In this case study in knowledge engineering and data mining, we implement a recognizer for two variations of the`bull¯ag' technical charting heuristic and use this recognizer to discover trading rules on the NYSE Composite Index. Out-of-sample results indicate that these rules are effective. q

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It is acknowledged by researchers and practitioners alike that risk reduction through portfolio diversification provides significant economic benefits. Less obvious is the size of the portfolio one would need to receive 50% or 90% of the possible benefits. If ownership of 100 securities is necessary to achieve half the possible risk reduction, diversification would be of practical use only for institutions and the extremely wealthy. Numerous empirical studies have examined this question, and most conclude that effective diversification is possible with a surprisingly small number of securities if the securities are chosen at random. The force of this evidence is reduced because all but two of these studies assigned equal weights to the securities selected for a portfolio. There can be no presumption that equal weights are optimal, and the evidence cannot be conclusive unless optimal weights are used. I. Earlier StudiesIn a seminal work in this area, Evans and Archer [4] concluded that there is relatively little economic justification for increasing portfolio sizes beyond ten or so randomly selected securities. Latane and Young [9] verified Evans and Archer's results, finding that an eight-stock portfolio achieves 85 percent of the possible gains through diversification. Fisher and Lorie [5] have also confirmed that increasing the number of stocks in a portfolio rapidly exhausts the variability present in a one-stock portfolio. For example, they found that while roughly 40% of the achievable reduction is obtained by holding two stocks, eight stocks reduce 80% of the dispersion. Sharpe [14, p. 130] agreed that "a little diversification can go a long way toward reducing risk." He suggested that a portfolio containing fifteen or so securities may be considered well-diversified. Elton and Gruber [2] reached the same conclusion from an analytical solution of the relationship between risk and portfolio size. Finally, Mokkelbost [12] also found that a major portion of the achievable reduction is accomplished when "relatively few" different securities are included in the portfolio.Two recent studies have questioned whether portfolios of only 10 to 20 securities sufficiently reduce variation. Lorie [10] argued that even small departures from perfect diversification create substantial amounts of risk. Concentrating on the variance in independent returns for different size portfolios, he showed that a choice of 50 stocks out of the Standard and Poor's 500 Index could produce annual returns that vary as much as four and one-half percentage points from the returns for the entire 500 stocks. Moreover, even as large a portfolio as 100 stocks might differ as much as three percentage points from the 500 stock index. Using Fisher and Lorie's earlier data, Upson, Jessup, and Matsumoto [15] make much the same point when they argue that small portfolios suffer