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This paper examines the common stochastic trends in daily equity returns in the United States, United Kingdom, Germany, France, and Japan. The study covers the period of the 1990s through early 2002. It provides an understanding of stochastic trends in the major equity markets, which is important when working with portfolio risk. It can prove to be beneficial to investors, and money managers. An understanding about how the different stock markets relate is imperative when designing and managing diversified portfolios. The characteristics of the stock markets are just one aspect examined in this paper, yet its major focus is the conditional volatility of stock returns. The ARCH model and a more generalized form of this model, the GARCH model are used to show the random variations in these markets. The sample data used in the study consist of daily closing prices from the various markets. The markets are the S&P 500 (U.S.), FOTSE 100 (U.K), DAX40 (Germany), CAC (France), and NIKKEI225 (Japan). The indexes range from November 26th, 1990 to March 21st, 2002. The sample data showed the market daily returns, squared returns, and correlations of the daily returns from the five markets. The daily returns represent the log diff