### Fibonacci Retracements – My 2nd Experiment,

This experiment is a follow up to my first test of Fibonacci retracement levels. In this experiment I am going to test how frequently the mid points between 38.2-50.0 and 50.0-61.8 are hit in comparison to the Fibonacci retracement levels themselves. The mid point between 38.2 and 50.0 is 44.1, and the mid point between 50.0 and 61.8 is 55.9.

In the example above a high of 1.51437 was formed on 25th of November 2009 and a low of 1.25229 was later formed on the 13th of July 2010. The Fibonacci retracement levels and the mid points between the Fibonacci levels are therefore –

61.8% 1.41425 (Fibonacci level)
55.9% 1.39880 (Mid point)
50.0% 1.38333 (Fibonacci level)
44.1% 1.36787 (Mid point)
32.8% 1.35241 (Fibonacci level)

In this example I would count the number of days that each of these levels was hit in the 200 trading days after the low on the 13th of July 2010. However, at the time of writing, I’m not able to do this as 200 trading days (about 1 year) has not elapsed since the 13th of July 2010.

### Fibonacci Retracement Levels Experiment II: The Results.

The total number of days each of the levels was hit is as follows –

61.8% Hit on 85 days (Fibonacci level)
55.9% Hit on 192 days (Mid point)
50.0% Hit on 136 days (Fibonacci level)
44.1% Hit on 171 days (Mid point)
38.2% hit on 100 days (Fibonacci level)

The full details of the tests that produced these totals are as follows –

EUR/USD 04/03/2009 to 25/11/2009, High 1.51437 Low 1.24560,
61.8% 6
55.9% 10
50.0% 6
44.1% 23
38.2% 18

EUR/USD 28/10/2008 to 18/12/2008, High 1.47190 Low 1.23300,
61.8% 8
55.9% 13
50.0% 15
44.1% 15
38.2% 23

EUR/USD 30/12/2004 to 15/11/2005, High 1.36700 Low 1.16920,
61.8% 8
55.9% 34
50.0% 17
44.1% 34
38.2% 2

GBP/USD 23/01/2009 to 05/08/2009, High 1.70422 Low 1.35030,
61.8% 8
55.9% 9
50.0% 22
44.1% 13
38.2% 5

GBP/USD 25/09/2008 to 23/01/2009, High 1.86680 Low 1.35030,
61.8% 5
55.9% 51
50.0% 11
44.1% 7
38.2% 2

GBP/USD 16/12/2004 to 28/11/2005, High 1.95520 Low 1.70470,
61.8% 14
55.9% 25
50.0% 9
44.1% 4
38.2% 2

USD/CHF 17/03/2008 to 21/11/2008, High 1.22960 Low 0.96420,
61.8% 16
55.9% 13
50.0% 12
44.1% 42
38.2% 25

USD/CHF 13/10/2006 to 17/03/2008, High 1.27680 Low 0.96420,
61.8% 14
55.9% 18
50.0% 10
44.1% 18
38.2% 13

USD/CHF 30/12/2004 to 16/11/2005, High 1.32870 Low 1.12850,
61.8% 6
55.9% 19
50.0% 34
44.1% 15
38.2% 10

### Trading Fibonacci Retracements II: My Conclusions.

Once again, Fibonacci retracement levels seem be far less likely to be hit than other levels (this time the levels were the mid points between the Fibonacci levels themselves). This, I believe, is more evidence that Fibonacci retracement levels do have some statistical significance and that the market price is likely to bounce off them. It should be noted however that so far I have only tested this on very large time frames. In these experiments the highs and lows have formed over several months or more and the test to see which levels were hit was done over the proceeding 200 trading days which is about a year.

Nevertheless, I hope this information proves to be useful to someone.

### What Are Fibonacci Retracements Levels

Fibonacci retracements are technical levels where the price is supposed to be statistically likely to retrace to.

The Fibonacci ratio (often called the golden ratio or the golden mean) appears all the time in nature as well as in art and architecture. The theory behind Fibonacci levels is that these levels (or ratios) that appear so frequently in nature, art and architecture also appear in the markets.

The most commonly used Fibonacci retracement levels in trading are 38.2%, 50.0% and 61.8%.

Advocates of using Fibonacci retracement levels in trading often claim that the price is drawn to retrace back to these levels and/or that these levels are statistically significant areas of support and resistance. Traders trying to pick market tops and bottoms often use Fibonacci retracement levels to try and help them to do it.

But do Fibonacci retracement levels really work like price magnets? Is the market price more likely to hit these levels than any others? And if not, do Fibonacci levels hold any sort of statistical significance at all?

To try and answer this question, I am going to take the 32.8%, 50.0% and 61.8% Fibonacci retracement levels between a major high and low like the one shown above. I will then compare how often the daily price movement is within one of these three Fibonacci levels in the proceeding 200-days after the major high and low is formed with how often the daily price movement is within one of three non-Fibonacci levels, 25.0%, 45.0% and 70.0%.

I could have picked any three levels between 0 and 100 for this experiment but 25.0%, 45.0% and 70.0% seemed as good any. Plus these three arbitrary retracement levels were not so near to 0 and 100 for the experiment to potentially be affected by the effects of support and resistance.

The idea behind this experiment is that if, as the exponents of Fibonacci in the markets claim, Fibonacci retracement levels have some significance; then the daily high and low (the daily price movement) should be either more likely or less likely to be between a Fibonacci level than between one of the three arbitrary levels I have chosen – more likely if the price is drawn magnetically to the Fibonacci levels and held there, and less likely if the Fibonacci levels act as support and resistance, magnetically drawing the price there only to quickly repeal it.

But one way or another, if Fibonacci levels have any significance then there should be a statistically significant difference between the likelihood of the daily price moving between one of the Fibonacci levels and one of the three arbitrary price levels that I have chosen. Now let’s do the experiment and see what the results are…

#### Experiment 1: EUR/USD 15/07/2008 to 28/10/2008, High 1.6038, Low 1.2330

 Retracement Level Number Of Times Hit 25.0 @ 1.3257 29 32.8 @ 1.3546 19 45.0 @ 1.3999 35 50.0 @ 1.4184 19 61.8 @ 1.4622 1 70.0 @ 1.4926 0

#### Experiment 2: EUR/USD 13/10/2006 to 08/12/2006, High 1.3364, Low 1.2483,

 Retracement Level Number Of Times Hit 25.0 @ 1.2703 5 32.8 @ 1.2772 9 45.0 @ 1.2879 4 50.0 @ 1.2924 15 61.8 @ 1.3027 14 70.0 @ 1.3100 15

#### Experiment 3: EUR/USD 15/11/2005 to 05/06/2006, High 1.2981, Low 1.1638,

 Retracement Level Number Of Times Hit 25.0 @ 1.1974 21 32.8 @ 1.2079 28 45.0 @ 1.2242 8 50.0 @ 1.2310 8 61.8 @ 1.2468 3 70.0 @ 1.2578 19

#### Experiment 4: EUR/USD 26/04/2004 to 30/12/2004, High 1.3670, Low 1.1759,

 Retracement Level Number Of Times Hit 25.0 @ 1.2237 27 32.8 @ 1.2386 13 45.0 @ 1.2619 8 50.0 @ 1.2715 1 61.8 @ 1.2940 25 70.0 @ 1.3097 17

#### Experiment 5: EUR/USD 03/09/2003 to 12/01/2004, High 1.2901, Low 1.0762,

 Retracement Level Number Of Times Hit 25.0 @ 1.1297 0 32.8 @ 1.1464 0 45.0 @ 1.1725 0 50.0 @ 1.1832 11 61.8 @ 1.2084 41 70.0 @ 1.2259 44

#### Experiment 6: EUR/USD 21/03/2003 to 27/05/2003, High 1.1931, Low 1.0502,

 Retracement Level Number Of Times Hit 25.0 @ 1.0859 8 32.8 @ 1.0971 4 45.0 @ 1.1145 8 50.0 @ 1.1217 12 61.8 @ 1.1385 9 70.0 @ 1.1502 20

#### Experiment 7: GBP/USD 23/01/2009 to 05/08/2009, High 1.7042, Low 1.3503,

 Retracement Level Number Of Times Hit 25.0 @ 1.4388 0 32.8 @ 1.4664 1 45.0 @ 1.5096 13 50.0 @ 1.5273 22 61.8 @ 1.5690 8 70.0 @ 1.5980 22

#### Experiment 8: GBP/USD 15/07/2008 to 23/01/2009, High 2.0158, Low 1.3503,

 Retracement Level Number Of Times Hit 25.0 @ 1.5167 8 32.8 @ 1.5686 2 45.0 @ 1.6498 44 50.0 @ 1.6831 3 61.8 @ 1.7616 0 70.0 @ 1.8162 0

#### Experiment 9: GBP/USD 09/11/2007 to 22/01/2008, High 2.1161, Low 1.9337,

 Retracement Level Number Of Times Hit 25.0 @ 1.9793 46 32.8 @ 1.9935 37 45.0 @ 2.0158 8 50.0 @ 2.0249 3 61.8 @ 2.0464 0 70.0 @ 2.0614 0

#### Experiment 10: GBP/USD 05/09/2005 to 28/11/2005, High 1.8503, Low 1.7047,

 Retracement Level Number Of Times Hit 25.0 @ 1.7411 35 32.8 @ 1.7525 29 45.0 @ 1.7702 21 50.0 @ 1.7775 15 61.8 @ 1.7947 1 70.0 @ 1.8066 1

#### Experiment 11: GBP/USD 07/09/2004 to 16/12/2004, High 1.9552, Low 1.7708,

 Retracement Level Number Of Times Hit 25.0 @ 1.8169 16 32.8 @ 1.8313 13 45.0 @ 1.8538 5 50.0 @ 1.8630 12 61.8 @ 1.8848 33 70.0 @ 1.8999 12

#### Experiment 12: GBP/USD 03/09/2003 to 18/02/2004, High 1.9143, Low 1.5609,

 Retracement Level Number Of Times Hit 25.0 @ 1.6493 0 32.8 @ 1.6768 0 45.0 @ 1.7199 0 50.0 @ 1.7376 0 61.8 @ 1.7793 22 70.0 @ 1.8083 25

#### Experiment 13: USD/CHF 21/01/2008 to 29/12/2008, High 1.2296, Low 1.0370,

 Retracement Level Number Of Times Hit 25.0 @ 1.0852 37 32.8 @ 1.1002 9 45.0 @ 1.1237 17 50.0 @ 1.1333 20 61.8 @ 1.1560 31 70.0 @ 1.1718 19

#### Experiment 14: USD/CHF 17/03/2008 to 21/11/2008, High 1.2296, Low 0.9642,

 Retracement Level Number Of Times Hit 25.0 @ 1.0305 0 32.8 @ 1.0512 3 45.0 @ 1.0836 45 50.0 @ 1.0969 12 61.8 @ 1.1282 16 70.0 @ 1.1499 25

#### Experiment 15: USD/CHF 16/11/2005 to 16/05/2006, High 1.3287, Low 1.1918,

 Retracement Level Number Of Times Hit 25.0 @ 1.2260 32 32.8 @ 1.2367 45 45.0 @ 1.2534 27 50.0 @ 1.2603 7 61.8 @ 1.2764 1 70.0 @ 1.2876 0

#### Experiment 16: USD/CHF 30/12/2004 to 16/11/2005, High 1.3287, Low 1.1285,

 Retracement Level Number Of Times Hit 25.0 @ 1.1786 0 32.8 @ 1.1942 1 45.0 @ 1.2186 18 50.0 @ 1.2286 34 61.8 @ 1.2522 6 70.0 @ 1.2686 11

## The Significance Of Fibonacci Retracement Levels: My Conclusion,

When I first totalled up the results of this experiment I was shocked, I had not expected the number of times the daily price moved between one of the Fibonacci levels to be much different from the number of times the daily price moved between one of the arbitrary levels I had chosen.

The results of the 16 experiments above were as follows –

Fibonacci levels –
32.8%: Hit 213 times.
50.0%: Hit 194 times.
61.8%: Hit 211 times.
Total number of times a Fibonacci level was hit: 618 times.

Non-Fibonacci levels –
25.0%: Hit 264 times.
45.0%: Hit 261 times.
70.0%: Hit 230 times.
Total number of times an arbitrary Non-Fibonacci level was hit: 755 times.

Whilst I probably haven’t done nearly enough samples on nearly enough different currencies pairs, or even experimented with enough arbitrary values to ‘prove’ it, the results of the test do seem fairly significant.

According to the results of this experiment, the price is 1.22 times more likely to hover between one of the arbitrary levels than a Fibonacci level.

In fact, none of the three Fibonacci levels tested was hit as often as any of the three arbitrary levels tested.

This result came as a great surprise to me and seems to suggest that Fibonacci levels quickly repeal the price whenever it reaches them, I would therefore conclude that Fibonacci levels probably act as support and resistance.

Of the three Fibonacci levels tested, the most popular one (50.0%) was hit the least number of times; this may explain why many traders use these levels (and especially the 50.0% level) to try and pick tops and bottoms. I still don’t believe it’s possible to consistently be able to pick market tops and bottoms, but the results of this experiment seem to suggest that if picking a top or bottom is what a trader is trying to do then while using Fibonacci levels will not make them always able to do this it probably improves their odds.

Have you tested the statistical significance of Fibonacci retracement levels in the markets yourself? If so, what experiments did you perform and what results did your experiments produce? And what conclusions have you been able to draw as a result? If you’ve any information you would like to share with me on this please do contact me and let me know. Hope to hear from someone more knowledgeable 🙂