Now we are interested in how the price moves in relation to the random normal distribution, and also how this changes over different time frames. Based on the previous analysis, we can make the conclusion that when prices keep moving inside a smaller number of deviations; it (the bar) tends to close near the equilibrium. Furthermore, when price moves away a certain amount of deviations from the equilibrium (if we compare it to the normal distribution, the equilibrium is the mean), the bar tend to close further away which indicates a trending scenario.

So, what does this mean? Basically it means that either the market moves sideways in a relatively narrow range most of the times, and when it breaks away from this range prices tend to move far away from the equilibrium. The probability for the price to move back to the equilibrium is still higher than the probability to move away, but compared with the random normal distribution this tendency has a higher probability than when random prices is used. In practice, this means that the trader can benefit from two kind of strategies – swingtrading/scalping will work great when the market is trading within a range, and trend following strategies when the market moves outside a certain number of deviations (based on the charts, the threshold is approximately 2.8 deviations).





As you can see in the graphs below, the 5m timeframe shows the highest tendency to act as a random normal distribution, while the H4 timeframe instead tend to either retrace to the equilibrium or trend far away. Please note that in this analysis we have not considered the time effect, it is only based on volatility. It is not impossible that the price tend to retrace to the equilibrium more often during low volatility times (such as during the night session) and to trend during the higher volatility times.





Nothing new, right? Perhaps not, but this analysis provide us with an interest idea for both positions sizing (which we will run a simulation on next) and also how to implement different kind of trading tactics based on the market scenarios. First, I want to explain some why: I assume most readers are familiar with the concept of normal distributions and standard deviation. Consider a simple strategy that is based solely on price, where we assume that the market move in a completely random fashion. This would mean that the probability of a certain move could be predicted with help of the normal distribution. The probability that the price would reach +1 standard deviation during the measured time unit is therefore 34.1%, and for +2 standard deviations is 13.6%. We will now look at the strategy where we go long at the beginning of the measure period, take a profit once +1 stdev is hit or a loss once the -2 stdev is hit. If this strategy was built on a bet, that we received one $1 dollar and risked $2 and if no level was hit the bet was cancelled, we would have a positive expectancy (0.341*1-0.136*2 = $0.69). Unfortunately, this is not how it works. Since the random normal distribution don’t have binary values, but instead is made up of a probability density function, this means that once our chosen period of time has ended we will end up with any value between $1 in profit and $2 in a loss, if none of the levels is reached. If we increase the levels in the previous test to binary steps each 1 stdev, we would instead have the expectancy of $-0.136 (0.341*1-0.341*1-0.136*1) since it is equally high probability that we end up with $1 as -$1, but then we also have the additional risk that the -$1 turns into a -$2. By running a monte carlo simulation of 10000 iteration to introduce non-binary steps we can see that this gives us an negative expectancy. This is because we limit our profit potential at the same time we have a higher potential to lose twice as much.

Now, how does this apply to the market? Since the market doesn’t move exactly as a random normal distribution as you can see in the graphs, we can’t apply this piece of theory direct to the market. In order to see how the same kind of strategy will work on the forex market, we need to try it with a probability density function that is similar to the markets distribution instead. However, this will take a lot of work and analysis to find such a probability density function, therefore we will not dig into that problem now and instead end this little article for now.

Best regards,
Johan Andréasson, System Investors