A note on the time–series relationship between market industry concentration and market volatility

Int. Fin. Markets, Inst. and Money 14 (2004) 105–115

A note on the time–series relationship between market industry concentration and market volatility Xuejing Xing∗ Department of Economics and Finance, School of Management and Information Systems, University of Missouri-Rolla, 101 Harris Hall, 1870 Miner Circle, Rolla, MO 65409-1250, USA Received 26 October 2002; accepted 16 April 2003

Abstract Using cross-sectional regression analysis, previous studies provide conflicting results regarding the relationship between market industry concentration and market volatility. This paper investigates this relationship in the time–series. Using data from twenty one developed markets and the world market, we find that this relationship is significant and positive in about 61% of the markets: the more concentrated the market, the more volatile the market. We also find that, in 70% of the markets, there exists a causal relationship between market industry concentration and market volatility and the direction of causality runs from the former to the latter. Our results suggest that market industrial structure is a significant factor in explaining market volatility. © 2003 Elsevier B.V. All rights reserved. JEL classification: E44; G15 Keywords: Market volatility; Industry concentration; EGARCH

1. Introduction Academics and professionals have long attempted to identify the factors that drive market volatility. As part of the efforts, researchers have asked whether market industrial structure is a significant factor in explaining the variance of stock market returns, as initiated by Lessard (1974). According to modern portfolio theory, there should exist a significant relationship between market industrial structure and market volatility. On the one hand, it is well ∗

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known that some industries are more volatile than others. A market tilting toward highly volatile industries should be more volatile. On the other hand, market industry concentration measuring the extent to which listed firms in a market disperse across industries should also play a role. The more concentrated within industries, the less diversified (more risky) the market portfolio is. Therefore, the market with higher industry concentration should be more volatile. Nevertheless, recent empirical studies find conflicting results. Some suggest that market industrial structure is an important factor in explaining market volatility. For example, Roll (1992) documents that industrial structure can explain approximately 40% of the volatility in market returns. Archanapalli et al. (1997) provide evidence consistent with the view that the industrial structure of national stock exchange indices is important for explaining cross-sectional return volatility differences. Cavaglia et al. (2000) report that the importance of industry factors in explaining portfolio risk has grown in recent years. Brooks and Catao (2000) demonstrate that industry sectors can explain 28% of portfolio return variation. Carrieri et al. (2002) show that global industry risk can be priced for certain industries, which implies a role of industrial structure in shaping market volatility. However, some other studies tell a different story. For instance, Ferson and Harvey (1993), Heston and Rouwenhorst (1994), and Griffin and Karolyi (1998) offer some evidence suggesting that market industrial structure can explain little of cross-country return variations. Why is there disagreement in empirical studies on a theoretically appealing story? One possibility is that this disagreement is due to the empirical approach applied in previous studies. Previous studies typically employ a cross-sectional regression framework.1 This cross-sectional regression approach may not be efficient in the sense that the estimated relation between market industrial structure and market volatility may not be precise and stable, because the sample size is small2 and because there are many market characteristics other than industrial structure that are strikingly different across markets but are hardly controlled for. If this is the case, it should not be surprising that there is disagreement in these empirical studies even if there actually exists a significant relationship between market industrial structure and market volatility. In this paper, we reexamine the relationship between market industrial structure and market volatility by taking a different approach. Instead of conducting cross-sectional analysis, we focus on the time–series relationship between the two variables. Time–series analysis has several advantages over the cross-sectional approach. First, as noted by Faff et al. (2002), time–series analysis can deliver a level of statistical power that may not be possible in a cross-sectional setting. For example, our time–series typically have as many as 1,400 observations, which are far more than those in any of previous cross-sectional studies. With more observations, our study has more power to reject the hypothesis that there is no relationship between market industrial structure and market volatility. Second, time–series analysis allows us to examine the relationship between market industrial structure and market volatility while addressing the time-varying nature of market volatility. In contrast, cross-sectional 1

For a detailed description of the typical cross-sectional framework, see Heston and Rouwenhorst (1994), and Griffin and Karolyi (1998). 2 Roll (1992), Heston and Rouwenhorst (1994), and Griffin and Karolyi (1998) use data from 24, 12, and 25 countries, respectively.

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studies can hardly have this luxury. Finally, time–series analysis enables us to circumvent the confounding factor problems suffered by cross-sectional studies. Thus, time–series analysis will provide us with new perspective on the relationship between market industrial structure and market volatility.3 Our sample includes 21 developed country markets and the world market, covering the period from January 1973 through May 2000. We use a Herfindahl industry concentration variable as a proxy for market industrial structure. This variable measures the extent to which the listed stocks in a market disperse across industries. Our time–series techniques are exponential generalized autoregressive conditional heteroskedasticity (EGARCH) models (Nelson, 1991) and vector autoregressive (VAR) models. We find that market industry concentration is significantly and positively related to market volatility in about 61% of the markets. We also find that, in 70% of the markets, there exists a causal relationship between market industry concentration and market volatility and the direction of causality runs from the former to the latter. Our results thus suggest that market industrial structure is a significant factor in explaining market volatility, which is consistent with Roll (1992). The remainder of the paper is separated into four sections. Section 2 describes data. Section 3 presents the methodology. Section 4 reports empirical results. Section 5 provides a summary and a conclusion.

2. Data 2.1. Sample description Weekly equity price indexes for 21 developed country markets and the world market are extracted from Datastream. These indexes are computed and maintained by Datastream itself. Accounting for over 90% of the total market capitalization in each country, Datastream country indexes are probably better than any other popular world indexes in terms of coverage,4 and thus could be more representative of the market behavior. We study only developed markets because Datastream country indexes cover a much longer period of time for developed markets than for emerging markets, making it possible to perform more precise time–series estimations. Furthermore, we use weekly data because they are supposed to be less noisy than daily data and more informative than monthly data. By using weekly data, we also expect to eliminate the problems of nonsynchronous trading and short-term correlation due to noise. Return indexes are approximated by taking the logarithmic difference of the price indexes. The majority of the market indexes start from 1973, with only four exceptions (Sweden 1980, Spain 1986, Finland 1988, and New Zealand 1988). The highest mean weekly dollar-denominated return (hereafter dollar return) (local-currency-denominated return, 3

Denis and Kadlec (1994) also argue that time–series analysis can provide new insights into issues that have been examined in a cross-sectional way. 4 By comparison, other popular country indexes usually have a lower level of tracking. For example, Dow Jones world indexes capture the target of 80% market capitalization for each market, S&P/IFC Global indexes cover about 70–75% of total market capitalization, and MSCI world indexes account for only 60% of total market capitalization.

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hereafter local return) is in Finland, at 0.33% (0.41%), and the lowest in New Zealand, at 0.03% (0.08%). For dollar (local) returns, 16 (18) of the 22 markets (including the world market) have significant negative skewness. Almost all the return series have fat tails, as indicated by the significant kurtosis. The Ljung-Box Q (16) statistics indicate significant serial correlations in 18 out of the 22 return series.5 2.2. Market industry concentration Following Roll (1992), we use a Herfindahl industry concentration variable to proxy for market industrial structure in each market.6 Specifically, the market industry concentration in country i is computed at each week as  n 
MVINDijt 2 INDit = (1) CAPit j=1

where INDit is the market industry concentration for country i at week t, MVINDijt the market value of industry j (j = 1, 2, . . . , n) in country i at week t, and CAPit country i’s total market capitalization at week t. Thus, the market industry concentration measures the extent to which the listed stocks in a market disperse across industries. Market industry data are obtained from Datastream. Datastream groups all listed stocks in a market into 10 major industry sectors (therefore, n = 10 for each market in the market industry concentration formula). These industry sectors are: resources; financial industries; basic industries; general industries; cyclical consumption goods; non-cyclical consumption goods; cyclical services; non-cyclical services; utilities; and information technology. It should be clear that market industry concentration, IND, ranges from 0.1 (all listed firms are equally distributed in 10 industry sectors) to 1 (all listed firms are concentrated on any of the 10 industry sectors). The bigger the industry concentration measure, the more concentrated the listed firms are. Columns 2–5 of Table 1 report several descriptive statistics for the market industry concentration measures in the 22 markets. Generally speaking, there are significant time–series variations in the industry concentration variable. For example, in Norway, market industry concentration ranges from 0.173 to 0.756 and in Austria from 0.153 to 0.539. In addition, industry concentration differs substantially across markets. Among the 22 markets, the world and the US have the lowest market industry concentration, 0.118. Ireland has the highest industry concentration, 0.384. Table 1 (columns 6–15) also presents the cross-sector industry distribution pattern in each market. The industry distribution across the 10 industry sectors in each market, measured by the ratio of the market value of all listed firms in a particular industry sector to the market value of all listed firms in a market, dramatically varies by country. For example, Norway concentrates on resources, with over 48% of its total market capitalization in resources. Italy is heavy in financial companies, with 53.4% market capitalization in financial firms. By comparison, US exhibits the least concentration among the 21 countries, with a maximum industry size of 17.8%, which is for non-cyclical consumer goods. 5 6

A detailed description of weekly returns in these markets is available from the author upon request. For a general discussion of the Herfindahl industry concentration measure, see Stigler (1968).

Table 1 Market industry concentration and industry distribution in 21 countries and the world market Industry concentration (mean)

Industry concentration (std)

Industry concentration (min)

Industry concentration (max)

Resources Financials Basic industries

General industries

Cyclical consumption goods

Non-consumption goods

Cyclical service

Non-cyclical service

Utilities Information technology

Australia Austria Belgium Canada Denmark Finland France Germany Hong Kong Ireland Italy Japan Netherlands New Zealand Norway Singapore Spain Sweden Switzerland UK US

0.277 0.299 0.208 0.163 0.248 0.231 0.144 0.200 0.326 0.384 0.350 0.146 0.238 0.233 0.309 0.333 0.227 0.191 0.354 0.158 0.118

0.066 0.082 0.028 0.024 0.034 0.061 0.021 0.021 0.035 0.100 0.078 0.012 0.038 0.041 0.132 0.056 0.029 0.027 0.063 0.013 0.011

0.204 0.153 0.172 0.132 0.192 0.159 0.117 0.159 0.231 0.229 0.203 0.122 0.178 0.180 0.173 0.233 0.191 0.151 0.266 0.137 0.106

0.470 0.539 0.309 0.247 0.373 0.513 0.218 0.254 0.380 0.568 0.590 0.194 0.378 0.344 0.756 0.455 0.325 0.275 0.558 0.184 0.160

0.408 0.019 0.236 0.213 0.000 0.002 0.160 0.000 0.001 0.011 0.023 0.017 0.361 0.028 0.480 0.001 0.079 0.017 0.000 0.153 0.113

0.203 0.422 0.267 0.178 0.215 0.145 0.103 0.282 0.469 0.387 0.534 0.240 0.241 0.230 0.104 0.476 0.361 0.464 0.232 0.204 0.098

0.131 0.202 0.137 0.173 0.037 0.228 0.119 0.177 0.008 0.270 0.078 0.143 0.048 0.212 0.083 0.019 0.085 0.107 0.045 0.107 0.071

0.033 0.131 0.058 0.072 0.101 0.111 0.174 0.246 0.179 0.021 0.051 0.125 0.087 0.011 0.087 0.121 0.030 0.132 0.102 0.080 0.093

0.005 0.004 0.001 0.004 0.036 0.001 0.117 0.108 0.004 0.035 0.135 0.108 0.005 0.021 0.003 0.000 0.002 0.106 0.009 0.010 0.051

0.082 0.136 0.023 0.069 0.242 0.123 0.145 0.045 0.004 0.192 0.005 0.072 0.144 0.131 0.061 0.110 0.035 0.012 0.522 0.172 0.178

0.118 0.025 0.047 0.082 0.330 0.067 0.076 0.035 0.117 0.072 0.029 0.134 0.082 0.101 0.125 0.201 0.037 0.022 0.045 0.171 0.120

0.016 0.002 0.032 0.018 0.038 0.050 0.068 0.054 0.124 0.010 0.121 0.040 0.025 0.231 0.005 0.068 0.146 0.004 0.005 0.076 0.088

0.004 0.042 0.199 0.056 0.000 0.002 0.003 0.044 0.091 0.000 0.019 0.059 0.000 0.034 0.031 0.000 0.223 0.011 0.037 0.024 0.074

0.000 0.018 0.001 0.135 0.001 0.272 0.036 0.009 0.004 0.001 0.005 0.062 0.007 0.000 0.021 0.005 0.002 0.126 0.003 0.004 0.113

Mean World

0.245 0.118

0.046 0.009

0.176 0.105

0.385 0.135

0.111 0.100

0.279 0.179

0.118 0.102

0.097 0.106

0.036 0.061

0.119 0.131

0.097 0.116

0.058 0.069

0.045 0.061

0.039 0.074

This table presents descriptive statistics for industry concentration (columns 2–5) and the average market share of each industry sector (columns 6–15) in each market over time. At each week within our sample period, we compute the Herfindahl industry concentration measure for each market as follows:

INDi =

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Country

10  MVIND 2
ij , CAPi j=1

where INDi is the industry concentration measure for country i, MVINDij the market value of industry j in country i, and CAPi is country i’s total market capitalization. The market share of each industry sector is measured by the ratio of the market value of all listed firms in a particular industry sector to the market value of all listed firms in a market. We use Datastream market industry data. Datastream groups all stocks listed in a market into 10 major industry sectors. The time period covered for each market is 1973–2000 except Sweden (1980–2000), Spain (1986–2000), Finland (1988–2000), and New Zealand (1988–2000).

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3. Methodology GARCH models (Bollerslev, 1986) have been very successful in modeling conditional volatility.7 However, conventional GARCH models are unable to capture the asymmetric effect of negative or positive returns on volatility. This effect, discovered by Black (1976), occurs when an unexpected drop in price increases volatility more than an unexpected increase in price of similar magnitude. The existence of this asymmetric effect implies that a symmetric specification on the conditional variance function as in a conventional GARCH model is theoretically inappropriate. To address this issue, Nelson (1991) introduces a modified GARCH model, the EGARCH model. In this paper, we take advantage of this EGARCH model to examine the time–series relationship between market industry concentration and market volatility. Specifically, we estimate the following modified EGARCH model with market industry concentration (IND) in both its mean and variance equations: Rit = αi + βi INDit + εit √ εit = hit eit eit ∼ N(0, 1) εi(t−1) log(hit ) = ωi + α1i log(hi(t−1) ) + α2i  + α3i hi(t−1)



  |εi(t−1) | 2  − + α4i INDit π hi(t−1)

(2)

where Rit is the stock market return for country i at week t, hit the conditional variance of market returns in country i at week t, and IND √ it the market industry concentration for country i at week t. Since the coefficient of εt−1 / ht−1 is typically negative,8 the EGARCH model is asymmetric: all else being equal, positive return shocks generate less volatility than negative return shocks.9 The coefficient α4 in the variance equation can be interpreted as a measure of the incremental information which market industry concentration contributes to changes in the conditional variance of return over time. Therefore, the hypothesis that market industry concentration is significantly related to market volatility can be tested by examining the statistical significance of the estimate of α4 . It is also important to know whether there is a causal relationship between market industry concentration and market volatility. If market industry concentration is a significant factor affecting market volatility, we would expect that market industry concentration cause market volatility. Thus, an investigation on the causality will provide further evidence on the true relationship between market industry concentration and market volatility. To examine the causal relationship, we apply the following bivariate, 24th order vector autoregressive (VAR) model:10 7

For a survey of the applications of ARCH models in finance, see Bollerslev et al. (1992). Cheung and Ng (1992) fit EGARCH models to 251 stock return series and find α2 < 0 for over 95% of the series. 9 Indeed, Engle and Ng (1993) find evidence suggesting that the EGARCH model is among the best of all GARCH-family models in modeling conditional volatility. 10 Darrat et al. (2003), Darbar and Deb (1999), Grier and Perry (1998), and others also apply a similar Granger causality test to GARCH-type volatility measures. Battalio et al. (1997) test the granger causality between a proxy for professional Small Order Execution System (SOES) trading and a measure of stock price volatility. 8

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  24  VOLit = ωi + 24 j=1 αij VOLi(t−j) + j=1 βij INDi(t−j) + εit    INDit = ω + 24 α VOLi(t−j) + 24 β INDi(t−j) + ε j=1 ij j=1 ij i it

111

(3)

where VOLit is the EGARCH market volatility for country i at week t and INDit the market industry concentration for country i at week t. Similarly, VOLi(t−j) and INDi(t−j) are the market volatility and industry concentration for country i at week (t − j), respectively. ωi , ωi , αij , αij , βij , and βij are simply constants. After estimating the VAR model, F-tests can be used to assess the predictive power of lagged industry concentration on market volatility and vice versa. In a market, if the F-test for the predictive power of lagged values of INDi (VOLi ) on VOLi (INDi ) is significant, then we can say that INDi (VOLi ) “Granger-causes” VOLi (INDi ).

4. Empirical results 4.1. EGARCH estimation results The estimation of the EGARCH model is performed by the method of maximum likelihood using the BHHH (Berndt et al. (1974)) numerical optimization algorithm. For each market, the sample period is from the first week of the Datastream country index starting year to 17 May 2000. To check the performance of our model, we conduct some specification tests on normalized residuals (i.e., residuals, εˆ t , divided by the square root of the conditional variance). We find that in 14 (or 63.6%) of 22 cases, the Ljung-Box Q statistics at 16 lags indicate no evidence of autocorrelation in the squared normalized residuals, thereby suggesting that our EGARCH model is reasonably well specified to capture the ARCH effects in most cases. Table 2 reports the estimated results with respect to the coefficients of industry concentration (IND) in the variance equation, both for dollar return series and for local return series.11 We find that, in most countries, market industry concentration is a significant factor in explaining market volatility over time. For the dollar return series, 13, or 59.1%, of the 22 markets (including the world) have a coefficient estimate of IND that is significant and positive. For the local return series, there are 14, or 63.6%, of the 22 markets with a significant, positive coefficient estimate of industry concentration. These results suggest that, in these markets, the higher the market industry concentration, the more volatile the market is. The only exception is Spain. We find a significant and negative coefficient estimate of industry concentration in Spain. This finding implies that, in Spain, market industry concentration is negatively related to market volatility. However, this is not surprising because Spain, in contrast to all other countries, has a very heavy weight of utilities in its industrial structure, which are a very stable industry. On average, Spain’s utility firms account for 22.3% of its total market capitalization; by comparison, the cross-sectional mean of the market share of utility firms in 21 countries is only 4.5% (see Table 1). It is highly likely that, in Spain, as the overall market industry concentration falls over time, 11

Detailed results regarding the entire model are available from the authors upon request.

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Table 2 The time–series relationship between market industry concentration and market volatility: EGARCH estimation results Country

Dollar returns α4

Australia Austria Belgium Canada Denmark Finland France Germany Hong Kong Ireland Italy Japan Netherlands New Zealand Norway Singapore Spain Sweden Switzerland UK US Worlda

0.355∗ 0.334∗∗∗ 0.135 1.367∗∗∗ 14.669∗∗∗ 1.806∗∗∗ 1.837∗∗ 0.848∗∗ 0.561∗∗∗ 0.565∗∗∗ 0.479∗∗∗ 0.730 0.731∗∗ 0.989∗ 0.077 −0.088 −1.181∗∗∗ 0.374 −0.162 0.204 0.048 1.495∗∗

Local returns α4

t-statistic

P-value

d.f.

1.67 3.99 0.45 2.92 16.5 2.62 2.53 2.07 2.69 3.57 2.83 1.23 2.26 1.81 1.25 −0.84 −2.73 0.61 −1.1 0.48 0.07 2.05

0.0952 0.0001 0.6497 0.0035 0.0000 0.0087 0.0115 0.0388 0.0071 0.0004 0.0047 0.2175 0.0240 0.0697 0.2122 0.4012 0.0064 0.5407 0.2725 0.6320 0.9425 0.0399

1401 1401 1401 1401 1401 606 1401 1401 1401 1401 1401 1401 1401 618 1036 1401 662 936 1401 1401 1401 1401

1.043∗∗∗ 0.190∗∗∗ 0.376 1.545∗∗∗ 14.683∗∗∗ 2.136∗∗ 1.033∗∗ 0.598∗∗ 0.412∗∗ 0.257∗∗ 0.244∗∗ 1.969∗∗∗ −0.010 0.912∗∗ 0.038 −0.101 −1.007∗∗ 0.769 0.186 1.629∗∗∗ 0.049 1.495∗∗

t-statistic

P-value

d.f.

3.15 3.53 0.92 3.19 19.62 2.28 2.16 1.97 2.04 2.52 2.18 3.34 −0.06 2.03 0.65 −1.00 −2.27 1.48 1.39 2.75 0.07 2.05

0.0016 0.0004 0.3600 0.0014 0.0000 0.0224 0.0306 0.0486 0.0414 0.0117 0.0293 0.0003 0.9560 0.0425 0.5176 0.3168 0.0233 0.1396 0.1649 0.0059 0.9420 0.0400

1401 1401 1401 1401 1401 606 1401 1401 1401 1401 1401 1401 1401 618 1036 1401 662 936 1401 1401 1401 1401

The time–series relationship between market industry concentration and market volatility is investigated by estimating the following modified exponential generalized autoregressive conditional heteroscedasticity (EGARCH) model: Rit =√ αi + βi INDit + εit εit = hit eit eit ∼ N(0, 1) εi(t−1) log(hit ) = ωi + αi1 log(hi(t−1) ) + αi2  + α3i hi(t−1)



|εi(t−1) |  − hi(t−1)

  2 + α4i INDit π

where Rit is the weekly market return for country i at week t, INDit the market industry concentration for country i at week t, and hit the conditional variance of market returns for country i at week t. The estimation is performed by the method of maximum likelihood using the BHHH (Berndt et al. (1974)) numerical optimization algorithm. The sample period is from the first week of the starting year (1973 except Sweden 1980, Spain 1986, Finland 1988, and New Zealand 1988) of the Datastream country index for a particular country through 17 May 2000. Reported in this table are the estimated coefficients of market industry concentration in the variance equation, α4 , t-statistics for the coefficients, P-values of the t-statistics, and the degree of freedom (d.f.) of the estimated model, both for dollar return indexes and for local return indexes. (Detailed results for the entire model are available upon request from the author.) a World: Datastream world index. ∗ Indicates significance at the 10% level. ∗∗ Indicates significance at the 5% level. ∗∗∗ Indicates significance at the 1% level.

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Table 3 F-tests from vector autoregressive (VAR) models for market industry concentration and market volatility Country

Dollar returns

Local returns

VOLa

Australia Austria Belgium Canada Denmark Finland France Germany Hong Kong Ireland Italy Japan Netherlands New Zealand Norway Singapore Spain Sweden Switzerland UK US Worldd

INDb

d.f.c

F-statistics

P-value

F-statistics

P-value

1.69∗∗ 1.80∗∗ 1.47∗ 1.78∗∗ 13.9∗∗∗ 3.65∗∗∗ 2.51∗∗∗ 1.24 1.62∗∗ 1.67∗∗ 2.53∗∗∗ 1.56∗∗ 1.32 1.61∗∗ 0.87 0.44 1.58∗∗ 1.53∗ 1.01 1.01 2.70∗∗∗ 1.79∗∗

0.0203 0.0103 0.0666 0.0119 0.0000 0.0000 0.0001 0.1925 0.0291 0.0228 0.0001 0.0413 0.1370 0.0334 0.6492 0.9913 0.0391 0.0502 0.4482 0.4547 0.0000 0.0111

1.08 1.91∗ 0.77 0.81 1.64∗∗ 0.75 1.21 1.35 4.35∗ 1.65∗∗ 1.12 1.58∗∗ 2.55∗ 1.27 0.92 0.77 2.38∗ 0.59 1.32 0.75 1.02 1.16

0.3647 0.0051 0.7836 0.7259 0.0271 0.8012 0.2184 0.1193 0.0000 0.0245 0.3166 0.0378 0.0001 0.1730 0.5696 0.7764 0.0003 0.9415 0.1357 0.7980 0.4369 0.2698

1336 1336 1336 1336 1336 541 1336 1336 1336 1336 1336 1336 1336 553 971 1336 597 866 1336 1336 1336 1336

VOLa

INDb

d.f.c

F-statistics

P-value

F-statistics

P-value

2.21∗∗∗ 1.86∗∗∗ 1.69∗∗ 2.37∗∗∗ 14.6∗∗∗ 5.39∗∗∗ 2.11∗∗∗ 1.54∗∗ 1.52∗ 1.46∗ 2.09∗∗∗ 1.84∗∗∗ 1.01 2.41∗∗∗ 0.87 0.29 1.20 1.21 0.77 1.11 2.70∗∗∗ 1.79∗∗

0.0007 0.0072 0.0202 0.0002 0.0000 0.0000 0.0014 0.0454 0.0526 0.0720 0.0016 0.0078 0.4524 0.0002 0.6494 0.9997 0.2355 0.2246 0.7739 0.3238 0.0000 0.0112

0.87 2.27∗ 0.67 1.05 2.12∗ 0.71 1.04 1.65∗∗ 4.75∗ 2.00∗ 0.88 2.07∗ 1.42∗∗∗ 1.19 0.97 0.67 2.71∗ 0.72 1.14 0.65 1.02 1.16

0.6424 0.0000 0.8809 0.3951 0.0012 0.8405 0.4109 0.0245 0.0000 0.0030 0.6262 0.0018 0.0846 0.2456 0.5084 0.8815 0.0000 0.8316 0.2866 0.9018 0.4365 0.2693

1336 1336 1336 1336 1336 541 1336 1336 1336 1336 1336 1336 1336 553 971 1336 597 866 1336 1336 1336 1336

The causal relation between market industry concentration and market volatility is investigated by estimating the following bivariate vector autoregressive (VAR) model:

 24 VOLit = ωi + 24 j=1 αij VOLi(t−j) + j=1 βij INDi(t−j)   24 24   INDit = ωi + j=1 αij VOLi(t−j) + j=1 βij INDi(t−j)

where VOLit is the EGARCH market volatility for country i at week t and INDit the market industry concentration for country i at week t. The estimation period is from the first week of the starting year (1973 except Sweden 1980, Spain 1986, Finland 1988, and New Zealand 1988) through May 17, 2000. F-statistics are used to test the joint significance of lagged VOL(IND) in explaining IND(VOL). a These columns report the results of F-tests for the joint significance of lagged IND in explaining VOL. b These columns report the results of F-tests for the joint significance of lagged VOL in explaining IND. c d.f.: degrees of freedom of the VAR model. d World: Datastream world index. ∗ Indicates statistical significance at the 10 level. ∗∗ Indicates statistical significance at the 5% level. ∗∗∗ Indicates statistical significance at the 1% level.

the market share of industries that are more volatile than utilities increases and thus market volatility rises as a result of the increasing domination of the more volatile industries in the market. Overall, our assessment of the EGARCH estimation results is that market industry concentration is significantly and positively related to market volatility: the higher the market industry concentration, the more volatile the market.

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4.2. VAR estimation results Table 3 presents the F-test results for the VAR model. In general, there are more cases in which the direction of causality runs from industry concentration to market volatility. In particular, when dollar returns are used, in 16, or 72.7%, of the 22 markets the F-tests for the predictive power of lagged values of industry concentration on market volatility are significant. In other words, in these 16 markets, market industry concentration “Granger-causes” market volatility. By contrast, in only 7, or 33.3%, of the markets the lagged values of market volatility may also be indicative of current industry concentration. When local returns are used, the story is qualitatively the same. Overall, our assessment is that, in general, there exists a causal relationship between market industry concentration and market volatility and the direction of causality runs from the former to the latter.

5. Summary and conclusion Cross-sectional studies report conflicting results on the relationship between market industrial structure and market volatility. In this paper, we examine this relationship in the time–series. We apply EGARCH models to weekly index return series for 21 developed markets and the world market from January 1973 through May 2000. We find a significant, positive relationship between market industry concentration and market volatility in about 61.3% of the markets. In addition, VAR estimation results indicate that, in 70% of the markets, there exists a causal relationship between market industry concentration and market volatility and the direction of causality runs from the former to the latter. Overall, our results suggest that market industrial structure is a significant factor in explaining market volatility, which is consistent with Roll (1992).

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