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In the currency market and the securities market, it is impossibleTrade without a carefully built trading system. Trading strategies can be different, and their profitability will be different. To assess the profitability of the system, the concept of mathematical expectation was introduced.

Mathematical expectation of the trading system

The mathematical expectation of a trading system canbe greater or less than 0. If the expectancy is above 0, then the system generates a profit. This does not mean that every perfect transaction will be profitable. But on a large number of transactions, the system will yield real profits. The higher the mathematical expectation of the trading system, the greater the profitability. The same goes for systems with a mathematical expectation of less than 0, but the result will be reversed. Some transactions made on such a system can be successful, but at a long distance the system will be unprofitable. You can not trade on such a system.

Calculation of the mathematical expectation

The expectation is calculated using the following formula: M = P + × V + - P- × V-. Here "P +" is the probability of profit per 1 trade, calculated as the ratio of the number of profitable trades to their total number. "V +" is the average profit per 1 transaction. Calculated as the ratio of total profit to the total number of transactions. "Р-" - the probability of obtaining a loss per transaction, is calculated as the ratio of the number of losing trades to their total number. Finally, "V-" is the average loss per transaction, equal to the ratio of the total loss to the total number of transactions. To make the calculations correct, at least a hundred transactions are required. The expectation can be calculated both on the basis of real trading, and when running the system on the tester - it is, for example, in the popular trading terminal Meta Trader 4. But the system rules must first be formalized, for this purpose a so-called trade advisor is written - a small program capable of independently open and close transactions on a given algorithm. The adviser is run on the history of trade, a lot of data is given out in the report on his work, including the expectation.

How to increase the mathematical expectation

The only way to increase it is tooptimization of trade rules. Many points are taken into account, among the main ones are the Stop Loss and Take Profit levels, a more precise definition of entry and exit points. Unfortunately, in the adviser many elements of the trading system can not be taken into account, so in practice, the effectiveness of the trading system usually has to be determined by the results of real trading or trading on a demo account. To determine the expectation in the trading terminal Meta Trader 4, you only need to order a report for a certain period of trading. To do this, open the "Trading history" tab, right-click on it and select "Save as detailed report".