It's arrivederci to Fibonacci, professor claims

A leading academic claimed yesterday to have debunked a key guiding principle widely used to try to gauge future movements of stock markets.

Roy Batchelor, professor of banking and finance at City University's Cass Business School in London, said analysis of the daily behaviour of the US Dow Jones index between 1914 and 2002 found no correlation with rules based on Fibonacci numbers.

He and the Cass researcher, Richard Ramyar, concluded that, contrary to beliefs held by many technical analysts, markets do not reverse at levels indicated by Fibonacci ratios.

Professor Batchelor said: "Nowadays, we think that most short-term movements in prices in financial markets are random. However, it is a natural human characteristic to look for patterns even in random data, and traders are under added pressure to rationalise their actions and display expertise.

"Theories of stock-market waves are manifestations of this illusion of control, the instinct that makes the dice harder when we want a high number."

The Fibonacci sequence of numbers first appeared in the work of the celebrated 13th-century mathematician, Leonardo Fibonacci da Pisa. His Liber Abacci, or Book of Calculation, of 1202 is credited as the first Western business text and helped popularise the decimal system and algebra in Europe.

The sequence, recently brought to popular consciousness in the bestseller The Da Vinci Code, is formed by successively adding two numbers to obtain the next in the chain. For example, 1, 1, 2, 3, 5, 8, 13, 21, 34, and so on to infinity. As the numbers become larger, the ratio of each number to the preceding one converges on 1.618 - the so-called "golden ratio". This number occurs naturally in the geometry of the pentagon, and Fibonacci sequences and ratios also arise in botany and physiology.

Ratios of 1.618:1 are argued to be aesthetically pleasing, and were used by architects and artists such as Le Corbusier and Mondrian.

In financial markets, Fibonacci ratios are mainly used in conjunction with Elliot Wave Theory, which claims that stock markets rise in three waves and fall in two. The idea is that if the market falls by 100 points, it is likely to rise by about 161.8 points or by some related ratio such as 61.8 points.