This post brings an end to my series on statistics in trading. If you are reading my blog for the first time, I highly recommend that you first read my posts about Standard Deviations, Bollinger Bands & Natural Distribution
The ZScore is the tool that brings all the statistic elements together, especially if we can use its values in the form of an Oscillator Indicator as you see below
The ZScore tells us how many standard deviations price is from a particular average. If price data is Naturally Distributed, which sometimes it is and sometimes it is not as much, the values would range primarily between -3 & +3, with most values ranging between -1.96 & +1.96.
In the chart above, we can see the ZScore indicator set with a period of 20 for the EURUSD Daily. Location above or below the zero line represent price either above or below the 20 period moving average since the value zero represents a zero deviation from the mean, price is located right at the average line.
It is worth noting that Bollinger Bands are usually set at 2 deviations from the mean. Based on this particular example above we can see how entering trades at such levels +1.96 or -1.96 delivered some decent profits. Such strategy is known as Mean Reversal.
The Formula to calculate the ZScore is quite simple. Z = (Price – Mean)/StdDev. An entire Spreadsheet & trading system can be built simply by having access to Price data, which is provided by most Central Banks, the ECB being the most natural distributed.
The ZScore can be calculated not only based on Price but also averages of price, aka Moving Average. In this case we would use a period for the price average which is much shorter than the period average we are focusing our trading.
In the example above we have a ZScore indicator set to calculate Z of an average. In this particular case we used a 20 period average of price and 100 period average as our main average. In order to provide a better visual representation we added two moving averages to the chart. 20 period in Green and 100 period in red.
As the ZScore indicator crossed over the zero value, we can see the shorter period average crossing above the longer period average, giving you an entry signal known as Average Crossover. The ZScore indicator remained positive while Price remained above the 100 average. An ideal situation here would have been to add a second ZScore indicator with a period of 20 which would have provided us with exits and re-entries as the value crossed below and above the zero line, representing price crossing below and above the 20 period average. A strategy known as Trend Continuation.
In the example above you may wonder why entering a Short at the +1.96 value provided a false signal as price continued to move upward. Mean Reversal strategies carry such risk. Eventually Price will reverse, but no one knows for certain when that will be. Mean Reversal strategies are better suited when Price is within a horizontal range rather than trending in one particular direction
The good news is, the ZScore indicator can also help us determine whether price is trending or not! For this purpose we can calculate the ZScore of the Standard Deviation itself. If values are moving downward we can determine the Standard Deviation is decreasing and thus price is consolidating while if the values are increasing we can determine an increase of the Standard Deviation which is usually followed when prices are trending in one particular direction.
In the example above we have a Z of Price indicator and below we have a Z of Std Deviation indicator. #1 was giving us a reversal entry signal but #2 was still increasing and therefore the entry signal was not confirmed. A few candles later #1 gave us a reversal entry signal again but this time it was confirmed by the #2 indicator showing a decline.
As you can see from the different examples above, the Z indicator offers a lot of ways to decipher the particular conditions of a particular traded instrument. We can, mathematically, define:
- The location of Price in reference to a an average to determine whether price is reaching oversold or overbought levels.
- The volatility of Price in reference to an average to determine whether price is entering consolidation or whether price is trending.
- The overall trend direction by examining the location of a shorter period average in reference to a longer period average
We spent countless hours working to create an indicator that would allow us to use the data that the ZScore provides in a visual format for us to determine what, when and for how long to trade a particular instrument. The ZScore Indicator Suite shown in the examples above is available for rental use for the MT5 platform.
I sincerely hope it enhances your trading performance. An entire system can be built with it