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that in the absence of insider information and in the presence of a cost to make trades or manage your portfolio, you can’t profit from any deviations from randomness.14 Nevertheless, Wall Street has a long tradition of guru analysts, and the average analyst’s salary, at the end of the 1990s, was about $3 million.15 How do those analysts do? According to a 1995 study, the eight to twelve most highly paid “Wall Street superstars” invited by Barron’s to make market recommendations at its annual roundtable merely matched the average market return.16 Studies in 1987 and 1997 found that stocks recommended by the prognosticators on the television show Wall $treet Week did much worse, lagging far behind the market.17 And in a study of 153 newsletters, a researcher at the Harvard Institute of Economic Research found “no significant evidence of stock-picking ability.”18

By chance alone, some analysts and mutual funds will always exhibit impressive patterns of success. And though many studies show that these past market successes are not good indicators of future success—that is, that the successes were largely just luck—most people feel that the recommendations of their stockbrokers or the expertise of those running mutual funds are worth paying for. Many people, even intelligent investors, therefore buy funds that charge exorbitant management fees. In fact, when a group of savvy students from the Wharton business school were given a hypothetical $10,000 and prospectuses describing four index funds, each composed in order to mirror the S&P 500, the students overwhelmingly failed to choose the funds with the lowest fees.19 Since paying even an extra 1 percent per year in fees could, over the years, diminish your retirement fund by as much as one-third or even one-half, the savvy students didn’t exhibit very savvy behavior.

Of course, as Spencer-Brown’s example illustrates, if you look long enough, you’re bound to find someone who, through sheer luck, really has made startlingly successful predictions. For those who prefer real-world examples to mathematical scenarios involving 101,000,007 random digits, consider the case of the columnist Leonard Koppett.20 In 1978, Koppett revealed a system that he claimed could determine, by the end of January every year, whether the stock market would go up or down in that calendar year. His system had correctly predicted the market, he said, for the past eleven years.21 Of course, stock-picking systems are easy to identify in hindsight; the true test is whether they will work in the future. Koppett’s system passed that test too: judging the market by the Dow Jones Industrial Average, it worked for eleven straight years, from 1979 through 1989, got it wrong in 1990, and was correct again every year until 1998. But although Koppett’s predictions were correct for a streak of eighteen out of nineteen years, I feel confident in asserting that his streak involved no skill whatsoever. Why? Because Leonard Koppett was a columnist for Sporting News, and his system was based on the results of the Super Bowl, the championship game of professional football. Whenever the team from the (original) National Football League won, the stock market, he predicted, would rise. Whenever the team from the (original) American Football League won, he predicted, the market would go down. Given that information, few people would argue that Koppett was anything but lucky. Yet had he had different credentials—and not revealed his method—he could have been hailed as the most clever analyst since Charles H. Dow.

As a counterpoint to Koppett’s story, consider now the story of a fellow who does have credentials, a fellow named Bill Miller. For years, Miller maintained a winning streak that, unlike Koppett’s, was compared to Joe DiMaggio’s fifty-six-game hitting streak and the seventy-four consecutive victories by the Jeopardy! quiz-show champ Ken Jennings. But in at least one respect these comparisons were not very apt: Miller’s streak earned him each year more than those other gentlemen’s streaks had earned them in their lifetimes.