Mathematical Expectations and Trading System Evaluation Methodology


Mathematical Expectations and Trading System Evaluation Methodology

Mathematical expectations play a great role in evaluating trading systems, in addition to fundamental and technical analysis, trading plays an important role in mathematics, more precisely, the capital Trade Management System. And, the main parameter of the system, the so-called Mathematical Expectation.
Traders may have full knowledge of technical analysis, is well aware of macroeconomics, realize what fundamental factors influence on the market, but if the trade is based on a negative mathematical expectation, then it will never be successful in this activity. Even if the transaction is closed with a profit of 8 to 10 from the transaction, it will still be a loss.
For example, if the profit from each deal amounted to 10 pips, while the loss of trade in the case of item 50, we get the following picture:
Earnings: 8 * 10 = 80 pips;
Losses: 2 * 50 = 100 pips;
Total: 80 - 100 = - 20 pips
Mathematical expectation is calculated by the formula:

Mathematical expectation = probability of making a profit in one transaction * Average profit - making the likelihood of losing a bargain average losses *

According to this formula, by our example above has a negative mathematical expectation :
8 * 10 - 50 * 2 = -20 <0
And, if, for example, a trader conquered profitable and unprofitable transactions, where each transaction in the profit and loss probability would be 50/50, and each of the lucrative deal would give it a 20-point win and one loss-making deal would give it a 10-point loss, then the trade of mathematical expectation would be positive:
20 * 0.5 - 0.5 * 10 5 => 0

How to calculate the mathematical expectation

For example, if we have the opportunity to close the deal with a profit of 40%, 3 GEL profit and lose 60% of transactions worth 1 loss, then our trade mathematical expectation is calculated as follows:
Mathematical expectation = (0.4 * 3) + (0.6 * (-1)) = 1.2 + (-0.6) = 0.6
As a result, it was found that our profit expectations for each transaction are about 60 cents. In other words, this is a trader's performance on the currency. A negative mathematical expectation of the case, but we would not talk about winning, but losing.

How to use the trade mathematical expectation factor

Mathematical expectation is an effective mechanism to test the profitability of a trading system.
In case, if the trader's trading system has a positive mathematical expectation, that is the trade capital increase. In addition, the higher the value of the mathematical expectation, the more quickly will increase its capital.
Trading system, the evaluation of other factors
Profit factor :
It is calculated by the formula, all the lucrative deals to divide the sum of all unprofitable transaction sum. It is believed that if the gain factor is not less than 1.6, then the trading system is profitable.
PF = S (Pi) / S (Li)
PF> 1.6
PF = TP / SL

Maximum loss (maximal drawdown или MIDD)

Maximum loss - it is time for a certain period of time deposits recorded a decrease in its maximum level.
Maximum loss shows the difference between maximum and minimum amounts of time for a certain period of time. The maximum rate of loss trading system helps us to better the rate. For example, some traders have concluded several deals during the period. Assuming its initial deposit of $ 1,000. In the first deal, he received a $ 50 profit, the amount of the loss is $ 10, $ 5 profit in the third, fourth and fifth of the loss of $ 20 to win $ 5. The result came out, the trader's deposits increased by $ 30 increments. At the same time the difference between the local maximum $ 1050 and $ 1025 to the local minimum wage, amounted to $ 25, which represents the maximum advantage of the losses.
Thus, the maximum loss shows the real risks sided trade. Sometimes, it may even exceed the trader's initial deposit. In this case, if it had originally been the winning trades and losing trades. Even if a trader has a positive trade balance, to say that its trading system is effective will not be correct.
Net profit ( Profit order in%)
It is calculated by the formula:
Net profit (%) = (Net profit / initial deposit) * 100%
As a result, we find out about what profits we trade system in percent, compared to the initial deposit.
Recovery Factor = Profit (%) / MIDD ( %)
The bigger the recovery factor, the greater the efficiency of the trading system. This indicator works quite well when we want to compare the different trading systems, to understand what their effectiveness.
Restoring factor shows how much higher the profit, the maximum loss. The higher recovery factor, the more quickly the trading capital increase after the defeat.
Comparing the two trading system to give priority to the restoration of more than a factor.
Consider the following example:
Gross profit account: $ 12,000
Gross loss account: $ 3,000
Net Income: $ 12,000 - $ 3000 = $ 9000
Maximum loss: $ 920
Recovery Factor: 9000/920 = 9.78
It is generally assumed that in order to be considered reliable and stable trading system is profitable, its recovery factor should not be less than 15 (the more, the better).

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