Interdependence of Nordic and Baltic Stock Markets Ulf Nielsson * Department of Economics, International Affairs Building, 118th Street and Amsterdam Avenue, NY, 10027, USA Abstract: The interdependence of the Nordic and Baltic stock markets is explored in light

of increased merger activity of stock exchanges over the sample period, 1996–2006. The results show surprisingly little interdependence between the Nordic and Baltic stock indices. In the short run, the response of each market to a shock in another is insignificant. In the longer term there is limited evidence of integration and only weak indication of convergence within the sample period. The stock markets seem no more integrated than they were at the outset of recent merger activity, suggesting that the levels of cooperation between the Nordic and Baltic exchanges have not been deep enough to produce increased interdependence. Keywords: Interdependence, integration, convergence, stock exchange merger, stock markets JEL codes: F36, G15

1. Introduction It has been established that the major stock markets of the world have been converging over the long run and becoming more interdependent.1 In recent years there has also been a tendency for stock market integration at a deeper level than price convergence. In Europe, these developments include the Euronext merger, the consolidation of the OMX group and ongoing discussions of consolidations of the New York Stock Exchange and Euronext, and potentially NASDAQ and London Stock Exchange.2 In light of this trend, it is natural to explore the relationship between increased merger activity and stock market integration (such as price convergence). Further, it is interesting to examine how the effect on international price interdependence differs depending on the form and level of stock exchange cooperation. This paper presents a case study which explores the relationships between the national stock markets of the Nordic and Baltic countries. The paper investigates whether these markets exhibit similar price characteristics and are converging over time, or if they are perhaps already fully integrated. The level of market integration has important implications for (i) the gains of international diversification and (ii) the effect of increased stock market * E-mail: [email protected]. Reykjavik University and PhD candidate at Columbia University. The author wishes

to thank Alexei Onatzki and two anonymous referees for very helpful comments and suggestions. Any remaining errors are my own. 1 See e.g. Taylor and Tonks (1989), Corhay et al. (1993), Fraser and Oyefeso (2005), Masih and Masih (2001),

Chelley-Steeley et al. (1998), Bessler et al. (2003), Kim et al. (2005), Phylaktis (1999). 2 Euronext is the merged stock exchange of former national exchanges in Belgium, France, Netherlands and Portugal.

OMX owns and operates 7 exchanges based in the Nordic and Baltic countries. NASDAQ is an American stock exchange with headquarters in New York.

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merger activity on market adjustments.3 For example, if prices of national stock markets co-move, there are limited gains to be made from international diversification which may have implications on the ability to attract global capital. In the extreme case of full stock market integration, risk adjusted stock returns will in fact be equal in all countries. Fraser and Oyefeso (2005) argue that this implies that the time may be right for increased merger activity between national stock exchanges, i.e. if stock markets are fully integrated then increased merger activity requires no stock market adjustments. If, however, markets do not trend together, it implies that stock markets must adjust while adapting to institutional changes that accompany increased merger activity. Hence, studying the level of market integration and interdependence is particularly interesting in light of recent merger activity and cooperation among stock exchanges. The econometric tools and techniques used to study the interdependence of stock markets have developed rapidly in the last two decades, partly explaining the extensive amount of research on the topic. Taylor and Tonks (1989) presented early evidence indicating that major stock markets of the world are converging, at least over the long-term. Since then the major stock exchanges of the United States and Europe have been analyzed in detail, and recently there has also been a lot of work done on the integration of stock exchanges in e.g. Africa and Asia.4 Although results differ in terms of direction of causation, short vs. long term effects, etc., there seems to be a broad agreement on some degree of convergence of most stock markets in the last decade. This paper adds to the current literature by presenting a case study of the Nordic and Baltic countries, i.e. the countries of Iceland, Norway, Denmark, Sweden, Finland, Latvia, Estonia and Lithuania. These countries have undergone increased institutional and operational cooperation in recent years, both in terms of the NOREX and OMX consolidations.5 Despite this active process of increased cooperation, the Nordic and Baltic countries have been subject to limited research. Earlier literature on the region includes the study of Malkamäki et al. (1992) who found no cointegration among stock indices in Scandinavia in 1988–90, but found that the Swedish stock market Granger caused other Scandinavian markets. Mathur and Subrahmanyam (1990, 1991) come to the same conclusion, but these studies present little evidence of Scandinavian markets significantly influencing outside markets. Malkamäki (1992) examines the interdependence of stock markets in Sweden, Finland and their biggest trading partners in the period 1974–89 and finds that the Scandinavian markets seem to be led by the German and the UK market. Interestingly, the influence of these stock markets on the two Scandinavian markets seems stronger than the influence of Sweden and Finland on each other. In short, these paper suggest that pre 1990 the interdependence of Scandinavian markets was limited. But due to recent developments in econometric techniques and in light of the recent increased merger activity, previous literature on the sample countries has become dated. 3 Taylor and Tonks (1989) also argue that the existence of cointegration in a speculative market implies a violation

of market efficiency. This follows from the existence of an error correction mechanism, i.e. from being able to use past prices to improve forecasts of current prices. More recent literature has however rejected this arguement of market inefficiency, since if fundamentals are cointegrated, then so are stock prices (Fraser and Oyefeso, 2005). 4 Hearn and Piesse (2002), Arshanapalli et al. (1995), Bessler et al. (2003), Bessler and Yang (2003), Yang et al.

(2003b), Phylaktis (1999). 5 All the Nordic and Baltic stock exchanges are members of the NOREX cooperation, which facilitates the usage

of a joint trading system and harmonization of regulations. The OMX consolidation goes beyond that, towards a formal merger of exchanges.

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Interdependence of Nordic and Baltic Stock Markets

This paper updates and extends existing research in response to these changes. Also, since the Nordic and Baltic stock markets are relatively small in size, accompanied with thin trading and potentially low efficiency, the behavior of these markets may be quite different from that of other, larger markets. The study adds the Baltic region to the analysis, since the Baltic countries have been involved in the merger activity initiated by the Nordic exchanges. Furthermore, examining the interdependence of Nordic and Baltic stock markets with respect to the depth of the stock exchange integration (e.g. NOREX versus OMX) provides not only answers to whether these stock markets are converging, but also helps addressing the question of why stock markets may be converging – e.g. if increased merger activity may be a driving factor. The paper extends on econometrics tools previously used to examine the sample countries. In particular, the study applies the generalized impulse response analysis of Koop et al. (1996) and Pesaran and Shin (1998) to estimate short-term causal linkages across stock markets. This methodology has the advantage over the more traditional orthogonalized approach (such as Cholesky factorization) that it is invariant to the ordering of variables when estimating a vector autoregressive model. Long run dynamics are explored using cointegration tests, principal component analysis and common factor models. The results show surprisingly little interdependence of the Nordic and Baltic markets. In the short run, the response of each market to a shock in another is insignificant. In the longer term there is some evidence of integration, although there is no indication of convergence within the sample period. The stock markets therefore seem no more integrated than they were at the outset of recent merger activity, suggesting that the levels of cooperation between the Nordic and Baltic exchanges have not been deep enough to produce increased interdependence. This lack of interdependence is surprising given the vast literature showing increased convergence and integration of other stock markets throughout the world. The paper proceeds in the next section by introducing the data and describing the cooperation networks of the Nordic and Baltic countries. Section 3 introduces the methodology used to analyse the long-run interdependence of stock markets, as well as the methodology applied in the short-run analysis. Section 4 outlines the results of the analysis and Section 5 concludes.

2. Data and Background Information The choice of sample countries is based on both geography and cooperation levels. There are primarily two stages of cooperation in the Nordic and Baltic countries. First, there is the NOREX alliance which was established in 1998 by the Swedish and Danish stock exchanges. Today all the Nordic and Baltic stock exchanges are members of the alliance. NOREX’s main area of cooperation is the usage of a joint trading system and the harmonization of regulations for trading and membership on the stock exchanges. The NOREX alliance is therefore concerned with facilitating interaction between exchanges, but without any implicit or formal merger activity. For example, the alliance encourages listed companies to list their securities on only one NOREX exchange, but still drives to provide easy access to all listed companies no matter where an investor may be located (The NOREX vision, 2006). The second form of cooperation among Nordic and Baltic stock exchanges is based on the Swedish–Finnish financial services company named OMX, which came into play in 2003 by a merger between the Swedish and Finnish stock exchanges. OMX now owns and operates six stock exchanges, i.e. the stock exchanges of Sweden, Finland, Denmark, Estonia, Latvia and

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Table 1. Date of membership in NOREX and OMX Iceland Norway Denmark Sweden Finland Estonia* Latvia* Lithuania**

NOREX

OMX

Jun. 2000 Oct. 2000 Jan. 1998 Jan. 1998 Dec. 2003 Dec. 2003 Dec. 2003 May 2005

Dec. 2004 Sep. 2003 Sep. 2003 Sep. 2003 Sep. 2003 May 2004

* In 2001 the Finnish stock exchange acquired ownership of the Estonian exchange and later, in August

2003, of the Latvian exchange. As a result these exchanges were automatically incorporated into NOREX and OMX along with the Finnish stock exchange. ** On May 30th 2005 the joint trading platform become operational in the Vilnius Stock Exchange. But it should be noted that membership in NOREX more or less follows from membership in OMX since most cooperation within NOREX is also effective in OMX.

Lithuania.6 Although the exchanges still retain their business names, they are not marketed as separate brands (Riga Stock Exchange History, 2006). OMX therefore steps further towards a full merger of stock exchanges than NOREX does and is in many ways an extension of the NOREX cooperation. The membership of each country in these two consolidations is summarized in Table 1. The table shows that the process of integration between the stock exchanges has been gradual within the sample period 1996–2006. The process of unification is likely to continue in the near future, since OMX is slowly extending the operational integration of its members and, for example, in September 2006 it was announced that the Iceland Stock Exchange intends to merge into OMX and, also, 3 weeks later OMX acquired a 10% stake in the Oslo Stock Exchange. Weekly data on the main stock exchange indices of the sample countries is obtained from Thomson Financial (Datastream) for a 10 year period, i.e. from May 1996 to May 2006.7 Each index in the sample thus consists of 520 observations, but due to limited data availability on Lithuania and Latvia, only Estonia is included in the sample of the 3 Baltic countries. Further description on the indices, summary statistics and correlation coefficients are reported in Appendix A and the index values over the sample period are depicted in Figure 1. Figure 1 hints towards partial co-movement of stock indices, at least in the long run. The correlation of index values (reported in Appendix A) varies considerably, the highest being between the stock indices of Sweden and Finland (0.953) and the lowest between Sweden and Estonia (0.232). Since Figure 1 gives limited insight into short run dynamics, it is informative to remove the permanent component from the stock indices and graph only the transitory component. Decomposing the stock market price series into their permanent and temporary component can provide insight into whether markets are driven by a common 6 On September 19, 2006 it was announced that the Icelandic Stock Exchange would merge into OMX. Since the

sample period ends in May 2006, the paper considers the Iceland Stock Exchange to be a NOREX member only. 7 The complete analysis in the paper was repeated using monthly data and no major changes in results arised. Also

note that using weekly data (instead of daily) may alleviate problems of serial correlation due to thin trading of stocks (Lo and Mackinley, 1998). This may very well be important given the relatively small and illiquid stock markets in the sample.

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Interdependence of Nordic and Baltic Stock Markets

Figure 1. Index values.

factor. It may also shed light on whether the extent and duration of temporary deviations from trend is relevant for diversification purposes. The transitory components of the stock indices are plotted in Figure 2 by applying a band-pass filter based on the Baxter and King (1995) methodology.8 8 Some data points are lost with this procedure, but it should be noted that applying the Hodrick–Prescott filter to

the series (which maintains the whole sample) yielded similar results. The frequency chosen for the band-pass filter is 1 (lower) and 6 (upper) weeks, with a MA component of 1 year. For intuition, the choice of frequency relates to the cycle length of weekly stock prices (rarely longer than 6 weeks) and the longer the MA component the smoother the output series.

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Figure 2. Transitory components of stock indices.

We observe in Figure 2 that there still seems to remain some level of interdependence of the stock indices, although perhaps less so than in Figure 1. Perhaps most noteworthy are transitory movements accompanying the boom in the late 90’s and the subsequent fall in 2000-01. The highest correlation between transitory components of the stock indices is between Sweden and Finland (0.906) and the lowest is between Estonia and Iceland (0.117). Taken together, Figures 1 and 2 suggest that there may be some degree of interdependence between the stock markets and the following sections are concerned with quantifying it.

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Interdependence of Nordic and Baltic Stock Markets

3. Methodology 3.1. Long Run Relationship The long run relationship between stock indices is explored by (a) testing for cointegration and (b) extracting unobservable (common) factors. To test for cointegration, the Johansen test is applied to determine the number of cointegrating vectors. The Johansen test asks how many common stochastic trends – or equivalently, how many cointegrating vectors – there are across the stock indices in the sample. The identification of the number of cointegration vectors is undertaken simultaneously to estimation (by maximum likelihood) of the shortrun dynamics between indices. In other words, the test estimates multivariate cointegrating systems based on an error correction mechanism of a vector autoregressive (VAR) model, which we can generally write as Yt = A1 Yt−1 + · · · + Ak Yt−k + εt ,

t = 1, 2, . . . , T .

(1)

In this setup the vector Y follows an autoregressive process of order k with Gaussian errors, where Ak is a n × n coefficient matrix. This can be rewritten in error correction form as Yt =

k−1


i Yt−i +



Yt−k + εt ,

(2)

i=1

 where the n × n matrix i = − kj =i+1 Aj represents the short-run dynamics and the n × n    matrix = ki=1 Ai − I represents the long-run impact matrix. The rank of determines the number of cointegrating vectors, i.e. it reveals the extent of integration across stock markets in the sample. The Johansen test statistic tests the null hypothesis of at most r cointegrating vectors and the process is sequentially repeated for r = 1, . . . , n − 1 until it fails to reject, where n is the number of stock indices in the sample. One advantage of the Johansen test is that efficiency of estimation is increased by simultaneously estimating the VAR system and the cointegrating relationship (Johansen, 1991). The long run relationship is also investigated by factor/component analysis. This involves using the correlation or covariance matrix of returns to extract unobservable factors from the series, which count for most of the variation in the data. There are various methods available for factor extraction. The two most common ones in financial analysis are principal component analysis and common factor analysis. The principal component analysis involves extracting those linear combinations (components) from the dataset that contribute most to its variance. The principal component analysis differs from common factor analysis in that it analyzes the total variance, whereas the latter analyzes common variance. In other words, the common factor model analysis is covariance oriented, i.e. it finds linear combinations of subsets of variables that share maximum common variation. The principal component analysis defines yi = w
i r, where r is a k-dimensional vector of returns and wi is a k-dimensional vector that is chosen such that yi and yj are uncorrelated for i = j and the variance of yi is as large as possible. In other words, the ith first principal component of r is the linear combination yi = w
i r that maximizes variance of yi subject to the constraint w
i w i = 1 and covariance of yi and yj being zero for j = 1, . . . , i − 1. It can be shown that the proportion of the total variance in r explained by the ith principal component

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is the ratio between the ith eigenvalue and sum of all eigenvalues of the covariance matrix of returns (Tsay, 2005). A disadvantage of the principal component analysis is that the number of components needed to explain variation in the data cannot be tested. A common factor model improves on the principal component analysis by allowing for such inference. A common factor model takes the general form r t = βf t + ε t ,

(3)

where r t is a k-dimensional vector of returns, β is a matrix of factor loadings (with βij being the loading of the ith variable on the j th factor), f t is a k-dimensional vector of factors and εit is the specific error of rit and i = 1, . . . , k. Equation (3) can be estimated by a maximum likelihood (ML) procedure, assuming joint normality of the common factors and specific errors. The ML method has desirable asymptotic properties and produces better estimates than principal component analysis in large samples. Again, the methodology also allows for testing the number of common factors and obtaining standard errors and confidence intervals for factor loadings (Tsay, 2005).

3.2. Short Run Relationship The short relationship between stock markets is examined by applying the generalized impulse response analysis, introduced by Koop et al. (1996) and Pesaran and Shin (1998). This differs from the traditional, orthogonalized impulse response analysis in one important way, i.e. the generalized approach is invariant to the ordering of the variables in the VAR system. The traditional impulse response analysis, such as the one based on Cholesky factorization for orthogonalization of VAR innovations, lacks this property, and hence yields different results depending on the ordering. This property of the generalized impulse analysis is therefore particularly useful in studies as this one, where economic theory gives little guidance on how to order the variables. Impulse response functions measure the time profile of the effect of shocks on the expected future values of variables in a dynamic VAR system. In other words, the impulse responses outline the reaction of one stock index to a shock in another. When the VAR system in Equation (1) can be rewritten as an infinite moving average process we get Yt =

∞


Ci εt−1 ,

t = 1, 2, . . . , T ,

(4)

i=0

where Ci is a matrix of moving average coefficients obtained recursively from Ai in Equation (1). Taking derivatives of this expression with respect to ε at a certain point in time gives an innovation term, i.e. the impulse response. Pesaran and Shin (1998) show that the generalized impulse response function, which measures the effect of one standard error shock to the j th equation at time t on expected values of Yt+p , is g

−1/2

ψj (p) = σjj

Cp ej ,

p = 0, 1, 2, . . . ,

(5)

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Interdependence of Nordic and Baltic Stock Markets

where σjj is the jj th element in the variance-covariance matrix  and ej is a n × 1 vector with unity as its j th element and zeros elsewhere. This is different from the more traditional impulse response function, ψjo (p) = Cp P ej

p = 0, 1, 2, . . .

(6)

which is obtained by using the Cholesky decomposition P P
= , where P is an n × n lower triangular matrix. The generalized impulse response functions are shown for the Nordic and Baltic stock indices in Section 4.2.

4. Results 4.1. Long Run Relationship As described above, the long run relationship between stock indices is explored by testing for cointegration and by extracting unobservable (common) factors. But first the augmented Dickey–Fuller test is used to verify that the series are indeed non-stationary, i.e. the test fails to reject non-stationarity for all series, but rejects non-stationarity after taking first differences (details reported in Appendix B). The appropriate lag length of the vector autoregressive (VAR) system is determined by the multivariate generalizations of the Akaike and Schwarz information criteria, which suggest a model with 3 or 1 lags, respectively. The analysis below proceeds with a VAR specification of 3 lags. The results of the Johansen cointegration test are reported in terms of both local currencies and the Swedish krona in Table 2. Both tables give Johansen trace statistics assuming an intercept but no deterministic trend in the cointegrating relationship (results are robust to including a linear trend). Since the development of stock exchange cooperation has been gradual throughout the sample period, there is no clear cut date at which to test for a structural break in the data. Also due to limited observations, the sample period is simply to short for it to be broken into more than two parts. Hence the sample is split into half at May 2001. At this point four countries were members of NOREX, but the OMX group was established 2 years later. The number of cointegrating vectors in each period is indicated in Table 2 by bold letters. The results show that there are 2 cointegrating vectors over the Table 2. Johansen test of cointegration Ho : No. of coint. vectors

Former period

Latter period

Whole period

Former period

Latter period

Whole period

None At most At most At most At most At most

106.74 66.32 40.68 23.14 13.05 4.11

91.34 54.42 30.47 14.79 6.45 0.47

117.10 75.47 46.66 23.65 9.10 0.03

101.93 58.27 36.18 20.07 10.09 3.97

97.95 54.33 25.87 12.85 4.73 0.67

126.73 74.97 44.04 20.47 9.65 0.00

1 2 3 4 5

Local currency

Swedish krona

No. of obs. 256 256 516 256 256 516 Start date 07/03/1996 06/27/2001 07/03/1996 07/03/1996 06/27/2001 07/03/1996 End date 05/23/2001 5/17/2006 05/17/2006 05/23/2001 5/17/2006 05/17/2006

Critical value (5%) 94.15 68.52 47.21 29.68 15.41 3.76

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Table 3. Principal component analysis of returns Eigenvalues

1 2 3 4 5 6

component components components components components components

No. of obs. Start date End date

Cumulative proportion of variation explained by components

Former period

Latter period

Whole period

Former period

Latter period

Whole period

2.31 0.17 0.92 0.81 0.46 0.34

2.66 1.01 0.96 0.84 0.31 0.23

3.10 1.00 0.91 0.41 0.36 0.21

0.39 0.58 0.73 0.87 0.94 1.00

0.44 0.61 0.77 0.91 0.96 1.00

0.52 0.68 0.84 0.90 0.97 1.00

259 6/12/1996 5/23/2001

260 5/30/2001 5/17/2006

519 6/12/1996 5/17/2006

259 6/12/1996 5/23/2001

260 5/30/2001 5/17/2006

519 6/12/1996 5/17/2006

whole period. Further, there is 1 cointegrating vector in the first period, while only 0 or 1 in the second period. There is therefore no indication of increased integration of the stock markets over the sample period. It is noteworthy that not only is there no evidence of increased integration, but there are only 2 cointegrating vectors among the 6 stock indices over the whole sample. This does not strike one as a particularly deep level of integration. For comparison, Bessler et al. (2003) use weekly data to find only 1 cointegrating vector among the markets of USA, S.Africa, Egypt, Morocco, Nigeria and Zimbabwe, while Fraser and Oyefeso (2005) use monthly data to find full integration of 8 cointegrating vectors among stock markets of USA, UK, Germany, France, Italy, Belgium, Spain, Denmark and Sweden. Of the few studies that focus on Scandinavian markets, Malkamäki et al. (1992) find no cointegration among indices when using daily returns over the 1988–90 period. The results of the principal component analysis are shown in Table 3. Over the whole period it can be seen that 4 factors are needed to explain over 90% of the variation in the data. Splitting the sample in half as before, shows that 5 factor are needed to explain over 90% of the variation in the former period, but 4 suffice in the latter. Comparing the explanatory power of each component in the two periods hints towards increased common variability among stock index returns, but the extra explanatory power in the latter period is only a few percentage points higher for each component. In short, the results slightly lean towards increased comovement of stock indices, but by no means strongly support it. Using monthly returns produces very similar results (not reported). A common factor model, such as the one described in Section 3.1, is also estimated. Unfortunately, for this particular data set, estimation of the common factor model produces communality estimates (portion of variance in returns contributed by the common factors) exceeding 1. This mathematical peculiarity, which is referred to as an ultra-Heywood case, renders a factor solution invalid. This happens when one or more eigenvalues, which are the variances of the factors, are negative in value.9 There are no available routes to address 9 More specifically, a Heywood case occurs when returns are perfectly correlated with a linear combination of the

factor returns so that the unique variance of a series is equal to zero (negative in ultra-Heywood case). The ML method is especially prone to Heywood cases since during the iteration process, a variable with high communality is given a high weight, which tends to increase its communality, which increases its weight, and so on. But here

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Interdependence of Nordic and Baltic Stock Markets

Table 4. Common factor analysis of returns Eigenvalues

1 component 2 components 3 components Ho : No. of factors At most 1 At most 2 No. of obs. Start date End date

Cumulative proportion of variation explained by components

Former period

Latter period

Whole period

Former period

Latter period

Whole period

2.473 0.375 0.168

2.837 0.542 0.170

1.043 2.756 0.177

0.820 0.944 1.000

0.799 0.952 1.000

0.262 0.955 1.000

259 6/12/1996 5/23/2001

260 5/30/2001 5/17/2006

519 6/12/1996 5/17/2006

13.89 2.54

χ 2 statistic* 23.21 1.29

24.34 2.31

259 6/12/1996 5/23/2001

260 5/30/2001 5/17/2006

519 6/12/1996 5/17/2006

* Degrees of freedom are 9 for testing at most 1 common factor and 4 for testing at most 2 factors. The corresponding critical values are 3.325 and 0.711.

a Heywood case, other than dropping factors associated with negative eigenvalues. Table 4 reports the results of the common factor analysis, where the factor space is reduced to 3 dimensions due to negative eigenvalues associated with other factors.10 The results are therefore of limited value and clearly not comparable to the results of the principal component analysis. Table 4 shows no evidence of increased explanatory power of common factors in the latter period of the sample and thus no indication of increased interdependence of the Nordic and Baltic stock markets in sample period. To sum up the long term relationship between indices, there seems to be limited interdependence among stock indices and there is no evidence for increased cointegration in the period of merger activity. It seems that any current cointegrating relationships were already established before 1996. A principal component analysis yields similar results, although there is some (weak) support of increased interdependence in variation of returns.

4.2. Short Run Relationship The short-run interdependence is more relevant for short term investors who are e.g. looking for diversification of risks. The short run dynamics are explored by e.g. analyzing the speed at which shocks are transmitted from one market to another, which indicates responsiveness of markets and the efficiency with which new information is transmitted between markets. Again the leading question is whether the increased merger activity and deeper level of cooperation has translated into contemporaneous co-movement of stock indices. the problem persists for other estimation techniques as well, such as an unweighted least-squares estimation. Using monthly data does not bypass Heywood cases either. Heywood cases actually occur fairly frequently in practice, see e.g. Cho and Taylor (1987), Cho et al. (1984) and Diamond and Simon (1990). See also Sentana (2000) for a nice mathematical description. 10 These results are produced using weekly returns.

Note that the common factor analysis assumes no serial correlation in returns, which is violated with weekly returns. However, in such cases one can remove the linear dynamic dependence of the data and apply factor analysis to the residual series. Fitting a VAR(4) model to returns removes the serial dependence and has hardly any effects on the corresponding correlation matrix (see Appendix B). Therefore the factor analysis can in this case be applied directly to the return series (Tsay, 2005).

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As described in Section 3.2, the methodology used to analyse the short run relationship of stock indices is the generalized impulse response analysis, credited to Koop et al. (1996) and Pesaran and Shin (1998). But additionally, it is useful first to briefly look at short run dynamics by testing for Granger causality between the series. This is both informative in terms of comparison to previous studies of the Nordic stock markets and it also has implications on what indices one might want to include in the vector autoregressive model previously presented. The results (reported in Appendix B) show that the Swedish stock index was most often a significant predictor of other stock indices in the sample period. This is consistent with previous work, which typically found the Swedish stock exchange to be leading other Scandinavian markets. Also, the Granger causality analysis indicates that overall the stock indices seem interrelated and no stock market is completely independent of other markets. This supports using all indices when specifying the vector autoregressive (VAR) model. The generalized impulse response functions (IRF), i.e. the response of one stock index to a shock in another, are obtained for all 6 stock indices. These responses to 1 standard deviation change in other stock indices are plotted in Figure 3. There are mainly two things to notice about Figure 3. First, the responses show longlasting effects on stock indices following a shock in other markets. After half a year the stock indices have in many cases not settled back to its pre-shock level. These long lasting effects are consistent with results of other studies (e.g. Masih and Masih, 2001). But secondly, even though the impact is generally long-lived, all responses are very small in scale, using a conventional definition of significant responses as those that exceed 0.20 unit standard deviations.11 Figure 3 indicates that not a single response can be deemed significant using this cutoff value. For example, the Finnish stock market responds most strongly to changes in the Swedish stock market (excluding the Finnish stock market itself, of course), peaking in the third week with a response value of around 0.10 units of standard deviations following a 1 unit innovation in the Swedish market. It is therefore of little value to wade through the shape of the responses, since the level of impact is in all cases smallish.12 It is informative to convert the responses into percentage changes of index values. For example, the 0.10 unit response of the Finnish stock market to the Swedish one, is equivalent to roughly a 2.6% change in the Finnish stock index. This may perhaps seem a significant, weekly response, but it is important to note that the stock indices have been quite volatile in the sample period and thus 1 standard deviation is a fairly large innovation (see summary statistics, Appendix A). In fact, a one standard deviation innovation in the Swedish market corresponds to roughly a 29% change in its stock index (using average values), making the 2.6% response of the Finnish market seem miniature. It should be noted that even though the stock markets hardly react to changes in other markets in the short run, these small responses accumulate over the long run. The responses of the four Scandinavian stock markets to each other become cumulative significant (above 0.2 units of st.dev.) after 3–5 weeks. So from this point of view the markets can be considered interdependent. But in general the responses are nevertheless low, there is for example stronger short-run interdependence between five emerging African stock markets as shown by Bessler et al. (2003). 11 This cutoff is suggested and used by e.g. Dekker et al. (2001), Bessler et al. (2003), Masih and Masih (2001)

and Yang et al. (2003b). 12 This result also holds true when using returns in Swedish krona terms.

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Interdependence of Nordic and Baltic Stock Markets

Figure 3. Generalized IRFs to 1 st.dev. innovation in stock mkt. indices.

As in Section 3, the sample is split in half to investigate whether the short run dynamics across stock markets have changed over the sample period. The results indicate that neither subperiod has significant responses. Hence there is no indication of increased interdependence in the short run as the stock exchanges have increased the level of cooperation.

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5. Concluding Remarks Given that the results indicate limited interdependence of stock markets and lack of strong evidence of convergence in times of increased cooperation, the obvious question to ask is what determines interdependence and convergence? Kim et al. (2005) find an unidirectional causality from the introduction of the European Monetary Union on European stock market integration. One can speculate if this may help to explain the lack of interdependence between the sample countries in this study, since only one country (Finland) in the sample is a member of the EMU. Masih and Masih (2001) postulate several other determinants of the interrelationship and integration among stock markets, such as deregulations, influence of multinational corporations, innovations in financial products and technology, etc. Determining the exact causes of stock market interdependence is an interesting (but tricky) battle left for future analysis. Future work may use a similar framework as is applied here to examine whether other stock exchange interactions of a deeper level have induced increased interdependence. For example, the Euronext merger between the stock exchanges of France, Belgium, Netherlands and Portugal is an interesting case, where the level of cooperation has been taken towards a fully formalized merger. It would be interesting to see if the interdependence has consequently become greater within the Euronext members and compare such an analysis to the Nordic and Baltic markets. Outside Europe there are further interesting, unexplored examples of increased merger activity. Besides ongoing discussions of transatlantic consolidations of the New York Stock Exchange or NASDAQ with either Euronext or the London Stock Exchange, many within country mergers have taken place, e.g. in Colombia, Japan, India, etc. With regards to the Nordic and Baltic markets, the weak interdependence of stock indices implies that there is still room for international diversification in the area. One might expect considerable market adjustment between the stock markets if the merger activity continues to deepen, since with further unification of exchanges the stock prices are bound to adapt to institutional changes.

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Appendix A Table 5. Data description Datastream Symbol

Currency

Description

Denmark Estonia

COSEASH ESTALSE

DKK EUR

Finland

HEXPORT

EUR

Iceland

ICEXALL

ISK

Norway

OSLOASH

NOK

Sweden

SWSEALI

SEK

The OMX Copenhagen all-share index. OMX Tallinn Index. Prices of shares listed in the Main and Investor lists of the Tallinn Stock Exchange. The base date of the Index is June 3, 1996 and the base is 100. All stocks listed on the Main list of the Helsinki Stock Exchange. Comprises all ICEX listed equities. Has been calculated and published daily since January 1993 (31 December 1997 = 1000). This is a capital-weighted yield index with a base of 100 on January 1st 1983. It comprises of all shares on the main list. The OMX Stockholm all-share index.

The indices are in local currency terms, except Finland and Estonia are reported in Euros. Start of sample period is due to data only being available through Datastream on 3 indices prior to 1996. Table 6. Summary statistics

Denmark Estonia Finland Iceland Norway Sweden Denmark Estonia Finland Iceland Norway Sweden

Mean

St.dev.

216.75 256.52 3200.94 1843.61 187.59 221.08

60.74 171.00 808.60 1209.62 73.92 63.46

0.23% 0.36% 0.19% 0.38% 0.23% 0.19%

2.26% 4.59% 2.90% 1.86% 2.73% 3.20%

Skewness Index points 0.83 1.29 0.67 1.71 1.92 0.67 Returns −0.54 −0.48 −0.65 −0.28 −0.79 −0.53

Kurtosis

JB stat.

3.51 3.52 3.09 5.03 6.62 2.98 6.16 10.32 5.94 5.72 5.32 5.34

240.63 1178.68 222.70 166.67 170.93 143.97

Table 7. Correlation of prices (index values) Denmark Estonia Finland Iceland Norway Sweden

Denmark

Estonia

Finland

Iceland

Norway

Sweden

1 0.742 0.723 0.857 0.939 0.724

1 0.334 0.898 0.859 0.232

1 0.505 0.650 0.953

1 0.921 0.421

1 0.587

1

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Table 8. Correlation of returns on stock indices Denmark Estonia Finland Iceland Norway Sweden

Denmark

Estonia

Finland

Iceland

Norway

Sweden

1 0.179 0.647 0.090 0.636 0.642

1 0.202 0.067 0.196 0.202

1 0.134 0.662 0.785

1 0.071 0.085

1 0.636

1

Appendix B Table 9. Augmented Dickey-Fuller test statistic for price series Denmark Estonia Finland Iceland Norway Sweden

Levels

1st difference

−0.993 −1.030 −1.456 0.798 1.284 −1.490

−22.529 −11.543 −22.291 −8.467 −21.160 −24.603

The 5% critical value is −3.418503 and the null hypothesis of non-stationarity is rejected if the test statistic is lower than critical value. In all cases the specification includes a constant and a time trend.

Table 10. Lag length specification for VAR model (prices) Lag

Akaike

Schwarz

0 1 2 3 4 5 6 7 8

70.065 47.678 47.610 47.569* 47.616 47.621 47.638 47.661 47.706

70.114 48.025* 48.256 48.513 48.858 49.161 49.476 49.797 50.139

* Indicates lag order selected by the criterion. Included observations: 512.

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Interdependence of Nordic and Baltic Stock Markets

Table 11. Correlation matrix for residuals after fitting a VAR(4) model to returns Denmark Estonia Finland Iceland Norway Sweden

Denmark

Estonia

Finland

Iceland

Norway

Sweden

1 0.159 0.635 0.059 0.641 0.652

1 0.173 0.016 0.171 0.193

1 0.105 0.667 0.803

1 0.053 0.066

1 0.643

1

This can be compared to Table 8 which shows correlation of returns.

Table 12. Granger causality test statistic – returns

. . . Denmark? . . . Estonia? . . . Finland? . . . Iceland? . . . Norway? . . . Sweden?

Denmark causes. . .

Estonia causes. . .

Finland causes. . .

Iceland causes. . .

Norway causes. . .

Sweden causes. . .

– 5.661 0.025 5.424 0.176 0.082

1.802 – 1.217 0.662 1.919 0.330

0.416 1.165 – 1.850 0.317 0.074

0.375 0.123 1.358 – 0.553 0.011

0.235 3.512 0.000 2.745 – 0.433

1.778 3.639 4.910 3.249 0.143 –

Bold letters indicate that one variable Granger causes another (10% sign. level). The null hypothesis is that x does not Granger cause y, i.e. that x does not contain information that helps to predict y. Rejection of this hypothesis is presented here as x causing y (knowing x helps predicting y). Granger causality is tested using a model specification with 1 lag (1 week forecasting horizon), determined by applying the Akaike and Schwarz criteria (see Table 10). In Table 13, the Granger causality test is presented using prices instead of returns. This is done in the spirit of Sims et al. (1990), who argue that differencing variables before carrying out the Granger causality tests may not be necessary. Now there are more significant causation relationships between indices, with the Danish and the Icelandic stock indices being the most frequent predictors of other stock indices in the sample period (here 3 lags are used, again determined by applying the Akaike and Schwarz criteria).

Table 13. Granger causality test statistic – prices

. . . Denmark? . . . Estonia? . . . Finland? . . . Iceland? . . . Norway? . . . Sweden?

Denmark causes. . .

Estonia causes. . .

Finland causes. . .

Iceland causes. . .

Norway causes. . .

Sweden causes. . .

– 1.348 0.463 3.227 2.753 3.723

3.028 – 1.054 1.952 2.764 0.528

0.560 1.448 – 1.108 0.964 4.152

9.316 2.078 2.626 – 11.118 2.158

1.485 1.427 0.791 0.554 – 1.184

1.203 1.336 3.288 1.474 0.476 –

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