CHARTING
In 1202, an Italian mathematician named Leonardo Pisano, better known by his nom de plume Fibonacci, published Liber abaci, a famous text that not only introduced the West to Arabic numbers but also described how a pair of rabbits would multiply under ideal circumstances. Assuming no rabbits die, growth of the total rabbit population follows a sequence of numbers beginning with 0, 1, and continuing to infinity. Each successive number is derived by adding the previous two (0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, and so on). The first couple of numbers are 1.5 times (or 50 percent more than) the preceding numbers, but the further out you go the closer each number comes to being 1.618 times (or 62 percent higher than) the one before and .618 times (or 38 percent less than) the one after - the so-called golden ratio. Mathematicians have discovered the Fibonacci sequence in a remarkable variety of natural systems, including the number of petals on a daisy, the spiral of a sea shell, the proportions of human anatomy - and, sometimes, the gyrations of the stock market.
Markets don't move straight up or straight down. There are always reactions after new highs or lows. Technical analysts, who study detailed stock charts, see these "retracements" unfolding in Fibonacci sequences. If, for example, an index doubles, a technician might expect it to give back 38 percent before heading up again.
How well does it work? Last fall the Dow rallied from an October low of 7,467 to a November high of 9,380. If you thought the rally was over, a Fibonacci buy signal would be set down at a 38 percent correction - 8,653. Turned out the market bottomed at 8,676 in December. Pretty damn close. You might expect the next advance to be either 38 percent or 50 percent or 62 percent of the October-November 1,913-point rally. Guess what? The market went up almost exactly 50 percent of that rally to a January peak of 9,648 and 38 percent of the previous decline. A double Fibbo.
Of course, as with any technical analysis, the validity of Fibonacci analysis depends a great deal on where the initial lines are drawn. "It's right at least 61.8 percent of the time," jokes Walter G. Murphy Jr., chief global technician for Merrill Lynch.
Any Bloomberg, Bridge, or TradeStation terminal can overlay Fibonacci lines. On the Web, try Fibonacci Trader. A 30-day trial costs $25, a real-time intraday package $986, and an end-of-day version $786.
Fibonacci Trader: www.fibonaccitrader.com.
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