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Chart Interpretation

# Fibo Retracement Phenomenon

Tom, you have occasionally mentioned Fibonacci retracement levels in your writings, but I have heard of published studies that refute the legitimacy of Fibonacci levels as retracement objectives.  If that is true, why do technicians still use them?

This is an excellent question, and I have read about a couple of those studies you mention, one which used several decades of DJIA history to look for evidence that Fibonacci retracement levels showed importance for the DJIA's movements.  One study was done by researchers at City University, and reported on by Financial Times columnist John Authers on Oct. 2, 2006, (FT.com subscription required).

The conclusion of that study was that, "the number of times the ratios between those peaks and troughs was anywhere close to a Fibonacci ratio was actually less than would have been predicted if the pattern were random."  That seems like a useful conclusion for technical analysts to know about, but it does not tell the full story.

One of the big problems with a test like this is that it only looks at the end points for price moves, which misses out on a lot of the importance that Fibonacci retracement levels can hold for the market.  I will show an example which illustrates this point below.

Another problem with the test design relates to the nature of chart structures.  A colleague who is an expert on Elliott Wave analysis (which I am NOT) once explained to me that it is terribly important to select the proper chart points from which to generate retracements to fit into the wave count objecives, and that these are not necessarily the highest nor lowest price points on a chart.  I cannot attest to that being the case, as I have not done my own thorough investigation, but it does make some sense.

Accordingly, it would come as no surprise that backtest results will be invalid or incorrect if improper high/low endpoints are used for calculating the retracements.  So any supposed "disproof" of the validity of Fibonacci retracement levels should itself be suspicious by virtue of the methodology used for selecting the end points from which to calculate the retracements.  Garbage in, garbage out.

There is also a logical problem involved in such studies stemming from an assumption that retracement end points are the only way in which Fibonacci ratios might matter.

Attached is a chart of the XAU, and it offers one of the best cases I have ever seen for believing in the importance of Fibo levels.  They may not have acted precisely as someone would preconceive that they should have, but they have definitely mattered.

The 0.382 retracement level did not halt the decline, and thus it would have been considered a failure in the study listed above.  Instead, the XAU gapped down through that retracement level in early December 2004, which is hardly what one would have wanted to see if one were expecting that level to offer support.  But then after that gap exhausted the selling pressure, the XAU rose back up to hover just under the ceiling represented by the 0.382 level for the rest of that month.  Clearly, the 0.382 level had importance for the XAU, but not necessarily as someone might have thought that it should.

When the decline resumed itself in early January 2005, it did get halted at the 0.618 retracement level, so call that one a success.

Interestingly, these same levels turned out to have mattered during the advance, before the top from which we measure the retracement was even put in.  For example, the 0.618 line marked a nice gap on the way up, and so the retracement to that level accomplished both a Fibo retracement and a gap closing. Talk about multi-tasking!

Now, having presented a chart in which the Fibo levels obviously (to the eye) do matter, I do not know how I would design a "test" to let a computer determine whether they matter elsewhere, or whether they matter universally.  I also do not know why one would need to.