# 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.

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4 Comments so far

1. Anatoly Veltman on November 23, 2007 4:34 am

In reference to your final assertion: there is plenty of evidence every trading day. I still have the statement for the only S&P order that I ever placed for Victor’s account. I shorted the \$440.35 pit high of 5/17/93. Despite quick subsequent intra-day drop of 3 handles, Victor ended up firing me - as my Fibonacci reversals remained un-tested against firm’s database… Over my 21 years of trading, I participated in hundreds of highs and lows - I’ll give you a couple of easily verifiable examples.

Comex Copper had double-bottom in 1999 at 61 cents, briefly revisited one more time in aftermath of the 9/11/01. From there, it took-off and never stopped until it hit \$4.16 on temporary limit-up bid 5/11/06. That all-time record was exact Fibonacci 685% multiple (of the near-61 cent lows)! So copper reversed and dropped into in Feb07 low of \$2.385 = precise 50% retracement of 0.61->4.16 rally! It then reversed on that low, and rallied 60% in one quarter!

USD/CAD rallied from sub-par in 1974, to reach its all-time high of 1.6180 in 2002. It’s been declining ever since and slid below par this year.

China Stock Index double-bottomed just below 1000 in 2005. It rallied straight-line from there to its Fibonacci 425% multiple (double-top at 4250) spring 2007. There, it reversed down and double-bottomed at 3417 (which was 23.6% retracement). It then reversed up, to rally to its 10/16/07 record of 5423. This final up-wave 3417->5423 equals precise 61.8% of the preceeding 1000->4250 wave! China reversed, to drop a 1000 points by now.

GOOG and AAPL make most of their reversals at FibNodes.

To prove that I’m not just retro-fitter: Dec Gold rallied from \$651.5 to \$848 in three months, and then quickly snapped back for its biggest correction this year. So our fund pre-placed a 773.5 bid and got filled in Asian session of Nov.20. Figure it for yourself, we were bidding 38.2% retracement of 651.5->848 up-wave. This proved the precise reversal point, and we just took profits near European open of Nov.23 session, in front of the tough 819.4 area. This area would equal 61.8% retracement of 848->773.4 move…

2. jim collins on November 23, 2007 7:06 pm

“There is no theoretical basis to believe that Fibonacci support and resistance levels hold any validity for traders. ” Which is completely irrelevant, because there is a lot of theoretical evidence that a lot of people believe and act on Fibonacci patterns and therefore it becomes self-fufilling (and actionable).

3. Anatoly Veltman on November 28, 2007 11:01 am

“self-fulfilling (and actionable)” - very poignant, Jim!

S&P futures took month-and-half to correct 1586.50->1406.30. It did so in a clear ABC zig-zag, where A low was 1492.60 and B high was 1558.50 . We bid 1406.50 on 11/27 = wave C extension: (1586.5-1492.6)x1.618 going down from 1558.50

Sorry to post here next morning: we’ve been busy aggressively shorting Gold and Crude yesterday, until this morning. We did post all recommendations in advance, on client website

4. Darren Tseng on August 24, 2009 12:26 am

I thought of this idea recently and I’m going to be using Fibonacci as a translation tool for applying sound to charts. I’ll offer the .MT4 indicator after and empirical data. It may or may not be useful in prediction….but it will be useful in pattern recognition and memorization.