Fun With Coin Tossing

It may sound weird but I really like playing with software that simulates distributions – it probably comes from when I had a semester free at Uni and simply took subjects that looked interesting. One of the ones I dropped into was Mathematical Ecology which is largely the mathematics of  natural distributions. I found it to be surprisingly interesting and since it involved no fieldwork and no one lecturing me as to why we shouldn’t treat possums as vermin and be able to either shoot them or drown them in a wheelie bin it was pretty much perfect.  Since then I have always viewed any system I encounter through the lens of much of what I learnt in this course and I have found markets to be wonderful subjects for analysis. Which is why I like modelling coin tosses – their variation based upon some tiny changes in initial conditions make for wonderfully diverse outcomes.

The chart below is an example.

Thus chart tracks the number of net heads over 10,000 iterations. Such things are wonderfully instructive because if I didnt tell you it was simply a distribution of coin tosses most would naturally see a price chart of some instrument. This is particularly true since I have plotted a moving average on the chart. Traders will see up trends, down trends, periods where price congests and all manner of things. What the chart highlights perfectly is the nature of clustering – you can see that there are clusters of heads and clusters of tails and this is useful because it serves to remind us that we operate at both the statistical whims of our system and of the market. LB and I have been doing a series of one day seminars recently that look at the problems that people who want to move to full time trader encounter and some of the potential solutions to those problems. One of the biggest problems we encounter is that new traders simply dont believe that they will encounter losing periods and if they do they think that their losing streak might be two or three trades before they are back on their way. If we think of the chart above as the number of losing trades you might have in a given period you can see that the ruthlessness of statistics tells a different story.

It is probably fair to say that in some way we all believe ourselves immune from population statistics. I am certain that the majority of smokers who develop lung cancer are surprised at their diagnosis. Yet it is known 90% of all lung cancer patients were smokers and that smoking causes 1 in 5 cancer deaths in Australia. Despite these horrible statistics many believe they are immune. Undoubtedly they are devastated when their shield of invulnerability is pieced by reality.  Decades ago when I first encountered this problem I dubbed this phenomena the myth of individual specialness. Each person believes that they are a special case and therefore exempt from the impact of large scale statistical measures. Traders are no different, the majority believe that they will never have streaks of losing trades and never enter drawdown. Unfortunately, this naivety is wonderful fodder for those out there who run one day seminars telling people that they can quit their day job and makes $100,000 with a $10,000 bank trading cryptocurrencies.

Trading is a simple profession, you spend most of your time trying not to go broke whilst waiting for the next big win. During the wait you are constantly reminded you are not that special.