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Quantifying Randomness

Why should we talk about randomness when trading the financial markets? First of all, we need to ask; what is random? When we consider something random, is it actually random or is it that we are just naive about the conditions or contributors of the system. Random to the observer is simply the outcome and is usually associated with something that is unpredictable or has no recognisable patterns. Let’s take a roll of a dice, we are certain that dice has 6 sides and when rolled we believe the outcome to be random. However, it might be the case that it is not random and we are just ignorant. If we can accurately measure all of the conditions that lead to the dice facing a certain side, then it stops being random and becomes certain.



The problem is that there are far too many initial and contributing conditions in the system and instruments are not sensitive enough to accurately measure them, let alone the accuracy of the size of the dice itself. However, in this light, the more times we roll the dice we find there are certain biases. For example: manufacturing faults giving asymmetry to the cube causing it to favour one side. This can then be seen after a number of throws. Patterns form and after a large number throws and can start moving from being random to becoming a determinable system.


Even with a coin toss we would believe there is only two possibilities; heads or tails. However, it has been calculated that a US nickel will land on its side once in every 6000 flips.

True randomness has “no discoverable cause”. The only one known to us is the very small world of quantum mechanics where there is no initial conditions for us to know. The only way to know an electron's position is the act of measuring it. It could be anywhere or in any position and is only measurable when it is observed. In other words, it is the act of observation which determines its position.


The poignant question here; are the markets random? Well no, they are not, however unless you know all of the contributing factors then they might as well be.



An interesting book written in the 1973 Random Walk Down Wall Street contends that the markets are completely random. Burton Malkiel suggests that one cannot predict the trend based on past history. - He conducted a study constituting of analyst’s prediction on a chart. When they found out that the chart was produced by a coin flip they were outraged. The chart, in fact looked very much like a real stock chart.


Critics of this randomness in price movement argued that the analysis is more than just technically based on the high, low, open and close. It can be predicted with a positive probability with Fundamental analysis and good risk reward ratios.


What is not random? – or the question; what is close to not random? To find a determinable system is to make sure a large enough source of information is gathered and tested against. Then to understand the biases that may make the tested data deceitful. These quantifiable results make the system determinable when using enough information covering all possible scenarios. Adjustments can be made to then make the system have a positive outcome.


How is this achieved? – A test of all possible scenarios plot a distribution curve and as long as the mode of the curve is creating a positive return then the system works well. The trick is to get the mode as positive as possible. Another way to see this is the profit factor; as long it is above 1 then the system is making money. (Profit Factor is the gross profit over gross loss. i.e. the return for every $1 invested).



The magicians disguise of course is the biases and information what is not available. Having a quantitative assessment of a system is not necessarily a guaranteed outcome. Depending on the depth of information, some factors are not included in quantitative testing. These include; swap rates, finance charge, slippage and latency. Biases include; look ahead bias, survivourships bias and manager bias.


The biggest of all is what I call “future bias” as there is always an unknown future event that can push the tails of the distribution out, reshaping the distribution curve.

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