eun shin(international trasmissions and movemants

JOURNAL OF FINANOIAL AND QUANTITATIVE ANALYSIS VOL 24, NO, 2, JUNE 1989

International Transmission of Stock MarketMovements

Cheol S. Eun an(j Sangdal Shim"

AbstractThis paper investigates the ititernational tratismission mechanism of stock market move-ments by estimating a nine-market vector autorcgression (VAR) system. Using simulatedresponses of the estimated VAR system, we (i) locate all the main channels of interactionsamong national stock markets, and (ii) trace out the dynamic responses of one market toInnovations in another. Generally speaking, a substantial amount of multi-lateral interac-tion is detected among national stock markets. Innovations in the U,S, are rapidlytransmitted to other markets in a clearly recognizable fashion, whereas no single foreignmarket can significantly explain the U.S. market movements. Also, the dynamic responsepattem is found to be generally consistent with the notion of informationally efficient in-temational stock markets.

I. Introduction

Since Grubel's work (1968), which expounded the benefits from intema-tiotial portfolio diversification, the relationship atnong national stock markets hasbeen analyzed in a series of studies, such as Granger and Morgenstem (1970),Ripley (1973), Lessard (1974), (1976), Panton. Lessig, and Joy (1976). and.more recently. Hilliard (1979), Despite the divergent empirical methods used,these studies generally found that (i) correlations among returns to national stockmarkets are surprisingly low, and (ii) national factors play an important role inthe return-generating process.' These findings were often cited as evidence sup-porting intemational, as opposed to purely domestic, diversification of invest-ment portfolios. As noted, the previous literature was mainly concerned withshowing that the interdependence of share price movements is much less pro-nounced among countries than within a country. Consequently, relatively littleattention was paid to the structure of interdependence among national stock mar-kets.

' College of Business and Management. University of Maryland, College Park, MD 20742, andKorea Development Institute, Seoul, Korea, respectively. The authors are grateful to two anonymousJFQA referees and JFQA Managing Editor Paul Malatesta for their valuable comments on earlierdrafts of the paper,

' These empirical lindings, however, were not unanimously confirmed by researchers, Agmon(1972), (1973), for example, found a substantial amount of relationship among the foursUKk marketsin his sample, i.e,, Germany, Japan, the U,K., and the U.S. Stock prices in non-U,S. countries werefound to respond to changes in the U,S, prices with no signiticant lags on a monthly basis. The use ofmonthly data, however, would obscure any lags lasting but a few days.

241

242 Journal of Financial and Quantitative Analysis

Careful examination of intemational stock market movements in recentyears suggests that there exists a substantial degree of interdependence amongnational stock markets. Furthertnore, unexpected developments in intemationalstock markets seem to have become important "news" events that influence do-mestic stock markets. To date, however, there exists no in-depth analysis of theinterdependence stmcture of national stock markets. The purpose of this paper isto provide such an analysis with a special emphasis on the intemational transmis-sion mechanism of stock market movements. Specifically, this paper addressesthe following issues:

(i) How much of the movements in one stock market can be explained byinnovations in other markets?

(ii) Does the U.S. stock market indeed influence other markets? Are thereany markets whose movements are causally prior to those of other mar-kets?

(iii) How rapidly are the price movements in one market transmitted to othermarkets?

In attempting to answer the above questions, we estimate a nine-market vec-tor-autoregressive system using daily rates of retum on the stock market indicesfrom the period January 1980 through December 1985, We use daily retum datato capture potential interactions, since a month or even a week may he longenough to obscure interactions that may last only for a few days. The nine mar-kets included in this study are Australia, Canada, France, Germany. Hong Kong,Japan. Switzerland, the United Kingdom, and the United States.' The vector-autoregressive analysis (VAR, henceforth), which was developed by Sims(1980), estimates unrestricted reduced form equations that have uniform sets ofthe lagged dependent variables of every equation as regressors. The VAR thusestimates a dynamic simultaneous equation system, free of a priori restrictions onthe structure of relationships. Since no restrictions are imposed on the stmcturalrelationships among variables, the VAR can be viewed as a flexible approxima-tion to the reduced fomi of the correctly specified but unknown model of theactual economic structure. Considering that the large-scale structural models arevery often misspecified, it seems to be appealing to use the VAR for the purposeof stylizing empirical regularities among time-series data.

Once our nine-market VAR system is estimated, we can trace out the dy-namic responses of each of the nine markets to innovations in a particular marketusing the simulated responses of the estimated VAR system. In addition, theinnovative accounting technique of the VAR allows us to measure the relativeimportance of each market in generating unexpected variations of retums to aparticular market and thus to establish causal ordering among national stock mar-kets. The empirical findings of our VAR analysis are thus expected to shed newlight on the interdependence structure of national stock markets, in general, and

' The nine markets included in this study are among ihe world's largest stock markets in lermsof capitalization value. These markets collectively account for about 93 percent of the world slockmarket index value (calculated by Morgan Stanley Capital Intemational Perspective) as of the end of1985, In addition, the nine markets coincide with those whose indices are reported by The WallStreetJournal on a daily basis.

Eun and Shim 243

the intemational transmission mechanism of stock market movements, in par-ticular.

In interpreting empirical results of VAR analysis, we recognize that nationalstock markets are operating in diverse time zones with different opening andclosing times, thereby making retum observations nonsynchronous. In this pa-per, we tackle the problem of nonsynchronism by first carefully examining thestructure of time differences, and then explicitly incorporating its implicationsinto the interpretation of empirical results. To illustrate this point briefly, sup-pose that the German stock market is influenced by developments in the U.S.stock market. Considering that for a given calendar day the German stock marketis closed before the U S . market opens, the German market would not be able torespond to a U,S. shock in the same day; instead, it would respond to the U,S,shock with a one-day lag. On the other hand, if the U,S, market is influenced bythe developments in the German market, the former should respond to a Germanshock in the same day in an efficient market. This is the case because the tradinghours of the German market precede those of the U,S.. providing the latter withan opportunity to react without delay. To recapitulate, despite the nonsynchro-nous nature of retum data employed, we can interpret the results of VAR analysisbased on the stmcture of time zone differences and therefrom obtain useful in-sights into the international transmission mechanism of stock market move-ments.

Our empirical results indicate that a substantial amount of multi-latera! in-teraction exists among national stock markets. As can be expected, the U.S.stock market tums out to be, by far. the most influential in the world. Innovationsin the U.S. stock market are rapidly transmitted to other markets in a clearlyrecognizable pattem, whereas no single foreign market can significantly explainthe U,S, market movements. The rather speedy transmission of a U,S. shock toother markets observed in this study generally supports the notion of informa-tionally efficient intemational stock markets.

The organization of the paper is as follows. Section II reviews the vectorautoregression methodology. Section III discusses data and a few related issues.The paper's main results are presented in Section IV. Section V offers a sum-mary and concluding remarks.

II. The VAR Model

The VAR model examined includes nine variables that are daily rates ofretum to the nine major national stock markets. The VAR model is expressed as

m

(1) Y(t) = C + YAis)Y(t-s) +e(t).

where Y(t) is a 9 x 1 column vector of daily rates of retum of the nine stockmarkets, and C and A(s) are, respectively, 9x 1 and 9 x 9 matrices of coeffi-cients, m is the lag length, and e{t) is the 9 x 1 column vector of forecast errors ofthe best linear predictor of Y{t) using all the past Y(s). By construction, eU) isuncorrelated with all the past Y(s). If this is combined with the fact that e(t) isalso a linear combination of current and past YU), e(t) is serially uncorrelated.


The iJth component of A(5) measures the direct effect that a change in the retumto the /th market would have on the /th market in ,v periods. As can be seen fromEquation (1). the right-hand side of each equation contains exactly the sameterms, i. e.. a constant, lagged value of each variable, and the error term.

Autoregressive systems such as (1), especially the coefficients of the regres-sion equations containing complicated cross-equation feedbacks are difficult todescribe intuitively. As shown by Sims (1980), it is better to analyze the sys-tem's reaction to typical random shocks or. equivalently. trace out the system'smoving average representation. By successive substituting on the right-hand sideof Equation (I), we can obtain a moving average representation as follows,

(2)

which represents Y(t) as a linear combination of current and past one-step-aheadforecast errors or "innovations,"-' The /,7th component of B(.s) shows the re-sponse of the /th market in A periods after a unit random shock in theyth marketand none in other markets.''

Although e{t) is serially uncorrelated by construction, the components ofeit) may be contemporaneously correlated. In order to observe the distinct re-sponse patterns the VAR system may display, it is useful to transform the errorterms. To achieve this, we choose a lower triangular matrix V and obtain theorthogonalized innovations u from e = Vu. It is noted that the transformed inno-vation u{t) has an identity covariance matrix, such that Eee' = S and W = S.Upon making an orthogonalized transformation to eU), Equation (2) can berewritten as follows.

(3)

.4-0

where C{s) - Bi.s)V. Then the ijih component of C(5) represents the impulse (orreflex) response of the /th market in s periods to a shock of one standard error inthejth market,^ A detailed description of the triangular orthogonalization proce-dure is provided in the Appendix.

' Innovations e(t) are detined ase w = n n - P \ Y { t ) \ Y l t - \ ) , > ' ( f - 2 ) . , , , I ,

where P denotes the linear least squares projection of Y(l) in the space spanned by \Ylt- I), YU-2)....]. As will be seen shortly, the moving average represenlalion of (2) enables us to trace out thereactions of inlemational stock markets to news, eU). in the form of unexpected developments in anational stock market.

•• The I jth component of Bl.s) represents the conditional expectation al time t of changes of ihe(th stock market returns in .( periods caused by a unil change in ihe /th markel. conditional on iheinformation available al time /,

"̂ To be consisleni with Ihe historical correlation pattem of innovations, we introduce a contem-poraneous shock in each equation thai is equal to Ihe corresponding element in ihe yth column ofmalrix V when we inlroduce one standard deviation shock in theyth markel. See the Appendix for adetailed exposition of this point.

Eun and Shim 245

Another advantage of using orthogonalized innovation is that we can alsoallocate the variance of each element in Y to sources in elements of u, since w isserially and contemporaneously uncorrelated. The orthogonalization provides thequantity, S/=(,C|(5), which is the component of forecast error variance in the7"+ 1 step ahead forecast of Y,, which is accounted for by innovations in K,, Thisdecomposition of forecast error variance provides a measure of the overall rela-tive importance of the markets in generating the fluctuations in stock retums intheir own and other markets,''

If one stock market is causally prior to other markets in the sense that theprice movements of the market affect subsequent price movements in other mar-kets, but are not affected by price movements of other markets in earlier periods,then the forecast errors of future retums of this influential market should bemostly accounted for by its own innovations, and should not be explained sub-stantially by the innovations of the other markets. The innovations of the influen-tial market should also explain a substantial fraction of the forecast error vari-ances of other markets,

III. Description of the Data

The data base used in this study consists of time series of daily stock marketindices at closing time, in terms of local currency units, of the world's nine majorstock markets, as calculated by Morgan Stanley Capital Intemational Perspec-tive. Geneva. It covers the period December 31. 1979, through December 20.1985. with a total of 1.560 observations. These stock market indices are trans-formed to daily rates of retum, which are then used in our VAR analysis. Poten-tial problems associated with any nonstationarity in the original sttKk marketindices can be alleviated by using the transfomied data. The stock market indicesused in this study do not double-count those stocks multiple-listed on foreignstock exchanges. Consequently, any observed interdependence among stockmarkets cannot be attributed to the multiple listings.

Given that national stock markets are generally operating in different timezones with different opening and closing times, their rates of retum on a givencalendar day may, in fact, represent the retums realized over different real timeperiods. For the purpose of interpreting the empirical results later on, it is impor-tant to know the operating hours of one market relative to other markets in a realtime scale. This infonnation is provided in Table I. which shows the openingand closing times of the major stock exchanges in New York time.

As can be seen in Table 1. all of the Asian-Pacific exchanges as well as twoEuropean exchanges, i.e,. Paris and Frankfurt, are closed when the New YorkStock Exchange (NYSE) opens for the day. On the other hand, the London andZurich exchanges operate from 4:30 a.m. to 10:30 a.m. by New York time, clos-ing half an hour after the NYSE has opened. When the European exchanges openfor the day, all of the Asian-Pacific exchanges are closed. The Toronto StockExchange, which is the last, along with the NYSE. to open for the day, operatesconcurrently with the NYSE.

'' Fora more detailed description of the VAR model, refer to Sims (1980).


TABLE 1

Opening and Closing Times of Major Stock Exchanges in New York Time

Exchange

AustraliaJapanHong KongU.K.SwitzerlandFranceGermanyCanadaUS.A,

Opening—Closing Time^

*8:00 p m -•8:00 p,m.-

*10:00p,m,-4:30 a m , -4:30 a m , -5:30 a.m,-5:30 a m , -

10:00 am. -10:00 a m -

1 00 am,2:00 a.m.3:30 am

10:30 a,m.10:30 am.8:30 am,7:00 a,m.4:00 p.m4:00 p,m.

a These times are as of December 1985, Asterisk (") denotes previous day in New York time.

IV. Empirical Results

In this paper, the lag length of VAR is chosen to be 15 trading days. We testa VAR with 15 lags in each variable against one with 20 lags, and we cannotreject the hypothesis that the restriction of excluding 16 through 20 lags holds, atthe usual 5-percent significance level. Neither can we reject the hypothesis thatall the coefficients of lags 21 through 25 periods are zero at the 5-percent signifi-cance level. All in all, there seems to be little, if any. feedback to the currentstock market retums from retums lagged more than 15 days. Thus, all the statisti-cal results presented below are based on the VAR with a lag of 15 trading days,which is equivalent to three weeks.''

A. Preliminary Discussion

Table 2 reports the contemporaneous correlations of the residual retumsamong the nine national stock markets. The residuals, or innovations, representabnormal stock market retums that were not predicted on the basis of all theinformation reflected in past returns. The contemporaneous correlations of theresidual retums reflect the degree to which new information producing an abnor-mal return in one market is shared by the other markets in the same calendar day.

Table 2 shows that, in general, the intra-regional pairwise correlations tendto be higher than the inter-regional correlations. For example, the U.S./Canadaexhibits the highest correlation, followed by Germany/Switzerland, whereas thecorrelations for such pairs as Canada/Japan and France/Hong Kong are close tozero. This pattem of contemporaneous correlations is consistent with what weexpect from the stmcture of time zone differences between pairs of markets. Thecorrelation pattem also may reflect the degree of economic integration betweencountries. This is so because the more integrated two economies are. the morestrongly the stock market movements in one country would be correlated to thosein another country. The unusually high correlation of U.S,/Canada seems to at-test to this factor.

^ Computer prcKessing lime with a large data set imposes another restriciion on the choice of thelag length. In our nine-markei VAR system, for each additional lag. the number of coefficients lo beestimated increases by 81,

Eun and Shim 247

In line with the general observations made above, the conteporaneous corre-lations of the U,S, with the Asian-Pacific and European markets, with the excep-tion of the U.K., are all low. Considering that the trading hours of these marketsprecede those of the U,S., development in these markets do not appear to havemuch impact on the U.S, market. The relatively high correlation ob.served be-tween the U S . and the UK, may reflect, at least in part, the fact that the twomarkets simultaneously operate for half an hour before the U,K, market closes.To recapitulate, a foreign market's correlation with the U.S, tends to get smallerthe farther away the market is from the U,S, This particular pattem of contempo-raneous correlations seems to suggest that the U,S, stock market influences otherstock markets. If the U.S. market were to be influenced, say. by the Japanesemarket, which closes before the U S . market opens, then the U.S. market couldhave responded to the Japanese developments in the same day. This, in tum,would have resulted in a higher contemporaneous correlation between the twomarkets.

AustraliaCanadaFranceGermanyHong KongJapanSwitzerlandU,K.U,S,A.

(AU)(CA)(FR)(GE)(HK)(JA)

(SW)(UK)(US)

TABLE 2

The Correlation Matrix of Residual Returns^

AU CA FR GE

1,000 0 045 0,068 0,0501,000 0 029 0,060

1,000 0,0781.000

HK

0.1240 062

- 0.0060 0861 000

JA

0.1270,0050.0950 1490.0791.000

SW

0 0690,1050.1140 2790.0400 1881,000

UK

0,0510,2050.0860 1360.0740 1040.1291.000

US

0,0350.6730 0220 0530.0880.0200.0830 17fi1.000

a Each entry in the table represents the contemporaneous correlation coefficient of theresidua! returns between a pair of countries, net of expected returns that are estimatedfrom the nine-market vector-autoregressive system using daily returns fronn the period1980.1-1985.12

B, Accounting National Stock Market Innovations

As previously mentioned, the forecast error variance of each stock marketcan be allocated to sources by using orthogonalized innovations. For each tnar-ket, the orthogonalization procedure provides the component of forecast errorvariance that is accounted for by innovations in each of the nine markets. Table 3provides the decomposition of 5-day. 10-day, and 20-day ahead forecasts ofstock market retums into fractions that are accounted for by innovations of differ-ent markets." Table 3 can thus be viewed as a summary that is useful in identify-ing the main channels of influence in the nine-market dynamic system. The moresalient features of Table 3 are discussed below.

" In this study, the orthogonalization is ordered as the U.S,. Ihe U.K,, Switzerland, Japan.Hong Kong, Germany. France, Canada, and Australia, When ihe different innovations are corre-laled. Ihe error variance decomposition could be sensitive to the order of variables for orthogonaliza-lion. To delemiinc the exogcneity of U.S. stock market returns, however, any ordering that puts theU,S. at the top would sufhce (See Doan and Litterman (1981). pp, 11-18), When we change theorder of variables, the U,S, still emerges as ihe dominant market.


Table 3 indicates that no national stock market is exogenous in that a mar-ket's own innovations fully account for its variance,'* On the contrary, a substan-tial amount of interaction is detected among national stock markets. At the hori-zon of 20 days, for example, the percentage of error variance of a national stockmarket attributable to collective innovations in foreign stock markets ranges from11,02 percent lor the U.S. to 52,02 percent for Canada, with the average of25.93 percent.

The results in Table 3 al.so indicate that the U,S, stock market is the tiiostinfluential in the world. While no single foreign market can explain more than 2percent of the U.S, error variance, the U,S, explains 6,43 percent (for HongKong) through 42,03 percent (for Canada) of the foreign market error variances,with the average of 16.78 percent. This U.S. average value is compared with2.56 percent and 2.15 percent, respectively, for Switzerland and the U.K,. thetwo relatively more influential foreign markets. Also, the U.S, innovations ac-count for about 89 percent of its own variance. No other market is so nearlyexogeneous in the sense defined above.

Switzerland turns out to be the most interactive market. Innovations in theSwiss market have repercussions in every other market and, at the same time,innovations in every other market are fed into the Swiss market. This highlyinteractive nature of the Swiss stcK'k market seems to reflect a high degree ofintegration of the Swiss economy with the world economy in general.

The pattern of interactions among Australia. Canada. Hong Kong, and theUK, revealed in Table 3 suggests that a British Commonwealth factor may bepresent. Innovations in the Canadian. Hong Kong, and U.K. markets collec-tively account for nearly 10 percent of the Australian variance. And about 6 per-cent of the Canadian variance is explained by innovations in Australia. HongKong, and the U.K,

Table 3 also provides evidence that the Japanese stock market, which iscomparable to the U.S. stock market in terms of capitalization value, acts like afollower in intemationai stock markets. Innovations in the Japanese market failto explain any substantial part of error variances of other markets. But the U.S.as well as the European markets, especially Switzerland and U.K,. exert substan-tial influence on the Japanese market. The European innovations collectively ac-count for about 9 percent of the Japanese variance, whereas the U.S, innovationsaccount for about 11 percent,

C, Dynamic Response Pattern

To obtain additional insight into the mechanism of intemational transmis-sion of stock market movements, we now examine the pattem of dynamic re-sponses of each of the nine markets to innovations in a particular market usingthe simulated responses of the estimated VAR system. To conserve space, weconcentrate on the responses of each of the nine markets to a shock in the U.S.market. Table 4 provides nomialized impulse responses of the nine markets to a

'' When we conduct the Granger (l%9) exogeneity test, the hypothesis that the U,S. or anysingle market is exogenous to olher markets is strongly rejected al the 5-percent significance level.The hypothesis thai ihe U.S, and Canada, as a bk)ck. arc exogenous also is rejected at the 5-pcrcentsigniticance level.

Eun and Shim 249

TABLE 3

Accounting National Stock Market Innovations^

MarketExplained

Australia

Canada

France

Germany

Hong Kong

Japan

Switzerland

U.K.

U.S,A.

Honzon(in days)

51020

51020

51020

51020

51020

51020

51020

51020

51020

AU

73,89720770,050 241 031,94

0.150,470,97

0.480.740.83

0 160.340.84

0.700.881.360,270,450,97

0,390,510,88

0,590.711.30

CA

2,803 243,49

51 7449,9247,98

0,440,530.79

0,410,590,88

0,401.201,43

0.430,570,93

0,580.631.65

1,011.251.66

1.191.702,24

FR

1.161 241 70

0.060.290 71

82.3880.0277.810.110.570,810310.380.67

0,240,711,26

0,471,401.83

0,160,751.45

0,180.261.00

By Innovations

GE

0.310 450.82

0.240,280,74

0,330,440,77

75.6473,4171,980.570.881 07

0.310.701.03

0,620,781,28

0.110.260,66

0,150.380 76

HK

1.171.642 06

0,391.131.60

0,971,641,97

0,780,891,17

90,3687.3884 49

0.821.221.67

0.470,691,020.440.981,200,841.061 32

JA

1.131.431.46

0300.490 851,111,241,36

0,851,391,65

0,550,961,46

81.1578,887622

0.270.741 24

0 220,811,38

0,370,681,28

in

SW

0,600.681,480,571,402,09

1.071,722,04

5,896,796.80

0.310,931.31

3,143.553 62

76.2373.8971,13

0,570.941.08

0.341.492.09

UK

3.503.944,03

0.851,432 05

0,661,111.57

1,591,812.01

1.051,702,30

2 542 572,871 141.351.38

82 7080.4577,94

0 070 561.02

US

15.4415.3114.89

45 5944 0442 03

12 8912 8312 72

14.2513.8013 88

6,286,23643

10.6810,9211.04

199320,0719,49

14 4014.0613,76

962793 1688 98

FMo

26,1127 9329 95

48 2650.0852 08

17.6219 982219

24 3626 5928.029.64

12.6215.51

18 8521,1223,7823,7726.1128,87

17 3019,5522,06

3 736 84

11.02

a Each entry in the table denotes the percentage of forecast error variance ol the left-handside market explained by the market at the top.

*> Each entry in the last column, FM, of the table denotes the percentage of forecast errorvariance of the left-hand side market explained collectively by the "foreign" markets.

typical shock, i.e., positive residuals of one standard deviation unit, in the U,S,These normalized impulse responses are the estimates of moving average coeffi-cients in Equation (3) divided by their standard errors,'" To facilitate the inter-pretation of Table 4, we plot the time paths of the normalized impulse responsesof the nine markets to a U.S, shock in Figure 1,"

As can be seen from examination of Figure 1. innovations in the U.S, stockmarket arc rapidly transmitted to all the other markets. All the European andAsian-Pacific markets respond to the U.S. shock most dramatically on day I and,thereafter, the responses rapidly taper off. Take the French response, for in-stance. Table 4 shows that the French impulse response to a U.S. shock is 0.40

'" The normalization procedure is necessary due to different variations of retums across stockmarkets. This procedure also makes it easy to interpret the empirical results, as the normalized re-sponses can be taken as the correlation coefficients,

' ' Impulse responses of the VAR system to shocks in other markets are available from the au-thors upon request.


on day 1, followed by -0 ,05 on day 2, and -0.01 on day 3. Since these foreignmarkets are either closed or about to be closed when the U.S, market opens, theyare expected to react to the U,S, shock with a one-day lag. This is exactly whatwe observe in Figure I, It also can be seen from Figure I that much of the adjust-ment of foreign stock prices to the U.S. shock is completed by day 2.

As can be seen from Table 4. the impulse response of the Canadian marketto a U.S, shock is 0.67 on day 0. followed by 0.21 on day 1. and 0.04 on day 2.This implies that, unlike other markets, the Canadian market responds moststrongly to the U.S. shock on day 0 when the U.S, shock occurs, and most of theadjustments are completed by day I. This result may reflect a high degree ofeconomic and financial integration and the free flow of information between thetwo countries, as well as the concurrent operation of their stock markets. Tosome extent, the U.K. market also reacts to the U.S. shock without lag. Becausethe two markets operate concurrently for half an hour a day. this result is asexpected. Unlike other markets, the U.K. seems to overreact somewhat to theU.S. shock on days 0 and !. which is subsequently corrected by a negative reac-tion on day 2.

Further examination of Figure I reveals some interesting regional patterns.As can be seen from the second column of Figure I. the three continental Euro-pean markets, i.e.. France. Germany, and Switzerland, respond to a U.S. shockin an almost identical fashion. They accommodate most of the U.S. shock on day1, The absence of noticeable responses beyond day I indicates that these Euro-pean markets are highly efficient in processing intemational news. In contrast,the third column of Figure I indicates that the Asian-Pacific markets, especiallyAustralia and Japan, are somewhat sluggish in their response to a U.S, shock;these markets continue to react noticeably through day 2.

Considering that both the Australian and Japanese markets are influenced bythe U.K. as well as U.S. markets, these seemingly sluggish responses are likelyto refiect the reactions of these markets to the (unpredicted) U,K, reaction to theU.S. shock, rather than market inefficiency. Because Australia and Japan aresituated between the U.S. and U.K. in terms of time zone, investors in these twocountries cannot observe the British reaction to the U S . shock on day 1 whiletheir national stock markets are still in session. In other words, the Australianand Japanese markets respond to a U.S, shock on day 1. without knowing ex-actly how the U.K, market may respond to the U,S. shock. In consequence, ifthe subsequently observed British reaction to the U.S. shock contains surprise,the Australian and Japanese markets would respond on day 2 to this indirect U.S.shock transmitted via the U.K. market. Granting that these "reactions to reac-tions" tnay last for a few days following the original shock, the market efficiencywould require that much of the responses to a shock should be completed in a fewdays.'2

'- This view seems io be supported when we examine the patterns of Australian and Japanesereactions to a U,K, shock that, unlike a US, shock, elicits little or no reaction to the indirect shockfed via d second market. Both the Australian and Japanese markets essentially complete their reac-tions to a U,K, shcxrk by day I, with no further noticeable responses. Given the time zone differencebetween these two countries and the U,K.. the observed response patterns are fully consistent withthe market efficiency.

Eun and Shim 251

In view of our finding that many of the responses are completed in abouttwo days after a shock, the pattern of impulse responses emerging from the VARanalysis seems to be broadly consistent with the notion of informational ly effi-cient intemational stock markets. This implies that it would be difficult to earnunusual profits by investing in a particular market based on the observed de-velopments in other markets. Finally, the leading role of the U.S. in the worldstock market is corroborated when the response pattem to a U.S. shock is cotn-pared with that to a U.K, shock. Unlike the case of a U.S. shock, the reaction ofother markets to a U.K, shock is found to be relatively weak. As previouslymentioned, however, a U,K. shock seems to have material influences on theAustralian and Japanese hiarkets.

fth Dayafter Shock

0123456789

1011121314151617181920

TABLE 4

Itnpulse Responses to the Unit Shock in the U.S.

AU

0.040 410 180.050 080 06

-0.020,000.030.01

- 0 0 10,02

- 0 0 10.020.03

- 0 010.010.01

-0.010,01001

CA

0.670.210.040.040.020.070,000.010.08

-0.04- 0 0 1-0.05

0.00-0.01

0 060.040.01

-0.010.01

-0.010 02

FR

0.020,40

-0.05-0,01

0 040.000.050.030.010.040.030.01

- 0 050.010.010.010.040.010.000,010.01

Impulse Responses in

GE

0.050.41

- 0 040 040 040.020.020 02

-0,010,000,020.040,00

-0,030.030.05

-0,01-0,02

0 000.00

-0,02

HK

0.090.220.080 030 060.01

-0,01-0.01

0.00-0.04-0.01-0.03

0.00-0.03

0.030 050,02

-0.01-0,01

0,010 00

JA

0.020.310.17

-0.020.020.010.070.01

-0,02-0.04-0,02

0 00- 0 06

0 050.00

-0.010 020 000.000.000 00

Market̂

SW

0,080 510.010.030 010.050 070 040,020 05

-0,02- 0 01

0,030.020 020 030 040,000 000010 00

UK

0 180.36

-0.100 070.03

- 0 0 10 020.010.03

-0.02-0.01

0.01-0.03-0.01

0 02-0.01

0.01-0.02

0.000.000.01

US

1 000,080.04

-0.01- 0 02-0.02

0.00-0.04

0,03-0,02

0.01- 0 04

0.000,000 000.020,000,000.00

-0,010,01

3 The /,/th entry in this table represents the normalized impulse response of the /th (column)market on the (th day (row) to the unit shock in the U,S. market. These entries are theestimates of moving average coefficients of the VAR system divided by their standarderrors.

V, Summary and Concluding Remarks

In this paper, nine time series of daily stock market retums were interpretedvia the vector autoregression (VAR) analysis in order to obtain insights into theinterdependence structure of major national stock markets. Emphasis was on un-derstanding the mechanism by which innovations in one stock market aretransmitted to other markets over time. Since no prior restriction is imposed, theVAR analysis enables us to locate all the main channels of transmission via simu-lated responses.

Since national stock markets operate in diverse time zones with the result


T T T T

T T T T

Eun and Shim 253

CO

a.J"6

T T T T


that return observations are nonsynchronous, we carefully examined the structureof time differences and explicitly took into consideration its implications in inter-preting empirical results of VAR analysis. Our evidence indicates that a substan-tial amount of interdependence exists among national stock markets. At the 20-day horizon, for example, innovations in foreign markets collectively account forabout 26 percent of the error variance of a national stock market on the average.Moreover, the U,S, stock market is found to be. by far, the most infiuential mar-ket in the world. No national stock market is nearly as influential as the U.S, interms ot its capability of accounting for the error variances of other markets. Thismay reflect the dominant position of the U,S, in the world economy, which prob-ably makes the country the most important producer of information affecting theworld stock market.

We analyzed the dynamic responses of each of the nine markets to innova-tions in a particular market, using the simulated responses of the estimated VARsystem. Against U.S. innovations, all the European and Asian-Pacific marketsresponded most strongly with a one-day lag and, thereafter, the responses ta-pered off rapidly. We find that most of the responses to a shock are completedwithin two days. The pattem of impulse responses emerging from the VAR anal-ysis, therefore, generally supports the notion of infonmationally efficient intema-tional stock markets.

Appendix: VAR Methodology

Using a simple example, this appendix describes the "triangular" ortho-gonalization procedure employed in our VAR analysis and the nature of theshock introduced to a variable to elicit impulse responses from other variables.We begin with the moving average representation of the VAR system.

Y(t) = > B{s)e{t-s) =

where, as previously defined. V is a lower triangular matrix. If we apply theorthogonalization procedure, e = Vu, to a simple case of three variables, weobtain

(A.2)

V,, 0

21

3i

22

.12

Let us now introduce a unit shock to the first variable, i.e,, [H| MT11 0 0]' . Then, (A.2) becomes

(A,3)

Eun and Shim 255

This result shows that each of the three variables is subject to a shock. To obtaina better understanding of the nature of these shocks, we apply the relationshipW ^ S(= £ce') to our three-variable case.

(A.4) 21

V.11

22

'32 .13

21

22

K

0

31

'32

33

CTj " 1 2

2

^ 2 1 ^ 2

CT,, O " ,31 " 3 2 " 3 .

= CT2P12, and V3,From (A.4). it can be shown that V,, = a, ,Consequently, (A.3) can be rewritten as

{A,5)

which shows the exact nature of the shocks. As shown in (A.5). when the firstvariable is subject to a "typical" shock, which is equal in magnitude to onestandard error of the first variable, each of the remaining variables is also subjectto a shock that is equal to its own (unit) standard error multiplied by its correla-tion with the first variable. By considering "'contemporaneous" shocks to othervariables, the VAR method can reproduce the "historical" pattem of interac-tions among variables.

For aunit shock tothe second variable, i.e.. l(j| »2 "3]' - (0 I 0J',(A,2)becomes

(A,6)

"0

^22

01/2

1/2

Analysis of a shock to the third variable is left to readers.


ReferencesAgmon, T, "The Relations among Equity Markets: A Study of Share Price Co-Movemenis in the

United States, United Kingdom. Germany and Japan." Journal of Finance. 27 (Sept. 1972),839-855.

"Country Risk: The Significance of Country Factor for Share Price Move-ments in the United Kingdom, Germany, and Japan," Journal of Business, 46 (Jan, 1973). 24-32.

Doan, T, , and R, Litterman, RATS Version 4.1. Minneapolis: Var Econometrics (1981).Granger, C. "Investigating Causal Relations by Econometric Models and Cross Spectral Methods."

Econometrica. 37 (July 1969), 429-438.Granger, C , and O, Morgenstem, Predictability of Stock Market Prices. MA: Lexington (1970),Grubel, H, "Internationally Diversified Portfolios: Welfare Gains and Capital Flows," American

Economic Review, 58 (Dec. 1968), I299- I3 I4 ,Grubel. H,, and K, Fadner, "The Interdependence of International Equity Markets." Journal of

Finance. 26 (March 1971), 89-94,Hilliard, J, "The Relationship between Equity Indices on World Exchanges." Journal of Finance,

34 [March 1979), 103-114,Lessard, D, "Wor ld , Country and Industry Relationships in Equity Retums: Implications for Risk

Reduction through International Diversification," Financial Analy.sts Journal. 32 (Jan./Feb.1976), 2-8.

"Wor ld . National and Industry Factors in Equity Retums." Journal of Fi-nance, 24 (May 1974), .379-391.

Levy, H., and M. Samat. "Intemational Diversification of Investment Portfolios," American Eco-nomic Review. 60 (Sept, 1970). 668-675,

Lupoletti, W,. and R. Webb, "Defining and Improving the Accuracy of Macroeconomic Forecasts:Contributions from a VAR M(xlel , " Journal of Bu.siness. 59 (April 1986). 263-285,

Panton, D,: V, t-essig; and O. Joy, "Comovements of Intemational Equity Markets: A TaxonomicApproach." Journal of Financial and Quantitative Analysis, t l (Sept, 1976), 415-432.

Ripley, D, "Systematic Elemenls in the Linkage of National Stock Market Indices." Reviewof Eco-nomics and Statistics. 55 (Aug. 1973), 356-361,

Sims, C. "Macroeconomics and Reality," Econometrica. 48 (Jan, 1980), 1-48,

eun shin(international trasmissions and movemants

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