How to calculate the mathematical expectation of a trading system

Calculating the mathematical expectation of a trading system is one of the first things that should be done to know if the system is capable of making money in the long term. Having a positive mathematical expectation is an indispensable condition that any moderately reliable system must meet.

The mathematical expectation measures the amount that is expected to be won or lost on average for each trade we do. For its calculation to be reliable, it is best that we take into account as many trades as possible.

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How to Measure a Trading System? – Ratios to assess your performance and risk

Example of equity drawdown

When you design a trading system, or you are looking to buy an automatic robot on the market, you must make decisions according to your preferences. The first thing you should ask yourself is: what am I looking for?

It is clear that you are looking to earn a lot of money, yes… this is what we all seek. But after a few losses and disappointments you learn that in Forex and other markets there are no magic methods and that the perfect trading system does not exist.

So, the right question is: how can you evaluate and compare different trading systems according to their risk level and potential benefit to know if they are viable for your use?

In this article we are going to review different statistical metrics to assess the performance of an investment system.

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Calculate the risk of ruin (or probability of success) of a trading system

Margin call risk curve


This is probably one of the most important articles for long-term success in trading that I have written so far. If I am not mistaken, this is the first time I have written about it, although the issue of risk of ruin is of the utmost importance in achieving long-term profitability. It is about evaluating, objectively, the risk I have of losing a certain percentage of the capital dedicated to investment and trading.

We have talked a lot in the past about drawdowns in general and in trading systems in particular. Specifically, we have explained the concept of the historical maximum drawdown as a risk measure of any kind.

When using a trading system in Forex and in other markets we must be able to answer two questions:

  • With a certain capital, what risk do I have of suffering catastrophic losses in the system/portfolio due to lack of funds?
  • If I want to risk only a certain capital, what probability of success do I have in the long term?

They are two questions that come to express the same thing, the relationship between the probability of long-term success and the capital available for the system/portfolio. Naturally we all know that the more we put in, the better, but it is about optimizing the use of money, right?

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What types of indicators do I need in my trading strategy?

As traders that we are, or pretend to be, we will spend most of the time looking for the best time to enter the market in a certain direction. In this search, we will use some tools such as technical indicators. From my point of view, any trader who bases his trading on technical analysis should use at least 4 types of indicators.

Well, rather, you should use those indicators that respond to the 4 basic trading needs: recognize the prevailing trend -> confirm the trend -> find the best entry -> find the best exit. These needs can be covered with the information of 1 or several indicators. Thus, I will classify the indicators into 4 categories according to the need they will cover, although this classification is for illustrative purposes only.

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Tom DeMark TD Sequential Trading Methodology

The sequential methodology of Tom DeMark or TD Sequential is a well-known indicator among traders that operate based on the techniques of this author, which has become known in recent years. In fact, this indicator is a mixture of a bit of everything, so it will be liked by both systematic traders and lovers of technical analysis, including those who like wave counts.

To calculate the TD Sequential, three phases are required:

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How to use stop loss orders? – Definition and main uses

The stop loss is a trading order placed in the broker to sell or buy a currency pair (or any other asset in a financial market) conditioned on the price reaching a certain value. It is mainly used to close an open transaction in case the price direction turns against it, hence its name. For example, if we have a buy position in the EUR/USD and put a stop loss at 50 pips below the entry price, our possible losses in case the price falls will be limited to 50 points (see how to calculate the value of a pip).

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Main Types of Trading Systems


We have already talked in other articles about the natural evolution of the Trader, from the beginning of his career in the markets until he obtains the knowledge and skills necessary to develop his own profitable Trading System, and now we are going to focus on the different types of trading systems that exist. Any person interested in the markets and trade successfully through a system is going to find a multitude of systems and methodologies of various types and characteristics, therefore we will present a classification as objective and simple as possible that allows the reader to know the main categories of trading systems that can be used.

The objective is merely didactic without offering any direct recommendation on a specific system, although the following information does offer advice on certain general aspects, especially when it comes to guiding the trader in the future development of systems. There are thousands of trading systems developed for all types of market conditions, and the best system is the one that each trader designs according to the strategy that gives the best results and makes him feel more comfortable. Do not expect to become a millionaire with the system that someone has sold you. Develop your own trading rules.

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What loss limit can I use in my trades?


Again, as long as I speak of losses, I must start this article by saying that  is completely impossible to avoid losses. Sooner or later they come to all traders. A good trader simply accept them consciously, which also involves applying systematic rules to keep the losses well controlled.

This article will not discuss the position of the stop loss, it will focus on the loss limit on volume that should be applied in all trades. That is, the maximum amount of money that would be lost if the operation goes wrong. Knowing this amount is essential to calculate the size of the trade.

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The scientific method in the development of trading systems

Tell me one thing: how do you validate your trading system? How can you be sure that by following these entry and exit signals from the market you will have profitable results? Just because you have executed a backtest and it has given you good results?

In today’s article I propose to rethink your way of working and begin to apply the scientific method as a procedure of development and validation of trading systems.

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Trading systems based on models


As we said in our previous article, we can classify trading systems into two groups: those based on models and those based on exploitation or data mining.

In this article we will discuss in detail the systems of the first type, defined as those who propose a model to represent the behavior of the market and from it, try to get benefits.

The algorithms that are part of this group are usually very simple in terms of the rules they use, although its development is usually relatively complex depending on the algorithm. The starting point of the models used for this type of strategy is the detection of a market inefficiency we want to exploit. Inefficiency produces an anomaly or a pattern on the price that can be described using a mathematical model that allows us to predict to some extent where the price will be in the next period based on a function based on historical price information.Let’s look at some of the most common strategies based on models.

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