Normal Distribution

On my About page I mentioned how my trading performance improved dramatically after discovering Brian Twomey on Twitter. Brian can hit targets like no one else. No indicators, no charts. All with pen, paper and a $5 calculator! How does he do it? A deep understanding of statistics and Interest Rates. Brian has written two books. One of them is available on Amazon, which I highly recommend and the other one is no longer avaialable

     

Without knowing much about statistics myself, I went deep down the rabbit hole determined to understand what Brian was talking about on his book about ZScore so I could apply it myself on my trading. Little did I know it wasn’t as difficult to understand as when I first looked at the image below on Brian’s book representing the curve of Normal Distribution

What does the theory of Normal Distribution says

According to Wikipedia, it is a graphical representation of the normal distribution theorem stating that “the averages of random variables independently drawn from independent distributions converge in distribution to the normal, that is, become normally distributed when the number of random variables is sufficiently large”.

According to Investopedia, The Normal Distribution, is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean.

In simple words, Normal Distribution tells us that, with enough data, an average can be calculated, represented by the zero point on the graph, from which the Standard Deviation of each data point can be calculated so we can determine how close or far from the mean each data point is. The beauty lies on how consistently symmetrical the data falls within a certain amount of deviations from the mean.

The theory tells us that, if the data is naturally distributed:

• 68.26% of the data points will fall between +1 & -1 standard deviations from the mean.
• 95.44% of the data will fall between +2 & -2 standard deviations from the mean.
• 99.72% of the data will fall between +3 & -3 standard deviations from the mean.
• ONLY 0.28% of the data will fall beyond +3 & -3 standard deviations from the mean

How can this information help you on your trading?

Well, if you knew that 99.72% of the time, the price of a currency or a stock travels between +3 and -3 Standard Deviations from the mean, wouldn’t you want to know exactly what point that is in your chart so you can mathematically draw perfect support and resistance lines? The answer is a DEFINITE YES!!!

However, it is a bit more complex than it sounds. First we need to determine what the mean is. The mean is a Simple Moving Average, which is the average of a selected range of prices, usually closing prices, by the number of periods in that range. With so many average periods known to traders, you can see how complex this can be, but not if you understand the following. Just like a shorter period average moves faster and closer to the price than a longer period average, a shorter period average produces more deviations than a longer period average.

Below is an example of Bollinger Bands with periods 20, 50, 100 & 200. As you will see, the shorter the period the more deviated price seems to move from the mean, easily touching the 3rd deviation band in red, while in the longer period, price seems to be traveling within 1-2 deviations from the middle line, the mean.

There is also the variable of which Time Frame to use which is a matter of personal style. It is important to know, once again, the shorter the time frame the more fluctuations. Don’t expect a define support and resistance levels at the +3 & -3 deviation from a 5 period average on a M5 chart!!!

With this new understanding of Normal Distribution, my hope is, you will be able to take more advantage of the Bollinger Bands indicator

On my next post I will close these statistical series by going over the Z Score. Once understood you will never need to see those Bollinger Bands on a chart in order to determine support and resistance as well as breakout points! More so, like Brian, if you ever run out of electricity or internet, you will still be able to calculate your entries and exits, perhaps even with more accuracy!!!