526 SAJEMS NS Vol 5 (2002) No 3 On the Long-Run Interdependence of Stock Markets: A Tale of Correlations, Auto- regressions and Decompositions Elna Moolman Department of Economics. University of Pretoria Suzanne McCoskey University of Pretoria and the United States Naval Academy ABSTRACT It seems as if national stock markets within certain groups of countries, for example within Europe and Asia, are interdependent. But to what extent are stock markets between these groups interdependent? Is it still possible to diversity among these groups, or have globalization tied world markets together to such an extent that diversification is no longer feasible? In this study we use time series techniques to analyze the interdependence among four of the most important groups of economies, namely Europe, Latin America, Asia and the US. This will show whether it is still possible to diversify between the stock markets of these groups of economies, since stock markets within these groups seem to be interdependent to such an extent that diversification within these groups is no longer possible. On a methodological level, we compare the results of the OLS-V AR with an FM-V AR model, which is a more robust estimation procedure in the presence of non-stationary or co integrated series. JEL GIO 1 INTRODUCTION Portfolio theory suggests that investing in less than perfectly correlated asset markets will result in greater diversification effects. This resulted in a search for diversification gains, which has been aggressively extended in investing internationally in the hope of additional diversification. In the mean time, financial globalization caused revolutionary and irreversible changes in financial markets. International capital transactions have accelerated, and innovations and deregulation have changed financial market structures. More instruments and markets have developed, and technological development has made a portfolio comprising international assets universal (Handley & Mills, 1996: 74). The ongoing relaxation of foreign investment restrictions and foreign exchange R ep ro du ce d by S ab in et G at ew ay u nd er li ce nc e gr an te d by th e P ub lis he r (d at ed 2 00 9) . SAJEMS NS Vol 5 (2002) No 3 527 controls in many countries has led to the speculation that world equity markets have become more integrated than ever, and that the diversification gain from investing internationally might have been reduced significantly. This calls for an examination of the intermarket relationships and dynamic linkages between international stock markets as the interdependence structure has important implications for market efficiency, profitable investment opportunities, risk diversification and international policy co-ordination. If markets are inefficient, the transmission of shocks from one market to another will involve systematic lagged responses that may be exploited by informed investors. On the other hand, lack of interdependence among markets will engender opportunities for risk diversification. Many studies have been conducted on the interdependence of different national stock markets, using different econometric techniques. For example, Masih and Masih (1997, 1999), Chowdhury (1994) and Palac-McMiken (1997) analyzed the interdependence among Asian markets while Dheeriya (1993) and Choudhry (1996) analyzed interdependence in Europe, and Christoffi and PericH (1999) and Choudhry (1997) analyzed interdependence among Latin American markets. Stock market interdependence in the emerging markets in Asia seems to be a widely accepted fact. Masih and Masih (1999) examined relationships among the stock markets of Thailand, Malaysia, the US, the UK, Japan, Hong Kong and Singapore from 1992 to 1997. The most important finding of their study is that Asian stock market fluctuations are mostly explained by the regional markets, rather than by the developed markets. They found that these markets are cointegrated, and their vector error correction modeling (VECM), variance decomposition and impulse response functions confirmed a high level of interdependence between these markets. Masih and Masih (1997) used the same econometric techniques, but a different group of Asian markets and data for the period 1982 to 1994. Consistent with their later findings (Masih & Masih, 1999), they found co integration among the markets of Taiwan, South Korea, Singapore, Hong Kong, the US, the UK, Germany and Japan. Again, their VECM, variance decomposition and impulse response functions confirmed a high level of stock market interdependence. Other authors examined different groups of Asian markets, but their results are consistent with those of Masih and Masih (1997, 1999) since they all found their respective stock market groups to be interdependent. Palac-McMiken (1997) found cointegration in the monthly ASEAN markets (Indonesia, Malaysia, the Philippines, Singapore and Thailand) during the period 1987 to 1995. Chowdhury (1994) used variance decomposition and impulse response functions R ep ro du ce d by S ab in et G at ew ay u nd er li ce nc e gr an te d by th e P ub lis he r (d at ed 2 00 9) . 528 SAJEMS NS Vol 5 (2002) No 3 to examine the relationships among Hong Kong, Korea, Singapore, Taiwan (that is, the Asian Newly Industrialized Economies (NIEs», Japan and the US, using daily data for the period January 1986 to December 1990. He found that the US led the NIEs and that there were significant linkages between the markets. In general, these studies used different techniques and different sample periods, but they all found that the emerging Asian markets are interdependent. Although there is substantially less literature on stock market interdependence in the emerging Latin American markets, all the available results indicate that the stock markets in this region are also interdependent. Christofi and Pericli (1999) used a vector autoregressive (V AR) model in their study on the stock markets of Argentina, Brazil, Chile, Columbia and Mexico from 1992 to 1997. They found significant spillover effects among these Latin American markets. Choudhry (1997) investigated interdependence among the stock markets of Argentina, Brazil, Chile, Colombia, Mexico and Venezuela, and by using cointegration techniques, found a common stochastic trend in these markets. Therefore, consistent with the results of the emerging Asian markets, the emerging Latin American markets are found to be interdependent. In a study on European stock prices, Choudhry (1996) used co integration techniques to analyze the long-run relationships, which should indicate the presence of common stochastic trends among indices. He used monthly data for the 1920s and 1930s of Czechoslovakia, France, Italy, Poland, Spain and Sweden. His results indicate a stationary long-run relationship during 1925-1936 and also during the pre-1929 crash period (1925-1929), but not during the post- crash period (1929-1936). Dheeriya (1993) used Geweke's causality test to study the direction of causality and feedback between the stock markets of Australia, Austria, Belgium, Canada, Denmark, France, Gennany, Ireland, Italy, Japan, Netherlands, Norway, Spain, Sweden, Switzerland, the UK and the US, by using daily data for 1987 and 1988. The impact of the stock market crash of October 1987 on other national stock markets is investigated by dis aggregating the data into pre- and post-crash periods. His results showed that almost all markets react to other markets' past and present movements. However, very few stock markets (only the US and UK) influenced other markets significantly, and the traditionally major markets of Japan, France and Canada, did not seem to be influential at all. From the literature it seems as if stock markets of countries within certain groups, for example within Europe, Latin America and Asia are interdependent. For example, Masih and Masih (1997, 1999) and Palac-McMiken (1997) detected interdependence among certain Asian stock markets, Chowdhury (1994) found interdependence among certain European stock markets and R ep ro du ce d by S ab in et G at ew ay u nd er li ce nc e gr an te d by th e P ub lis he r (d at ed 2 00 9) . SAJEMS NS Vol 5 (2002) No 3 529 Christoffi and PericH (1999) indicated interdependence among Latin American stock markets. But to what extent are stock markets within these groups interdependent? The results suggest that the gains from diversification within these groups of countries have decreased significantly. Is it then still possible to diversify among these groups, or are they so interrelated that diversification is no longer feasible? In this study we analyze the interdependence among some of the well-known groups of economies, namely Europe, Latin America, the US and Asian economies. This will show whether it is still possible to diversify between the stock markets of these groups of economies, since stock markets within these groups seem to be interdependent to such an extent that diversification within these groups is no longer possible. We use time series techniques to address several important issues regarding the long-term relationships among major stock market groups. In particular, we use Granger causality tests, vector autoregressive (V AR) analysis, impulse response functions and variance decompositions. The first issue is quite simply whether a direction of causality can be determined amongst the different groups of stock exchanges. This issue is addressed through tests for Granger causality, which test the null hypothesis that one stock market does not Granger cause another stock market. This test is conducted for every possible combination of stock markets, in every possible direction of causality to determine between which stock markets there is causality and in which direction. Secondly, it can be asked whether the stock markets inform forecasts of other stock markets. For this variance decompositions can be used, which describe the proportion of the forecast error variance that can be explained by each stock market including the stock market itself. If almost all the forecast error variance is explained by innovations in the series itself, the series is largely exogenous. This would indicate that the particular stock market is not interdependent on the other markets, but is determined exogenously. On the other hand, if a substantial part of the forecast error variance of a series is explained by innovations in other series, it suggests that the variable is not exogenous but interrelated with the other markets. Thirdly, we use vector autoregression (VAR) analysis to analyze the dynamic interactions among the markets. We will initially estimate the VAR model with ordinary least squared (OLS), and then check these results against that of an FM-V AR estimation, which is a more robust estimation procedure in the presence of non-stationary and cointegrated series. If dynamic interactions are found, impulse response functions can be used to track the length of the dynamic shocks to the system. R ep ro du ce d by S ab in et G at ew ay u nd er li ce nc e gr an te d by th e P ub lis he r (d at ed 2 00 9) . 530 SAJEMS NS Vol 5 (2002) No 3 The article is outlined as follows: Section 2 summarizes the data and section 3 explains the theory of stock market interdependence. Section 4 summarizes the time series techniques used in the study. The empirical results are given in section 5, and section 6 provides some concluding thoughts. 2 THE DATA It is a well-known fact in econometrics that the span of the data, and not the frequency, should be taken into account when looking at long-term trends (Hatanaka, 1996: 25). By using annual data for a relatively long period - 34 years instead of 1 or 2 years like most of the studies we are able to look at long-run trends instead of short-run fluctuations, which may not be persistent or may reflect special circumstances. The long span of the data also makes it possible to compare performance over a number of market cycles. We use the stock market indices of 4 of the major groups of countries, namely Europe, the US, Latin America and the Asian economies. The Standard and Poor 500 index is used to represent the US stock market index. The indices of the United Kingdom, Germany, France, Italy, Switzerland, Netherlands, Belgium, Spain, Denmark, Norway and Sweden are included in the European index. The Latin American index includes Argentina, Brazil, Chile, Columbia, Mexico, Peru and Venezuela and the Asian index includes Hong Kong, India, Israel, Malaysia, Pakistan, Philippines, Singapore, South Korea and Taiwan. These aggregated indices were obtained from Global Financial Data (http://www.globalfindata.com). In order to make the indices directly comparable, all the indices are measured in US dollars. The indices are capitalization-weighted annual stock price indices for 1919 1999 (except for Latin America and Asia where data was only available since 1936 and 1967 respectively), with 1969 as the base year. By looking at the graphs of the composite indices in Figure I, several broad patterns emerge. In general, there has been a significant increase in all the indices since the globalization of the nineties. However, the US and European indices show a steady increase while the Asian and Latin American indices were extremely volatile during their increases. When the US is compared with Europe, the difference is relatively small, except for a slightly larger gap during the period 1982 to 1992. Similarly, there has been a remarkable co-movement between the Latin American indices. R ep ro du ce d by S ab in et G at ew ay u nd er li ce nc e gr an te d by th e P ub lis he r (d at ed 2 00 9) . SAJEMS NS Vol 5 (2002) No 3 531 Figure 1 Stock market indices of Asia, Europe, Latin America and the US .... ,_ 3000 J 1200 2000 800 10"" 400 Q 0 '" :IQ 30 -ASlA. -EUROPE 4000 ,_ 3000 1200 :IQQQ BOO 100Q ..,. 0 :IQ 30 - LA nH AMEfUCA -us The simple correlations between these groups (see Table 1) suggest very high correlations between these groups. It also shows very high correlation between the relatively undeveloped stock markets of Asia and Latin America, and between the developed stock markets of the US and Europe. Table 1 Correlations between stock market groups, 1967-1999 Asia Europe Latin America US Asia 0.859554 0.912211 0.801067 Europe 0.859554 1.000000 0.885803 0.990116 Latin 0.912211 0.885803 1.000000 0.865556 America US 0.801067 0.990116 0.865556 1.000000 3 THEORETICAL EXPLANATION OF STOCK MARKET INTERDEPENDENCE In general, there are three categories of explanations as to why there is co- movement among different stock markets. The first category is the so-called R ep ro du ce d by S ab in et G at ew ay u nd er li ce nc e gr an te d by th e P ub lis he r (d at ed 2 00 9) . 532 SAJEMS NS Vol5 (2002) No 3 contagion effect, which is the part of stock market co-movement that cannot be explained by economic fundamentals. The second category is economic integration, which means that the more the economies of two countries are integrated, the more interdependent or integrated their stock markets will be. Economic integration includes not only trade relationships, but also co- movement in the economic indicators that influence stock market returns, such as interest rates and inflation. The third and last category includes stock market characteristics that influence the extent of stock market interdependence, namely industrial similarity, volatility and market size. In general, therefore, the extent of interdependence between two stock markets (or groups of stock markets) should be a function of the following variables: 3.1 Contagion Contagion, as defined by the academic profession, is the co-movement of asset markets not caused by a common movement of fundamentals (Wolf, 1998: 220). Contagion is not measurable in itself, but rather estimated with the residual from the co-movement that is not explained by fundamentals. There are two broad categories of literature on this field, either based on informational factors or based on institutional factors (op. cit.: 220). The category of informational factors is based on the well-known comparison between the stock market and the Keynesian "beauty contest", where each judge votes the way he thinks the other judges will vote. In the same way, investors will sell their investments in a specific asset class if they believe that other investors will sell their investments in that asset class. This provides some explanation of the herd behavior of stock market traders which leads to a sell-off of emerging market securities if a sufficient number of investors believe that other investors have become disenchanted with the emerging markets asset class. The herd behavior of investors will lead to a widespread decline or upswing in emerging markets, and if this widespread movement is not caused by fundamentals, it is, by definition, contagion. The category of institutional factors focuses on issues such as forced redemption and two-stage investment strategies (op. cit.: 221). A substantial proportion of the inflows to the equity markets of emerging countries come through open- ended mutual funds. When these funds are faced with large-scale withdrawals or a reduction in inflows, they may be forced into redemption. Global mutual funds will then sell off their assets in the most liquid markets. In other words, if these markets were not affected previously. they will be affected by the forced redemption. This redemption thus creates a contagion effect in which several markets decline simultaneously without justifying changes in fundamentals. The same occurs when global mutual funds try to exploit perceived mispricing via R ep ro du ce d by S ab in et G at ew ay u nd er li ce nc e gr an te d by th e P ub lis he r (d at ed 2 00 9) . SAJEMS NS Vol 5 (2002) No 3 533 purchases in the most downtrodden markets, financed through sales of equities in less-affected markets (op. cit.: 221). With two-stage strategies, some fraction of the overall portfolio is allocated to the emerging-market category, and is then sub-allocated according to some index weighting. This provides the second of the institutional explanations for contagion to the extent that first-stage decisions, even if motivated by factors relevant to some emerging markets, may also affect markets for which these factors are of little importance (Chuhan, 1994). 3.2 Economic Integration From a macroeconomic perspective, there are two broad categories of economic variables that influence the degree of stock market interdependence, namely the extent of bilateral trade and factors that influence stock prices according to the cash flow model. 3.2.1 Bilateral trade When two countries have a strong bilateral trade relationship, their economies and stock markets are expected to be highly interdependent. If a substantial portion of country A's total exports are exported to country B, then a downswing in country B will cause a decline in its imports from country A. There will be a decline in country B's stock market associated with the domestic downswing in country B, and at the same time a decline in country A's stock market due to the reduction in exports to country B. The stock markets of the two countries will thus exhibit a co-movement due to their bilateral trade ties. The more important the trade ties, the higher the degree of co-movement in the stock markets. Therefore, the bilateral trade relationship between two countries is expected to explain some of the correlation or co-movement between their stock markets. 3.2.2 The cash flow model Stock prices (P) can be written as the expected discounted stream of dividends: p = E(c) k (1) where c is the dividend stream and k is the discount rate. It follows trivially that the systematic forces that influence stock prices, and hence returns, are those that influence the discount factors, k, or the expected cash flows, E(c) (Chen et al. 1986). Any factor that influences the stream of cash flows or the discount R ep ro du ce d by S ab in et G at ew ay u nd er li ce nc e gr an te d by th e P ub lis he r (d at ed 2 00 9) . 534 SAJEMS NS Vo15 (2002) No 3 rate will systematically influence stock prices. Since the seminal article by Chen et al. (1986), the influence of interest rates and inflation on the discount rate, and of industrial production growth on the expected cash flows - and hence on stock prices has been well established. These macroeconomic variables influence the stock market performance of an individual country, which means that in two countries in which these variables are similar, the stock market performance will be similar. For example, if the interest rates of two countries show the same trend over time, perhaps due to similar monetary policies, the effect of interest rates on stock prices will cause a co-movement in the two stock markets. Therefore, larger interest rate, growth and inflation differentials will cause a smaller amount of co-movement. 3.3 Stock Market Characteristics Apart from the economic variables discussed in the previous section, several other variables have been discussed in the literature as having the potential to influence the extent of stock market correlation. These factors are stock market size, stock market volatility and industrial similarity. 3.3.1 Size The effect of the size of a firm on its stock market performance is a welI- documented phenomenon (see for example Banz, 1981; Berk, 1996; Keppler & Traub, 1993; Asness et al., 1996). Smaller firms command higher returns due to less liquidity and the higher transaction costs associated with trading their equity. By extension, the size of a national equity market may reflect its stage of development, and may also indicate the degree of market liquidity and the level of information cost and transaction cost associated with trading equity in that market. From this perspective, a large disparity in market sizes may indicate large differences in the liquidity, information costs and transaction costs between the two markets, which should result in less co-movement. 3.3.2 Volatility The basic principle on which all investment models are based is that the returns on any asset should be a positive function of its risk. According to the capital asset pricing model (CAPM) of Sharpe (1964) and Lintner (1965), stock market returns should be a positive function of the risk of the stock market, where risk is measured as the volatility or variance of the returns. Since the returns of any stock market are a function of its volatility, two markets with more or less the same volatility should be more interdependent than two markets with substantially different volatilities. R ep ro du ce d by S ab in et G at ew ay u nd er li ce nc e gr an te d by th e P ub lis he r (d at ed 2 00 9) . SAJEMS NS Vol 5 (2002) No 3 535 3.3.3 Industrial similarity The effect of industrial similarity on stock market correlation has received a substantial amount of attention in the literature (e.g. Serra, 2000; Wolf, 1998; Roll, 1992). The performance of any index is partly determined by sectoral composition, and partly obscured by idiosyncratic noise (Wolf, 1998: 224). For example, consider two emerging market indices dominated by equities in a single sector, say petroleum. A decrease in the world demalld for oil may lead to a substantial decrease in the equity prices of oil companies in both economies. Thus, when two markets are both dominated by the same type of industry, their stock markets will reveal co-movement to the extent that the general performance of their stock markets is based on that industry. This does not only happen in the extreme case when two markets are dominated by the same sector, but also the extent of industrial similarity between the two stock markets generally increases the extent of their co-movement. A priori theory therefore suggests the following about the relevant variables and their coefficients: + Interdependence= f{Trade, inflation differential, interest rate differential, size + differential, volatility differential, growth differential, industrial similarity}; (i) Trade: The more important the trade relationship between two countries, the more correlated their stock markets should be. (li) Inflation differentials: Since inflation influences stock prices, the inflation differential of two countries is expected to influence the extent of interdependence between their stock markets negatively. The bigger the inflation differential, the bigger the difference in stock prices will be, and hence the lower the level of interdependence between the markets. (iii) Industrial production growth: Industrial production growth influences stock market behavior through the cash flow model, and therefore the difference between two countries' industrial production growth rates will be negatively correlated with the extent of their stock market correlation. (iv) Interest rates: Interest rates influence the discount factor of the cash flow model and hence stock prices. Therefore, the interest rate differential between two countries should be negatively correlated with their stock market correlation. (v) Size: Since the size of a stock market reflects its liquidity and transaction costs and therefore influences stock prices, the size difference between any countries' stock markets will have a negative relationship with the correlation of their stock markets. R ep ro du ce d by S ab in et G at ew ay u nd er li ce nc e gr an te d by th e P ub lis he r (d at ed 2 00 9) . 536 SAJEMS NS Vol 5 (2002) No 3 (vi) Volatility: The risk of a stock market is measured by its volatility, and stock prices are positively influenced by volatility since investors demand higher returns for tolerating higher risk. This means that in two stock markets whose volatilities converge (diverge), the prices should also converge (diverge). Therefore, the correlation between two stock markets should be a negative function of the ratio of their volatilities. (vii) Region: Stock markets within a region can be interdependent due to policy coordination, or simply due to contagion caused by investors' treatment of the asset markets within a region as one asset class. Therefore, the correlation between two countries that are in the same region is expected to be higher than that of two countries in different regions. 4 TESTING METHODOLOGY 4.1 Granger Causality Yl causes another time series XI in the Granger sense if series Xl can be predicted better by using past values of series YI than by using only the historical values of series XI' To test whether YI Granger eauses Xt, Granger (\969) proposed the following regression equation: ax. = Co + IdjtJ.YH + IcjtJ.Xt _i + v, 1=1 j~1 (2) where m is the appropriate autoregressive lag length as determined by the Akaike and Schwartz criteria, and VI is white noise. The test for Granger causality is testing the null that YI does not Granger cause XI> by comparing the following f-statistic to the relevant critical values of the F(m, T-2m-l) distribution: F (SEER -SSEu)!m SSE,,!(T-2m-l) (3) \\ here SSE R is the sum of squared residuals from a restricted regression equation, in other words no lagged YI in equation X, SSEu is the sum of squared residuals from equation X, and T is the number of observations. R ep ro du ce d by S ab in et G at ew ay u nd er li ce nc e gr an te d by th e P ub lis he r (d at ed 2 00 9) . SAJEMS NS Vol 5 (2002) No 3 537 4.2 Vector Autoregressive Analysis (V AR) The V AR modeling technique is an effective means of characterizing the dynamic interactions among economic variables by reducing dependence on the potentially inappropriate theoretical restrictions of structural models. The general V AR specification can be written as: (4) where XI is a (n xl) vector containing each of the n variables included in the VAR Ao is a (n x 1) vector of intercept terms Ai is a (n x n) matrix of coefficients et is a (n xl) vector of error terms The t-statistic computed for the coefficients of each of the lagged variables indicate whether that particular lagged variable is significant in explaining some of the variation in the relevant dependent variable. Since only lagged values of the endogenous variables appear on the right-hand side of each equation, there is no issue of simultaneity, and OLS is generally regarded as an appropriate estimation technique. However, although OLS is consistent, it may be biased. As described by Phillips (1995), fully modified (FM) estimation of the VAR model should improve the OLS results in the presence of non-stationary regressors, 1(1) processes and even cointegrating relationships. In addition, the FM-estimation procedure is valid without pre-testing for the exact cointegrating relationships or even the number of unit roots in the system. The FM-procedure specifically takes into account the possible serial correlation and endogeneities of the system. In this study, we will initially estimate the V AR model with OLS, and then use the FM-VAR procedure outlined by Phillips (1995) to verify its robustness. 4.3 Impulse Response Functions Impulse response functions characterize the dynamic structure of the estimated model by showing how each endogenous variable responds over time to a shock in that variable and in every other endogenous variable. It traces the effect of a one standard deviation shock to one of the innovations on current and future values of It he endogenous variables, in other words, it trades the response of the endogenous variables to such shocks (Pindyck & Rubinfield, 1991: 385). In other words, it can be used to analyze the persistence of shocks in the system, as R ep ro du ce d by S ab in et G at ew ay u nd er li ce nc e gr an te d by th e P ub lis he r (d at ed 2 00 9) . 538 SAJEMS NS Vol 5 (2002) No 3 well as the return of the variables to equilibrium levels after shocks in the system. In the same way that a autoregressive (AR) process can be written as a moving average (MA) process, a vector autoregressive (V AR) model can be written as a vector moving average (VMA). For example, equation X can be written as ., XL == J.l + L