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On the riskiness of the world's stock markets
288
European Journal of Operational Research 53 (1991) 288-296 North-Holland
Theory and Methodology
On the riskiness of the world's stock markets M a r k k u J. M a l k a m ~ i k i
Bank o f F inland, P.O. Box 160, SF-O0101 Helsinki, Finland Teppo Martikainen
and Jukka Perttunen
University of Vaasa, School of Business Studies, P.O. Box 297, SF-65101 Vaasa, Finland Received July 1989; revised January 1990
Abstract: The main aim of this paper is to study the riskiness of the world's stock markets. This is carried out by applying the concepts of the two main asset pricing models: the Capital Asset Pricing Model (CAPM) and the Arbitrage Pricing Model (APM). Certain obvious risk categories among world stock markets exist. Three major potential reasons for the existence of these different risk categories are reported. Firstly, economic trade and currency areas seem to affect the riskiness of different stock markets, with North American, European and Oceanic stock exchanges quite clearly creating their own separate factors. Secondly, the level of institutional development of a given stock market also appears to be a factor determining its riskiness. Thin stock markets, such as those of Finland and Mexico seem to exhibit a different price behaviour of their own. Thirdly, the combined effect of different time zones and efficiency is discussed, especially in the case of the UK stock markets vs. other European stock markets.
Keywords: Finance
I. Introduction This paper aims to study the riskiness and stock price behaviour of 24 world stock markets. This will be carried out applying the risk concepts of the two main asset pricing models: the Capital Asset Pricing Model (CAPM) and the Arbitrage Pricing Model (APM). In the first phase, we will study the sensitivity of each of the stock markets to the movements of the world-wide market portfolio. This sensitivity is measured by determining the beta coefficient for each security market, applying Sharpe's (1964) market model. In the second phase, we will define which of the world stock markets belong to the same risk category. This will be carried out through estimating sys-
tematic risk components of the APM using factor analysis (see e.g. Roll and Ross, 1980). The CAPM and the APM are the most widely used equilibrium models to be found in modern financial literature. These models assume that the expected return of a security is linearly related to its systematic risk. In the CAPM, the systematic risk is measured by the so-called beta coefficient. This measure represents the covariance of the security return with the return of the market portfolio divided by the variance of the return of the market portfolio. In the APM, the systematic risk of a security is split in to several systematic risk components i.e. the sensitivities to unknown common factors (see e.g. Copeland and Weston, 1988, pp. 193-239).
0377-2217/91/$03.50 © 1991 - Elsevier Science Publishers B.V. (North-Holland)
M.J. Malkamiiki et al. / On the riskiness of the world's stock markets
In the international applications of the CAPM, a typical approach has been to determine the market portfolio as a world-wide market portfolio. Assuming that currency hedging is fully available, this world market portfolio can be regarded as the optimal risky portfolio (Solnik, 1988, p. 27). In this approach the international systematic risk component of an individual stock has been determined by measuring its sensitivity to this international market portfolio (see e.g. Solnik, 1974; Adler and Dumas, 1983). The International Arbitrage Pricing Model was formulated by Solnik (1983), and has been tested e.g. by Cho, Eun and Senbet (1986). They reported that, in the IAPM, the number of common factors between different countries is dependent on the degree of their economic integration. In addition, a number of studies have reported positive relationships in returns across different stock exchanges (see e.g. Jaffe and Westerfield, 1985a, 1985b; Mourik, 1988; Arnott and Henriksson, 1989; and Hamao, Masulis and Ng, 1989). In this paper we concentrate on the riskiness of stock markets as a whole. It is extremely im-
289
portant for investors to notice the general characteristics and riskiness of stock returns in different stock markets. This is due to the fact that in recent years barriers against international capital movements have been lowered whilst at the same time global on-line information to support portfolio decisions has become widely available. International portfolio diversification is thus a viable option, even for private investors.
2. The data
In this study we will use the Financial Times Actuaries World Indices published daily by the Financial Times in co-operation with Goldman, Sachs & Co, and Wood MacKenzie & Co since March 1987. The indices are presented for 24 individual countries, 10 regions of the world, and the world as a whole. Indices in local currencies as well as in US dollars and in pounds sterling are included. Taking the international investor's point of view, we have used indices in dollar form. The base value for the indices is 100 = Dec. 31, 1986.
Table 1 Basic statistical p r o p e r t i e s of stock returns Country
Mean
Std-dev
Skewness
Kurtosis 0.390
Australia
0.0013
0.0126
- 0.307
Austria
0.0001
0.0065
- 0.326
1.406
Belgium Canada
0.0010 0.0003
0.0102 0.0075
0.944 - 0.116
6.036 3.125
Denmark Finland
0.0013 0.0007
0.0084 0.0091
- 0.262 0.175
2.356 0.938
France West G e r m a n y
0.0012 0.0007
0.0099 0.0108
- 0.056 - 0.124
0.003 1.979
Hong Kong
0.0007
1.446
0.0007 0.0005
0.0101 0.0102 0.0122
- 0.066
Ireland Italy
- 0.425 - 0.022
3.603 0.845
Japan Malaysia Mexico Netherlands New Zealand
0.0012 0.0008 0.0018 0.0005 - 0.0005
0.0095 0.0101 0.0235 0.0084 0.0145
- 0.026 - 0.164 0.790 - 0.366 - 0.192
0.775 1.805 4.918 1.344 2.218
Norway Singapore S o u t h Africa
0.0009 0.0006 - 0.0006
0.0129 0.0106 0.0174
- 0.406 - 0.335 - 0.196
2.622 3.715 1.006
Spain Sweden Switzerland United Kingdom USA
0.0004 0.0013 - 0.0002 0.0001 0.0003
0.0084 0.0095 0.0108 0.0085 0.0100
-
0.229 0.404 1.451 0.386 1.188
2.360 2.100 8.322 0.310 8.411
The World Index
0.0007
0.0061
- 0.351
1.307
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However, the index for Finland has only been published since Dec. 31, 1987. Country indices are calculated as weighted arithmetic means of stock prices, normalised to the same base period (Goldman, Sachs & Co, 1987). Weighting equates to relative market values. Our data consists of daily returns for the year 1988. The returns have been measured using differences in logarithmic stock market indices. The basic statistical properties of stock returns are presented in Table 1. The skewness and especially the kurtosis measurements indicate a certain departure from the normality assumption required for the following statistical analysis. These kinds of deviations from the normality assumption occur commonly when calculations are based on daily returns (see e.g. Hawawini and Michel, 1984, pp. 18-28). However, they indicate that the empirical results in the study must be considered with a relatively moderate level of caution.
3. Empirical results 3.1. R i s k i n e s s o f single s t o c k m a r k e t s
In the first phase we study the riskiness of each individual stock market, applying the risk concept of the CAPM. This is carried out by estimating the beta coefficient for each stock market, applying Sharpe's market model: r,, = a i + Bir,,, + ei,,
(1)
where r,, = the return on a stock market i at time t; a, = the intercept term; ,8, = the estimate of the beta coefficient of stock market i; r,,, = the return of the world market portfolio at time t; ei, = a random-error term. In order to study the stability of the beta coefficients, we divided the whole data into two mutually exclusive subperiods. The market portfolio required was determined using the value-weighted world index introduced by the Financial Times. The OLS-estimates of beta coefficients for each stock market are presented in Table 2. The results in Table 2 indicate that the beta coefficients for the Japanese and US stock markets have typically been higher than those of the other
Table 2 Estimated beta coefficients for each stock market Country
Beta Whole
Subperiod 1
Subperiod 2
Australia Austria Belgium Canada Denmark Finland France West G e r m a n y Hong Kong Ireland Italy Japan Malaysia Mexico Netherlands New Zealand Norway Singapore South Africa Spain Sweden Switzerland United Kingdom USA
0.643 0.421 0.503 0.570 0.427 0.239 0.589 0.809 0.611 0.517 0.680 1.215 0.508 0.080 0.637 0.388 0.512 0.576 0.362 0.565 0.694 0.605 0.807 0.954
0.543 0.287 0.467 0.598 0.241 0.126 0.378 0.822 0.615 0.470 0.670 0.988 0.556 0.448 0.558 0.277 0.701 0.614 0.250 0.541 0.702 0.630 0.664 1.315
0.774 0.583 0.538 0.534 0.647 0.356 0.840 0.828 0.622 0.571 0.712 1.465 0.459 - 0.330 0.729 0.511 0.306 0.567 0.501 0.599 0.701 0.588 0.975 0.545
Mean Std-dev
0.580 0.228
0.561 0.255
0.610 0.304
stock markets. This observation is apparently due to the fact that these two stock markets have the highest weights in the world market index used in the study, representing the major part of the value-weighted index. Thus, the values of their beta coefficients tend to move upwards. On the other hand, the values of the beta coefficients of the stock markets with smaller weights tend to move downwards. This phenomenon is also usually found in studies where a value-weighted market index is applied to thin stock markets (compare Hawawini and Michel, 1984). The negative beta coefficient of the Mexican stock market in the second subperiod may be due to the fact that its index consists of only 14 stocks. Thus, the reliability of the Mexican index behaviour may be quite poor. One of the main problems when estimating beta coefficients for single stocks has been the problem of instability. Relative instability of the beta coefficients can also be reported in our study. The Spearman rank correlation coefficient be-
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291
stock returns. In this approach the systematic risk components have been estimated measuring each stock's sensitivities to these macro-economic factors (see e.g. Chen, Roll and Ross, 1986). The second method has been to estimate the systematic risk components and unknown factors simultaneously by factor analysis (see e.g. Roll and Ross, 1980). In this study, the factor analysis approach is used to determine the global common factors that explain the returns of world stock markets and also to estimate the systematic risk components of each individual stock market. The following factor analysis model is used to estimate these common factors and the systematic risk components for each stock market:
tween betas from subperiod 1 and subperiod 2 was 0.38 which differs from zero at 7% significance level. This indicates that predicting future beta coefficients using historical return series is apparently difficult. The empirical evidence indicates that the same problems observed when estimating betas at the single stock level are also present when measuring betas at the stock market level. Thus, the reliability and usability of the systematic risk measurements estimated using this approach are obviously not very high in global asset allocation.
3.2. Risk categories of the world's stock markets When estimating the systematic risk components of the APM, two main approaches have been presented in literature. The first has been the use of pre-specified macro-economic variables in order to determine the general factors that explain
r , , - ~ t , = b i l F l , + b , 2 F 2 , + . ' . +b, kFkt+e,,, where r,, = the return on a stock market i at time t; /,, = the mean return of stock market i;
Table 3 C l a s s i f i c a t i o n p a t t e r n of stock e x c h a n g e s ( l o a d i n g s over 0.35 in b o l d text) Country
Factor
1
Communality
2
3
4
0,747 0.733 0.692 0.672 0.646 0.612 0.593 0.577 0.576 0.572 0.445 0.436 0.196
0.162 0.241 0.101 0.263 0.021 0.050 0.202 - 0.010 0.215 0.283 0.281 0.179 0.826
0.068 - 0.064 - 0.044 0.097 0.102 0.002 0,072 0.263 0.046 0.152 0.128 0.320 0.018
- 0.290 0.137 0.119 - 0.156 0.385 0.342 0.146 - 0.243 0.210 0.022 - 0.436 - 0.007 - 0.145
0.180 0.217 0.279 0.059 0,081 - 0,197 0,441 0,487 0.142 0.346 0.039
0.816 0.668 0.633 0.554 0 . l 34 0.097 0.094 0.180 - 0.075 0.271 0.043
- 0.022 0.172 0.143 0.139 0.768 0.722 0.583 0.537 0.455 - 0.089 - 0.122
- 0.094 -0.191 0.161 0.309 - 0.177 - 0.129 0.029 - 0.354 0,390 0.499 0.354
Variance explained
5.367
3.096
2.289
1.609
R a t e of determination
0.224
0.129
0.095
0.067
West Germany Spain Belgium Switzerland Austria Denmark Italy France Japan Sweden Norway Ireland Singapore Malaysia Hong Kong Australia New Zealand Canada USA United Kingdom Netherlands South Africa Finland Mexico
0.673 0.618 0.505 0.554 0,576 0.493 0.419 0.461 0.424 0.431 0.483 0.325 0.741 O.708 0.559 O.528 0.425 0.646 0.586 0.544 0,684 0.385 0.450 0.143
Cumulative 0.515
(2)
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M.J. Malkamiiki et al. / On the riskiness of the worM's stock markets
Eigenvalue
Factor Figure 1. Results of the scree-test.
b,j = the sensitivity of stock market i to the j-th common factor; /~, = the value of the j-th common factor at time t; E i t = a random-error term. The varimax-rotated factor patterns from the principal component factor analysis based on the covariance matrix of the stock market returns are reported in Table 3. (The four-factor solution is selected based on the results of the scree-test presented in Figure 1.) The first thing to notice in Table 3 is that most of the European stock exchanges are loaded to the first empirical factor. This indicates a strong positive empirical relationship between stock returns in these European countries. Japan is also loaded to this European factor. The second factor in Table 3 clearly represents the Oceanic factor consisting of Singapore, Malaysia, Hong Kong, Australia and New Zealand. Also Japan has its second highest loading on this factor.
The third factor can be seen to represent the North American stock exchanges, since both the USA and Canada have their highest loadings on this factor. Furthermore, these two stock exchanges do not have any high loadings on the other empirical factors. Regarding the European exchanges, the United Kingdom and the Netherlands are situated on this third factor. However, it should be noticed that they also have high loadings on the first, European factor. The fourth factor consists of the highest loadings of Finland and Mexico, both of which are relatively thin stock markets, the number of stocks in their indices also being low (Finland 26, Mexico 14), which might well be the underlying reason for the index behaviour of these countries. However, it should be noted that Finland also has a strong loading on the European factor. Austria, Norway and South Africa also have strong loadings on the fourth factor. All of these five countries have relatively thin stock markets and are not commonly included when international portfolios are diversified. The main interpretation of the factors thus seems to be the geographical locations of stock exchanges. There exists a wide range of potential reasons why stock markets located in the same geographical area typically have high loadings on the same factor. First, North America, Europe and Asia can be seen to represent the main economic areas of the world. Within these areas constraints and regulations imposed by national governments, technological specialisation, and cultural and sociological factors etc. are relatively similar. Therefore, it is expected that stock prices behave homogeneously within these areas (see e.g. Solnik, 1988, pp. 38-43). Secondly, the economic areas presented above are also dominated by different currencies. The US dollar is obviously the most commonly used currency in international trading and in portfolio investments. As is widely known, the holdings of dollar dominated investments or positions have been subject to relatively high risks during our research period. As the uncertainty on the US dollar increases, more investments are likely to be transfered to yen and D-mark based securities. These currencies have been extremely strong whereas the rate of sterling has been more uncertain during the research period. This might partly explain why the International Stock Exchange of
M.J. Malkamiiki et al. / On the riskiness of the world's stock markets
between the NYSE and the International Stock Exchange in London is only four hours. Opening price quotations on the New York Stock Exchange may thus have some effect on trading in the U K if its markets are efficient, i.e. new published information is reflected in stock prices without a time lag. Where this is the case, a stock market is said to be efficient in the semi-strong sense. Several empirical studies have indicated that the UK markets exhibit this semi-strong form of efficiency (see e.g Hawawini and Michel, 1984). This might well be a potential explanation for the empirical finding that the UK stock market has its highest loading on the US factor. Other European stock exchanges do not have the same opportunity to react so rapidly to the US information due to their five hour time difference and their call auction trading mechanisms. The third explanation is thus not only the time zones but also the degree of sophistication of trading mechanisms on the stock exchanges, i.e. the structural (institutional) ef-
Table 4 Transformation
matrix
between
empirical
terns of stock exchanges from subperiods Factor
pat-
1 and 2
Subperiod 2
1 Subperiod
classification
2
3
4
1
0.718
0.150
2
0.016
0.964
0.002
3
0.682
0.164
0,314
4
0.135
- 0.146
0,834
1
-0.454
293
0,505 0,266 -0,640 0,515
London has its highest loading on the same factor as the USA. Following this explanation, it is important to recognize that both Japan and Germany have very low loadings on the North American factor. The third explanation for the geographical factors may be the different time zones i.e. different stock exchange hours. Before trading on the New York Stock Exchange starts, the trading in Tokyo has already closed. However, the time difference
Table 5 Residual matrix and abnormal Country
transformation
Factor
1 Australia
for subperiod 2 Abnormal
2
3
transformation
4
0.093
- 0.297
0.220
- 0.143
Austria
- 0.273
0,242
- 0.030
0.241
0.192
Belgium
- 0.120
- 0.097
- 0.243
0.076
0.089 0.026
Canada Denmark Finland France West Germany Hong Kong
0.166
0.046
- 0.079
0.007
- 0.132
- 0.470
0.174
- 0.373
0.332
0.500
0.093
0.085
- 0.177
0.029
0.048
0.140
- 0.280
0.231
0.052
0,031
- 0.364 0.049
- 0.008 -0.098
-0.127
0.096
0.166
- 0.138
- 0.060
0.059
Ireland
- 0.226
0.189
0.199
- 0.120
0.141
ltaly
- 0.243
0.159
0.093
0.052
0.095
0.048
0.247
0.167
0.152
0.114 0.125
Japan Malaysia
0.121
- 0.082
0.075
0.313
Mexico
- 0.093
0.308
0.098
0.802
Netherlands
-0.106
New Zealand
-0.064
0.216
0.757
-0.214
0.108
- 0.299
0.099
-0.272
0.196
- 0.035
0.002
- 0.092
Norway
0.090
0.188
0.280
Singapore
0.109
- 0.067
0.070
0.151
0.044
South Africa
0.108
- 0.035
0.151
- 0.508
0.294
Spain
- 0.047
0.160
- 0.060
- 0.043
0.033
Sweden
- 0.297
0.220
- 0.143
0.282
0.237
Switzerland
0.242
- 0.030
0.241
- 0.320
0.220
United Kingdom
- 0.097
- 0.243
0.076
- 0.044
0.076
USA
- 0.079
0.007
- 0.132
0.471
0.245
0.818
0.639
0.691
1.977
4.126
Abnormal transformation
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294
ficiency of the stock markets. The low trading volume on other European stock markets may also explain the result above. An interesting question arising from our study is that of the stability of the relationships between different stock exchanges. To test the stability of the obtained results we divided the research period again into two subperiods. The factor patterns from these subperiods are presented in Appendices A and B. In order to study the similarity of the factor patterns produced, we applied transformation analysis. Transformation analysis was initially presented by Ahmavaara (1954) and has been mainly applied in Finnish political and sociological studies. In finance literature, it was first introduced by Yli-Olli (1983) for determining the na-
ture and medium-term stability of the classification patterns of financial ratios. Transformation analysis in testing similarities between created factor patterns is preferred to traditional correlation and congruency analysis because of the fact that by this method we can obtain a regression type model for the shifting of variables from one factor to another (for a deeper presentation of the method see Yli-Olli and Virtanen, 1989). The results presented in Table 4 indicate that the factors representing European, Oceanic, and North American stock exchanges have been relatively similar in both subperiods. The North American factor has changed its position from the fourth factor to the third factor in the second subperiod. This, however, does not mean any in-
Appendix A Table A Classification pattern of stock exchanges. First subperiod Country
C ommuna l i t y
Factor 1
2
3
0.683 0.657 0.628 0.618 0.599 0.588 0.449 0.382 0.143 0.088 0.042 0.273 0.184 0.384 0.026 0.417 0.408 0.022 0.007 0.213 0.106 0.257 0.224 0.118
- 0.006 0.163 0.293 0.289 0.222 0.099 0.279 -0.107 0.813 0.813 0.723 0.612 0.505 0.429 0.308 0.144 0.226 0.177 0.020 0.171 0.137 0.041 -0.174 0.267
0.026 0.146 - 0.048 0.408 - 0.107 0.356 0.243 -0.362 0.167 0.246 0.306 0.187 - 0.096 0.238 0.690 0.686 0.686 0.620 0.574 - 0.161 0.273 0.219 0.105 0.319
Variance explained
3.539
3.353
3.192
2.308
Rate of determination
0.147
0.140
0.133
0.096
Austria Japan Finland Spain Denmark Belgium Italy Mexico Malaysia Singapore Hong Kong Australia New Zealand Sweden Norway West Germany Switzerland Netherlands France USA Canada United Kingdom South Africa Ireland
-
4
-
0.159 0.109 0.167 0.070 0.075 0.058 0.108 0.084 0.067 0.059 0.114 0.034 0.026 0.192 0.132 0.072 0.154 0.538 0.171 0.763 0.733 0.658 0.348 0.335
0.492 0.491 0.510 0.632 0.425 0.485 0.350 0.296 0.715 0.732 0.632 0.485 0.299 0.425 0.588 0.670 0.711 0.706 0.359 0.683 0.642 0.548 0.213 0.299
Cumulative 0.516
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295
Appendix B Table B Classification pattern of stock exchanges. Second subperiod Country
1 Denmark Austria Belgium France Sweden Spain
Communality
Factor 2
3
4
0.820
- 0.056
0.005
0.060
0.802
0.082
- 0.092
0.100
0.679 0.668
0.779
0.025
- 0.039
0.135
0.627
0.775
0.098
0.186
0.004
0.644
0.768
0.147
0.203
- 0.028
0.654
0.764
0.103
- 0.151
0.134
0.635
Italy
0.750
0.067
- 0.129
0.150
0.607
West Germany Netherlands Ireland Switzerland Japan United Kingdom Norway Singapore Malaysia
0.731
0.276
0.213
0.205
0.698
0.589
0.262
0.437
0.131
0.624
0.578
0.055
0.128
0.219
0.401
0.543 0.541
0.277 0.314
- 0.082 0.005
0.227 0.186
0.430 0.426
0.520
0.184
0.424
0.383
0.632
0.421
0.199
0.035
- 0.006
0.218
0.143 0.118
0.869 0.863
0.018 - 0.029
- 0.018 0.097
0.777 0.769 0.457
Hong Kong USA
Canada South Africa N ew Zealand Australia Finland Mexico Variance explained Rate of determination
0.170
0.558
0.312
0.136
- 0.078
0.052
0.815
- 0.036
0.674
0.165 0.168
0.076 - 0.200
0.778 0.070
0.097 0.687
0.647 0.545
0.114 0.245 0.308 0.130
0.438 0.521 0.119 0.076
0.000 0.033 - 0.262 - 0.315
0.601 0.547 0.311 - 0.363
0.566 0.631 0.274 0.254
6.821
2.797
2.108
1.812
0.284
0.117
0.088
0.076
Cumulative
stability, and the interpretation of this factor is relatively clear. The fourth factor seems to be more unstable in nature. This is not especially surprising since this factor consists of thin stock exchanges. In order to obtain further information concerning the similarities of classification patterns of different stock exchanges over time, we determined the residual matrix to define the abnormal transformation between factor patterns of successive subperiods. This residual matrix is presented in Table 5. An interesting observation is the high abnormal transformation of the Mexico Stock Exchange. The reason for this exceptional behaviour of the Mexico Stock Exchange has been discussed earlier.
0.565
The other stock markets seem to have more similar factor loadings in both subperiods.
4. Summary The main purpose of this paper was to study the riskiness of the world's stock markets. This was carried out by applying the concepts of the two main asset pricing models: the Capital Asset Pricing Model (CAPM) and the Arbitrage Pricing Model (APM). We found certain obvious risk categories to exist among the world's stock markets. Most of the European, Oceanic and North American stock
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exchanges created their own regionally specific factors. Also thin stock markets, such as Finland and Mexico, seemed to exhibit a price behaviour of their own. Several fundamental and technical features were assumed to be beyond the observed risk categories. Firstly, economic trade and currency areas seemed to affect the riskiness of different stock markets. North American, European and Oceanic stock exchanges quite clearly created their own separate factors. Secondly, the state of institutional development of a stock market seemed also to affect its riskiness. Thin stock markets, such as Finland, Mexico, New Zealand and South Africa, seemed to have a price behaviour of their own. Thirdly, the combined effect of the different time zones and efficiency was analysed, especially in the case of the U K stock markets vs. other European markets. The main implication of our study for decision-makers, i.e. investors, is that they can reduce the unsystematic risk of their portfolios by diversifying in stocks listed in different geographical areas. It should be emphasized, however, that the relatively short time period covered, obviously makes any generalised interpretation of the results very difficult.
Acknowledgements The authors wish to thank Dr. Peter Nyberg from The Bank of Finland and an anonymous referee for their useful comments. The financial support by Suomen Arvopaperi markkinoiden Edist~imiss~i~itio is also gratefully acknowledged.
References Adler, M., and Dumas, B. (1983), "International portfolio choice and corporation finance. A survey", Journal of Finance 38/1, 41-50. Ahmavaara, Y. (1954), "Transformation analysis of factorial data", Annales Academiae Scientiarum Fennicae Series B 88/2. Arnott, R.D., and Henriksson, R.D. (1989), "A disciplined approach to global asset allocation", Financial Analysts Journal 45/3, 17-28.
Brown, R.J. (1988), "A comparison of market efficiency among stock exchanges", Journal of Business Finance and Accounting 15/3, 373-384. Chen, N-F., Roll, R., and Ross, S.A. (1986), "Economic forces and the stock market", Journal of Business 59/3, 383-403. Cho, D.C., Eun, C.S., and Senbet, L.W. (1986), "International arbitrage pricing theory: an empirical investigation", Journal of Finance 41/2, 313-329. Copeland, W., and Weston, J. (1988), Financial Theory and Corporate Policy, Addison-Wesley, New York. Goldman, Sachs & Co (1987), The FT-actuaries World Indices: An Introduction, New York. Hamao, Y., Masulis, R.W., and Ng, V. (1989), "Correlations in price changes and volatility across international stock markets", Paper presented to the 16th Annual Meeting of the European Finance Association, Stockholm 31.8.1989. Hawawini, G.A., and Michel, P.A. (eds.) (1984), European Equity Markets: Risk, Return and Efficiency, Garland Publishing Inc. New York. Jaffe, J., and Westerfield, R. (1985a), "Patterns in Japanese common stock returns: day of the week and turn of the year effects", Journal of Financial and Quantitative Analysis 20/2, 261-272. Jaffe, J., and Westerfield, R. (1985b), "The week-end effect in common stock returns: international evidence", Journal of Finance 40/2, 433-454. Lease, R., and Lewellen, W.G. (1982), "Market efficiency across securities exchanges", Journal of Economics and Business 12, 101-109. Mourik, T.J. (1988), "Systematic patterns in recent stock returns. An analysis of the efficiency of stock markets on the basis of the FTA indices", Paper presented at the Workshop on Equity Pricing and Portfolio Management, Brussels 6.12.1988. Roll, R., and Ross, S.A. (1980), "An empirical investigation of the arbitrage pricing theory", Journal of Finance 35/5, 1073-1102. Sharpe, W.F. (1964), "Capital assets prices: a theory of market equilibrium under conditions of risk", Journal of Finance 19/3, 425-442. Solnik, B. (1974), "An equilibrium model of the international capital market" Journal of Economic Theory July/August 500-524. Solnik, B. (1983), "International arbitrage pricing theory", Journal of Finance May 449-457. Solnik, B. (1988), International Investments, Addison-Wesley, Reading, MA. Yli-Olli, P. (1983), "The empirical classification of financial ratios and the stability of the classification", Proceedings of the University of Vaasa. Research Papers 95. Yli-Olli, P., and Virtanen, I. (1989), "On the long-term stability and cross-country invariance of financial ratio patterns", European Journal of Operational Research 39, 40-53.
European Journal of Operational Research 53 (1991) 288-296 North-Holland
Theory and Methodology
On the riskiness of the world's stock markets M a r k k u J. M a l k a m ~ i k i
Bank o f F inland, P.O. Box 160, SF-O0101 Helsinki, Finland Teppo Martikainen
and Jukka Perttunen
University of Vaasa, School of Business Studies, P.O. Box 297, SF-65101 Vaasa, Finland Received July 1989; revised January 1990
Abstract: The main aim of this paper is to study the riskiness of the world's stock markets. This is carried out by applying the concepts of the two main asset pricing models: the Capital Asset Pricing Model (CAPM) and the Arbitrage Pricing Model (APM). Certain obvious risk categories among world stock markets exist. Three major potential reasons for the existence of these different risk categories are reported. Firstly, economic trade and currency areas seem to affect the riskiness of different stock markets, with North American, European and Oceanic stock exchanges quite clearly creating their own separate factors. Secondly, the level of institutional development of a given stock market also appears to be a factor determining its riskiness. Thin stock markets, such as those of Finland and Mexico seem to exhibit a different price behaviour of their own. Thirdly, the combined effect of different time zones and efficiency is discussed, especially in the case of the UK stock markets vs. other European stock markets.
Keywords: Finance
I. Introduction This paper aims to study the riskiness and stock price behaviour of 24 world stock markets. This will be carried out applying the risk concepts of the two main asset pricing models: the Capital Asset Pricing Model (CAPM) and the Arbitrage Pricing Model (APM). In the first phase, we will study the sensitivity of each of the stock markets to the movements of the world-wide market portfolio. This sensitivity is measured by determining the beta coefficient for each security market, applying Sharpe's (1964) market model. In the second phase, we will define which of the world stock markets belong to the same risk category. This will be carried out through estimating sys-
tematic risk components of the APM using factor analysis (see e.g. Roll and Ross, 1980). The CAPM and the APM are the most widely used equilibrium models to be found in modern financial literature. These models assume that the expected return of a security is linearly related to its systematic risk. In the CAPM, the systematic risk is measured by the so-called beta coefficient. This measure represents the covariance of the security return with the return of the market portfolio divided by the variance of the return of the market portfolio. In the APM, the systematic risk of a security is split in to several systematic risk components i.e. the sensitivities to unknown common factors (see e.g. Copeland and Weston, 1988, pp. 193-239).
0377-2217/91/$03.50 © 1991 - Elsevier Science Publishers B.V. (North-Holland)
M.J. Malkamiiki et al. / On the riskiness of the world's stock markets
In the international applications of the CAPM, a typical approach has been to determine the market portfolio as a world-wide market portfolio. Assuming that currency hedging is fully available, this world market portfolio can be regarded as the optimal risky portfolio (Solnik, 1988, p. 27). In this approach the international systematic risk component of an individual stock has been determined by measuring its sensitivity to this international market portfolio (see e.g. Solnik, 1974; Adler and Dumas, 1983). The International Arbitrage Pricing Model was formulated by Solnik (1983), and has been tested e.g. by Cho, Eun and Senbet (1986). They reported that, in the IAPM, the number of common factors between different countries is dependent on the degree of their economic integration. In addition, a number of studies have reported positive relationships in returns across different stock exchanges (see e.g. Jaffe and Westerfield, 1985a, 1985b; Mourik, 1988; Arnott and Henriksson, 1989; and Hamao, Masulis and Ng, 1989). In this paper we concentrate on the riskiness of stock markets as a whole. It is extremely im-
289
portant for investors to notice the general characteristics and riskiness of stock returns in different stock markets. This is due to the fact that in recent years barriers against international capital movements have been lowered whilst at the same time global on-line information to support portfolio decisions has become widely available. International portfolio diversification is thus a viable option, even for private investors.
2. The data
In this study we will use the Financial Times Actuaries World Indices published daily by the Financial Times in co-operation with Goldman, Sachs & Co, and Wood MacKenzie & Co since March 1987. The indices are presented for 24 individual countries, 10 regions of the world, and the world as a whole. Indices in local currencies as well as in US dollars and in pounds sterling are included. Taking the international investor's point of view, we have used indices in dollar form. The base value for the indices is 100 = Dec. 31, 1986.
Table 1 Basic statistical p r o p e r t i e s of stock returns Country
Mean
Std-dev
Skewness
Kurtosis 0.390
Australia
0.0013
0.0126
- 0.307
Austria
0.0001
0.0065
- 0.326
1.406
Belgium Canada
0.0010 0.0003
0.0102 0.0075
0.944 - 0.116
6.036 3.125
Denmark Finland
0.0013 0.0007
0.0084 0.0091
- 0.262 0.175
2.356 0.938
France West G e r m a n y
0.0012 0.0007
0.0099 0.0108
- 0.056 - 0.124
0.003 1.979
Hong Kong
0.0007
1.446
0.0007 0.0005
0.0101 0.0102 0.0122
- 0.066
Ireland Italy
- 0.425 - 0.022
3.603 0.845
Japan Malaysia Mexico Netherlands New Zealand
0.0012 0.0008 0.0018 0.0005 - 0.0005
0.0095 0.0101 0.0235 0.0084 0.0145
- 0.026 - 0.164 0.790 - 0.366 - 0.192
0.775 1.805 4.918 1.344 2.218
Norway Singapore S o u t h Africa
0.0009 0.0006 - 0.0006
0.0129 0.0106 0.0174
- 0.406 - 0.335 - 0.196
2.622 3.715 1.006
Spain Sweden Switzerland United Kingdom USA
0.0004 0.0013 - 0.0002 0.0001 0.0003
0.0084 0.0095 0.0108 0.0085 0.0100
-
0.229 0.404 1.451 0.386 1.188
2.360 2.100 8.322 0.310 8.411
The World Index
0.0007
0.0061
- 0.351
1.307
290
M.J. Malkamiiki et al. / On the riskiness of the worM's stock markets
However, the index for Finland has only been published since Dec. 31, 1987. Country indices are calculated as weighted arithmetic means of stock prices, normalised to the same base period (Goldman, Sachs & Co, 1987). Weighting equates to relative market values. Our data consists of daily returns for the year 1988. The returns have been measured using differences in logarithmic stock market indices. The basic statistical properties of stock returns are presented in Table 1. The skewness and especially the kurtosis measurements indicate a certain departure from the normality assumption required for the following statistical analysis. These kinds of deviations from the normality assumption occur commonly when calculations are based on daily returns (see e.g. Hawawini and Michel, 1984, pp. 18-28). However, they indicate that the empirical results in the study must be considered with a relatively moderate level of caution.
3. Empirical results 3.1. R i s k i n e s s o f single s t o c k m a r k e t s
In the first phase we study the riskiness of each individual stock market, applying the risk concept of the CAPM. This is carried out by estimating the beta coefficient for each stock market, applying Sharpe's market model: r,, = a i + Bir,,, + ei,,
(1)
where r,, = the return on a stock market i at time t; a, = the intercept term; ,8, = the estimate of the beta coefficient of stock market i; r,,, = the return of the world market portfolio at time t; ei, = a random-error term. In order to study the stability of the beta coefficients, we divided the whole data into two mutually exclusive subperiods. The market portfolio required was determined using the value-weighted world index introduced by the Financial Times. The OLS-estimates of beta coefficients for each stock market are presented in Table 2. The results in Table 2 indicate that the beta coefficients for the Japanese and US stock markets have typically been higher than those of the other
Table 2 Estimated beta coefficients for each stock market Country
Beta Whole
Subperiod 1
Subperiod 2
Australia Austria Belgium Canada Denmark Finland France West G e r m a n y Hong Kong Ireland Italy Japan Malaysia Mexico Netherlands New Zealand Norway Singapore South Africa Spain Sweden Switzerland United Kingdom USA
0.643 0.421 0.503 0.570 0.427 0.239 0.589 0.809 0.611 0.517 0.680 1.215 0.508 0.080 0.637 0.388 0.512 0.576 0.362 0.565 0.694 0.605 0.807 0.954
0.543 0.287 0.467 0.598 0.241 0.126 0.378 0.822 0.615 0.470 0.670 0.988 0.556 0.448 0.558 0.277 0.701 0.614 0.250 0.541 0.702 0.630 0.664 1.315
0.774 0.583 0.538 0.534 0.647 0.356 0.840 0.828 0.622 0.571 0.712 1.465 0.459 - 0.330 0.729 0.511 0.306 0.567 0.501 0.599 0.701 0.588 0.975 0.545
Mean Std-dev
0.580 0.228
0.561 0.255
0.610 0.304
stock markets. This observation is apparently due to the fact that these two stock markets have the highest weights in the world market index used in the study, representing the major part of the value-weighted index. Thus, the values of their beta coefficients tend to move upwards. On the other hand, the values of the beta coefficients of the stock markets with smaller weights tend to move downwards. This phenomenon is also usually found in studies where a value-weighted market index is applied to thin stock markets (compare Hawawini and Michel, 1984). The negative beta coefficient of the Mexican stock market in the second subperiod may be due to the fact that its index consists of only 14 stocks. Thus, the reliability of the Mexican index behaviour may be quite poor. One of the main problems when estimating beta coefficients for single stocks has been the problem of instability. Relative instability of the beta coefficients can also be reported in our study. The Spearman rank correlation coefficient be-
M,J. Malkamiiki et al. / On the riskiness of the world's stock markets
291
stock returns. In this approach the systematic risk components have been estimated measuring each stock's sensitivities to these macro-economic factors (see e.g. Chen, Roll and Ross, 1986). The second method has been to estimate the systematic risk components and unknown factors simultaneously by factor analysis (see e.g. Roll and Ross, 1980). In this study, the factor analysis approach is used to determine the global common factors that explain the returns of world stock markets and also to estimate the systematic risk components of each individual stock market. The following factor analysis model is used to estimate these common factors and the systematic risk components for each stock market:
tween betas from subperiod 1 and subperiod 2 was 0.38 which differs from zero at 7% significance level. This indicates that predicting future beta coefficients using historical return series is apparently difficult. The empirical evidence indicates that the same problems observed when estimating betas at the single stock level are also present when measuring betas at the stock market level. Thus, the reliability and usability of the systematic risk measurements estimated using this approach are obviously not very high in global asset allocation.
3.2. Risk categories of the world's stock markets When estimating the systematic risk components of the APM, two main approaches have been presented in literature. The first has been the use of pre-specified macro-economic variables in order to determine the general factors that explain
r , , - ~ t , = b i l F l , + b , 2 F 2 , + . ' . +b, kFkt+e,,, where r,, = the return on a stock market i at time t; /,, = the mean return of stock market i;
Table 3 C l a s s i f i c a t i o n p a t t e r n of stock e x c h a n g e s ( l o a d i n g s over 0.35 in b o l d text) Country
Factor
1
Communality
2
3
4
0,747 0.733 0.692 0.672 0.646 0.612 0.593 0.577 0.576 0.572 0.445 0.436 0.196
0.162 0.241 0.101 0.263 0.021 0.050 0.202 - 0.010 0.215 0.283 0.281 0.179 0.826
0.068 - 0.064 - 0.044 0.097 0.102 0.002 0,072 0.263 0.046 0.152 0.128 0.320 0.018
- 0.290 0.137 0.119 - 0.156 0.385 0.342 0.146 - 0.243 0.210 0.022 - 0.436 - 0.007 - 0.145
0.180 0.217 0.279 0.059 0,081 - 0,197 0,441 0,487 0.142 0.346 0.039
0.816 0.668 0.633 0.554 0 . l 34 0.097 0.094 0.180 - 0.075 0.271 0.043
- 0.022 0.172 0.143 0.139 0.768 0.722 0.583 0.537 0.455 - 0.089 - 0.122
- 0.094 -0.191 0.161 0.309 - 0.177 - 0.129 0.029 - 0.354 0,390 0.499 0.354
Variance explained
5.367
3.096
2.289
1.609
R a t e of determination
0.224
0.129
0.095
0.067
West Germany Spain Belgium Switzerland Austria Denmark Italy France Japan Sweden Norway Ireland Singapore Malaysia Hong Kong Australia New Zealand Canada USA United Kingdom Netherlands South Africa Finland Mexico
0.673 0.618 0.505 0.554 0,576 0.493 0.419 0.461 0.424 0.431 0.483 0.325 0.741 O.708 0.559 O.528 0.425 0.646 0.586 0.544 0,684 0.385 0.450 0.143
Cumulative 0.515
(2)
292
M.J. Malkamiiki et al. / On the riskiness of the worM's stock markets
Eigenvalue
Factor Figure 1. Results of the scree-test.
b,j = the sensitivity of stock market i to the j-th common factor; /~, = the value of the j-th common factor at time t; E i t = a random-error term. The varimax-rotated factor patterns from the principal component factor analysis based on the covariance matrix of the stock market returns are reported in Table 3. (The four-factor solution is selected based on the results of the scree-test presented in Figure 1.) The first thing to notice in Table 3 is that most of the European stock exchanges are loaded to the first empirical factor. This indicates a strong positive empirical relationship between stock returns in these European countries. Japan is also loaded to this European factor. The second factor in Table 3 clearly represents the Oceanic factor consisting of Singapore, Malaysia, Hong Kong, Australia and New Zealand. Also Japan has its second highest loading on this factor.
The third factor can be seen to represent the North American stock exchanges, since both the USA and Canada have their highest loadings on this factor. Furthermore, these two stock exchanges do not have any high loadings on the other empirical factors. Regarding the European exchanges, the United Kingdom and the Netherlands are situated on this third factor. However, it should be noticed that they also have high loadings on the first, European factor. The fourth factor consists of the highest loadings of Finland and Mexico, both of which are relatively thin stock markets, the number of stocks in their indices also being low (Finland 26, Mexico 14), which might well be the underlying reason for the index behaviour of these countries. However, it should be noted that Finland also has a strong loading on the European factor. Austria, Norway and South Africa also have strong loadings on the fourth factor. All of these five countries have relatively thin stock markets and are not commonly included when international portfolios are diversified. The main interpretation of the factors thus seems to be the geographical locations of stock exchanges. There exists a wide range of potential reasons why stock markets located in the same geographical area typically have high loadings on the same factor. First, North America, Europe and Asia can be seen to represent the main economic areas of the world. Within these areas constraints and regulations imposed by national governments, technological specialisation, and cultural and sociological factors etc. are relatively similar. Therefore, it is expected that stock prices behave homogeneously within these areas (see e.g. Solnik, 1988, pp. 38-43). Secondly, the economic areas presented above are also dominated by different currencies. The US dollar is obviously the most commonly used currency in international trading and in portfolio investments. As is widely known, the holdings of dollar dominated investments or positions have been subject to relatively high risks during our research period. As the uncertainty on the US dollar increases, more investments are likely to be transfered to yen and D-mark based securities. These currencies have been extremely strong whereas the rate of sterling has been more uncertain during the research period. This might partly explain why the International Stock Exchange of
M.J. Malkamiiki et al. / On the riskiness of the world's stock markets
between the NYSE and the International Stock Exchange in London is only four hours. Opening price quotations on the New York Stock Exchange may thus have some effect on trading in the U K if its markets are efficient, i.e. new published information is reflected in stock prices without a time lag. Where this is the case, a stock market is said to be efficient in the semi-strong sense. Several empirical studies have indicated that the UK markets exhibit this semi-strong form of efficiency (see e.g Hawawini and Michel, 1984). This might well be a potential explanation for the empirical finding that the UK stock market has its highest loading on the US factor. Other European stock exchanges do not have the same opportunity to react so rapidly to the US information due to their five hour time difference and their call auction trading mechanisms. The third explanation is thus not only the time zones but also the degree of sophistication of trading mechanisms on the stock exchanges, i.e. the structural (institutional) ef-
Table 4 Transformation
matrix
between
empirical
terns of stock exchanges from subperiods Factor
pat-
1 and 2
Subperiod 2
1 Subperiod
classification
2
3
4
1
0.718
0.150
2
0.016
0.964
0.002
3
0.682
0.164
0,314
4
0.135
- 0.146
0,834
1
-0.454
293
0,505 0,266 -0,640 0,515
London has its highest loading on the same factor as the USA. Following this explanation, it is important to recognize that both Japan and Germany have very low loadings on the North American factor. The third explanation for the geographical factors may be the different time zones i.e. different stock exchange hours. Before trading on the New York Stock Exchange starts, the trading in Tokyo has already closed. However, the time difference
Table 5 Residual matrix and abnormal Country
transformation
Factor
1 Australia
for subperiod 2 Abnormal
2
3
transformation
4
0.093
- 0.297
0.220
- 0.143
Austria
- 0.273
0,242
- 0.030
0.241
0.192
Belgium
- 0.120
- 0.097
- 0.243
0.076
0.089 0.026
Canada Denmark Finland France West Germany Hong Kong
0.166
0.046
- 0.079
0.007
- 0.132
- 0.470
0.174
- 0.373
0.332
0.500
0.093
0.085
- 0.177
0.029
0.048
0.140
- 0.280
0.231
0.052
0,031
- 0.364 0.049
- 0.008 -0.098
-0.127
0.096
0.166
- 0.138
- 0.060
0.059
Ireland
- 0.226
0.189
0.199
- 0.120
0.141
ltaly
- 0.243
0.159
0.093
0.052
0.095
0.048
0.247
0.167
0.152
0.114 0.125
Japan Malaysia
0.121
- 0.082
0.075
0.313
Mexico
- 0.093
0.308
0.098
0.802
Netherlands
-0.106
New Zealand
-0.064
0.216
0.757
-0.214
0.108
- 0.299
0.099
-0.272
0.196
- 0.035
0.002
- 0.092
Norway
0.090
0.188
0.280
Singapore
0.109
- 0.067
0.070
0.151
0.044
South Africa
0.108
- 0.035
0.151
- 0.508
0.294
Spain
- 0.047
0.160
- 0.060
- 0.043
0.033
Sweden
- 0.297
0.220
- 0.143
0.282
0.237
Switzerland
0.242
- 0.030
0.241
- 0.320
0.220
United Kingdom
- 0.097
- 0.243
0.076
- 0.044
0.076
USA
- 0.079
0.007
- 0.132
0.471
0.245
0.818
0.639
0.691
1.977
4.126
Abnormal transformation
M.J. Malkamiiki et al. / On the riskiness of the world's stock markets
294
ficiency of the stock markets. The low trading volume on other European stock markets may also explain the result above. An interesting question arising from our study is that of the stability of the relationships between different stock exchanges. To test the stability of the obtained results we divided the research period again into two subperiods. The factor patterns from these subperiods are presented in Appendices A and B. In order to study the similarity of the factor patterns produced, we applied transformation analysis. Transformation analysis was initially presented by Ahmavaara (1954) and has been mainly applied in Finnish political and sociological studies. In finance literature, it was first introduced by Yli-Olli (1983) for determining the na-
ture and medium-term stability of the classification patterns of financial ratios. Transformation analysis in testing similarities between created factor patterns is preferred to traditional correlation and congruency analysis because of the fact that by this method we can obtain a regression type model for the shifting of variables from one factor to another (for a deeper presentation of the method see Yli-Olli and Virtanen, 1989). The results presented in Table 4 indicate that the factors representing European, Oceanic, and North American stock exchanges have been relatively similar in both subperiods. The North American factor has changed its position from the fourth factor to the third factor in the second subperiod. This, however, does not mean any in-
Appendix A Table A Classification pattern of stock exchanges. First subperiod Country
C ommuna l i t y
Factor 1
2
3
0.683 0.657 0.628 0.618 0.599 0.588 0.449 0.382 0.143 0.088 0.042 0.273 0.184 0.384 0.026 0.417 0.408 0.022 0.007 0.213 0.106 0.257 0.224 0.118
- 0.006 0.163 0.293 0.289 0.222 0.099 0.279 -0.107 0.813 0.813 0.723 0.612 0.505 0.429 0.308 0.144 0.226 0.177 0.020 0.171 0.137 0.041 -0.174 0.267
0.026 0.146 - 0.048 0.408 - 0.107 0.356 0.243 -0.362 0.167 0.246 0.306 0.187 - 0.096 0.238 0.690 0.686 0.686 0.620 0.574 - 0.161 0.273 0.219 0.105 0.319
Variance explained
3.539
3.353
3.192
2.308
Rate of determination
0.147
0.140
0.133
0.096
Austria Japan Finland Spain Denmark Belgium Italy Mexico Malaysia Singapore Hong Kong Australia New Zealand Sweden Norway West Germany Switzerland Netherlands France USA Canada United Kingdom South Africa Ireland
-
4
-
0.159 0.109 0.167 0.070 0.075 0.058 0.108 0.084 0.067 0.059 0.114 0.034 0.026 0.192 0.132 0.072 0.154 0.538 0.171 0.763 0.733 0.658 0.348 0.335
0.492 0.491 0.510 0.632 0.425 0.485 0.350 0.296 0.715 0.732 0.632 0.485 0.299 0.425 0.588 0.670 0.711 0.706 0.359 0.683 0.642 0.548 0.213 0.299
Cumulative 0.516
M.J. Malkamiiki et al. / On the riskiness of the world's stock markets
295
Appendix B Table B Classification pattern of stock exchanges. Second subperiod Country
1 Denmark Austria Belgium France Sweden Spain
Communality
Factor 2
3
4
0.820
- 0.056
0.005
0.060
0.802
0.082
- 0.092
0.100
0.679 0.668
0.779
0.025
- 0.039
0.135
0.627
0.775
0.098
0.186
0.004
0.644
0.768
0.147
0.203
- 0.028
0.654
0.764
0.103
- 0.151
0.134
0.635
Italy
0.750
0.067
- 0.129
0.150
0.607
West Germany Netherlands Ireland Switzerland Japan United Kingdom Norway Singapore Malaysia
0.731
0.276
0.213
0.205
0.698
0.589
0.262
0.437
0.131
0.624
0.578
0.055
0.128
0.219
0.401
0.543 0.541
0.277 0.314
- 0.082 0.005
0.227 0.186
0.430 0.426
0.520
0.184
0.424
0.383
0.632
0.421
0.199
0.035
- 0.006
0.218
0.143 0.118
0.869 0.863
0.018 - 0.029
- 0.018 0.097
0.777 0.769 0.457
Hong Kong USA
Canada South Africa N ew Zealand Australia Finland Mexico Variance explained Rate of determination
0.170
0.558
0.312
0.136
- 0.078
0.052
0.815
- 0.036
0.674
0.165 0.168
0.076 - 0.200
0.778 0.070
0.097 0.687
0.647 0.545
0.114 0.245 0.308 0.130
0.438 0.521 0.119 0.076
0.000 0.033 - 0.262 - 0.315
0.601 0.547 0.311 - 0.363
0.566 0.631 0.274 0.254
6.821
2.797
2.108
1.812
0.284
0.117
0.088
0.076
Cumulative
stability, and the interpretation of this factor is relatively clear. The fourth factor seems to be more unstable in nature. This is not especially surprising since this factor consists of thin stock exchanges. In order to obtain further information concerning the similarities of classification patterns of different stock exchanges over time, we determined the residual matrix to define the abnormal transformation between factor patterns of successive subperiods. This residual matrix is presented in Table 5. An interesting observation is the high abnormal transformation of the Mexico Stock Exchange. The reason for this exceptional behaviour of the Mexico Stock Exchange has been discussed earlier.
0.565
The other stock markets seem to have more similar factor loadings in both subperiods.
4. Summary The main purpose of this paper was to study the riskiness of the world's stock markets. This was carried out by applying the concepts of the two main asset pricing models: the Capital Asset Pricing Model (CAPM) and the Arbitrage Pricing Model (APM). We found certain obvious risk categories to exist among the world's stock markets. Most of the European, Oceanic and North American stock
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exchanges created their own regionally specific factors. Also thin stock markets, such as Finland and Mexico, seemed to exhibit a price behaviour of their own. Several fundamental and technical features were assumed to be beyond the observed risk categories. Firstly, economic trade and currency areas seemed to affect the riskiness of different stock markets. North American, European and Oceanic stock exchanges quite clearly created their own separate factors. Secondly, the state of institutional development of a stock market seemed also to affect its riskiness. Thin stock markets, such as Finland, Mexico, New Zealand and South Africa, seemed to have a price behaviour of their own. Thirdly, the combined effect of the different time zones and efficiency was analysed, especially in the case of the U K stock markets vs. other European markets. The main implication of our study for decision-makers, i.e. investors, is that they can reduce the unsystematic risk of their portfolios by diversifying in stocks listed in different geographical areas. It should be emphasized, however, that the relatively short time period covered, obviously makes any generalised interpretation of the results very difficult.
Acknowledgements The authors wish to thank Dr. Peter Nyberg from The Bank of Finland and an anonymous referee for their useful comments. The financial support by Suomen Arvopaperi markkinoiden Edist~imiss~i~itio is also gratefully acknowledged.
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