1 RB 62.0 42.0 02.0 51.0 30.0- 00.1 LC 10.0 30.0 50.0- 30.0- 00.1 XM 96.0 74.0 16.0 00.1 DB 17.0 05.0 00.1 KU 77.0 00.1 SU 00.1 DW = GS ,senippilihP ehT = HP ,aisyalaM = YM ,aisenodnI = DI :swollof sa era sedoc yrtnuoc ehT .snruter ssecxe ytiuqe fo xirtam noitalerroc eht swohs elbat ehT =DB,ocixeM=XM,elihC=LC,lizarB=RB,anitnegrA=RA,nawiaT=AT,aeroKhtuoS=OK,napaJ=PJ,gnoKgnoH=KH,dnaliahT=HT,eropagniS 9991rebmetpeS51hguorht0991lirpA11morfdetupmocsinoitalerrocehT .dlroW=DWdna,aciremAfosetatSdetinU=SU,modgniKdetinU=KU,ynamreG .snoitavresbo394folatotarof 25

xirtaM ecnairavoC :3 elbaT DW SU KU DB XM LC RB RA AT OK PJ KH HT GS HP YM DI 74.2 07.1 53.1 03.2 33.0- 05.2 31.5 51.3 35.0 19.6 90.3 23.8 36.51 84.7 73.1 13.31 08.73 DI 97.2 01.2 14.2 19.2 50.0 13.2 74.0 38.1 21.0 81.6 81.3 61.8 39.31 89.8 54.0 29.52 YM 58.0- 29.0- 66.0- 71.0 52.0- 31.1- 09.0 44.0 53.0 81.1- 79.0- 49.0- 43.0- 58.0- 49.81 HP 04.2 47.1 02.2 92.2 34.0 07.1 54.0 45.1 50.0 03.4 09.2 59.5 14.9 16.8 GS 73.3 97.2 30.3 88.3 03.0- 26.3 79.4 25.4 43.0- 27.9 80.3 34.9 78.13 HT 20.3 06.2 60.3 10.3 62.0- 60.3 35.0 92.2 06.0 59.5 36.2 49.21 KH 39.3 24.1 14.2 67.2 54.0 37.0 63.0- 76.0- 24.0 74.4 33.01 PJ 40.3 92.2 23.2 64.2 33.1- 05.2 85.1- 31.1- 51.1 05.82 OK 61.0- 61.0- 37.0- 75.1- 16.2- 17.0- 50.0 18.0 93.82 AT 52.0 88.0 60.0- 78.0- 73.2- 84.4 93.21 75.33 RA 76.0 48.0 90.1 35.0 26.2- 80.4 92.15 RB 34.1 64.1 73.1 01.1 84.0- 52.01 LC 40.0 03.0 64.0- 43.0- 14.02 XM 28.2 01.2 99.2 54.5 DB 95.2 40.2 83.4 KU 95.2 27.3 SU 40.3 DW = GS ,senippilihP ehT = HP ,aisyalaM = YM ,aisenodnI = DI :swollof sa era sedoc yrtnuoc ehT .snruter ssecxe ytiuqe fo xirtam ecnairavoc eht swohs elbat ehT =DB,ocixeM=XM,elihC=LC,lizarB=RB,anitnegrA=RA,nawiaT=AT,aeroKhtuoS=OK,napaJ=PJ,gnoKgnoH=KH,dnaliahT=HT,eropagniS 9991rebmetpeS51hguorht0991lirpA11morfdetupmocsiecnairavocehT .dlroW=DWdna,aciremAfosetatSdetinU=SU,modgniKdetinU=KU,ynamreG .snoitavresbo394folatotarof 26

Table 4: Capital Market Integration and Contagion Hypotheses Tests Hypothesis No Contagion Regional Contagion I RegionalContagionII Capital Market Integration Failed to Reject Failed to Reject Failed to Reject (W = 19.2437) (W = 18.6342) (W = 20.1045) (χ2 16,0.95 =26.2962) (χ2 16,0.95 =26.2962) (χ2 16,0.95 =26.2962) Contagion Rejected Rejected Failed to Reject (LM = 1085.3471) (LM = 719.8412) (LM = 310.5128) (χ2 480,0.95 =532.0754) (χ2 380,0.95 =426.4537) (χ2 300,0.95 =341.3951) Thetableshowsteststatisticsforthecapitalmarketintegrationandcontagionhypotheses. Thenullhypothesisfor capitalmarketintegrationisthattheinterceptsinthemeanassetexcessreturnsequationareequaltozero,C=0. The test is performed by a robust Wald test. The statistics are distributed Chi-square with 16 degree of freedom (χ2 16). No Contagionistherestrictedmodelunderthehypothesisofnocontagion(SeeFigures3and4). Regional Contagion IistherestrictedmodelunderthehypothesisofRegionalContagionI(SeeFigures5and6). Regional ContagionIIistherestrictedmodelunderthehypothesisofRegionalContagionII(SeeFigures7and8). Thetest ofthesignificanceoftime-varyingbetafromtheRegional Contagion IImodelisperformedbyarobustWaldtest. The statistic rejected the insignificance of the information variables at the 95% confidence interval (W =75.2641 withχ2 48,0.95=65.1708). AllrobuststandarderrorsarecalculatedfromH−1SH−1,whereH istheHessianandS istheouterproductofthegradients(BollerslevandWooldridge(1992)). 27

Table 5: Residual Diagnostic Skewness Kurtosis QZ12 QZS12 Indonesia -0.1502 3.9951 20.2487 7.1637 Malaysia 0.0811 5.9328 7.9994 16.4642 The Philippines 0.0058 7.0881 21.2241∗ 9.3204 Singapore -0.1112 6.7947 6.0906 9.4237 Thailand 0.3837 4.7586 8.1127 10.2757 Hong Kong -0.4917 3.9000 25.2641∗ 12.6672 Japan 0.4112 4.0790 17.7374 12.8364 South Korea 0.3959 6.2182 21.0784∗ 12.1812 Taiwan 0.1330 4.1144 32.7031∗ 20.2043 Argentina 0.3267 4.8636 17.2749 12.5983 Brazil -0.0973 3.7207 13.9712 10.9624 Chile 0.1034 3.9489 42.8892∗ 16.0026 Mexico -0.3479 5.4702 15.8771 15.9115 Germany -0.4945 4.8430 17.7358 46.5423∗ U.K. 0.0156 4.7310 13.5782 20.9752 U.S. -0.6058 4.9795 28.5025∗ 42.8582∗ ThetableshowsteststatisticsforstandardizedresidualimpliedfromtheconditionalCAPMmodelwithtimevarying beta (Regional Contagion II). Standardized residual is computed from U t −1 Υt, where UtU t (cid:1) =Σt. Ut isanuppertriangularmatrixandΣt isthecovariancematrix. Allseriesarefrom11April1990through 15September1999foratotalof493observations. ThelasttwocolumnsshowLjung-Boxteststatisticsfor 12th-order serial correlation of standardized residual (QZ12) and standardized residual squared (QZS12). Theχ2(12)criticalvaluesare18.5493(10%),21.0261(5%),and26.2170(1%). ∗ indicatesthecoefficientis significantatthe95%confidenceinterval. 28

Table 6: Estimates of the GARCH(1,1)-M for the World Market Portfolios zt m =α0+α1σm 2 ,t+ηt σm 2 ,t =γ0+γ1ηt 2 −1+ γ2σm 2 ,t−1 Time-Invariant Time-Varying t-Dist. (ν =5) α0 0.1716 0.1156 0.0414 (0.1723) (0.1462) (0.1741) α1 0.0433∗ 0.0394∗ 0.0575∗ (0.0145) (0.0124) (0.0314) γ0 0.1650∗ 0.1457∗ 0.2355∗ (0.5170) (0.0497) (0.0647) γ1 0.1898∗ 0.1784∗ 0.1546∗ (0.0414) (0.0378) (0.0254) γ2 0.7460∗ 0.7714∗ 0.7689∗ (0.0427) (0.0394) (0.0378) Skewness -0.0431 -0.4468 -0.4342 Kurtosis 4.0362 4.0368 3.9122 QZ12 15.2254 15.0791 14.6522 QZS12 12.4223 11.4934 12.6377 The table shows estimates of the market portfolio equation. The equation is estimated via Quasi-Maximum Likelihood (QMLE). The robust standard errors are in parentheses. Robust standard errors are computed from H−1SH−1, where H is the Hessian and S is the outer product of the gradients. Time-Invariant shows results from the Regional Contagion II model with time-invariant beta. Time- VaryingcolumnshowsresultsfromtheRegional Contagion IImodel withtime-varyingbeta. t-Distcolumnshowsresultsfromanunivariateestimationofthemarketportfoliovolatilityundertheassumption that ηt has a conditional t-distribution with 5 degrees of freedom (ν = 5). Skewness and Kurtosis show the estimates of skewness and kurtosis of the standardized residuals. QZ12 and QZS12 show Ljung-Boxteststatisticsfor12th-orderserialcorrelationoftheresidualandresidualsquared,respectively. Theχ2(12)criticalvaluesare 18.55(10%), 21.03(5%), and 26.22(1%). ∗ indicates the coefficient is significantatthe95%confidenceinterval. 29

All countries 0.4 0.3 0.2 0.1 0 −0.1 1993 1995 1998 noitalerroC Asia 0.4 0.3 0.2 0.1 0 −0.1 1993 1995 1998 noitalerroC Latin America 0.5 0.4 0.3 0.2 0.1 0 −0.1 −0.2 1993 1995 1998 noitalerroC Germany−U.K.−U.S. 1 0.8 0.6 0.4 0.2 0 1993 1995 1998 noitalerroC Asia and Latin America 0.2 0.15 0.1 0.05 0 −0.05 −0.1 1993 1995 1998 noitalerroC Asia and Germany−U.K.−U.S. 0.5 0.4 0.3 0.2 0.1 0 −0.1 −0.2 1993 1995 1998 noitalerroC Latin America and Germany−U.K.−U.S. 0.3 0.2 0.1 0 −0.1 −0.2 1993 1995 1998 noitalerroC Figure 1: Equally-weighted average of cross-country correlations The figure shows equally-weighted average excess return rolling cross-country correlations. The rolling window is 24 weeks. The name on top of each figure indicates the equally-weighted average correlations in that group of countries. All countries consists ofAsia, LatinAmerica, andGermany-U.K.-U.S.. AsiaincludesIndonesia, Malaysia, ThePhilippines, Singapore, Thailand, Hong Kong,Japan,SouthKorea,andTaiwan. Latin AmericaincludesArgentina,Brazil,Chile,andMexico. 30

(cid:15) (cid:1) (cid:10) (cid:16) (cid:2) (cid:5) (cid:3) (cid:14) (cid:4)(cid:5) (cid:2) (cid:17) (cid:1) (cid:6) (cid:14) (cid:7) (cid:12) (cid:2) (cid:5) (cid:2) (cid:8) (cid:9) (cid:10) (cid:13) (cid:4)(cid:14) (cid:5) (cid:12) (cid:11)(cid:12) (cid:5) (cid:10) (cid:13) (cid:8) (cid:2) (cid:5) (cid:1) (cid:18) (cid:19) (cid:3) (cid:14) (cid:5) (cid:20) (cid:4)(cid:14) (cid:12) (cid:3) (cid:10) (cid:16) (cid:4)(cid:16) (cid:2) (cid:1) (cid:14) (cid:12) (cid:5) (cid:2) (cid:13) (cid:4)(cid:14) (cid:12) Figure 2: Relationship between Capital Market Integration and Contagion ThefigureshowsrelationshipsbetweenCapitalMarketIntegrationandContagionconcepts. This papertestsforcontagion undertheassumptionofcapital marketintegration (Test of Contagion Hypothesis). 31

(cid:1) (cid:1) (cid:2) (cid:1) (cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:3) (cid:1)(cid:2) (cid:3) (cid:4) (cid:5) (cid:6) (cid:7) (cid:8) (cid:9) (cid:6) (cid:6) (cid:10) (cid:11) (cid:5) (cid:10) (cid:12) (cid:9) (cid:13) (cid:13) (cid:14) (cid:15) (cid:14) (cid:16) (cid:17) (cid:3) (cid:18) (cid:15) (cid:2) (cid:19) (cid:10) (cid:19) (cid:7) (cid:4) (cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:6) Figure 3: Idiosyncratic conditional covariance matrix: No Contagion (cid:1) (cid:1) (cid:1) (cid:1) (cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:3) (cid:1) (cid:1) (cid:2) (cid:1)(cid:1)(cid:2)(cid:3) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:2) (cid:4)(cid:4)(cid:2)(cid:3) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:2) (cid:5)(cid:5)(cid:2)(cid:3) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:2) (cid:6)(cid:6)(cid:2)(cid:3) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:2) (cid:7)(cid:7)(cid:2)(cid:3) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:2) (cid:8)(cid:8)(cid:2)(cid:3) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:2) (cid:9)(cid:9)(cid:2)(cid:3) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:2) (cid:10)(cid:10)(cid:2)(cid:3) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:2) (cid:11)(cid:11)(cid:2)(cid:3) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:2) (cid:1)(cid:12)(cid:1)(cid:12)(cid:2)(cid:3) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:2) (cid:1)(cid:1)(cid:1)(cid:1)(cid:2)(cid:3) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:2) (cid:1)(cid:4)(cid:1)(cid:4)(cid:2)(cid:3) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:2) (cid:1)(cid:5)(cid:1)(cid:5)(cid:2)(cid:3) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:2) (cid:1)(cid:6)(cid:1)(cid:6)(cid:2)(cid:3) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:2) (cid:1)(cid:7)(cid:1)(cid:7)(cid:2)(cid:3) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:2) (cid:1)(cid:8)(cid:1)(cid:8)(cid:2)(cid:3) (cid:4) (cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:6) (cid:2) Figure 4: Restrictions on the idiosyncratic conditional covariance matrix (Ωt = RtR t ): No Contagion 32

  Ω t =  S I T S n i o h n d u e g o t a n h p es o i r E a P e , , a h M s T il t i h a p a l A p a il y i a n s s n i e i a a s d : , , E H J T a a o a p i n s w a t g n an ,K K A o o s r n e ia g a : , , L A C a h rg t il e i e n n , t M i A n e a m x , i B e co r ra ic z a il : , G U. e S r . man, U.K.,  Figure 5: Idiosyncratic conditional covariance matrix: Regional Contagion I (cid:1) (cid:1) (cid:1) (cid:1) (cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:3) (cid:1) (cid:1) (cid:2) (cid:1)(cid:1)(cid:2)(cid:3) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:2) (cid:1)(cid:4)(cid:2)(cid:3) (cid:1) (cid:1) (cid:2) (cid:4)(cid:4)(cid:2)(cid:3) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:2) (cid:1)(cid:5)(cid:2)(cid:3) (cid:1) (cid:1) (cid:2) (cid:4)(cid:5)(cid:2)(cid:3) (cid:1) (cid:1) (cid:2) (cid:5)(cid:5)(cid:2)(cid:3) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:2) (cid:1)(cid:6)(cid:2)(cid:3) (cid:1) (cid:1) (cid:2) (cid:4)(cid:6)(cid:2)(cid:3) (cid:1) (cid:1) (cid:2) (cid:5)(cid:6)(cid:2)(cid:3) (cid:1) (cid:1) (cid:2) (cid:6)(cid:6)(cid:2)(cid:3) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:2) (cid:1)(cid:7)(cid:2)(cid:3) (cid:1) (cid:1) (cid:2) (cid:4)(cid:7)(cid:2)(cid:3) (cid:1) (cid:1) (cid:2) (cid:5)(cid:7)(cid:2)(cid:3) (cid:1) (cid:1) (cid:2) (cid:6)(cid:7)(cid:2)(cid:3) (cid:1) (cid:1) (cid:2) (cid:7)(cid:7)(cid:2)(cid:3) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:2) (cid:8)(cid:8)(cid:2)(cid:3) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:2) (cid:8)(cid:9)(cid:2)(cid:3) (cid:1) (cid:1) (cid:2) (cid:9)(cid:9)(cid:2)(cid:3) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:2) (cid:8)(cid:10)(cid:2)(cid:3) (cid:1) (cid:1) (cid:2) (cid:9)(cid:10)(cid:2)(cid:3) (cid:1) (cid:1) (cid:2) (cid:10)(cid:10)(cid:2)(cid:3) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:2) (cid:8)(cid:11)(cid:2)(cid:3) (cid:1) (cid:1) (cid:2) (cid:9)(cid:11)(cid:2)(cid:3) (cid:1) (cid:1) (cid:2) (cid:10)(cid:11)(cid:2)(cid:3) (cid:1) (cid:1) (cid:2) (cid:11)(cid:11)(cid:2)(cid:3) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:2) (cid:1)(cid:12)(cid:1)(cid:12)(cid:2)(cid:3) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:2) (cid:1)(cid:12)(cid:1)(cid:1)(cid:2)(cid:3) (cid:1) (cid:1) (cid:2) (cid:1)(cid:1)(cid:1)(cid:1)(cid:2)(cid:3) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:2) (cid:1)(cid:12)(cid:1)(cid:4)(cid:2)(cid:3) (cid:1) (cid:1) (cid:2) (cid:1)(cid:1)(cid:1)(cid:4)(cid:2)(cid:3) (cid:1) (cid:1) (cid:2) (cid:1)(cid:4)(cid:1)(cid:4)(cid:2)(cid:3) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:2) (cid:1)(cid:12)(cid:1)(cid:5)(cid:2)(cid:3) (cid:1) (cid:1) (cid:2) (cid:1)(cid:1)(cid:1)(cid:5)(cid:2)(cid:3) (cid:1) (cid:1) (cid:2) (cid:1)(cid:4)(cid:1)(cid:5)(cid:2)(cid:3) (cid:1) (cid:1) (cid:2) (cid:1)(cid:5)(cid:1)(cid:5)(cid:2)(cid:3) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:2) (cid:1)(cid:6)(cid:1)(cid:6)(cid:2)(cid:3) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:2) (cid:1)(cid:6)(cid:1)(cid:7)(cid:2)(cid:3) (cid:1) (cid:1) (cid:2) (cid:1)(cid:7)(cid:1)(cid:7)(cid:2)(cid:3) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:2) (cid:1)(cid:6)(cid:1)(cid:8)(cid:2)(cid:3) (cid:1) (cid:1) (cid:2) (cid:1)(cid:7)(cid:1)(cid:8)(cid:2)(cid:3) (cid:1) (cid:1) (cid:2) (cid:1)(cid:8)(cid:1)(cid:8)(cid:2)(cid:3) (cid:4) (cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:6) (cid:2) Figure 6: Restrictions on the idiosyncratic conditional covariance matrix (Ωt = RtR t ): Regional Contagion I 33

  Ω t =  A I p K n i o n s d n i e o a g s n : , , e J s S i a a i p n , a g n a M , p K o a r l o a e y r , e s a i T a , , h T a a i T i l w a h n a e d n , P H hi o li n p g - L A C a h rg t il e i e n n , t M i A n e a m x , i B e co r ra ic z a il : , G U. e S r . man, U.K.,  Figure 7: Idiosyncratic conditional covariance matrix: Regional Contagion II (cid:1) (cid:1) (cid:1) (cid:1) (cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)(cid:3) (cid:1) (cid:1) (cid:2) (cid:1)(cid:1)(cid:2)(cid:3) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:2) (cid:1)(cid:4)(cid:2)(cid:3) (cid:1) (cid:1) (cid:2) (cid:4)(cid:4)(cid:2)(cid:3) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:2) (cid:1)(cid:5)(cid:2)(cid:3) (cid:1) (cid:1) (cid:2) (cid:4)(cid:5)(cid:2)(cid:3) (cid:1) (cid:1) (cid:2) (cid:5)(cid:5)(cid:2)(cid:3) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:2) (cid:1)(cid:6)(cid:2)(cid:3) (cid:1) (cid:1) (cid:2) (cid:4)(cid:6)(cid:2)(cid:3) (cid:1) (cid:1) (cid:2) (cid:5)(cid:6)(cid:2)(cid:3) (cid:1) (cid:1) (cid:2) (cid:6)(cid:6)(cid:2)(cid:3) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:2) (cid:1)(cid:7)(cid:2)(cid:3) (cid:1) (cid:1) (cid:2) (cid:4)(cid:7)(cid:2)(cid:3) (cid:1) (cid:1) (cid:2) (cid:5)(cid:7)(cid:2)(cid:3) (cid:1) (cid:1) (cid:2) (cid:6)(cid:7)(cid:2)(cid:3) (cid:1) (cid:1) (cid:2) (cid:7)(cid:7)(cid:2)(cid:3) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:2) (cid:1)(cid:8)(cid:2)(cid:3) (cid:1) (cid:1) (cid:2) (cid:4)(cid:8)(cid:2)(cid:3) (cid:1) (cid:1) (cid:2) (cid:5)(cid:8)(cid:2)(cid:3) (cid:1) (cid:1) (cid:2) (cid:6)(cid:8)(cid:2)(cid:3) (cid:1) (cid:1) (cid:2) (cid:7)(cid:8)(cid:2)(cid:3) (cid:1) (cid:1) (cid:2) (cid:8)(cid:8)(cid:2)(cid:3) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:2) (cid:1)(cid:9)(cid:2)(cid:3) (cid:1) (cid:1) (cid:2) (cid:4)(cid:9)(cid:2)(cid:3) (cid:1) (cid:1) (cid:2) (cid:5)(cid:9)(cid:2)(cid:3) (cid:1) (cid:1) (cid:2) (cid:6)(cid:9)(cid:2)(cid:3) (cid:1) (cid:1) (cid:2) (cid:7)(cid:9)(cid:2)(cid:3) (cid:1) (cid:1) (cid:2) (cid:8)(cid:9)(cid:2)(cid:3) (cid:1) (cid:1) (cid:2) (cid:9)(cid:9)(cid:2)(cid:3) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:2) (cid:1)(cid:10)(cid:2)(cid:3) (cid:1) (cid:1) (cid:2) (cid:4)(cid:10)(cid:2)(cid:3) (cid:1) (cid:1) (cid:2) (cid:5)(cid:10)(cid:2)(cid:3) (cid:1) (cid:1) (cid:2) (cid:6)(cid:10)(cid:2)(cid:3) (cid:1) (cid:1) (cid:2) (cid:7)(cid:10)(cid:2)(cid:3) (cid:1) (cid:1) (cid:2) (cid:8)(cid:10)(cid:2)(cid:3) (cid:1) (cid:1) (cid:2) (cid:9)(cid:10)(cid:2)(cid:3) (cid:1) (cid:1) (cid:2) (cid:10)(cid:10)(cid:2)(cid:3) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:2) (cid:1)(cid:11)(cid:2)(cid:3) (cid:1) (cid:1) (cid:2) (cid:4)(cid:11)(cid:2)(cid:3) (cid:1) (cid:1) (cid:2) (cid:5)(cid:11)(cid:2)(cid:3) (cid:1) (cid:1) (cid:2) (cid:6)(cid:11)(cid:2)(cid:3) (cid:1) (cid:1) (cid:2) (cid:7)(cid:11)(cid:2)(cid:3) (cid:1) (cid:1) (cid:2) (cid:8)(cid:11)(cid:2)(cid:3) (cid:1) (cid:1) (cid:2) (cid:9)(cid:11)(cid:2)(cid:3) (cid:1) (cid:1) (cid:2) (cid:10)(cid:11)(cid:2)(cid:3) (cid:1) (cid:1) (cid:2) (cid:11)(cid:11)(cid:2)(cid:3) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:2) (cid:1)(cid:12)(cid:1)(cid:12)(cid:2)(cid:3) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:2) (cid:1)(cid:12)(cid:1)(cid:1)(cid:2)(cid:3) (cid:1) (cid:1) (cid:2) (cid:1)(cid:1)(cid:1)(cid:1)(cid:2)(cid:3) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:2) (cid:1)(cid:12)(cid:1)(cid:4)(cid:2)(cid:3) (cid:1) (cid:1) (cid:2) (cid:1)(cid:1)(cid:1)(cid:4)(cid:2)(cid:3) (cid:1) (cid:1) (cid:2) (cid:1)(cid:4)(cid:1)(cid:4)(cid:2)(cid:3) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:2) (cid:1)(cid:12)(cid:1)(cid:5)(cid:2)(cid:3) (cid:1) (cid:1) (cid:2) (cid:1)(cid:1)(cid:1)(cid:5)(cid:2)(cid:3) (cid:1) (cid:1) (cid:2) (cid:1)(cid:4)(cid:1)(cid:5)(cid:2)(cid:3) (cid:1) (cid:1) (cid:2) (cid:1)(cid:5)(cid:1)(cid:5)(cid:2)(cid:3) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:2) (cid:1)(cid:6)(cid:1)(cid:6)(cid:2)(cid:3) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:2) (cid:1)(cid:6)(cid:1)(cid:7)(cid:2)(cid:3) (cid:1) (cid:1) (cid:2) (cid:1)(cid:7)(cid:1)(cid:7)(cid:2)(cid:3) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:2) (cid:1)(cid:6)(cid:1)(cid:8)(cid:2)(cid:3) (cid:1) (cid:1) (cid:2) (cid:1)(cid:7)(cid:1)(cid:8)(cid:2)(cid:3) (cid:1) (cid:1) (cid:2) (cid:1)(cid:8)(cid:1)(cid:8)(cid:2)(cid:3) (cid:4) (cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:5)(cid:6) (cid:2) Figure 8: Restrictions on the idiosyncratic conditional covariance matrix (Ωt = RtR t ): Regional Contagion II 34

All countries 0.4 0.3 0.2 0.1 0 −0.1 1993 1995 1998 noitalerroC Asia 0.4 0.3 0.2 0.1 0 −0.1 1993 1995 1998 noitalerroC Latin America 0.5 0.4 0.3 0.2 0.1 0 −0.1 −0.2 1993 1995 1998 noitalerroC Germany−U.K.−U.S. 1 0.8 0.6 0.4 0.2 0 1993 1995 1998 noitalerroC Asia and Latin America 0.2 0.15 0.1 0.05 0 −0.05 −0.1 1993 1995 1998 noitalerroC Asia and Germany−U.K.−U.S. 0.5 0.4 0.3 0.2 0.1 0 −0.1 −0.2 1993 1995 1998 noitalerroC Latin America and Germany−U.K.−U.S. 0.3 0.2 0.1 0 −0.1 −0.2 1993 1995 1998 noitalerroC Figure 9: Conditional correlations implied from the CAPM: Regional Contagion II The figure shows both equally-weighted average conditional correlations implied from the conditional CAPM with timevaryingbetaundertheRegionalContagionIImodel(solidline)andshowstheequally-weightedaveragerollingcross-country correlations(dashedline). Therollingwindowis24weeks. Thenameontopofeachfigureindicatestheequally-weighted averagecorrelationsinthatgroupofcountries. SeedescriptioninFigure1forthenotationofeachgroup. 35

All countries 0.4 0.3 0.2 0.1 0 −0.1 1993 1998 noitalerroC Asia 0.4 0.3 Conditional Correlation 0.2 0.1 0 −0.1 Contribution from the Market Portfolio −0.2 1993 1998 noitalerroC Conditional Correlation Contribution from the Market Portfolio Latin America 0.4 0.2 0 −0.2 −0.4 1993 1998 noitalerroC Germany−U.K.−U.S. 1 Conditional Correlation 0.8 0.6 0.4 Contribution from the Market Portfolio 0.2 0 1993 1998 noitalerroC Conditional Correlation Contribution from the Market Portfolio Figure 10: Contribution of the World Market Portfolio to the conditional correlation: Regional Contagion II The figure shows the contribution of the World Market Portfolio to the conditional correlation (solid line). Correlations are equally-weighted average conditional correlations implied from the conditional CAPM with time-varying beta under the Regional Contagion II model (dashed line). The name on top of each figure indicates the equally-weighted average correlationsinthatgroupofcountries. SeedescriptioninFigure1forthenotationofeachgroup. 36

)tekraM ytiuqE( noitubirtsid−t .S.V ateB gniyraV−emiT htiw II noigatnoC lanoigeR 02 51 01 5 0 8991 7991 5991 4991 3991 1991 0991 ytilitaloV II noigatnoC lanoigeR .tsiD−t ytilitaloV oiloftroP tekraM dlroW ehT :11 erugiF 37