# Fibonacci Ratios in Trading and Music, from Phil McDonnell

November 23, 2007 |

The beauty of the Fibonacci mathematical sequence and its cousin the golden ratios are indisputable. Mr. Glazier poses a very interesting question. First let examine one of his premises - that the market is self similar at all time scales.

Empirically speaking this is not quite true but appears to be approximately true. The market does somewhat resemble a log normal distribution but with a bit more peakedness and fat tails. It does seem to converge to a more normal distribution as time is increased. Perhaps this is caused by the fact that all distributions with finite variance eventually converge to the normal or log normal.

One interesting property of the normal distribution is that it is self-similar at different time scales. So if the market is normal at say time scales of a week then periods longer than that will be normal as well. They will simply be the sum of normal variables which is known to be normal as well. So we get the result that the market is both self similar and scales to longer time frames. So perhaps there is a grain of truth to that part of Mr. Glazier's assertions..

Let us consider the question of the magical 1.618 and its reciprocal .618. In fact these numbers really result from an underlying logarithmic growth pattern of the Fibonacci series. Check the logs on your scientific calculator. The natural log of 1.618 is .48 and the log of .618 is -.48. The reason for this is that it is a ratio relationship.

So too with music. All musical harmonies are based on ratios of the notes. Simple integer ratios sound pleasant to the ear. So if the market is really growing with a long term compounded drift then it is really nothing more than a process based upon equal ratios just as music is.

Therefore if the log normal model adequately explains the self similarity and the scale invariance of the market distribution then does that necessarily imply that Fibonacci levels will offer better than random turning points. Unfortunately the answer is emphatically no! If the model is a random log normal one then the turning points are also quite random. It is as simple as that.

There is no theoretical basis to believe that Fibonacci support and resistance levels hold any validity for traders. So the only possible rationale might be that one finds that they work empirically. To date no such credible evidence has ever been seen.

`SELECT * FROM wp_comments WHERE comment_post_ID = '2432' AND comment_approved = '1' ORDER BY comment_date`