The authors examine the validity of the empirical rule connecting the randomness of high frequency stock prices to its future performance in a bully market conditions. For this purpose, the U.S. market in the period of 1993-1997 is chosen for investigation. The rule was first discovered in a bear market of 2007-2009 in Tokyo market, as one of the useful applications of the RMT-Test which is a new tool to measure the randomness of given time series based on the random matrix theory, showing that the stock of the highest randomness is more profitable than the Nikkei Average Price throughout the following year. The previous analysis was limited to the period of bear market, and inclusive analysis for a wider market conditions are necessary in order to establish the validity of the rule.
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