Fibbonaci: Little Evidence

Well finally got around to looking for evidence of Fibbonaci retracement in stock markets... which would have been the logical place to start this investigation ;-)

BP (LSE) data from 2003 to 2011 was used.

Data was transformed into a simple stochastic oscillator STO: price as a percentage of High/Low range for the preceding period (p).

1) Method: The number of days in at each percentage point was summed.

Result: With p=10,20 the graph has 3 noticeable points.

i) Price spends most of its time just below the High >80% (about 1.2% of the time for each STO percentage point). This is near a subtracted Fib point.

ii) Price spends the next longest duration (0,.75% time / STO point) at about 20% of the range. This is near one of the Fib points.

iii) Price spends the least time (about 0.6%) in the middle of its range.

Conclusion: This crude measure would expect movement to Fib levels to show up as longer time at these levels with the price moving fast through other levels. This is not in the data. However bouncing off these levels would not show up in this measure.

2) Method: The Gradient was calculated as the regression slope between the preceding week and the subsequent week.

Result: Gradients are negative and fastest near the Low and positive and fastest near the High. They oscillate in the middle band. A moving average smooth of the curve shows that they are flat at 60%. This is a Fib level.

Conclusion: The flat level at 60% is as expected. The data is not fine enough to conlcude anything however. It also suggests that movements out of the range occur at high speed, while there is fluctuation within the range. Little peak at 70% suggests that prices travel fast through here to the 60% range and 80% range.

3) Method: Same but with average volume.

Result: Volumes decline as the price moves up through the range, with a peak before 20%. Thus suggests that people trade based on ranges like this with buyers buying in expecting the price to rise again into the range and sellers afraid that it will fall below the last low.

4) Same with Volume x Gradient

Result: Movement into stock positions increases as the price rises and accelerates upward as it approaches tops. Peaks at 35% and 70% of range.

Conclusion: No evidence of Fib here. It suggests that it is safe to add into high volume upward trends even near the local high because the gradient down is less. Conversely it is dangerous to add to low volume downward trends... as I discovered in gas last year where I threw away 20% of my portfolio!

Now there are two ways to do Fib. Time to examine the other one.

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Taking the trend into account with High/Low calculated from the previous 40day period gives these results. It was calculated on actual prices of the BP graph not on LN - that was a mistake above. After a falling trend the SSTO was calculated normally, but after a rising trend the 100-SSTO was calculated since Fib retracement is calculated from the most recent reversal point back in time.

Fib retracement means that prices bounce off the retracement lines which means that days with this closing price ought to be rarer than random.

Instead the below trend is found which is essentially a probability distribution as this measure actually captures the volatility!

Rather than days at each level the average absolute gradient (calculated as regression through each point and week either side). This measures the rate at which the price was changing (either going up or down) at each point. At Fib levels, if they do resist movement, the gradient ought to slow down.

The 3 middle black bars are the main Fib levels (38.2,50,61.8) with 78.6 an official additional and 23.6 a logical 5th.

With some imagination there are periodic sudden increases in gradient (sudden acceleration) before Fib levels but certainly no indication of a slowing down.

Next up would be a distribution of turning points... but given that the stock market is fractal and turning points occur ever second, minute, hour, day... what scale do we chose? and how do we approach the issue of scale?... it is not exactly a 3rd dimension since scales are discrete (we choose maybe a 9day, 20 day, 50day moving average) but which scale would be best and why? .... to come back on this one.