# Cumulative Harmonic Rotations After a 2 Standard Deviation Rotation for the ES (S&P500 E-mini)

While doing my Harmonic Rotation and Pullback and Continuation Studies, I was wondering if after a large harmonic rotation (Greater than 2 Standard Deviations) the ES would generally tend to continue in the same direction as that move. The thinking behind this being that a large harmonic rotation would be a signal of new value, and many people have said that “markets have inertia”, so it would be logical to think that the markets will continue to move in that direction.

I wanted to test this theory on the ES and from a Day Trading mindset. I took my Harmonic Rotation Study for the ES, which found all moves in 1 direction without a 1 point pullback (4 ticks on the ES, or \$1), and then I summed the following Harmonic Rotations that happened after that rotation. I summed the following 2, 4, 6, 8, 10, 20 and 50 rotations after a large rotation. I did even numbers because the market will need to rotate in the opposite direction, before rotation again and continuing in the same direction as the large rotation. This keeps the analysis even between up and down rotations.

I also adjusted the data to normalize between upward and downward rotations. Thus a positive cumulative rotation means that it is in the same direction as the large rotation, while a negative cumulative rotation means in the opposite direction as the large rotation.

Here’s the data:

First 2 rotations after: There is a slight positive bias in the same direction, but quite small.  The standard deviation is also quite large considering the original  Harmonic Rotation study found that 68.2% of all rotations were 1.75 points or lower and 95% of all rotations were 3.5 points and lower. With a 3.49 standard deviation, it would seem that the rotations are generally larger right after a large rotation.

The data then indicates that the cumulative rotations afterwards are against the original rotation. 4 rotations is almost even, and then it continues to drop.

This data would indicate that it may be better to fade a large rotation, but only after 2 or 4 rotations after the large one.

Given that I am currently lumping ALL rotations greater than 2 Standard Deviations, my next question would be, “Does the likelihood of a continuation move increase as the initial rotation size increases? It’s an interesting theory, but it is limited to a very small set of rotations. Here’s a scatter plot chart of the cumulative 4 rotations vs the initial rotation size:

Pretty obvious there is no real correlation. Looks like it’s back to the drawing board! 🙂