a multivariate garch model of international transmissions of stock returns and volatility

16
A Multivariate GARCH Model of International Transmissions of Stock Returns and Volatility: The Case of the United States and Canada Author(s): G. Andrew Karolyi Reviewed work(s): Source: Journal of Business & Economic Statistics, Vol. 13, No. 1 (Jan., 1995), pp. 11-25 Published by: American Statistical Association Stable URL: http://www.jstor.org/stable/1392517 . Accessed: 15/03/2012 15:25 Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at . http://www.jstor.org/page/info/about/policies/terms.jsp JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact [email protected]. American Statistical Association is collaborating with JSTOR to digitize, preserve and extend access to Journal of Business & Economic Statistics. http://www.jstor.org

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Page 1: A Multivariate GARCH Model of International Transmissions of Stock Returns and Volatility

A Multivariate GARCH Model of International Transmissions of Stock Returns and Volatility:The Case of the United States and CanadaAuthor(s): G. Andrew KarolyiReviewed work(s):Source: Journal of Business & Economic Statistics, Vol. 13, No. 1 (Jan., 1995), pp. 11-25Published by: American Statistical AssociationStable URL: http://www.jstor.org/stable/1392517 .Accessed: 15/03/2012 15:25

Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at .http://www.jstor.org/page/info/about/policies/terms.jsp

JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range ofcontent in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new formsof scholarship. For more information about JSTOR, please contact [email protected].

American Statistical Association is collaborating with JSTOR to digitize, preserve and extend access to Journalof Business & Economic Statistics.

http://www.jstor.org

Page 2: A Multivariate GARCH Model of International Transmissions of Stock Returns and Volatility

@ 1995 American Statistical Association Journal of Business & Economic Statistics, January 1995, Vol. 13, No. 1

A Multivariate GARCH Model of

International Transmissions of

Stock Returns and Volatility: The Case of the United States and Canada

G. Andrew KAROLYI Max M. Fisher College of Business, The Ohio State University, Columbus, OH 43210

This study examines the short-run dynamics of returns and volatility for stocks traded on the New York and Toronto stock exchanges. The main finding is that inferences about the magnitude and persistence of return innovations that originate in either market and that transmit to the other mar- ket depend importantly on how the cross-market dynamics in volatility are modeled. Moreover, much weaker cross-market dynamics in returns and volatility prevail during later subperiods and especially for Canadian stocks with shares dually listed in New York. Implications for international asset pricing, hedging strategies, and regulatory policy are discussed.

KEY WORDS: Multivariate; ARCH; International; Stock returns.

The growing international integration of financial markets has prompted several recent empirical studies to examine the mechanism through which stock market movements are transmitted around the world. These studies evaluate how stock returns in one national stock market influence those of another stock market and their implications for pricing of se- curities within those markets, for hedging and other trading strategies, and for regulatory policies within their financial markets. These issues have been of heightened interest in the wake of the October 1987 international crash that saw large, correlated price movements across most stock mar- kets. As a result, various regulations and institutional rules were introduced to dampen the cross-market impact of large stock-price movements. Roll (1989) surveyed the regulatory policies that have been designed to mitigate against "exces- sive" market volatility, such as futures-market price limits, margin requirements, and transaction taxes, in 23 countries.

In this study, I examine the short-run dependence in price movements for stocks traded on the Toronto Stock Exchange (TSE) and the New York Stock Exchange (NYSE). Specif- ically, I focus on the dynamic relationship between daily stock returns and stock-return volatility for the Standard and Poor (S&P) 500 and TSE 300 stock indexes from April 1981 through December 1989. The North American context has received attention in several recent studies in the finance liter- ature, such as those of Booth and Johnston (1984), Jorion and Schwartz (1986), Alexander, Eun, and Janakiranan (1988), Mittoo (1993), and Foerster and Karolyi (1993), which have examined the extent to which these two markets are finan- cially integrated. Their motivation for studying the case of the United States and Canada arises from the similarity of market structures and regulation and the absence of controls on the free flow of capital between the countries. Indeed,

these studies generally found, using international versions of the Capital Asset Pricing Model (CAPM) or Arbitrage Pricing Theory (APT), that Canadian securities are priced to reflect their risk exposure to the larger North American market rather than just the Canadian market, especially in the 1980s.

My interest in the North American context for examina- tion of the short-run dynamics of stock returns and volatility is, however, further motivated by three institutional features of these markets. First, unique to these two stock markets is the fact that they represent the two largest national markets in terms of equity capitalization with perfectly synchronous trading hours. The experiment in this article is then able to circumvent the problem of disentangling the confound- ing effects of nonsynchronous trading hours and correlated price changes and volatility. This focus is important be- cause most studies of international dependence in stock re- turns (e.g., Eun and Shim 1989; Hamao, Masulis, and Ng 1990; Koch and Koch 1991) have determined that systematic lagged cross-market adjustments are typically short-term-- that is, no longer than one day. Second, a vast majority of all interlisted stocks on U.S. exchanges are Canadian based, comprising 42% of the total number of foreign stocks listed on the NYSE and the American Stock Exchange (AMEX) and 53% of the total market capitalization of foreign stocks, as of December 1990 (American Stock Exchange 1991; New York Stock Exchange 1991). Moreover, approximately 133 of about 1,200 companies listed on the TSE are interlisted on U.S. exchanges, trading of which comprises about 57% of the TSE's total-dollar trading volume (Toronto Stock Ex- change 1990). Classifying Canadian stocks as interlisted or purely domestic allows my study to formulate a controlled experiment of the impact of different types of barriers to inter-

11

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12 Journal of Business & Economic Statistics, January 1995

national investment on the dynamic relations between price movements 'across national stock markets. Finally, through daily news reports, market regulators, traders, and the gen- eral investing public in Canada have become sensitized to market movements in the United States and their impact on Canadian markets (e.g., Financial Post headlines "TSE 300 lags Dow on the Week," December 12, 1992; "U.S. Bull only a Steer in Canada," August 3, 1992; "Sun Shines on Bay Street: Market Healthy Despite Chilly Blast from U.S.," July 6, 1992).

My methodology is also different from the previous ef- forts just cited in that I examine the dynamic relationship be- tween the U.S. and Canadian daily stock-market returns and return volatilities using a bivariate generalized autoregres- sive conditional heteroscedastic (GARCH) model, a family of statistical models originally developed by Engle (1982) and Bollerslev (1986). With this model, I test not only how rapidly stock-return innovations originating in the U.S. and Canadian markets transmit to the other market but also how rapidly the volatility of these innovations transmits to the other market by simulating the impulse responses of the esti- mated bivariate GARCH model. Earlier studies examined the correlation of asset-price changes across international mar- kets. Hilliard (1979), Eun and Shim (1989), von Fursten-

berg and Jeon (1989), Roll (1988, 1989), and Koch and Koch (1991) all focused on the contemporaneous and lagged corre- lation in daily closing-price changes across major stock mar- kets, usually including Canada and the United States. These studies ignored, however, the changing conditional volatility of stock price changes and, more importantly, the interna- tional spillovers of these price-change volatilities that might be occurring at the same time. In a study similar to this one, Hamao et al. (1990) used autoregressive conditionally het- eroscedastic models to demonstrate the different dynamics for spillover effects in price changes and volatilities between the United States and Japan and found that shocks that origi- nate in the United States are larger and more persistent. Lin, Engle, and Ito (in press) used similar techniques to study such spillover effects, but they explicitly modeled the non-

synchronous trading hours in these markets and found much weaker results.

I confirm that the bivariate GARCH model is a reason- able representation of the linkages between stock-price move- ments in the U.S. and Canadian markets. In fact, inferences about the magnitude and persistence of the stock-returns shocks that originate in either market and that transmit to the other market are shown to depend importantly on how we model the cross-market dynamics in the conditional volatili- ties of the respective markets. Specifically, tests using mul- tivariate GARCH models indicate that the effects of shocks from S&P 500 index returns for the TSE 300 index returns and volatility are smaller and less persistent than those mea- sured with traditional vector autoregressive (VAR) models. Second, using a subperiod analysis, I show that the effects of S&P 500 returns shocks on Canadian stocks have dissi- pated over the decade of the 1980s, a finding consistent with the evidence in other studies of growing financial integration

between the two markets. Finally, I show that the dynamics of the impact of U.S.-based stock-return innovations on port- folios of interlisted and noninterlisted Canadian-based stocks are measurably different. This evidence suggests that invest- ment barriers faced by U.S. traders interested in Canadian stocks--due to differences in disclosure requirements, re- strictions on ownership of foreign securities (e.g., 10% limit for Canadian pension funds), or perhaps tax considerations-- do indeed affect the short-term dynamics of lagged price ad- justment of those stocks to information shocks that arise in the U.S. markets.

Section 1 offers some preliminary analysis of the data. Section 2 presents the econometric approach. Section 3 ex- hibits the main results. Section 4 assesses the differences in linkages across markets for interlisted and noninterlisted Canadian-based stocks. Section 5 summarizes the main re- sults and discusses their implications.

1. PRELIMINARY ANALYSIS

1.1 Data

The data used in the study consist of time series of daily stock-market indexes at the close of the markets (4:00 p.m. Eastern), in terms of local currency, for the S&P 500 and TSE 300. Both market aggregates are value-weighted com- posite indexes of a large cross-section of listed stocks. The TSE 300 comprises Canadian-owned stocks that have been continuously listed for at least three years and that have total market values of over $3 million and annual dollar trading volume in excess of $1 million. Care is taken to eliminate control blocks of more than 20% of outstanding shares in the calculation of market value weights (Hatch and Robin- son 1989). These data are obtained from Reuters Datalink and the Index Section of the Toronto Stock Exchange for the period April 1, 1981, through December 29, 1989. I consider daily returns for which the respective close-to-close trading periods in New York and Toronto are perfectly aligned, gen- erating a total of 2,133 observations. When multiple-day returns arise as a result of weekends or holidays observed by either market, these observations are accounted for in my estimation procedures by means of a dummy variable. My analysis is performed with both own currency and U.S. dollar-denominated returns, where the latter employ the daily 4:15 p.m. (Eastern) New York market midpoint quotes for the Canadian dollar, also obtained from Reuters. Note that the results report only those experiments performed with U.S. dollar-denominated returns, although results from ex- periments using own-currency returns are obtainable from me. Finally, I eliminate from the sample the four influ- ential daily returns-October 16, 19, 20, and 21-around the market crash when, it appears, the distribution of returns differs dramatically from the distribution on the other days in the sample. The model estimates and inference tests in this study are also influenced by these four observations. I chose to focus on the long-run dynamic patterns in stock re- turns and volatility for these two markets; readers specifically

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Karolyi: A GARCH Model of International Transmissions 13

interested in the global market linkages around the episode of October 1987 can consult Roll (1989) and Bennett and Kelleher (1988).

The stock-market indexes in this study do not double-count stocks interlisted on either market so that, for example, no Canadian-based interlisted stocks of the TSE 300 index are members of the S&P 500 index. Any measurable interdepen- dence between the markets cannot be attributed to multiple listings of stocks.

1.2 Some Diagnostics

Table 1 presents a wide range of descriptive statistics for the daily stock-index returns of the S&P 500 and TSE 300 for the full sample period and for two equally divided subperiods and the post-October-1987 period. The sample moments for all returns series indicate empirical distributions with heavy tails relative to the normal distribution. There is some neg- ative skewness, especially in the S&P 500 returns, and zero excess kurtosis is confidently rejected for all series and in all subperiods at the 95% level. The overall statistics are notably influenced by the post-October-1987 period, even without the omitted returns around the crash period itself.

The sample autocorrelation functions for the daily raw- returns series and their respective squared-returns series up to two lags with Ljung-Box (LB) statistics up to 6 and 12 lags are also exhibited. As seen in previous studies, the autocor- relations in the stock indexes are statistically different from 0 for the first and possibly higher lags. Due to the large sam- ple size of this analysis, the appropriate criteria for statistical significance for sample statistics and estimated coefficients are unclear. I highlight throughout the text and tables critical values at the 5% significance level but caution the readers that a more conservative cutoff may be appropriate (Zellner 1984, chap. 3). The LB statistics for the raw and squared returns se- ries reject the null hypothesis of white noise easily. Note that the magnitude of the first-order autocorrelation coefficient for the TSE 300 index is larger, which, given the lower trading volume and frequency in the TSE 300 stocks, suggests that the presence of asynchronous trading of component stocks in the index may be spuriously inducing the serial correla- tion in the series (Muthuswamy 1989). The autocorrelation for the squared daily returns may be evidence of nonlinear dependence in the returns series possibly due to changing conditional volatility over time. The ARCH models of Engle (1982) have been developed to capture second-order nonlin- ear dependence in which the first and second moments of returns depend on past values. Finally, the lead and lag cor- relations for the raw and squared returns series for the S&P 500 and TSE 300 confirm a significantly positive and large contemporaneous association and in the one-period lead from the S&P 500 to the TSE 300. The apparent asymmetry of the relation with stronger transmissions of movements from New York to Toronto concurs with the findings of Eun and Shim (1989) and others. Although a crude diagnostic, this effect indicates that cross-market influences can be revealed in the volatility of the returns as well as the mean returns themselves. This confirms the importance of building the

additional structure for the conditional volatility of returns, as in the multivariate GARCH (M-GARCH) framework pro- posed in this study.

2. THE ECONOMETRIC APPROACH

In this section, I introduce the bivariate GARCH model, describe the numerical maximum likelihood techniques used to estimate the system, and illustrate the impulse response analysis. The tests in this article are based on the ARCH family of models developed by Engle (1982) and general- ized (GARCH) by Bollerslev (1986). These models have been empirically shown to capture reasonably well the time variation in the volatility of daily and monthly stock returns (Bollerslev, Chou, and Kroner 1992). Moreover, in its mul- tivariate form, it has been applied successfully for asset re- turns by Bollerslev, Engle, and Wooldridge (1988), Schwert and Seguin (1990), Lin et al. (in press), Chan, Chan, and Karolyi (1991), Chan, Karolyi, and Stulz (1992), and Engle and Susmel (1993).

2.1 The Bivariate GARCH Model

The following bivariate GARCH model is posited for the joint processes governing the daily rates of return for the S&P 500 and TSE 300 stock indexes:

P

r, = a + E pr,_, + DIHOL, + D2WKND, + e,, p=1

e, I R- N(0, H,) (1) and

K L

H, = 'T + FkH,_kFk + G'e,_- e,G k=1 1=1

+ V'VHOL, + V2V2WKND,, (2)

where the daily index returns are the logarithm of the stock price relative for the S&P 500 (ri,) and the TSE 300 (r2t) and the returns vector is denoted by r' = [ri,, r2t]. The residual vector is given by e' = [Lt, 2t], with its corresponding con- ditional covariance matrix {H,}i = hi,,. e, is represented as a column vector of forecast errors of the best linear predictor of r, conditional on past information, denoted by ft, 1, and including the P lagged values of r,. The parameter vectors and matrices of the mean returns equation (1) are defined as a' = [al,a2] for the constant and {.Ip}i = di, for the matrix of coefficients with the p lagged returns. The parameter ma- trices for the variance equation (2) are defined as {r}0 = y, which is restricted to be upper triangular, and free matrices

{Fk}1 =j;j, k and {Gi}i = go, for lags k and I, respectively. The dummy-variable specification for mean returns and

variances in this model follows the approach of Baillie and Bollerslev (1989) to isolate the daily spillovers of stock re- turns and volatility for the markets when close-to-close trad- ing hours are perfectly aligned. This is in contrast to Cheung and Kwan (1992), who compared the average volatility for TSE 300 stock-index returns on days in which New York is

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14 Journal of Business & Economic Statistics, January 1995

Table 1. Summary Statistics for Daily Returns on the Standard & Poor 500 and Toronto Stock Exchange 300 Stock Indexes

Overall period Subperiods Apr/8 1-Dec/89 Apr/81-Jun/84 Jul/84-Oct/87 Nov/87-Dec/89

Statistics (2,127 obs.) (793 obs.) (793 obs.) (541 obs.)

S&P 500 returns

Mean .054 .016 .094 .054 Std. dev. 1.012 .948 .862 1.276 (Tstat of mean) 2.463* .487 3.070 .978 Skewness -.230* .483* -.237* -.626* Kurtosis 8.780* 2.415* 2.279* 11.533* Raw returns correlations

Rho (lag = 1) .062* .102* .100* .000 Rho (lag = 2) -.016 .005 -.030 -.025 LB(6) 34.232* 9.545 1.819 41.591* LB(12) 37.541* 13.684 18.480 46.881*

Squared returns correlations Rho (lag = 1) .176* .032 .086* .194* Rho (lag = 2) .100* .003 -.014 .112* LB( 6) 675.633* 56.323* 11.422 222.571* LB(12) 753.015* 89.252* 17.093 239.819*

TSE 300 returns

Mean .030 -.023 .075 .045 Std. dev. .923 1.019 .693 1.062 (Tstat of mean) 1.519 -.639 3.035* .979 Skewness -.242* .280* .039 -.921* Kurtosis 12.934* 2.765* 2.538* 24.629* Raw returns correlations

Rho (lag = 1) .130* .251* .267* -.125* Rho (lag = 2) .080* .042 .064* .136* LB( 6) 61.060* 59.519* 62.878* 45.340* LB(12) 64.646* 59.681* 66.873* 54.011*

Squared returns correlations Rho (lag = 1) .339* .102* .153* .394* Rho (lag = 2) .176* .141* .055* .181* LB(6) 708.123* 42.042* 32.413* 241.015* LB(12) 784.990* 59.683* 41.551* 263.189*

S&P 500 and TSE 300 returns cross-correlations

Raw returns Rho (lag = -2) .055* .041 .008 .099* Rho (lag = -1) .198* .271* .236* .097* Rho (lag = 0) .661* .712* .599* .661* Rho (lag = +1) -.049* .032 .069* - .214* Rho (lag = +2) .011 -.007 -.020 .048*

Squared returns Rho (lag = -2) .155* .024 -.023 .186* Rho (lag = -1) .196* .076* .130* .218* Rho (lag = 0) .764* .632* .438* .817* Rho (lag = +1) .301* .052* .064* .360* Rho (lag = +2) .119* .063* -.027 .133"

NOTE: * indicates significance at the 5% level. LB(n) denotes the Ljung-Box test of significance of autocorrelations of n lags. Rho (lag = j) denotes a lag correlation coefficient between the TSE 300 return and the jth lag of the S&P 500 return (j less than 0 is leading correlation from S&P 500 to TSE 300).

open and closed. I, therefore, define

D,= dl2 J(3)

for HOL,, a dummy variable equal to 1 for days that follow holidays in either market, and 0 otherwise. D2 is similarly

defined for a Monday seasonal dummy, WKND,, to isolate day-of-the-week effects. In the variance equation, the param- eter matrices, V1 and V2, correspond to the dummy variables for holidays HOL, and weekends WKND,, respectively, and are restricted to be upper triangular, similar in construction to the constant matrix r.

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Karolyi: A GARCH Model of International Transmissions 15

Equation (1) models the index returns as a VAR process, such as were employed to study the international transmis- sions of stock-market movements by Eun and Shim (1989), von Furstenburg and Jeon (1989), and Koch and Koch (1991). The multivariate structure allows us to measure the effects of an innovation in the stock returns of one market on its own lagged return and that of the other market. For example, the i,jth component of P,, measures the direct effect that a change in the return to the jth market would have on the ith market in p days. Because of the complicated cross-equation feedbacks built into such an autoregressive system, measur- ing the system's response to a typical random shock requires us to trace out the appropriate moving average representation, as shown by Sims (1980). More discussion of the impulse response analysis follows in Subsection 2.4.

Conditional on this dependence structure in the mean returns, the residual vector is bivariate normally distributed with conditional covariance matrix H,. Equation (2) models the dynamic process of H, as a linear function of its own K past values, Ht-k, as well as L past values of squared in- novations, e,_te'_,, both of which allow for own-market and cross-market influences in the conditional variances. This model was originally proposed by Baba, Engle, Kraft, and Kroner (1989) (BEKK). The important feature of this speci- fication is that it builds in sufficient generality, allowing the conditional variances and covariances of the two stock mar- kets to influence each other, and, at the same time, it does not require estimation of many parameters [eight for the bi- variate system with (L, K) = (1, 1)]. Even more importantly, perhaps, the BEKK process guarantees by construction that the covariance matrices in the system are positive definite.

Sequential testing procedures are used to determine the order, P, of the VAR process, as well as for the conditional variance equation, L and K in a BEKK process. In this article, I justify the specification for the conditional mean returns and conditional volatility equations using the optimal lag-length algorithm with the Akaike information criterion.

2.2 Other Conditional Variance Processes

To measure the sensitivity of the analysis to the specifi- cation of the BEKK conditional variance process, the study also employs other specifications. The simplest specifica- tion corresponds to that of a traditional VAR system in which the residual vector, e,, is white noise with a constant co- variance matrix, H, = H. This process is nested within the BEKK model by restricting the F and G matrices to be 0. This comparison represents an important check of the stabil- ity of a full information maximum likelihood system such as M-GARCH. Moreover, it affords us an opportunity to bench- mark the findings of earlier studies of international transmis- sions of stock returns that employ different specifications.

I also explore an alternative bivariate GARCH specifica- tion employed previously by Baillie and Bollerslev (1987), Schwert and Seguin (1990), and Chan et al. (1991):

h1 ,= C2 1

L h22,t k=l , t-k =1 2, t-lI

and h12,t = p[hi, th22, t1/2, (5)

where A' = [ala2], {Bk}ij = bij,k, and {CI}1 = cij,1, for lags k and 1, respectively. This model imposes an assump- tion of a constant correlation matrix of returns (p) over time. This parameterization ensures that H, is positive semidef- inite and also offers a parsimonious representation for the tests that follow. Note also that this specification allows for own-market and cross-market influences in the conditional variances through the off-diagonal coefficients in each of the Bk and C, matrices. We denote this model the GARCH-CC process to contrast with the GARCH-BEKK process.

Finally, I consider a specification in which the cross-market influences in the conditional variance process are restricted to be 0. That is, I estimate a univariate GARCH process for the conditional variances, while at the same time allowing for spillovers in the returns equation. This is similar to the GARCH-CC process, except that the correlation coefficient, p, and the off-diagonal coefficients in each of the Bk and Ct matrices are constrained to be 0. I denote this the univariate GARCH model and use it to gauge how important modeling of the cross-market influences in the conditional variance process will be for measuring the short-run dependence in the mean returns.

2.3 Estimation

Given a sample of T observations of the returns vector, r,, the parameters of the bivariate systems are estimated by computing the conditional log-likelihood function for each time period as

L,(O) = - log 27r - logI H,j -t e()H- 1()e,(()

(6) and

T

L() = EL,(8), (7) t=l

where 8 is the vector of all parameters. Numerical maxi- mization of the log-likelihood function following the Berndt, Hall, Hall, and Hausman (1974) algorithm yields the maxi- mum likelihood estimates and associated asymptotic standard errors. The standard errors and associated t values reported in this article are, however, those calculated using the quasi- maximum likelihood methods of Bollerslev and Wooldridge (1992), which are robust to the density function underlying the residuals. To perform residual diagnostics, standardiza- tion is based on a Cholesky decomposition of the conditional covariance matrix at each period t.

2.4 Impulse Response Analysis

To illustrate the dynamics of the bivariate GARCH system for the conditional mean returns of U.S. and Canadian stock markets, I solve for the impulse response functions implied by the system. The impulse response coefficients can be obtained for the conditional mean returns as in traditional

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"16 Journal of Business & Economic Statistics, January 1995

Table 2. Estimates From Dynamic Models of Daily Returns on the S&P 500 and TSE 300 Stock Indexes from April 1981 to December 1989, VAR Model and M-GARCH BEKK Model

VAR model M-GARCH BEKK model Equation 1 Equation 2 Equation 1 Equation 2

S&P 500 returns TSE 300 returns S&P 500 returns TSE 300 returns

Parameters Lag Coef. t value Coef. t value Coef. t value Coef. t value

S&P 500 -1 .1686 [5.79]* .1990 [7.64]* .0573 [2.64]* .1985 [9.60]* -2 -.0617 [-2.09]* -.0424 [-1.61] .0180 [.81] .0270 [1.28] -3 -.0825 [-2.81]* -.0212 [-.81] -.0663 [-2.99]* -.0145 [-.69] -4 -.0851 [-2.89]* -.0580 [-2.20]* -.0047 [-.21] .0260 [1.23] -5 .0049 [.17] -.0009 [-.03]

TSE 300 -1 -.1658 [-5.12]* -.0136 [-.47] -.0478 [-2.10]* .1213 [5.60]* -2 .1067 [3.28]* .1292 [4.43]* .0510 [2.23]* .0961 [4.42]* -3 -.0183 [-.56] -.0305 [-1.04] -.0225 [-.98] -.0230 [-1.05] -4 .1024 [3.14]* .1175 [4.03]* -.0225 [-.98] .0085 [.39] -5 -.0522 [-1.64] -.0289 [-1.01]

Constant .0837 [3.40]* .0726 [3.30]* .0804 [3.23]* .0494 [2.09]* WKND dummy -.1510 [-2.69]* -.2974 [-5.91]* -.1749 [-3.07]* -.3332 [-6.15]* HLDY dummy .1312 [1.31] .2202 [2.45]* .1284 [1.26] .1986 [2.05]*

Adj R2 .0349 .0692 .0103 .0807 DW 1.9973 2.0026 1.9975 2.0007 Skewness -.2662* -.3143* -.1332 -.3092* Kurtosis 4.9442* 1.0554* 2.7001 5.2469* Returns residuals

LB(6) .0973 .1180 1.6599 5.2902 LB(12) 4.2034 4.2191 4.7732 13.0350

Squared returns residuals LB(6) 342.1167* 659.4262* 12.0861 36.5527* LB(12) 432.2920* 762.9053* 13.6191 38.1322*

Ftests of block of lags S&P 500 11.5644 (.00) 13.8256 (.00) 1.6410 (.07) 8.9172 (.00) TSE 300 9.8361 (.00) 7.7861 (.00) 1.4825 (.12) 5.4894 (.00)

Log-likelihood 14,941.3342 15,204.8753

NOTE: Quasi-maximum likelihood t values (in brackets) based on Bollerslev and Wooldridge (1992) are employed. Skewness, kurtosis measures, and autocorrelations are computed for standardized residuals. F statistics (with p values in parentheses) denote tests of exogeneity of block of lags. A * indicates significance at the 5% level. The specifications and estimation procedures for each model are described in the text.

VAR models by successively substituting on the right side of Equation (1) to generate a moving average representation (Sims 1980) as follows:

00

r, = R,e,_, (8) s=

which represents rt as a linear combination of current and past one-step-ahead forecast errors or innovations. The i,jth component of R, shows the response of the ith market in s pe- riods after a standardized unit random shock in thejth market and none in other markets. To observe the distinct response patterns of the system, the errors are transformed to orthogo- nalize the innovations using a Cholesky factorization in which a lower triangular matrix V is selected so that V-'HV -' = I and used to compute new innovations, vt = V-'et. Making an orthogonalized transformation to v,, Equation (8) can be rewritten as

r, = RsVv,_, = QSv_, (9) s=O s=O

where the i,jth component of Q, represents the impulse re- sponse of the ith market in s periods to a shock of one standard error in thejth market. The responses can be thought of as the

estimates of the moving average coefficients in Equation (1), though they are normalized by dividing by their standard er- rors to control for different variations in returns across the two stock markets. The impulse response functions for the bivariate and univariate GARCH processes apply the same procedures to their standardized residuals series, which have been corrected for time-varying conditional heteroscedastic- ity, as implied by their respective models. One caveat about impulse response analyses derives from the difficulty in com- puting appropriate standard-error bands (Runkle 1987) and from their sensitivity to the underlying model specification (Braun and Mittnik in press). These studies imply that, if these error bands are large, inferences about the relative mag- nitude of responses across models will be problematic.

3. RESULTS

3.1 Primary Results

Tables 2 and 3 report the results of fitting the VAR, univari- ate GARCH and the BEKK and CC bivariate GARCH models to the S&P 500 and TSE 300 index returns. In each case, I report the coefficient estimates for the various models with associated robust t values, adjusted R2 measures, likelihood-

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Karolyi: A GARCH Model of International Transmissions 17

Table 3. Estimates From Dynamic Models of Daily Returns on the S&P 500 and TSE 300 Stock Indexes from April 1981 to December 1989, M-GARCH CC Model and Univariate GARCH Model

M-GARCH CC model Univariate GARCH model

Equation 1 Equation 2 Equation 1 Equation 2 S&P 500 returns TSE 300 returns S&P 500 returns TSE 300 returns

Parameter Lag Coef. t value Coef. t value Coef. t value Coef. t value

S&P 500 -1 .0600 [2.76]* .1884 [8.75]* .1079 [3.56]* .1304 [4.32]* -2 .0191 [.86] .0334 [1.52] -.0095 [-.31] -.0382 [-1.27] -3 -.0638 [-2.89]* -.0196 [-.90] -.0294 [-.97] -.0171 [-.57] -4 -.0032 [-.15] .0312 [1.42] -5

TSE 300 -1 -.0544 [-2.48]* .1012 [4.66]* -.0642 [-2.12]* - .0713 [2.36]* -2 .0466 [2.12]* .0832 [3.83]* .0181 [.59] .0687 [2.27]* -3 -.0316 [-1.43] - .0274 [-1.26] .0164 [.54] .0207 [.68] -4 -.0228 [-1.04] .0289 [1.33] -5

Constant .0812 [3.24]* .0542 [2.18]* .0819 (3.31]* .0959 [3.89]* WKND dummy -.1706 [-2.98]* -.3155 [-5.57]* -0.1578 [-2.79]* - .3229 [-5.73]* HLDY dummy .1310 [1.28] .2037 [2.01]* .1138 [1.12] .2105 [2.08]*

Adj R 2 .0116 .0662 .0049 .0470 DW 1.9978 2.0040 1.9982 2.0008 Skewness -.2714* .1548 -.1505 .3392* Kurtosis 5.4505* 11.1014* 4.8471* 15.2530* Returns residuals

LB(6) .0703 2.2342 .2585 .0927 LB(12) 1.8102 5.9626 2.6846 4.7869

Squared returns residuals LB(6) 91.4459* 147.7939* 17.6840* 224.8783* LB(12) 94.1430* 148.5949* 19.5341 245.3134*

F tests of block of lags S&P 500 1.6329 (.08) 7.8140 (.00) 1.9922 (.04) 2.6289 (.01) TSE 300 1.8206 (.04) 4.0736 (.00) 1.2201 (.28) 1.8175 (.06)

Log-likelihood 15,196.4238 15,186.5012

NOTE: Quasi-maximum likelihood t values (in brackets) based on Bollerslev and Wooldridge (1992) are employed. Skewness, kurtosis measures, and autocorrelations are computed for standardized residuals. F statistics (with p values in parentheses) denote tests of exogeneity of block of lags. A * indicates significance at the 5% level. The specifications and estimation procedures for each model are described in the text.

function values, and various residual diagnostics. I do not

report the coefficient estimates for the conditional variance dynamics to conserve space, though they are available on re- quest. Finally, I compute tests of the joint significance of a block of lags (block exogeneity test) for the returns of one market in terms of F statistics, reported with associated p val- ues. Note that these F statistics are not computed using the quasi-maximum likelihood estimate of the coefficient covari- ance matrix but with restricted and unrestricted coefficients of determination, as in traditional VAR studies.

For each model, I estimate lag lengths that correspond to the optimal number as determined by the Akaike criterion. This resulted in five lags for the VAR, four lags for the BEKK and CC bivariate GARCH models, and three lags only for the univariate GARCH model. Similarly, though not reported, the Akaike criterion dictated that the conditional variance process be governed by a lag (L, K) structure of (1, 3) for the CC model (16 parameters) and the univariate model (8 parameters) and of (1, 1) for the BEKK model (8 parameters).

The patterns in the coefficients of the matrices 4 that cap- ture the dependence of the index returns on their lagged values are different across models. In general, the estimates for the

first-order lags are quite different for the VAR model than for any of the GARCH models. For example, the coefficient val- ues for the own-market lags of the S&P 500 range from .1686 for the VAR model to .0573 for the BEKK GARCH model, though all are statistically significant. On the other hand, for the TSE 300 returns, the coefficient estimates for the own- market lagged returns range from an insignificant -.0136 in the VAR model to .1213 for the BEKK GARCH model. More interesting, however, is the variability across models in inferences about the cross-market dependence in returns. Whereas the VAR and GARCH models agree on a large and significant value of about .1990 for the dependence of TSE 300 returns on lagged S&P 500 returns, the VAR models ap- pear to overestimate the dependence of S&P 500 returns on lagged TSE 300 returns with a significant value of -.1658 as compared with the GARCH estimates all around -.0500. This finding is consistent with VAR models estimated by Eun and Shim (1989) in which they determined that in accounting for the total forecast error variance for U.S. market returns, a surprisingly large 33% of the foreign (eight different mar- kets in total) market component derives from the Canadian returns. Finally, higher-order lags of the VAR system appear

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18 Journal of Business & Economic Statistics, January 1995

0.25 0.25 Model A - VAR Model B - M-GARCH BEKK

0 . ................................................................................................................ 0.1 ................................................................................................................ 0.1--------------------- ............................................................................................................... 0.1----------------------------------- ................................................................................................................0................. 0.1 5 ------?--------?--- ------------------------- 0,1

0,1- -I---- --------?------------- --- - --------- 0.15

-0.15 --------------- ---- 1------- -0.1 05

1 2 3 4 5 6 7 11 12 1 2 3 4 5 6 7 8 9 10 11 12 0.25 O.L-

Model C - M-GARCH CC Model D - Univarlate GARCH

0,15 -------------? - ------------------ 0-1

0,1 ----------------------------- 0.1

.----................---------------------------- 0.05-........ O,5..o ........ ... ................................................. ............................

0* .I . O

-0.1 -------------------------- -01 ...............................................- ........................................... ...................

-0.15- 11 -0.15 1 11 1 - I 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 7 9 10 11 12

Figure 1. Impulse Response Coefficients for Daily S&P 500 Stock-Index Returns April 1981 to December 1989, up to 12 Lags Following Unit-Return Shock Originating in S&P 500 (domestic, solid line) and TSE 300 (foreign, dotted line) Markets. Estimates are from VAR and M-GARCH models of Tables 2 and 3.

to be statistically significant in contrast with the GARCH models. For example, though the GARCH models rarely yield statistically significant coefficient estimates for higher than two lags either for own-market or cross-market returns, those of the VAR model are almost all significant up to the fourth lag.

The residual diagnostics indicate that the M-GARCH mod- els obtain a better fit to the returns process. The distribu- tional coefficients reveal still significant nonnormality for the VAR model with large negative skewness and excess kurtosis. These models do appear to absorb the dependence in the auto- correlations of the residuals for both series, but higher-order dependence in the squared residuals remains. In contrast, the residuals from the bivariate GARCH models approach nor- mality, with insignificant excess skewness and only slightly positive excess kurtosis. The BEKK model also captures the structure in the raw and squared residuals autocorrelations, with LB X2 statistics unable to reject white noise at the 5% significance level for the S&P 500 returns, though not for the squared TSE 300 returns residuals. Wald tests (not reported in the table) were conducted of the null hypothesis that the

conditional variance dynamics in the bivariate and univariate GARCH models are 0. That is, the VAR model was proposed as a restricted alternative to the more general GARCH mod- els. The X2 statistics (degrees of freedom) yielded values of 526.9 (8), 510.2 (16), and 490.3 (8) for the BEKK, CC, and univariate GARCH models, respectively, all of which represent p values less that .0001.

Tables 2 and 3 also present results on zero exclusion or block exogeneity tests of the null hypothesis that no cross- market spillovers of stock-return innovations exist. I imple- ment these tests using the F statistic with degrees of free- dom equal to the number of restrictions imposed on the system and the number of parameters in the unconstrained system. The VAR model indicates that the null hypothe- sis of zero cross-market spillovers can be easily rejected in both directions. That is, not only are the five lags of S&P 500 returns statistically important predictors of TSE 300 re- turns, but so are the five lags of TSE 300 returns for the S&P 500 returns. This is counterintuitive and likely due to model misspecification, as seems to be the case when con- sidering the bivariate and even univariate GARCH models.

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Karolyi: A GARCH Model of International Transmissions 19

25Model A - VAR 25Model B - M-GARCH BEKK Model A - VAR

..............................................................................................................

0 .5 ................................................................... ............................................. .a ,

0.1

0 01

......................... ................................................ -......................................................................................

0.Q5 .... ............... .................. -....

-G151........................................................ -Q

-0-10, 5 ' "' ,.. -

1 3 5 7 8 9 10 1' 112 12 3456 7 8 9101112 a025 0.25

Model C - M-GARCH CC Model D - Untvariate GARCH 0.2 .......................................--- -------- 2-..........................................

Q . ................................................... ................................................ 0.1 ......................................................... .....................15 015-..................................... ri1 - .-- \---.------------'-'-'-"- """ "'--- 0,1

0 0

-0 5 ................................................................................................................. -Q 0 5 ................................................................................................................

-Q...................................................... •-Q............................... ......... .. _Q 15-L---1-11-- 1- a5 II--------.-1 1 -aI I

1 2 3 4 5 6 7 8 9 10 11 12 1 2 4 5 6 7 8 9 10 11 12 Figure 2. Impulse Response Coefficients for Daily TSE 300 Stock-Index Returns April 1981 to December 1989, up to 12 Lags Following

Unit-Return Shock Originating in TSE 300 (domestic, solid line) and S&P 500 (foreign, dotted line) Markets. Estimates are from VAR and M-GARCH models of Tables 2 and 3.

For example, in the BEKK process, the F statistic associated with the null of zero cross-market spillovers from lagged TSE 300 returns to future S&P 500 returns cannot be rejected (p value of .1233). Interestingly, the statistical importance of the lagged S&P 500 returns for future TSE 300 returns is confirmed for all four models estimated, though the magni- tude of the F values are considerably smaller for the GARCH models.

The evidence in Tables 2 and 3 suggests that the dynamics of the conditional volatility processes builds important struc- ture into the data. As shown in the residual diagnostics and block exogeneity tests, inferences about the statistical impor- tance of cross-market spillovers of returns between the S&P 500 and TSE 300 market returns do appear to be sensitive to the conditional volatility dynamics.

3.2 Impulse Response Analysis To illustrate the dynamics of the VAR and bivariate and

univariate GARCH models for S&P 500 and TSE 300 mar- ket returns, we computed the simulated responses of the esti-

mated systems to innovations originating in each market us- ing an impulse response analysis. The normalized response functions implied by the four models are plotted in Figure 1 for the S&P 500 market returns and in Figure 2 for the TSE 300 market returns. Both figures indicate that the innova- tions in these markets are rapidly transmitted across markets with the most dramatic responses usually on day 1 and later responses tapering off. One contrast between S&P 500 and TSE 300 response functions is the absolute and relative mag- nitude of the domestic and foreign responses at the first and even subsequent lags. For the S&P 500, the average response is generally within a band of .10 around 0 for both domes- tic and foreign shocks, which are likely to be insignificant (Runkle 1987). Moreover, the magnitude of responses to do- mestic shocks are on average larger than for foreign shocks, consistent with findings of Eun and Shim (1989). For the TSE 300 returns, the responses are larger at the first lag, in general, and especially those from the foreign shocks that originate in the S&P 500 returns. This finding is consistent across all four models, although the sizes of the response coefficients are smaller for the GARCH CC and univariate GARCH models.

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20 Journal of Business & Economic Statistics, January 1995

Table 4. Subperiod Estimates From Dynamic Models of Daily Returns on the S&P 500 and TSE 300 Stock Indexes

Apr/81-Jun/84 JuV8 4-Oct/87 Nov/87-Dec/89 793 obs. 793 obs. 541 obs.

Equation 1 Equation 2 Equation 1 Equation 2 Equation 1 Equation 2 S&P 500 returns TSE 300 returns S&P 500 returns TSE 300 returns S&P 500 Returns TSE 300 Returns

Parameters Lag Coef. t value Coef. t value Coef. t value Coef. t value Coef. t value Coef. t value

S&P 500 -1 .1128 [3.15]* .2748 [8.08]* .1002 [2.78]* .2231 [6.57]* -.0349 [-.80] .0992 [2.35]* -2 .0257 [.69] -.0168 [-.48] -.0447 [-1.20] -.0111 [-.32] .0293 [.66] .0669 [1.58] -3 -.0137 [-.37] .0645 [1.82] .0036 [.10] .0318 [.91] -.1813 [-4.18]* -.1355 [-3.24]* -4 -.0021 [-.06] -.0137 [-.39] -.0224 [-.60] .0033 [.09] -.0728 [-1.64] .0460 [1.08]

TSE 300 -1 -.0592 [-1.58] .1647 [4.63]* .0175 [.46] .1654 [4.61]* -.0791 [-1.74] .0703 [1.61] -2 .0204 [.54] .0625 [1.74] .0086 [.22] .0636 [1.75] .0906 [1.99]* .1204 [2.74]* -3 .0474 [1.26] .0083 [.23] -.0231 [-.60] -.0424[-1.17] -.0634 [-1.39] .0048 J.11] -4 -.0365 [-.97] .0141 [.40] -.0770 [-2.00]* .0396 [1.09] .0287 [.63] -.0683 [-1.56]

Constant .0421 [1.05] .0520 [1.37] .1302 [3.33]* .0368 [1.00] .0561 [1.05] .0607 [1.18] WKND dummy -.2245 [-2.45]* -.4524 [-5.21]* -.1752 [-2.00]* -.2724 [-3.30]* -.0585 [-.47] -.2089 [-1.73] HLDY dummy 0783 [.50] .1021 [.69] .1178 [.76] .2857 [1.95] .1770 [.71] .3095 [1.30]

Adj R2 .0123 .1346 .0106 .0848 .0400 .0455 DW 1.9975 1.9909 1.9979 2.0105 1.9950 1.9723 Skewness .3203* -.0355 -.1652 -.0072 -.8751* -.1141 Kurtosis 1.5222 1.9533 1.8439 .8381 9.0747* 12.6153 F tests of block of lags

S&P 500 1.2811 (.24) 6.7345 (.00) 1.4950 (.14) 5.2378 (.00) 2.4424 (.02) 2.6568 (.01) TSE 300 1.1207 (.34) 3.3304 (.00) 1.0922 (.37) 3.1943 (.00) 1.7827 (.06) 2.8837 (.01)

Log-likelihood 20,13.6487 38,422.9087 24,266.8386

NOTE: See Tables 2 and 3 for notation and symbols.

3.3 Subperiod Analysis

Studies by Booth and Johnston (1984), Jorion and Schwartz (1986), Alexander et al. (1988), Mittoo (1993), and Foerster and Karolyi (1993) empirically examined the extent of integration or segmentation of the financial markets in Canada and the United States. Their motivation for consid- eration of the North American case arose from the similarity of market structures and regulation, and from the absence of many controls on capital flows. The tests took the form of empirical investigations of how domestic and foreign mar- ket risk is priced for portfolios of stocks traded on the TSE and NYSE in accordance with international versions of asset- pricing models such as the CAPM or APT. The evidence is generally consistent with a growing degree of integration be- tween the financial markets over the decade of the 1980s (Mittoo 1993). An important supplementary hypothesis that I test in this section is whether this recent phenomenon can be observed in the short-term dynamics of the S&P 500 and TSE 300 returns and volatility.

Table 4 presents subperiod results of the BEKK GARCH model for the S&P 500 and TSE 300 returns series. The model is estimated with four lagged returns for each market and us- ing an (L, K) lag structure of (1,1) in the conditional volatil- ity process, as in Section 2. The subperiods correspond to two equally divided periods before the October 1987 market crash (1981-1984 and 1984-1987) and one post-crash period (1987-1989). The coefficient estimates associated with the

first lagged returns show an attenuation over time. For the S&P 500 returns, the coefficient for the own-market lagged return falls from a value of .1128 to a statistically insignif- icant -.0349. Less dramatically, the first own-market lag for TSE 300 returns falls from .1647 to .1204. The more interesting pattern across subperiods, however, is in terms of cross-market dependence in which the coefficient of future TSE 300 returns on the lag-one S&P 500 returns falls from .2748 to only .0992. The cross-market influence of TSE 300 returns for subsequent S&P 500 returns is, as expected, weak over the entire horizon.

This diminishing cross-market dependence of TSE 300 returns on the U.S. market shocks is further demonstrated in the block exogeneity tests, shown at the bottom of Ta- ble 4. Whereas the F statistics associated with the null hypothesis that the block of lagged S&P 500 returns have no predictive power for TSE 300 returns can easily be re- jected in the earlier two subperiods, this is not the case in the post-crash period, at least at the 1% significance level. Figures 3 and 4 plot the impulse response functions for the S&P 500 and TSE 300 returns, respectively, in response to own-market and foreign-market returns shocks. The re- sponse function for the S&P 500 returns show no dramatic changes over time and, overall, are well within a band of .1 around 0. These responses are likely to be statistically in- significant. By contrast, the TSE 300 response functions show larger changes over the three subperiods, with the first day lagged response of around .30 in the 1981-1984

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Karolyi: A GARCH Model of International Transmissions 21

Q3 Subperlod: Apr/81 - Jun/84

a 25 ................................................................................................................

a 2 .................................................................................................................

a 15 ................................................................................................................

015

- i -

1 2 3 4 5 6 7 8 9 10 11 12

a3 Subperiod: JuV/84 - Oct/87

a 25 ...............................................................................................................

a 2 . ................................................................................................................

Q i15 ................................................................................................................

0,25-

02

03

-,O5 ................ ... ............... ....................................

-Q i ...................... ................................ ............................................... . . -Qi

-al 1

1 2 3 4 5 6 7 8 9 10 11 12

Q3 Subperlod: Nov/87 - Dec/89

0 25 - ?-- ?-------------

(3a 1 5 ....................................o............................................... 0 0...........................

. 5...... . '............-............

02

01

1 2 3 4 5 6 7 8 9 10 11 12

Figure 3. Impulse Response Coefficients for Daily S&P 500 Stock-Index Returns, Subperiod Results, up to 12 Lags Following Unit-Return Shock Originating in S&P 500 (domestic, solid line) and TSE 300 (foreign, dotted line) Markets. Subperiod estimates corre- spond to those of Table 4.

a3 Subperlod: Apr/81 - Jun/84

02

ai

Subpe-rod: Jul/84 - Oct/87

Q2-

-015

1 2 3 4 1 6 7 1 10 11 12

a3-

Subpedod: Nov/87 - Dec/89

l 25 ...........................................................................................

02

0

Figure 4. Impulse Response Coefficients for Daily TSE 300 Stock-Index Returns, Subperiod Results, up to 12 Lags Following Unit-Return Shock Originating in TSE 300 (domestic, solid line) and S&P 500 (foreign, dotted line) Markets. Subperiod estimates corre- spond to those of Table 4.

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22 Journal of Business & Economic Statistics, January 1995

subperiod falling to only .10 in the most recent 1987-1989 subperiod.

Overall, the short-run dependence of returns on Canadian stocks to innovations or shocks that arise in New York ap- pears to have diminished over time. I interpret this subperiod evidence as consistent with the findings in other studies of the North American capital market that demonstrate growing financial market integration during the 1980s.

4. INTERLISTED AND NONINTERLISTED CANADIAN STOCKS

Many Canadian firms have chosen to simultaneously list their stocks on the major U.S. market exchanges in addi- tion to Canadian markets over the past two decades. The usual arguments put forward by firms relate to the enhanced marketability of their securities, better access to new funds at lower cost, and a greater profile for Canadian products sold in the U.S. market. Switzer (1986), Mittoo (1992), and Foerster and Karolyi (1993) have examined the benefits and costs of listing Canadian stocks in U.S. markets. Two critical facts are important. First, of all foreign-based companies listed on U.S. exchanges, Canadian-based firms represent the largest foreign-stock contingent. Second, a large frac- tion (as of December 1990, about 133 of 1,200 companies) of all listed securities on the TSE are interlisted on the NYSE, AMEX, or NASDAQ exchanges. Moreover, these comprise some of the largest TSE-listed companies in terms of capi- talization and total-dollar trading volume. In fact, the TSE

has established direct electronic trading links with the AMEX that allows for two-way trading in their 30 Canadian-based in- terlisted stocks. Orders can be routed either way between the exchanges using the Market Order Trading System (MOST) of the TSE or the Post Execution Reporting (AUTOPER) sys- tem of AMEX. The TSE has a similar though less important trading link with the Midwest Stock Exchange in Chicago.

The pattern of spillovers in returns and volatilities across the U.S. and Canadian markets and globally can arise from many different barriers to investments across national mar- kets such as the quality of financial reporting due to differ- ential accounting disclosure standards, tax considerations, foreign ownership restrictions, or just the difficulty of ob- taining information about foreign stocks. For U.S. investors, interlisted Canadian stocks, however, are subject to the same listing requirements and are as easy to trade as domestic U.S. stocks. One way to gauge the economic importance of these investment barriers is to examine the patterns of spillovers of returns and volatilities from U.S. markets to interlisted versus purely domestic Canadian stocks. In the studies by Jorion and Schwartz (1986) and Mittoo (1993) stronger evidence of seg- mentation (versus integration) was uncovered in the pricing of purely domestic versus interlisted Canadian stocks rela- tive to a North American market. A second reason to exam- ine separately interlisted and noninterlisted TSE 300 stocks arises from the study by Bertero and Mayer (1989), which

proposed that the degree of correlatedness across the world's stock markets is related to the trading of overseas securi- ties and, in particular, the fraction of cross-listed securities.

Table 5. Estimates From Dynamic Models of Daily Returns on the S&P 500 Stock Index and Portfolios of Interlisted and Domestic TSE 300 Stocks

Interlisted TSE stocks Domestic TSE stocks

Equation 1 Equation 2 Equation 1 Equation 2 S&P 500 returns Portfolio returns S&P 500 returns Portfolio returns

Parameters Lag Coef. t value Coef. t value Coef. t value Coef. t value

S&P 500 -1 .1287 [4.44]* .1163 [3.97]* .1147 [4.63]* .2513 [1.09]* -2 -.0566 [-1.94] -.0594 [-2.02]* -.0308 [-1.21] -.0151 [-.59] -3 -.0292 [-1.00] .0031 [.10] -.0412 [-1.63] .0072 [.28] -4 .0113 [.39] .0275 [.93] -.0001 [-.01] .0287 [1.13]

TSE 300 -1 -.0627 [-2.19]* .0576 [1.99]* -.0604 [-2.46]* -.0634 [-2.57]* -2 .0595 [2.06]* .0790 [2.71]* .0395 [1.61] .1027 [4.16]* -3 -.0144 [-.50] -.0159 [-.54] .0030 [.12] .0166 [.67] -4 -.0097 [-.34] -.0072 [-.25] .0111 [.45] .0380 [1.54]

Constant .0880 [3.62]* .0481 [1.96]* .0842 [3.51]* .0692 [2.87]* WKND dummy -.1638 [-3.00]* -.1726 [-3.13]* -.1533 [-2.84]* - .2520 [-4.64]* HLDY dummy .1314 [1.17] .2747 [2.43]* .1399 [1.27] .2956 [2.66]*

Adj R2 .0116 .0286 .0116 .0648 DW 1.9971 1.9982 1.9977 2.0009 Skewness -.0372 .0351 -.0729 .1801" Kurtosis 3.0689* 1.4663 3.3361* 3.5270* F tests of block of lags

S&P 500 4.9807 (.00) 2.0497 (.02) 5.4090 (.00) 2.6023 (.00) TSE 300 1.7090 (.13) 2.5073 (.03) 1.8572 (.10) 5.7375 (.00)

Log-likelihood 62,206.4209 36,472.1287

NOTE: See Tables 2 and 3 for notation and symbols.

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Karolyi: A GARCH Model of International Transmissions 23

Q3- Intertlsted TSE 300 Stocks

QL25i .............................................................................................................................

00 .............. ...................................

015

Non-antedisted TSE 300 Stocks

OL25 ................................................................................................................

0Q 2 ............................................................................................................................

0Q 15 ......... .................................................................................... .............

- 1 2 3 4 5 6 7 8 1-0 11 12

1 2O534...7..10 1 12

1 2 3 4 5 7 8 1 10 11 12

Figure 5. Impulse Response Coefficients for Daily Returns on Portfolios of Interlisted and Domestic TSE 300 Stocks up to 12 Lags Following Unit-Return Shock Originating in TSE 300 (domestic) and S&P 500 (foreign) Markets. Estimates correspond to those of Table 5.

Barclay, Litzenberger, and Warner (1990) examined the im- portance of this element for average market volatility in the New York and Tokyo markets.

In this section, I repeat the experiments of Section 3 for two portfolios of large, actively traded TSE 300 stocks that are interlisted or "purely domestic." The interlisted portfolio comprises Alcan Aluminum, Canadian Pacific, Moore Cor- poration, Inco, Northern Telecom, and Placer Dome, each of which trade on the NYSE. They represent, as of Decem- ber 31, 1989, 15.92% of the total market capitalization of the TSE 300. The matched sample of large, actively traded, purely domestic stocks includes Canadian Tire, Imasco, No- randa, Power Corporation, Stelco, and Thomson Corpora- tion, which total 6.88% of the capitalization of the TSE 300. This supplementary test is also important because I control for the effects of asynchronous trading of component secu- rities in either the aggregate TSE 300 index or its subport- folios. Studying the model estimates for two portfolios of actively traded TSE stocks will help to determine whether

the conditional returns and volatility dynamics uncovered in the previous subsection are simply statistical artifacts of a lagged response by Canadian stocks to shocks originating in U.S. markets because of the many small TSE 300 stocks that trade infrequently.

Table 5 reports the estimates of the bivariate GARCH- BEKK model for the interlisted and noninterlisted portfolios with the S&P 500. The main contrasting feature of the in- terlisted and noninterlisted portfolios is the significant and much larger positive dependence of the portfolio return on the one-day lagged S&P 500 returns. The coefficient value of .2513 is more than double that of the interlisted portfo- lio of .1163. The block exogeneity tests at the bottom of Table 5 also confirm the greater importance of the lagged S&P 500 returns for subsequent returns of the domestic TSE stocks (F statistic of 20.6023) than for those of the interlisted TSE stocks (F statistic of 2.0497). Finally, Figure 5 dis- plays the impulse response coefficients for the two portfo- lios of TSE 300 stocks in response to both own-market and foreign-market shocks. Whereas for the interlisted stocks the foreign market shock generates a response equivalent in magnitude at the first and subsequent lags to that of a do- mestic shock, the foreign-market shock has a much greater immediate impact for the noninterlisted stocks. Despite po- tentially large standard-error bands that surround these im- pulse response functions, the economic impact of the U.S. shocks appears to be demonstrably larger for noninterlisted Canadian stocks.

In sum, our results suggest that the magnitude and per- sistence of the innovations originating in S&P 500 stock re- turns that have an impact on subsequent returns of interlisted stocks are smaller than those of noninterlisted stocks in the Canadian markets. Furthermore, we find evidence that the dynamics of the spillovers in the returns uncovered cannot be directly attributed to the phenomenon of asynchronous trading of portfolio securities because our results obtain for returns on portfolios of large and actively traded TSE stocks as well as for broad-based market-index returns.

5. CONCLUSIONS

5.1 Main Findings

This article examines the structure of short-run dynam- ics of returns and volatility for stocks traded on the TSE and the NYSE for the period from 1981 to 1989. The ex- periment is designed to account for the fact that these mar- kets trade simultaneously so that our measures of return and volatility spillovers between markets are not affected by mea- surement problems due to nonsynchronous trading hours in the two markets. The study employs multivariate GARCH techniques to capture the mechanism by which stock-returns innovations in one market have an impact on not only the conditional market returns but also the conditional market volatility of the other market. I also exploit the fact that many Canadian stocks interlist on U.S. exchanges to explore the importance of different types of linkages between markets

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24 Journal of Business & Economic Statistics, January 1995

that interlisted and noninterlisted stocks face. The main re- sults can be summarized as follows:

1. A bivariate GARCH model is a useful representation of the joint process governing S&P 500 and TSE 300 re- turns. Inferences about the magnitude and persistence of the return innovations that originate in either market and that transmit to the other market depend importantly on how the cross-market dynamics in the conditional volatilities of the respective markets are modeled.

2. The cross-market patterns in S&P 500 and TSE 300 returns and volatilities have changed over time. During the latter part of the 1980s, the magnitude of shocks originating in New York have had a diminished impact on subsequent TSE 300 returns.

3. The impact of S&P 500 stock-return innovations on portfolios of interlisted versus noninterlisted TSE 300 stocks are distinctly different. The magnitude and persistence of S&P 500 shocks are greater for subsequent returns of non- interlisted stocks. This suggests that investment barriers re- lated to differential accounting disclosure standards, foreign- ownership restrictions, and tax considerations may be impor- tant for understanding the dynamics of comovements in stock prices around the world.

4. Spurious autocorrelation in the returns series for the large S&P 500 and TSE 300 aggregate indexes due to asyn- chronous trading of component securities likely cannot ex- plain the structure of cross-market dependence in conditional mean returns or volatility.

5.2 Implications

These results have important implications for the global pricing of securities, for hedging and other trading strategies, and for regulatory policies within these two financial markets. If one accepts that the short-run cross-market dependence in the security returns and volatilities are significant, then we need to assess the impact of these international spillovers for our understanding of the degree of integration or segmenta- tion in the pricing of Canadian and U.S. securities within the global North American context. Most of the tests of interna- tional asset-pricing models ignore the time-varying nature of conditional expected returns and their covariance or variance risks, including those that focus on the U.S. and Canadian markets (Jorion and Schwartz 1986; Mittoo 1993). Future re- search needs to evaluate how sensitive are conclusions about the extent of integration or segmentation in these markets in the context of models that allow for the dynamics uncovered in this study.

We also need to understand the dynamics of conditional volatilities in these markets and how they influence hedging behavior using, for example, Canadian derivative securities, such as the TSE 35 index options and futures contracts and the more popular TIPS (index participation certificates), all trading on the TSE. For example, one of the difficulties with these contracts is their low liquidity, particularly in contrast with that of the Chicago Mercantile Exchange's S&P 500 index futures and futures options contracts. With a better understanding of the short-term dynamics of TSE 300 and

S&P 500 market returns, future research can examine the viability of cross-hedging trading strategies using the liquid, U.S.-based derivative contracts for traders with exposure to Canadian market risk.

Finally, our finding that the magnitude of shocks that orig- inate on the NYSE and that spill over to the TSE has been previously overstated in several studies may provide useful guidelines for regulatory policy in the Canadian securities industry. For example, the adoption by the NYSE in 1988 of limits on large negative daily price movements, known as "circuit breakers," led to the introduction of similar measures on markets around the world, including the TSE. The Brady Commission's Report of the Presidential Task Force on Mar- ket Mechanisms (1988) originally recommended downside price limits in the stock-index futures and options markets and trading halts in all markets at price levels equivalent to 250- and 400-point declines in the Dow Jones Industrial Av- erage from the previous day's close. The benefits and costs of these policies have been debated in various committee reports sponsored by the Commodity Futures Trading Commission (Kuhn, Kuserk, and Locke 1990) and the NYSE's Market Volatility and Investor Confidence Panel Report (1990). Var- ious U.S. securities, futures, and options exchanges adopted these recommendations in October 1988, followed the next year by the Board of Governors of the Toronto Stock and Fu- tures Exchanges, which adopted circuit breaker rules identi- cal to those of the NYSE (Toronto Futures Exchange Notice to Members TS89-21, August 15, 1989). Interestingly, though, the TSE's circuit breakers are triggered, similarly to those of the NYSE, by down moves of the Dow Jones Industrial Average and not of any TSE-based aggregate. Because the evidence in this study demonstrates that the influence on the volatility of Canadian financial markets of U.S.-based stock- price movements is weaker than previously understood and has diminished over time, the rationale behind these regula- tory policies should be seriously reexamined.

ACKNOWLEDGMENTS

Financial support was provided by a seed grant from The Ohio State University, a Faculty Research Grant from the Embassy of Canada, and the Dice Center for Finan- cial Economics at Ohio State University. I am grateful for comments from both Editors John Geweke and George Tauchen, an anonymous associate editor, two anonymous referees, Warren Bailey, Stephen Foerster, David Johnson, Eric Kirzner, Francis Longstaff, Marlene Puffer, Rena Stulz, Justin Wood, and participants at the September 1992 North- ern Finance Association meetings and at Wilfrid Laurier University. Discussions with Keith Boast, Director of the Toronto Stock Exchange's Market Listings Division, and Craig Hurl of the Derivative Markets group were helpful. Bong Chan Kho provided capable research assistance. Re- maining errors are my own responsibility. All correspon- dence to G. Andrew Karolyi, Fisher College of Business, The Ohio State University, 318 Hagerty Hall, 1775 College Road, Columbus, OH 43210-1309. Phone: (614) 292 -1875.

[Received November 1991. Revised June 1994. ]

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