Head and Shoulders Pattern

For my inaugural post, I would like to discuss the venerable “head and shoulders” pattern.  You have probably seen this pattern before.  The example below is made-up data, but it has the familiar features – a head, shoulders, neckline, and price target.

HS1 What you see here is simply a rise and fall with some noise over it.  That’s why it works.  Consider the following trajectory.  This is a parabola, the path taken by a long fly ball.  Since it’s a stock price and not a baseball, you should consider the point at which you would be willing to bet on a continued descent.  I would say that falling through $90, around day 63, the odds are good.

HS2In the next chart, I have taken the parabola and overlaid three periods of a sine wave.  Actually, for the timeframe depicted, it’s a negative cosine.  This represents an oscillating intermediate term trend with a period of one month.

HS3You can see that the head and shoulders are an artifact of this monthly oscillation.  An oscillation is, by definition, trend neutral.  Our parabola is still the prevailing trend.

Now, if you go short on day 63, you may still be correct but the oscillation will move against you for the next two weeks.  The only way to be “sure” is to wait for that third wave to turn down and breach the neckline.

The measured move is how far you can expect to ride the downtrend before discovering that our parabola is maybe not a parabola but another longer sine wave.  There is a guy called Fourier who can break any series down into a collection of superposing sine waves.

HS4I produced that first chart by adding some random noise to the sine wave.  Yes, the Excel RAND function.  For the purpose of trading a pattern that takes months to emerge, the daily ups and downs are just noise.


In real life, you can’t see through the noise like this and, if you could, it wouldn’t be a perfect sine wave.  But you can plot a 10-day exponential moving average.

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