This paper investigates the nature of the volatility process among security prices for US, Europe and the Pacific Rim capital markets using a new data set that removes the problem of disparate index composition associated with aggregate stock market index series. We use the common ARCH-feature testing methodology, recently developed by Engle and Kozicki (Journal of Business Economics 11, pp. 369-380, 1993), to examine the issue of a common volatility process among asset prices of nine industry groups from three economic regions of the world economy. It is found that industry-return series exhibit intra-industry common time-varying volatility process. The evidence is consistent with the view that world capital markets are related through their second moments implying that a world common time-varying variance specification seems to be appropriate in modeling asset prices. While our empirical evidence suggests that investors can form constant-variance portfolios by investing within an industry across regions, they will be better off if they invest across regions and industries rather than diversify within an industry across different geographical regions. That is, the industrial mix of global investment portfolios accounts for a substantial proportion of the international diversification benefits. Finally, our results appear to be consistent with Roll (Journal of Finance, 47, pp. 3-41, 1992) view that the industrial structure of national stock exchange indices is important for explaining cross-sectional return volatility differences. (C) 1997 Elsevier Science Ltd.