It has been a while since my last blog, not sure if I can still write some thoughts down on a paper, so let's try=))

During our trading journey, we often wonder how the market behaves on the price charts. Every one of us employ different methods and views so he can trade his edge comfortably. Some of which can be the market harmonics or market geometry trading... One law stated by very well-known Alan Hall Andrews says that the market reaches the median line in 80% of time (hopefully I remember that one correctly). And there are certainly more of these.

The question which immediately arises is: **“Is there any research which could confirm that there certainly are universal laws in price charts of financial assets?”**

The answer is surprisingly - Yes. We talk about **Scaling Laws** here, for more information see (Müller et al. [1990], Guillaume et al. [1997], Glattfelder et al. [2010]) on which academic works is this article mostly based on and are used as a primary source of further informations. There are **17 laws in total**, and they can bring a further understanding of financial markets behavior. I am going to talk about 3 of them, for me, the most mind boggling.

Beforehand it is necessary to explain what those authors define as **directional change** (DC) and **overshoot phase** (OS). Firstly, a directional change is identified (of pre-set value, be it 1.7% in this case) from the last price extreme. When this event occurs, afterwards we measure the overshoot phase, until the new directional change event occurs. And so on all over again. See figure one.

Figure 1: Directional change and overshoot phase with its fractal nature

Further presented scaling laws could be written with formulas which corresponds to the scaling laws generally. To make this more entertaining let’s skip the math and present the results which holds in many markets. Reader can find the math and proofs in mentioned works above.

**First Scaling Law:**

Just to mention - is set at the beginning. Be it any reasonable positive number. Then, further equation holds on FX (proved by academic researchers) and on crypto currencies (proved by me, results can be sent via PM).

It basically states, that if we chose 1.7% directional change, the overshoot phase is in average equal to this size. Important to mention, this hold for the average length of overshoot phase. But still works pretty well.=))

**Second Scaling Law:**

Translated into English. The average duration of overshoot phase will be twice the bigger as average duration of directional phase.

**Third Scaling Law:**

Translated into English. Let’s assume we define a tick change of 0.1%. Then the average number of those 0.1% tick in our 1.7% DC will be twice as bigger in the overshoot phase as the average number of those tick in the directional change.

**Short conclusion for traders:**

The moral for traders could be - if your trading resolution is targeting around 1.7% market moves, then, if you try to capture them after the DC, then you should be more patient because the market will not move so quickly, but in average it should make the move (which does not tell much about a certain move hehe)=)) So, patience, patience=))

**Further research suggestions:**

Some of my thoughts after playing around with this concept.

It is notable, that when we choose different size for up and down directional changes (i.e. DC from low is e.g. 1% and from high we measure 2%), then those laws hold too, but in the opposite way I would expect. I.e. The OS phase is in average equal to DC but for the OS which occurred before DC. Which says, if you want to grow for 2% in average you must fall 2% certainly. Sounds more like a life to me :D

## Comments

What would represent "Be it any reasonable positive number." this is a bit stretched?

Yes it is a bit stretched statement. Sorry. The word "reasonable" should be explained.

Let's assume the EURUSD moves 20% in one year (1Y candle), therefore setting DC to 15% would not produce enough of DCs (as well as overshoot phases). However, when we use something reasonable let's say 0.5% for DC, we will have enough of observation to statisticaly prove those laws really works as defined.

So, the answer is - for FX majors, picking any number from interval ( 0% ; 5% ) (the 5 is questionable ofc) would converge the average return of overhoot phase in reasonable time period to the chosen value.

If one choose 2.5% for DC, the average overshoot phase will also be of 2.5% and so it holds for any reasonable number we choose=)) (unreasonable number - hundreds of procent and more?)

As it works with averages, for us, traders, it does not bring any edge. However, Glattfelder and Olsen defined a Coast Line trader, which is a market making system with some backtests showing it is working well.