The theory of quantitative trading
This book consists of a selection of articles divided into three main themes: Statistics, Quantitative Trading, Psychology. These three arguments are indispensable for the development of a quantitative trading system. The order of the articles was chosen so as to constitute a single logical reasoning that develops progressively.
“The difference between an amateur trader and a professional trader is that the first is obsessed by the result while the second is obsessed by the knowledge”
Introduction
The first step that you must take when you want to learn how to develop a quantitative trading system is to answer the following question: what characteristics must a system have to represent the theoretically most difficult situation possible where to make predictions?
The first characteristic that this system must possess is that of having a very low ratio between the deterministic component and the random component. Therefore, the random component must overcome the deterministic component.
The second characteristic that we need to determine concerns the number of degrees of freedom. This parameter determines how much difficult it is to test hypotheses. This consideration derives from the fundamental problem of statistics defined as follows: “A statistical data does not represent useful information, but becomes useful information only when it is shown that it was not obtained randomly”. Therefore, given a result, the probability of obtaining it randomly decreases as the degrees of freedom of the system increase. Consequently, systems with a low number of degrees of freedom are particularly dangerous, because it is particularly easy to get good results randomly and therefore you risk overestimating an investment strategy. For this reason, a system that wants to be as difficult as possible where making predictions must have a low number of degrees of freedom.
The third characteristic we have to choose is if to consider the system as ergodic (stationary) or non-ergodic (non-stationary). This choice is easy because it is much more difficult to make forecasts on a non-ergodic system. Indeed, in this case, past results may not be significant with respect to future results.
In conclusion, the system that represents, from the theoretical point of view, the most difficult situation in which to make predictions is a system in which there is a predominant random component, with a low number of degrees of freedom and not ergodic. Is there a system that has all these 3 characteristics? The answer is yes indeed, the financial markets represent a system that respects all these conditions.
I started this book with this consideration because I believe that the most important thing to understand, for any person who wants to develop a quantitative trading system, is to know that you are facing the most difficult situation theoretically possible where to make predictions.
It is this awareness that must guide us in the study of the financial markets. Without this awareness, we will inevitably be led to underestimate the difficulty of the problem and this will lead us to make mistakes.
