Mathematical Expectancy… A Basic Powerful Concept in System Design and Development

Through my last few posts I have mentioned the concept of mathematical expectancy , a very important and useful concept which many people seem to be unfamiliar with. The objective of today’s post is to talk a little bit about the concept of mathematical expectancy and its usefulness, pointing out why it is such a fundamental and useful tool in the development of long term profitable trading systems and a key step in the evaluation of any given entry logic. I will start the post with the definition and purpose of mathematical expectancy and I will then continue with some examples and concepts which will show you why the analysis of mathematical expectancy is extremely important and a necessary step in the design of any given trading system.

Many of you may have wondered how successful traders come out with a good entry logic for their trading systems, being manual or automated. How can these people know the chances of success of a given entry logic and use it within their system development ? Many people who are new to automated or manual trading usually have an over-focusing – with little analysis – on the entry logic completely neglecting the development of the money management part. Not only does this pave the way towards the development of unprofitable systems but it doesn’t help that the way in which the entries are developped is non-systematical and statistically not rigurous. usually you’ll find that people develop a given entry logic based on visual observations of a VERY limited number of market situations and then modify the entries in forward/live testing as they fail under current conditions. This speaks about the lack of knowledge of this novice developers and the way in which they view market and long term profitability.

A simple question then arises. Is there a way to systematically evaluate different entries to know which entry is better, which time frame is better and what exit strategies may be more suitable ? The answer comes in the form of mathematical expectancy analysis- an absolutely simple- yet absolutely powerful technique which allows you to evaluate the POTENTIAL (different from the profitability which comes into play when money management is implemented !!) of a given entry logic. So what is exactly mathematical expectancy and how does it play a role in system development ?

The mathematical expectancy analysis is simply a technique which allows you to know the extent to which the market is bound to move in a certain direction after a given entry is taken. The analysis is fairly simple, you mark every entry for a given logic on a chart and then you mark a set given number of bars into the future. So for example, if you want to evaluate the mathematical expectancy of a moving average cross on a 10 bar period you simply mark each entry and then you mark the tenth bar after the entry. After doing this you determine the high/low of this ten period after the entry. This gives you the maximum the market moved in favor of your entry and against your entry during this period. When you do this over a very large sample size you can determine the average movement in favor and against you and you will be able to tell if the mathematical expectancy of your system is positive or negative. This marks the potential of your entry.

This analysis is very versatile and very important. By changing the number of periods in the analysis you can see if your strategy is better at capturing short or long movements and what timeframe fits your strategy best. For example, some systems may have negative mathematical expectancy on a small number of periods while the mathematical expectancy may be positive under larger periods meaning that the system is better fit at capturing long term movements than short term movements. This analysis also allows you to design appropiate exit techniques for a given entry logic since you know what the average movement against and in favor of your entry is you can calculate an adaptive SL or TP such that in average you will hit the TP and miss the SL.

It is of course terribly difficult to explain all the aspects of mathematical expectancy within a single post reason why I only meant to give a small introduction to the topic within this post so that people interested in system design may know that this technique exists and has a paramount importance in the development of a system’s entry logic. Within my website – in Asirikuy- I have made several videos explaining both the theory and practical aspects of evaluating mathematical expectancy over a 10 years period, in additon I have also coded an EA to allow people to evaluate any given entry logic . If you aren’t interested in Asirikuy then at least you now know this tool exists and you can either make your own EA to evaluate this aspect or you can do your own research to find more information on the subject :o).