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Bulkowski's Head-and-Shoulders Symmetry

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Written by and copyright © 2005-2019 by Thomas N. Bulkowski. All rights reserved. Disclaimer: You alone are responsible for your investment decisions. See Privacy/Disclaimer for more information. Some pattern names are the registered trademarks of their respective owners.

My book, Encyclopedia of Chart Patterns Second EditionEncyclopedia of Chart Patterns 2nd Edition book., discusses the head-and-shoulders chart pattern in detail including performance statistics. I show a picture of it on the right.

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This page examines the head-and-shoulders patterns for symmetry, answering the question if a right shoulder is farther away than the left, does performance suffer?



Head-and-Shoulders Symmetry Summary

I read in Picture of Markman's book. Swing Trading: Power strategies to cut risk and boost profits, by Jon Markman that head-and-shoulders patterns with an extended right shoulder tend to perform less well. This page proves that Terry Bedford (the person to which the finding is attributed), is right. Head-and-shoulders tops and bottoms with extended right shoulders perform less well than do those with the left shoulders farther from the head, by 37.4% to 35.9%.

I also looked at pattern symmetry. Unsymmetrical head-and-shoulders tops perform better than their more symmetrical looking counterparts, with rises averaging 23.8% versus 22.8% for more symmetrical patterns. Head-and-shoulders bottoms show the reverse: symmetrical patterns work better than their ugly counterparts: 38.1% versus 34.9% average rise.


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Head-and-Shoulders Symmetry Methodology

The three views of a head-and-shoulders top chart pattern, show for symmetry.

The chart shows three varieties of head-and-shoulders top chart patterns. The top one shows a symmetrical pattern, with an equal distance between the head and shoulders. The middle figure shows the right shoulder farther from the head than the left shoulder. The bottom illustration shows the reverse, with the left shoulder farther from the head than the right shoulder.

I started with my database of known-good head-and-shoulders patterns: tops and bottoms, simple and complex. The data used 500 stocks covering the period from mid 1991 to mid 1996 and additional stocks both no longer trading and those more recent (from 1991 to June 2008). The test used well over a thousand stocks, but many symbols were duplicated between the three databases. When the testing finished, only data from 678 unique stocks qualified, but those yielded 2,117 patterns. The period covers both bull and bear markets, with the bear market in the S&P 500 index from March 2000 to October 2002 and the bull market is everything else.

Once I had the data, it was just a matter of analyzing it. I computed the time between the left shoulder and head and head and right shoulder. For a complex head-and-shoulders top, or bottom, I used the shoulder farthest from the head. I added together the head-and-shoulder tops and complex head-and-shoulders tops to keep the sample counts high. I also did this for the simple and complex bottoms (the word simple means a head-and-shoulders top/bottom when contrasted to the complex variety).

Once I had the distances, I just divided the two to form a ratio. A ratio of 1.00 was perfectly symmetrical. For example, if the left shoulder had 49 days to the head, and the right shoulder was also 49 days away, the ratio would be 1.00 (49/49). An unsymmetrical triangle would be anything not symmetrical. By that, let's take another example and widen the range to 1.2 to 0.80. Any ratio falling within 1.2 to 0.8 would be symmetrical and anything outside of that range would not be symmetrical. For example, let's use the shoulder to head distances of 29 and 34 days. The ratio is 29/34 or .85, which falls within the 0.8 to 1.2 range. Flipping the distances around, 34 and 29, results in a ratio of 1.17 (34/29) which is still within range, so it is also symmetrical. Days 26 and 16 would not be symmetrical because the ratio is 26/16 or 1.63 and 16/26 is .62, which is also outside of the symmetrical range.

To prove that patterns with an extended right shoulder underperform, I compared the ratio of left shoulder to right shoulder distances. A ratio higher than one means that the left shoulder is farther away from the head; a ratio below 1 means the right shoulder is farther away. Knowing this, I just computed the average rise (for bottoms) or decline (for tops) of the two groups.

For each ratio range, we can map the performance of the head-and-shoulders pattern to get a sense of which symmetrical/non-symmetrical patterns work best and which ones don't. This may sound complex but it isn't. A table shows which ones outperform and you will see a pattern as the range widens. You can also take an average of the results to get a sense of how symmetry works for symmetrical patterns and the ugly ones.

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Head-and-Shoulders Symmetry Results

The median distance from the left shoulder to the head is 28 days and from the head to right shoulder is 29 days. The averages are nearly as close, 35 to 37 days apart, respectively. The numbers suggest that many of the patterns in the three databases I used are symmetrical.

To prove that patterns with an extended right shoulder perform worse than do those with an extended left shoulder, I compared the two as described in the Methodology. I found that the average post-breakout rise for head-and-shoulders bottoms from patterns with an extended left shoulder was 37.4% (420 samples) compared to an average rise of 35.9% (606 samples) for patterns with an extended right shoulder.

For head-and-shoulders tops, the trend was similar: 23.3% (501 samples) versus 22.5% (590 samples) for extended left and right shoulders, respectively. In other words, simple or complex head-and-shoulders tops or bottoms with an extended right shoulder underperform.

I created a range of ratios to look at and mapped the average rise or decline from the breakout to the ultimate high or low, depending on whether or not the pattern was a bottom or top, respectively. The following table shows the results for head-and-shoulders tops and complex head-and-shoulders tops (combined to keep the sample counts high).

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MaxMinAvg Drop %SamplesAvg Drop %Samples

Ignore the first few rows and the last one because the sample count is too small. When the ratio between the left shoulder and right shoulder distances range between 1.10 and 0.90, we see that a head-and-shoulders top or complex head-and-shoulders top results in an average drop of 24.6% after the breakout. Head-and-shoulders with the shoulders less symmetrical than the 1.10 to 0.90 range show drops averaging 22.4%.

As you scan down the columns, the results flip from the symmetrical patterns doing well until the max ratio is less than 1.30 and it switches to the non-symmetrical patterns from there on. If you average the numbers with triple digit sample counts, we find that symmetrical patterns have post-breakout drops averaging 22.8% but non-symmetrical patterns show declines averaging 23.8%. Thus, the more unsymmetrical a head-and-shoulders top appears, the better it tends to perform.

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The following table shows the results for head-and-shoulders bottoms and complex head-and-shoulders bottoms. Ignore any row with less than 3 digit sample counts. For the high sample count rows, the table shows that symmetrical patterns outperform the non-symmetrical counterparts in every case. The average of the rows also confirms this: 38.1% average rise for symmetrical patterns versus an average rise of 34.9% for non-symmetrical patterns.

Symmetrical head-and-shoulders bottoms outperform.

MaxMinAvg Drop %SamplesAvg Drop %Samples

-- Thomas Bulkowski

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Written by and copyright © 2005-2019 by Thomas N. Bulkowski. All rights reserved. Disclaimer: You alone are responsible for your investment decisions. See Privacy/Disclaimer for more information. Some pattern names are the registered trademarks of their respective owners. Your momma is so fat that the shadow of her ass weights 100 pounds!