Bill: It wouldn't be so bad if this kind of thinking affected only kids. This guy Paulos wrote the book (literally!) on mathematical idiocy. He's right, but only within a very narrow concept of information. We clearly pay financial advisors in order to improve the odds of our investment decisions, not to simply ignore their recommendations and throw dice. Just like we go to doctors because we think it will improve our chances of getting better (I heard a statistic recently, that until 1911, you were better off _not_ going to a doctor when you were sick, because the doctor was more likely to harm you than whatever disease that you had). Henry ----- http://www.forbes.com/forbes/2003/0512/050_print.html On My Mind Is Insider Trading So Bad? John Allen Paulos, 05.12.03, 12:00 AM ET Look at elementary principles of probability, and you'll discover it's not. It's natural to take an indignant stance toward the corporate fraud and excesses that have dominated business news the last couple of years. This is especially so if you've lost your shirt on a stock like WorldCom, as I unfortunately did. Yet an elementary probability puzzle suggests that one argument against insider trading and stock manipulation--that it costs investors money--is not quite as compelling as it seems. (There are, of course, other arguments against these practices.) The puzzle involves those standbys of probability professors--coins, both fair and biased. It asks: Which of the following two situations would you prefer to be in? In the first one you're given a fair coin to flip and are told that you will receive $1,000 if it lands heads and lose $1,000 if it lands tails. In the second, you're given a very biased coin to flip--you don't know in which direction it's biased--and must decide whether to bet on heads or tails. If it lands the way you predict, you win $1,000 and, if not, you lose $1,000. Although you might prefer to flip the fair coin, your chances of winning are 50% in both situations, since you're as likely to pick the biased coin's "good" side as its "bad" side. Now consider a second pair of schematic bets involving stocks, entities whose behavior is usually indistinguishable from that of coins. In the first situation you buy a stock that is being offered in a randomly fluctuating market and your earnings will be $1,000 if it rises the next week and -$1,000 if it falls. (In the short run, probabilities of different outcomes with stocks are pretty symmetric.) In the second, you're told that there is evidence of insider trading and manipulation and that this will bring about--you don't know which--either a $1,000 rise or a $1,000 fall in the price of the stock the next week. Given this information, you must decide whether to buy or sell (that is, short) the stock. If you guess correctly, your earnings are $1,000 and, if not, they're -$1,000. Once again, your chances of winning are 50% in both situations. In each of these pairs the unfairness of the second situation is more apparent than real. Although cognitive psychologists know that most people try to avoid them, you have the same chance of winning in the second situation as you do in the first. Insider trading and stock manipulation are wrong for other reasons (the undermining of investor confidence and, arguably, the disproportionate share of returns accruing to insiders), but I maintain that they can be viewed as simply two among the many unpredictable factors affecting the price of a stock. Depending on investors' actions, they're as liable to cut one way as the other. Of course, insider trading and stock manipulation are not equivalent offenses. Legal theorist Henry Manne goes further and advocates the outright legalization of insider trading, arguing that it would make for more efficient markets. Even if the law were to be liberalized along these lines, it would not shelter a looter who cooked the books and then sold his overvalued shares to innocents. It probably would decriminalize the actions of ImClone's Sam Waksal and other users of inside information. The fact is that there are insurmountable logical problems with the very notion of insider trading. It's illegal for an insider to buy on learning of his company's secret scientific breakthrough. But if this same person changes his plans to sell the stock after finding out about the breakthrough, he has violated no rule. When I fall into discussions with woebegone investors in WorldCom and other infamous companies, I hear self-righteous condemnations of cooked books, manipulated earnings and analyst/company collusions. In a sense, however, these investors merely picked the wrong coin. A few years ago they were just as likely to have profited enormously from cooked books. As in many other areas of life, people are much quicker to see themselves as victims of bad guys than as beneficiaries of bad guys. John Allen Paulos, mathematics professor at Temple University, author of Innumeracy and A Mathematician Plays The Stock Market.