Harmonic Rotations are best described as the ebb and flow of prices of any given product within the market; in theory there is a natural expansion and contraction of prices similar to how we breathe. The market is in a constant auction to discover price, and participants act on the current market by anticipating higher or lower prices. The idea is if a rotation breaks out of its natural behavior it’s the first sign of an unusual occurrence, for instance trading at the open can cause a very expanded first rotation. Let's consider figure 1: the DAX on the 9th of August 2016 in which it traded up >2% and closed a >150 pts gapzone standing from the start of 2016.

Figure 1: DAX on August 9 2016, 08:00AM - 22:00PM (GMT+1), harmonic rotations with minimum rotation of 10 points, timeframe 1M; |

With the restriction of 10 points as a minimum rotation there were 18 rotations on the 9th of August. The average up and down rotations were 46 and 19 points respectively with an average rotation time of 40 and 42 minutes respectively. As the DAX started trading out of the value and out of the range set by the previous trading session, DAX took some big deep expanded breaths followed by minor contractions. All very interesting, but how can information on harmonic rotations be of value in our trading plans and our actual trading.

An excellent read on how a fellow trader (@adeyf69) uses statistics (among other rotations data) in his trading is: http://takingonetradeatatime.com/2015/10/29/how-i-use-statistics-in-my-trading/; Short recap of Adey's post with emphasis on the relevancy of studying rotations:

- Statistics can provide extra context to your trade plan.
- Statistics can help you decide whether a trade is worth taking. The harmonic rotation is useful as a gauge of strength of the current rotation taking place.
- Statistics can boost the win rates of your trades and the overall expectancy of your setups. Statistics on rotations can be used as an input for sensible scales and stops.

We consider a small sample size harmonic rotations study on the DAX with the following input:

- Product: DAX CFD;
- Data provider: IG Markets;
- Date: 1st of August 2016 - 12th of August 2016 (# 10 trading sessions);
- Time: 08:00 AM (GMT+1) - 22:00 PM (GMT+1);
- Timeframe: 1 minute;
- # Bars: 7;
- Minimum rotation: 10 points (20 ticks in equivalent DAX future).

The output is shown in figures 2 and 3 with the statistics and a harmonic rotation histogram respectively. Although the sample size is small with 355 rotations in 10 trading sessions the histogram reveals that the most common rotation is in between 14 and 16 points with the 1 standard deviation area given by 10 to 26 points. A rotation outside 26 points can therefore be considered large. Next step is to incorporate these statistics in our trading plan (use as an input for stops and targets) and a follow up study can be done on the unusual occurences (eg. rotations after macro releases, rotations after break out of yesterdays value area and range, etc.).

Figure 2: DAX Harmonic Rotation Statistics, first column shows hour of trade starting with 08:00 AM to 09:00 AM GMT+1 |

Figure 3: DAX Harmonic Rotation Histogram, point of control in RED, 1 sigma value area in ORANGE, 2 sigma value area in YELLOW |

More information on rotations (background, guide to DIY in excel, ideas how to exploit the information rotations statistics give):