Tossing a Coin and Trend Following

Following on the topic of probabilities, I thought on making a post regarding the relationship between tossing a coin and a trend following system.

Many authors have addressed this particular subject, and I will try my best to share my view on the issue.
The event of tossing a coin is a classic example on how probabilities can be explained.

Every time someone tosses a coin there's 50% chances for head and 50% chances for tail. Nothing new.

The first interesting conclusion is that they are totally independent events.

This simply means that even after tossing a coin 10 times and getting heads in all of these attempts, the next time you toss the same coin ( the 11th attempt), there will be a 50%-50% probability of getting either head or tail.

Now, what is the relationship between these statistic events of tossing a coin and trading?

The act of tossing a coin and analysing its outcomes is what makes the foundation of a sound trend following trading system. For that matter, it is also the foundation for mean-reversion systems. However, for the purposes of this blog, I will focus on trend following systems.

Coming back to the coin toss issue. Whenever we toss a coin repeatedly, the outcome wil not always be H(head) or T(tail) perfectly alternating like the following distribution:

HTHTHTHTHTHTHTHTHT: 50% H - 50% T

In a sequence of 20 tosses, we could have sequences such as:

HTTTTTHHTHTHHHTHTTH: 50% H - 50% T

THHHHHHHHHTTTTTTHHT: 50% H - 50% T

TTTTTTTTTTTTTTTTTTHT: 5% H - 95% T

HHHHHHHHHHHHHHHHT: 95% H - 5% T

The only thing we really "know" is that in the very long term, the distribution will be approximately 50% H - 50% T in average. This is a statistic observation called "The Law of The Large Numbers".

However, it's close to impossible to predict what will be the distribution of events in the very short term. This is why there's a tendency for novice traders to observe short term technical patterns that fall in the statistic observation called: "The Law of The Small Numbers". For example: If a currency pair, for the last two weeks had breakouts on the 30min. bar chart, than, the novice trader, turns this into some kind of law and thinks he has found a true gold mine. Big mistake.

I don't want to get away from the main subject. So lets get back to it.

Trend following strategies 'believe' that the distributions do not alternate perfectly towards the mean as HTHTHTHTHT, on the contrary, these strategies look out for discrepancies in the distribution concentrated in one direction or the other relative to the mean. This is what we call trend.

Therefore, trend followers observe imbalances in events of price they being random or not. Therefore, whenever there's a discrepancy, trend follower jump into the trend until the trend reverts back towards the mean thus invalidating the original trend according to one criteria.

It's up to one's criteria to determine, as a trend follower, to observe these distributions and its imbalances as to guide on: where to enter the market, where to cut losses and where to take profits.

As previously mentioned, I will try my best to post my criteria for trend following trading.

Best,
M.