Bigger Games -the peculiarities of financial statistic

written by Sergey Tarassov

1. How many times some phenomenon should occur for taking it into account as the phenomenon that affects the stock market?
2. How many winning trades do we need to have to be sure that %X trading strategy is reliable?
3. Why a trading system that worked good enough for several years in a row does not work anymore?
4. Why the weather is so unpredictable last years?

All these questions have something in common. Mathematically speaking they are questions about the sample size, the amount of analyzed  phenomena. I can substitute all these questions to one: what is the sufficient value of the sample size?

First of all I will answer to this question as a recent University graduate would do. The answer would be:

We need to have a sample size 30 at least, this is the minimal number that allows to apply the standard statistics formulas. In other words we need to have the phenomena that take place 30 times at least, or 30 trades at least.

The guy who has spent many years dealing with financial markets data would give a different answer. Here it is:

I am sorry, this is not a good news. Even if your trading system is confirmed by 100 trades (as an example) or even 500 trades - you cannot be sure that this trading system will work so good in the future. We have to accept the risk, we cannot avoid it just using classical statistics' formulas. This is a reality of financial statistics.

This statement needs some comment. The classical statistics was born from a game theory; in most cases this kind of statistics assumes the NORMAL distribution of the analyzed phenomena. More info about this issue you can find in this article: http://www.timingsolution.com/TS/Articles/cds/index.htm

When we deal with real phenomena, especially the phenomena that involve human activity, the classical normal distribution (in most cases) does not work anymore. While the classical statistics can be considered as a variation of dicing of the ideal coin, the real statistics that describes the events of human activity can be compared to a dicing of the coin, but this is not a random dicing. This dicing  uses some special rules that involve some other BIGGER game. Accordingly, this big game is a part of one more, even bigger, game. Dicing our coin this way, we can get some effects that cannot be explained by classical statistics' approach. For example, while dicing our coin, we can get 50  heads in a row, however this fact still can be not random, it might be caused by some other, bigger, game.

As an example, analyzing the Dow Jones Industrial index in 2009-2010, we can always find some aspect that coincided with Dow moving up. We can even provide the formal statistical analysis and get very good results, but - this aspect stopped working beyond the year 2010. Where is a mistake here? Why the aspect that worked well before does not work now? The answer is: we simply have considered this phenomenon as an event with one degree of freedom while in reality this phenomenon has more dimensions. To get the true answer, we have to consider the history of DJI in 2009-2010 as a part of a BIGGER GAME. Some hints to that BIGGER game can be found among fundamental factors. In 2009-2010, Dow is still affected by US stimulus plan, while this plan itself is a part of another BIG GAME - Great Financial Crisis of 2007-2009; in turn, the Great Financial Crisis refers us to another BIG GAME - the reform conducted by Ronald Reagan in the beginning of 1980s. So, when doing our research of financial markets, we always should remember the bigger picture.

BTW, the weather follows the same rules; it involves many big astronomical/geological/geophysical factors. The weather looks unpredictable simply because we are not able to see the whole picture now. We observe the symphony of many BIG GAMES and because very often we do not understand  most of these GAMES yet, they look unpredictable for us and even scare us.