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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The Calmar Ratio – Profitability and Risk Indicator

The Calmar Ratio is an indicator that is designed to measure and compare the performance of an investment portfolio or trading system.

The interesting thing about this ratio is that it summarizes how the profitability of the period has been with respect to the assumed risk.

Although it is a less known indicator than the Sharpe ratio, the Calmar ratio is currently widely used in the financial industry. It was first published in 1991 in the Futures magazine and was developed by Terry W. Young; precisely its name comes from the acronym formed from the name of the newsletter that the author sent to his clients, called CALifornia Managed Accounts Report. The Calmar ratio is defined as the ratio between the annualized profitability of the system and its maximum drawdown in absolute value. 

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The Sortino Ratio – good and bad volatility in your investments

The Sortino Ratio

To correctly analyze the performance of investments in the stock market and other financial markets, it is always advisable to relate profitability with respect to risk. One of the most used ratios for this is the Sharpe ratio. But today we will see that it is possible to further refine this measure using the Sortino ratio. Both ratios serve to measure the expected return of an investment fund, calculated on the expected return of an asset without risk, however, they present a series of subtle differences that we are going to show next.

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What is a Robust Trading System?

The difficult part to begin to trade in any market is to define the strategy or trading system that we are going to apply to make money, as there are many trading systems but:

  • Which trading systems are really robust?
  • What are the main features of robust trading system?

We will start by solving the second question. We will be trading with robust trading system as long as we have verified that any fair value we assign to the variables that define our system, end up producing gains in the trading account.

Just the opposite to define a trading system that is not robust. This situation occurs when you have been able to verify that with certain values your system has worked incredibly well, however with other values for the variables, it has been a ruin for your account.

We can do a practical exercise to evaluate the robustness of two well-known trading strategies:

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