Not So Magical Numbers

Some technical analysts rely on an arcane 13th century arithmetic series, called the Fibonacci sequence. A recent study says that it is false belief

Many traders believe that clues to where the market is headed lie in the work of Leonardo of Pisa, a mathematician who lived in the 12th and 13th century. Leonardo, widely known as Fibonacci, had produced a sequence by adding consecutive numbers in a series starting with 1 and 2. It goes as: 1, 2, 3, 5, 8, 13 and so on. Intriguingly, the numbers in this series crop up frequently in nature. There are leaves that grow in this sequence as also shells that are patterned along this sequence. Most interestingly, if you divide each number with the next one, you inexorably move towards 1.618. This is supposed to be the golden ratio in architecture and design, most famously exemplified by the nude man with his arms stretched in Leonardo Da Vinci’s painting of the Vitruvian Man. The Fibonacci magical sequence has also been glorified in “The Da Vinci Code”. Financial traders have long invested a great deal of belief in the golden ratio and the Fibonacci numbers. They believe that markets will retrace 61.8% of a previous leg or go up to 1.618% of the previous move. When this does not work, they use 50% and 38.2% as well, which are supposed to be other important Fibinacco percentages.

Fibonacci worshippers are part of a gang called chartists, or more pompously, technical analysts. They believe that past patterns in prices can provide clues to the future price movements. Some detect and follow patterns such as “cup and handle” or “double bottom”. Some others follow waves, which supposedly move according to the magical Fibonacci numbers and ratios, the most arcane and mysterious of the TA tools. The belief in Fibonacci sequence is so great that the chartists track whether the number of weeks that have elapsed following a move, is a Fibonacci number. For instance, if it is the 13th week after the market has started rising, it could mean that it is time for a correction. Well, none of this is ever tested. The believers selectively remember the times when it has worked and not when it has not worked.

What if someone statistically tested the usefulness of Fibonacci sequence? Professor Roy Batchelor and Richard Ramyar of the Cass Business School did and found no evidence that Fibonacci numbers work in American stock markets. They looked at all major moves of the Dow Jones Industrial Average between 1914-2002 and found no indication that moves reverse at the 61.8% level, or follow any other pattern.

The researchers go beyond the failure of Fibonacci to predict prices and reject the idea that TA works at all. “The root of the problem is the failure of technical analysts to specify their trading rules and report trading results in a scientifically acceptable way. Too often, rules are so vague and complex as to make replication impossible,” they write.

Indeed, one of the biggest beets noires of TA, Victor Niederhoffer, has tested every TA indicator over his 45 years of trading. So far, not one has passed the test of statistical significance. What Victor found instead were haphazard anecdotes, confident assertions, and appeals to authority. He too believes that practitioners and advocates of TA fail to follow standard scientific procedure in presenting and evaluating its techniques.

If you divide each number with the next one,
you inexorably move towards 1.618.
This is supposed to be the golden ratio in architecture and design.
Financial traders have long invested a great deal of belief in this ratio