[fibonnachi] and the herd mentality

This post takes large chunks from an article by Carolyn Cohn, of Reuters, Friday, July 21, 2006, [with the sensationalism extracted] and adds from other sources:

Leonardo Fibonacci of Pisa published a book in 1202 which calculated the reproductive cycles of pairs of rabbits and showed that they followed a pattern 1-1-2-3-5-8-13-21 - a sequence where the sum of any two consecutive numbers equals the next highest number.

When the ratio of a number to the ones closest is taken over time, it tends to 1.618, which has now entered mythology as a magic or Golden Ratio. It is approximately:

1.6180339887

It enters the fields of music, sculpture, painting, book design and a host of other fields, including architecture. Therefore pyramid devotees will find it in the measurements there.

Even in my field of sailing, an approximation can be found. The usual height of the mast these days is 1.6 times the boat's length [my designs have two masts at 1:1]. Google 1.618 and it's interesting.

Accountant Ralph Nelson Elliott. the 1930s, developed his own theory based on Fibonacci numbers called Elliott wave analysis, which said the market followed a repetitive pattern, with each cycle made up of a five-wave rise followed by a three-wave fall.

Elizabeth Miller, of Redtower Research in Aberdeenshire, said the Dow Jones stock index collapse from the dot-com boom that peaked in 2000 followed a Fibonacci pattern.

"Fibonacci retracements work on pretty much everything, but they work particularly well with stock markets - it's natural mathematics."

61.8 is among the key price retracement targets for modern traders of currencies, stocks and commodities. The ratio is known as the "golden mean" for its universal applications. Another key retracement is 38.2 percent, which is 1 divided by 1.618 squared.

Midas Banned, on goldismoney, gives an example with HUI from March, 2003 then goes on to say:

To give credit where credit is due, this observation was first discussed in detail by W. D. Gann (1878-1955). Since the late great Gann had only a slide rule, not a calculator, he used the 5/8 level, which is .625, and almost exactly matches .618......."

Tom Pelc, chief technical strategist at RBS Financial Markets in London, finds Fibonacci patterns in recent moves in London's FTSE stock index.

"If you look at the FTSE's decline in May and June and its bounce since then, it's struggling right now at exactly the 61.8 percent retracement," he said in mid-July.

However, detractors, as you'd expect, scoff at this:

Use of Fibonacci can become something of a self-fulfilling prophecy for stock markets where there is a crowd mentality and where everyone starts to watch out for the same levels.

"It's amazingly common to read sentences written by technical analysts involving Fibonacci ratios," said Roy Batchelor, professor of banking and finance at Cass Business School in the City.

"The evidence on this is contrary. People will show you a picture where it happened, not the 100 pictures where it did not happen -- but it's got entertainment value.

We suffer from the illusion of control, that things have to have an explanation - people hate randomness."