### Mathematical Trading Strategy Spetsnaz for the EURUSD Currency pair,Calculating the mathematical expectation of success

Still, the drawdowns can be lengthy — The longest drawdown seen under back-testing was more than days. The ratio of profit-to-drawdown when using this strategy is similar to that of buying-and-holding stocks, and during back-testing the ratio was about 0.

Risk management for multicurrency trading strategies using ME. By knowing the average MFE and MAE values, a forex trader can program a multicurrency mechanical system to exit a trade at a profit target or stop-loss point determined by adding a calculated number of pips beyond the Maximum Favorable Excursion or Maximum Adverse Excursion values.

On average, in order to win over time the forex trading system must reach the profit goal more often than it touches the stop-loss exit level. For example, if my system is seeing an average MAE of 35 pips and an average MFE of 55 pips, there is a tradable opportunity.

The profit target may be projected for 50 pips, which is 5 pips less than MFE, and the stop-loss exit can be set at 30 pips, which is 5 pips beyond the MAE. As mentioned earlier, a mechanical trading system can easily use Average True Range ATR as a volatility-dependent tool to calculate MAE and MFE in order to set exit points. The system determines the entry price plus or minus a percentage of the ATR that is workable according to the ME analysis.

To have a large enough sample, I usually set the ATR to calculate the previous 15 or 20 time frames. So, if a trade moves in a favorable direction for 55 pips, and if the current ATR is 85 pips, the move is not reported as 55 pips; instead, the MFE is reported as In order to fine-tune forex trading results according to volatility, the mechanical trading system can set the profit targets and stop-loss points at varying levels.

Still, this system is likely to reach target profit levels more often than stop-loss levels, and winners should be larger as long as target profits are set larger than stop-losses. For all trades, the calculated number of pips for target profits and stop-losses is always based on volatility just at the moment of the trade, as reflected by the ATR. When a signal arises, the trading system checks the value of current ATR, then calculates the exact number of pips to reach target profit and stop-loss levels.

Using this system, my average trade duration is about 25 days. In summary, this basic multicurrency forex trading strategy takes advantage of a positive, high ME shared across the four major currency pairs.

The entries, profit targets and stop-loss points are all based on ME. Stoploss is not set. When one of the trades is closed by TP, another trade is opened again in the same direction with the same take-profit of points. And you do not close the trade with the current minus, leave it as it is. That is, if a buy trade is closed, then hold a sell and open a new buy with a take-profit of points. And repeat these actions until the end of the trading day.

The next day, open two trades again at the current market. And yesterday's unprofitable trade is averaged so that for each trade involved in averaging there would be points. For example, suppose we opened Buy and Sell at 1. The price went up points and closed at the price of 1.

For Sell, the current minus is points. We do not touch it. The price rises by another points and Buy is closed at 1. For Sell, the current minus is equal to points. And this should be done while the price is moving in one direction. One of the simplest and most effective position sizing models is a fixed fractional model. Once you have determined how much you plan to risk on a per trade basis, then you would start by determining where the most logical stop should be placed on a particular trade.

One you have located a level where you plan on placing your stop loss , measure the distance in pips between this level and your intended entry. Then jot that number down and keep it handy. Now the next step is to determine the value of each pip. We have discussed how to calculate the value of a pip in the previous section.

Once you have this value, you are ready to calculate your position size. Here is the trading math behind Position Sizing:. Trade Expectancy is one of the most important metrics that a trader should be aware of. But what does it mean?

In a nutshell, trade expectancy is the average profit or loss that can be expected on each trade based on your average Win Percentage, Avg Win Size and Avg Loss Size. Here is the mathematical formula for Trade Expectancy:. Typically trend following systems tend to have low win rates, but relatively large average wins compared to average losses.

This time we will look at a Mean Reversion strategy. Mean reversion strategies tend to have higher win rates, and the average wins and losses are somewhat similar. Many traders make the mistake of only relying on win rates when evaluating trading systems. How many times have you entered positions in multiple currency pairs and noticed that their price movements were related?

To understand this better, you have to know what currency correlation is and how it can impact the overall risk in your portfolio. Currency correlation is a statistical measure of how different currency pairs move in relationship to each other. Currency correlations can be positive, meaning that two currency pairs move in the same direction. Currency correlations can be negative, meaning that two currency pair move in opposite directions. And finally, currency correlation can be neutral, meaning there is no discernible price relationship between the two currency pairs.

The forex mathematics behind currency correlation can be quite complicated, so we will not get into that in this lesson. But fortunately for us, we do not need to know the trade math because there are many currency correlation tools available in the market that makes it easy for use to do our correlation analysis. Most currency correlation tools are presented in a table format. Remember that a positive value means that the pairs move in the same direction, while a negative value means they have an inverse relationship.

As traders, we know that we will have losing trades and that they are a natural part of trading. Essentially, maximum drawdown is the maximum loss in equity that our portfolio incurs over a period of time. It is the largest drop from a previous equity peak to the lowest point after the peak. We can calculate the maximum drawdown after a new peak has been put in place on the equity curve. Here is the math formula for calculating Maximum Drawdown:.

What is your Maximum Drawdown in this scenario? So, the Max Drawdown in this case is Drawdowns can be very dangerous to the financial health of a trader because, as your drawdown increases the return needed to recover becomes larger and larger. Let take a look at the table below:. As you can see, the larger the max drawdown or capital loss the higher the percentage gain is needed to recover the losses. This is one reason why it is critical for traders to trade small so that they can try to keep drawdowns to a tolerable level.

Some forex traders use the same trading strategy for all currencies, while others use entirely different strategies depending on the currency pairs being traded. Or, traders may use multiple strategies with multiple forex pairs, in order to perhaps increase profits while reducing the risk of drawdown resulting from over-concentration on a single strategy.

And, testing may show increased risk from overlapping or correlated drawdowns when disparate forex strategies are merged together. Using algorithms, a trading system can check currency pairs and perform specific operations according to input parameters. A multicurrency, multi-system EA can be crafted in order to assess all trading strategies side-by-side. This may be helpful in case only a single EA is permitted to access a given account.

It can be challenging to develop a forex trading system that works well across different currency pairs under a variety of conditions. Most of the widely-known systems for multicurrency trading are based on trend-following strategies, such as Donchian-channel breakouts, and are designed to profit from very long-term trends. And, trades must become winners during fairly short time periods. If not, then trading correlated pairs may create a risk of over-concentration and excessive drawdown.

Mathematical expectation predicts the likelihood that a forex trade will win. A well-programmed EA can use ME tools to help build systems that work across multiple currency pairs. Recently, traders have become more aware of the drawbacks that arise when using data-mining techniques to back-test and fine-tune strategies for forex trading systems. Alternative system-development methods like System Parameter Permutation SPP are now available and can help traders avoid the issue of data-mining bias.

If done carefully, SPP or data mining will help build a set of good-quality indicators to generate signals across the four major currency pairs. Then, the expert advisor calculates Mathematical Expectation to see whether the trade is likely to be profitable or not. Entry and exit points are calculated by the mechanical trading system using mathematical expectation adjusted for current volatility. Mathematical Expectation ME is a statistic that measures the greatest temporary profit that a trade experienced the entire time it remained open.

It was first popularized under the Optimal-F position-sizing and money-management rules developed by Ralph Vince.

The equation is:. ME is defined according to the concepts of Maximum Favorable Excursion MFE and Maximum Adverse Excursion MAE. Maximum Favorable Excursion is the greatest balance on a favorable trade before a forex trade is closed out, regardless of final closing price during the time period, whether daily, hourly or minutely.

MFE is the highest positive balance achieved while the trade was open. Maximum Adverse Excursion is the largest unrealized or temporary loss during a trade, regardless of whether the trade was closed out as a loser or not. MAE is the lowest negative balance on the trade while it was open. In order to quantify and analyze the ME from a given forex pair, traders can simply calculate average MFE and average MAE for a large number of past trades.

Mathematical Expectation equals Maximum Favorable Excursion minus Maximum Adverse Excursion. If average MFE is larger than average MAE, then the Mathematical Expectation is positive. The larger the ratio between MFE and MAE for a given currency pair, the more favorable is the outlook for a potential trade.

Those parameters can be set independently by the mechanical trading system based on ME adjusted for volatility, as discussed later in this article. After determining the entry point and trade direction, the mechanical trading system calculates MFE and MAE values generally first at 10 bars beyond the entry price, then 15 bars beyond, then 20 bars beyond the entry price.

My simplest multicurrency trading strategy uses daily charts and relies on a combination of three price-based rules, and only a few parameters that use mathematical expectation to predict success. The rules for long and short trades are as follows:. This system reverses the trade when the signal changes. Another parameter of this system is the stop-loss trigger which is set at a value just slightly more than the fifteen-day or twenty-day average true range ATR.

This value is updated each time a new signal is received in the same direction. This simple multicurrency forex trading system has shown decent results in real trading, and back-testing over a twenty-year period shows that it would have enjoyed profitable results for at least sixteen out of the twenty years tested.

It has shown a reward-to-risk ratio of about 1. Still, the drawdowns can be lengthy — The longest drawdown seen under back-testing was more than days. The ratio of profit-to-drawdown when using this strategy is similar to that of buying-and-holding stocks, and during back-testing the ratio was about 0.

Risk management for multicurrency trading strategies using ME. By knowing the average MFE and MAE values, a forex trader can program a multicurrency mechanical system to exit a trade at a profit target or stop-loss point determined by adding a calculated number of pips beyond the Maximum Favorable Excursion or Maximum Adverse Excursion values.

On average, in order to win over time the forex trading system must reach the profit goal more often than it touches the stop-loss exit level.

For example, if my system is seeing an average MAE of 35 pips and an average MFE of 55 pips, there is a tradable opportunity. The profit target may be projected for 50 pips, which is 5 pips less than MFE, and the stop-loss exit can be set at 30 pips, which is 5 pips beyond the MAE.

As mentioned earlier, a mechanical trading system can easily use Average True Range ATR as a volatility-dependent tool to calculate MAE and MFE in order to set exit points. The system determines the entry price plus or minus a percentage of the ATR that is workable according to the ME analysis. To have a large enough sample, I usually set the ATR to calculate the previous 15 or 20 time frames.

So, if a trade moves in a favorable direction for 55 pips, and if the current ATR is 85 pips, the move is not reported as 55 pips; instead, the MFE is reported as In order to fine-tune forex trading results according to volatility, the mechanical trading system can set the profit targets and stop-loss points at varying levels.

Still, this system is likely to reach target profit levels more often than stop-loss levels, and winners should be larger as long as target profits are set larger than stop-losses.

For all trades, the calculated number of pips for target profits and stop-losses is always based on volatility just at the moment of the trade, as reflected by the ATR. When a signal arises, the trading system checks the value of current ATR, then calculates the exact number of pips to reach target profit and stop-loss levels.

Using this system, my average trade duration is about 25 days. In summary, this basic multicurrency forex trading strategy takes advantage of a positive, high ME shared across the four major currency pairs. The entries, profit targets and stop-loss points are all based on ME.